- Book Chapters
- Journal Papers
- Conference Papers
- Peer-Reviewed Educational Software
- PhD Dissertations
- MS Thesis

## Book Chapters

### 2017

- A. T. Becker, “Chapter 1 – controlling swarms of robots with global inputs: breaking symmetry,” in Microbiorobotics (second edition), Second Edition ed., M. Kim, A. A. Julius, and K. U. Cheang, Eds., Boston: Elsevier, 2017, pp. 3-20.

[Bibtex]`@incollection{2017beckermicrochapter, Abstract = {Roboticists, biologists, and chemists are now producing large populations of simple robots, but controlling large populations of robots with limited capabilities is difficult, due to communication and onboard-computation constraints. This chapter provides controllability proofs for control of mobile robots that move in a 2D workspace where each robot receives exactly the same control inputs. We focus on two types of control: when control inputs are the desired angular and linear velocity for the robots, and secondly when control inputs are the desired direction and speed for the robots. Both use broadcast control inputs: the first uses control inputs specified in the local reference frame of each robot, while the second uses control inputs specified in the global reference frame. Each method allows steering each robot to a desired goal location in O(n2) time, but the second option enables a class useful of swarm manipulation tasks to be accomplished efficiently.}, Address = {Boston}, Author = {Aaron T. Becker}, Booktitle = {Microbiorobotics (Second Edition)}, Doi = {10.1016/B978-0-32-342993-1.00006-9}, Edition = {Second Edition}, Editor = {Minjun Kim and Anak Agung Julius and U Kei Cheang}, Isbn = {978-0-323-42993-1}, Keywords = {Microrobot, Nanorobot, Global inputs, Nonprehensile, Under actuation}, Pages = {3 - 20}, Publisher = {Elsevier}, Series = {Micro and Nano Technologies}, Title = {Chapter 1 - Controlling swarms of robots with global inputs: Breaking symmetry}, Url = {http://www.sciencedirect.com/science/article/pii/B9780323429931000069}, Year = {2017}, pdf = {2017beckermicrochapter.pdf}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/B9780323429931000069}, Bdsk-Url-2 = {https://doi.org/10.1016/B978-0-32-342993-1.00006-9}}`

- P. S. S. Kim, A. T. Becker, Y. Ou, D. H. Kim, A. A. Julius, and M. Kim, “Chapter 11 – magnetic swarm control of microorganisms,” in Microbiorobotics (second edition), Second Edition ed., M. Kim, A. A. Julius, and K. U. Cheang, Eds., Boston: Elsevier, 2017, pp. 221-243.

[Bibtex]`@incollection{KIM2017221, Abstract = {Tetrahymena pyriformis is a single cell eukaryote that can be modified to respond to magnetic fields, a response called magnetotaxis. Naturally, this microorganism cannot respond to magnetic fields, but after modification using iron oxide nanoparticles, cells are magnetized and exhibit constant magnetic dipole strength. In experiments, a rotating field is applied to cells using a two-dimensional approximate Helmholtz coil system. Using rotating magnetic fields, we characterize discrete cells' swarm swimming which is affected by several factors. The behavior of the cells under these fields is explained in detail. After the field is removed, relatively straight swimming is observed. We also generate increased heterogeneity within a population of cells to improve controllability of a swarm, which is explored in a cell model. By exploiting this straight swimming behavior, we propose a method to control discrete cells utilizing a single global magnetic input. Successful implementation of this swarm control method would enable teams of microrobots to perform a variety of in vitro microscale tasks impossible for single microrobots, such as pushing objects or simultaneous micromanipulation of discrete entities.}, Address = {Boston}, Author = {Paul Seung Soo Kim and Aaron T. Becker and Yan Ou and Dal Hyung Kim and Anak Agung Julius and MinJun Kim}, Booktitle = {Microbiorobotics (Second Edition)}, Doi = {10.1016/B978-0-32-342993-1.00018-5}, Edition = {Second Edition}, Editor = {Minjun Kim and Anak Agung Julius and U Kei Cheang}, Isbn = {978-0-323-42993-1}, Keywords = {, Iron oxide nanoparticles, Magnetotaxis, Swarm control, Microrobot}, Pages = {221 - 243}, Publisher = {Elsevier}, Series = {Micro and Nano Technologies}, Title = {Chapter 11 - Magnetic swarm control of microorganisms}, Url = {http://www.sciencedirect.com/science/article/pii/B9780323429931000185}, Year = {2017}, Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/B9780323429931000185}, Bdsk-Url-2 = {https://doi.org/10.1016/B978-0-32-342993-1.00018-5}}`

### 2014

- A. Becker, E. D. Demaine, S. P. Fekete, G. Habibi, and J. McLurkin, “Reconfiguring massive particle swarms with limited, global control,” in Algorithms for sensor systems, P. Flocchini, J. Gao, E. Kranakis, and F. Meyer auf der Heide, Eds., Berlin, Heidelberg: Springer berlin heidelberg, 2014, p. 51–66.

[Bibtex]`@incollection{becker2014-reconfiguring-massive-particle, Abstract = {We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal such as gravity or a magnetic field. Upon activation of the field, each particle moves maximally in the same direction, until it hits a stationary obstacle or another stationary particle. In an open workspace, this system model is of limited use because it has only two controllable degrees of freedom---all particles receive the same inputs and move uniformly. We show that adding a maze of obstacles to the environment can make the system drastically more complex but also more useful. The resulting model matches ThinkFun's Tilt puzzle.}, Address = {Berlin, Heidelberg}, Author = {Becker, Aaron and Demaine, Erik D. and Fekete, S{\'a}ndor P. and Habibi, Golnaz and McLurkin, James}, Booktitle = {Algorithms for Sensor Systems}, Editor = {Flocchini, Paola and Gao, Jie and Kranakis, Evangelos and Meyer auf der Heide, Friedhelm}, Doi={10.1007/978-3-642-45346-5_5}, Isbn = {978-3-642-45346-5}, Pages = {51--66}, Publisher = {Springer Berlin Heidelberg}, Title = {Reconfiguring Massive Particle Swarms with Limited, Global Control}, Year = {2014}, pdf = {becker2014-reconfiguring-massive-particle.pdf}}`

## Journal Papers

##### (**bold face **for lab members)

### 2020

- H. Zhao, L. Julien, M. Feucht, O. Bailey, and A. Becker, “3d path-following using mrac on a millimeter-scale spiral-type magnetic robot,” Ieee robotics and automation letters, pp. 1-1, 2020.

[Bibtex][Video]`@ARTICLE{2020icra-mrac-swimmer, author={H. {Zhao} and L. {Julien} and M. {Feucht} and O. {Bailey} and A. {Becker}}, journal={IEEE Robotics and Automation Letters}, title={3D Path-Following using MRAC on a Millimeter-Scale Spiral-Type Magnetic Robot}, year={2020}, volume={}, number={}, pages={1-1}, abstract={This paper focuses on the 3D path-following of a spiral-type helical magnetic swimmer in a water-filled workspace. The swimmer has a diameter of 2.5 mm, a length of 6 mm, and is controlled by an external time-varying magnetic field. A method to compensate undesired magnetic gradient forces is proposed and tested. Five swimmer designs with different thread pitch values were experimentally analyzed. All were controlled by the same model reference adaptive controller (MRAC). Compared to a conventional hand-tuned PI controller, their 3D path-following performance is significantly improved by using MRAC. At an average speed of 50 mm/s, the path-following mean error of the MRAC is 3.8 +/- 1.8 mm, less than one body length of the swimmer. The versatility of this new controller is demonstrated by analyzing path-following through obstacles on a helical trajectory and forward & backward motion.}, keywords={Medical Robots and Systems;Model Learning for Control}, doi={10.1109/LRA.2020.2969159}, ISSN={2377-3774}, pdf={2020icra-mrac-swimmer.pdf}, month={}, video={https://youtu.be/U3xE5grzTLc},}`

- A. Schmidt, V. M. Baez, A. T. Becker, and S. P. Fekete, “Coordinated particle relocation using finite static friction with boundary walls,” Ieee robotics and automation letters, vol. 5, iss. 2, pp. 985-992, 2020.

[Bibtex][Video]`@ARTICLE{2020coordinated-relocations-finite-friction, author={A. {Schmidt} and V. M. {Baez} and A. T. {Becker} and S. P. {Fekete}}, journal={IEEE Robotics and Automation Letters}, title={Coordinated Particle Relocation Using Finite Static Friction With Boundary Walls}, year={2020}, volume={5}, number={2}, pages={985-992}, abstract={We present theoretical and practical methods for achieving arbitrary reconfiguration of a set of objects, based on the use of external forces, such as a magnetic field or gravity: Upon actuation, each object is pushed in the same direction until it collides with an obstruction. This concept can be used for a wide range of applications in which particles do not have their own energy supply. A crucial challenge for achieving any desired target configuration is breaking global symmetry in a controlled fashion. Previous work made use of specifically placed barriers; however, introducing precisely located obstacles into the workspace is impractical for many scenarios. In this letter, we present a different, less intrusive method: making use of the interplay between static friction with a boundary and the external force to achieve arbitrary reconfiguration. Our key contributions are a precise theoretical characterization of the critical coefficient of friction that is sufficient for rearranging two particles in triangles, convex polygons, and regular polygons; a method for reconfiguring multiple particles in rectangular workspaces, and deriving practical algorithms for these rearrangements. Hardware experiments show the efficacy of these procedures, demonstrating the usefulness of this novel approach.}, keywords={Manipulation planning;underactuated robots}, doi={10.1109/LRA.2020.2967275}, ISSN={2377-3774}, month={April}, pdf={2020coordinated-relocations-finite-friction.pdf}, video={https://youtu.be/hSa4EmjHXAI},}`

### 2019

- S. Shahrokhi, L. Lin, and A. T. Becker, “Planar orientation control and torque maximization using a swarm with global inputs,” Ieee transactions on automation science and engineering, vol. 16, iss. 4, pp. 1980-1987, 2019.

[Bibtex]`@ARTICLE{2019planar-orientation-torque, author={S. {Shahrokhi} and L. {Lin} and A. T. {Becker}}, journal={IEEE Transactions on Automation Science and Engineering}, title={Planar Orientation Control and Torque Maximization Using a Swarm With Global Inputs}, year={2019}, volume={16}, number={4}, pages={1980-1987}, abstract={This paper studies the torque applied by a large number of particles on a long aspect-ratio rod. The particles are all pushed in the same direction by a global signal. We calculate the force and torque generated by three canonical position distributions of a swarm: uniform, triangular, and normal. The model shows that for a pivoted rod the uniform distribution produces the maximum torque for small swarm standard deviations, but the normal distribution maximizes torque for large standard deviations. In the simulation, we use these results to design proportional-derivative controllers to orient rigid objects. We conclude showing the experiments with up to 97 hardware robots to evaluate our theory in practice.}, keywords={control system synthesis;mobile robots;optimisation;PD control;position control;statistical distributions;torque control;swarm standard deviations;proportional-derivative controllers;planar orientation control;torque maximization;long aspect-ratio rod;canonical position distributions;pivoted rod;global input swarm;hardware robots;Torque control;Particle swarm optimization;Robot kinematics;Position control;Robot sensing systems;Swarm control;torque control;underactuated robots}, doi={10.1109/TASE.2019.2925908}, ISSN={1558-3783}, month={Oct}, pdf={2019planar-orientation-torque.pdf}}`

- S. Shahrokhi, J. Shi, B. Isichei, and A. T. Becker, “Exploiting nonslip wall contacts to position two particles using the same control input,” Ieee transactions on robotics, vol. 35, iss. 3, pp. 577-588, 2019.

[Bibtex]`@ARTICLE{2019-exploiting-non-slip-wall-contacts, author={S. {Shahrokhi} and J. {Shi} and B. {Isichei} and A. T. {Becker}}, journal={IEEE Transactions on Robotics}, title={Exploiting Nonslip Wall Contacts to Position Two Particles Using the Same Control Input}, year={2019}, volume={35}, number={3}, pages={577-588}, abstract={Steered particles offer a method for targeted therapy, interventions, and drug delivery in regions inaccessible by large robots. For example, magnetic actuation of particles has the benefits of requiring no tethers, being able to operate from a distance, and in some cases allows imaging for feedback (e.g., MRI). This paper investigates position control of particles using uniform forces (the same force is applied everywhere in the workspace). Given a controllable field that can generate bidirectional forces in three orthogonal directions, steering one particle in three-dimensional (3-D) is trivial. Adding additional particles to steer makes the system underactuated because there are more states than control inputs. However, the walls of in vivo and artificial environments often have surface roughness such that the particles do not move unless actuation pulls them away from the wall. In the previous work, we showed that the individual two-dimensional (2-D) position of two particles is controllable using global inputs in a square workspace with nonslip wall contact [1]. Because in vivo environments are usually not square, this paper extends the previous work to all convex workspaces, and shows how this could be extended to 3-D positioning of neutrally buoyant particles. We investigate analytically an idealized variant of this problem with nonslip boundaries and control inputs that are applied uniformly to all particles in the workspace. This paper also implements the algorithms in 2-D using a hardware setup inspired by the gastrointestinal tract.}, keywords={actuators;biological organs;feedback;medical robotics;motion control;position control;surface roughness;square workspace;nonslip wall contact;neutrally buoyant particles;control input;steered particles;targeted therapy;drug delivery;magnetic actuation;position control;bidirectional forces;artificial environments;global inputs;3D positioning;in vivo environments;gastrointestinal tract;surface roughness;large robots;Force;Magnetic resonance imaging;Aerospace electronics;Position control;Hardware;Robot sensing systems;Configuration space;motion control;path planning for multiple robot systems;underactuated robots}, doi={10.1109/TRO.2019.2891487}, ISSN={1941-0468}, month={June}, pdf={2019-exploiting-non-slip-wall-contacts.pdf},}`

- A. T. Becker, E. D. Demaine, S. P. Fekete, J. Lonsford, and R. Morris-Wright, “Particle computation: complexity, algorithms, and logic,” Natural computing, vol. 18, iss. 1, p. 181–201, 2019.

[Bibtex]`@article{2019particle-computation-complexity, title={Particle computation: complexity, algorithms, and logic}, author={Becker, Aaron T and Demaine, Erik D and Fekete, S{\'a}ndor P and Lonsford, Jarrett and Morris-Wright, Rose}, abstract = {We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). Upon activation of the field, each particle moves maximally in the same direction until forward progress is blocked by a stationary obstacle or another stationary particle. In an open workspace, this system model is of limited use because it has only two controllable degrees of freedom—all particles receive the same inputs and move uniformly. We show that adding a maze of obstacles to the environment can make the system drastically more complex but also more useful. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and, nand, nor, and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2 × 1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits.}, journal={Natural Computing}, volume={18}, number={1}, pages={181--201}, year={2019}, publisher={Springer}, url = {https://link.springer.com/article/10.1007/s11047-017-9666-6}, doi={https://doi.org/10.1007/s11047-017-9666-6}, ISSN={1567-7818}, }`

### 2018

- J. Leclerc, B. Isichei, and A. T. Becker, “A magnetic manipulator cooled with liquid nitrogen,” Ieee robotics and automation letters, vol. 3, iss. 4, pp. 4367-4374, 2018.

[Bibtex]`@ARTICLE{2018magneticmanipulatorliquidnitrogen, author={J. {Leclerc} and B. {Isichei} and A. T. {Becker}}, journal={IEEE Robotics and Automation Letters}, title={A Magnetic Manipulator Cooled With Liquid Nitrogen}, year={2018}, volume={3}, number={4}, pages={4367-4374}, abstract={Miniature robots manipulated by external magnetic fields could enable less invasive surgeries. Magnetic tools, capsules, or medication can be controlled inside a human body using electromagnets. However, resistive magnetic devices able to produce strong magnetic fields in a large volume inefficiently use space and energy. This letter presents the design and testing of a magnetic manipulator cooled with liquid nitrogen. This technique reduces the electrical resistance of copper wires. It, therefore, reduces the amount of heat generated to produce a given magnetic field. Liquid nitrogen-cooled electromagnets are smaller than air-cooled ones and use less power. This letter examines how both effects scale with the size of the workspace. The system presented possesses six electromagnets and its ability to control a robot is demonstrated experimentally.}, keywords={cooling;electromagnets;magnetic devices;magnetic fields;medical robotics;micromanipulators;surgery;copper wires;capsules;air-cooled electromagnets;liquid nitrogen-cooled electromagnets;electrical resistance;strong magnetic fields;resistive magnetic devices;human body;magnetic tools;invasive surgeries;external magnetic fields;miniature robots;magnetic manipulator;Manipulators;Nitrogen;Electromagnets;Medical robotics;Force control;Medical robots and systems;force control;micro/nano robots}, doi={10.1109/LRA.2018.2863358}, ISSN={2377-3774}, month={Oct}, pdf={2018magneticmanipulatorliquidnitrogen.pdf},}`

- A. T. Becker, S. P. Fekete, P. Keldenich, D. Krupke, C. Rieck, C. Scheffer, and A. Schmidt, “Tilt assembly: algorithms for micro-factories that build objects with uniform external forces,” Algorithmica, p. 1–23, 2018.

[Bibtex]`@article{2018tilt-assembly, title={Tilt assembly: Algorithms for micro-factories that build objects with uniform external forces}, author={Becker, Aaron T and Fekete, S{\'a}ndor P and Keldenich, Phillip and Krupke, Dominik and Rieck, Christian and Scheffer, Christian and Schmidt, Arne}, journal={Algorithmica}, pages={1--23}, year={2018}, publisher={Springer}, doi={https://doi.org/10.1007/s00453-018-0483-9}, ISSN={0178-4617}, abstract={We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield micro-factories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle. Particles bond when forced together with another appropriate particle. Due to the physical and geometric constraints, not all shapes can be built in this manner; this gives rise to the Tilt Assembly Problem (TAP) of deciding constructibility. For simply-connected polyominoes P in 2D consisting of N unit-squares (“tiles”), we prove that TAP can be decided in 𝑂(𝑁log𝑁) time. For the optimization variant MaxTAP (in which the objective is to construct a subshape of maximum possible size), we show polyAPX-hardness: unless P = NP, MaxTAP cannot be approximated within a factor of Ω(𝑁13) ; for tree-shaped structures, we give an Ω(𝑁12) -approximation algorithm. For the efficiency of the assembly process itself, we show that any constructible shape allows pipelined assembly, which produces copies of P in O(1) amortized time, i.e., N copies of P in O(N) time steps. These considerations can be extended to three-dimensional objects: For the class of polycubes P we prove that it is NP-hard to decide whether it is possible to construct a path between two points of P; it is also NP-hard to decide constructibility of a polycube P. Moreover, it is expAPX-hard to maximize a sequentially constructible path from a given start point.} }`

- A. Schmidt, S. Manzoor, L. Huang, A. T. Becker, and S. P. Fekete, “Efficient parallel self-assembly under uniform control inputs,” Ieee robotics and automation letters, vol. 3, iss. 4, pp. 3521-3528, 2018.

[Bibtex]`@ARTICLE{2018-schmidt-efficient-parallel-self-assembly, author={A. {Schmidt} and S. {Manzoor} and L. {Huang} and A. T. {Becker} and S. P. {Fekete}}, journal={IEEE Robotics and Automation Letters}, title={Efficient Parallel Self-Assembly Under Uniform Control Inputs}, year={2018}, volume={3}, number={4}, pages={3521-3528}, abstract={We prove that by successively combining subassemblies, we can achieve sublinear construction times for ``stages'' assembly of microscale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance in the context of programmable matter and self-assembly for building high-yield microfactories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles bond when forced together with a compatible particle. Previous work considered sequential composition of objects, resulting in construction time that is linear in the number N of particles, which is inefficient for large N. Our progress implies critical speedup for constructible shapes; for convex polyominoes, even a constant construction time is possible. We also show that our construction process can be used for pipelining, resulting in an amortized constant production time.}, keywords={computational complexity;self-assembly;uniform control inputs;subassemblies;sublinear construction times;microscale objects;programmable matter;high-yield microfactories;uniform external forces;compatible particle;constructible shapes;constant construction time;amortized constant production time;parallel self-assembly;pipelining;Shape;Self-assembly;Production;Robots;Tiles;Containers;Computational geometry;underactuated robots;additive manufacturing}, doi={10.1109/LRA.2018.2853758}, ISSN={2377-3774}, month={Oct},}`

- J. Leclerc, A. Ramakrishnan, N. V. Tsekos, and A. T. Becker, “Magnetic hammer actuation for tissue penetration using a millirobot,” Ieee robotics and automation letters, vol. 3, iss. 1, pp. 403-410, 2018.

[Bibtex]`@ARTICLE{2018leclerc-magnetic-hammer, author={J. {Leclerc} and A. {Ramakrishnan} and N. V. {Tsekos} and A. T. {Becker}}, journal={IEEE Robotics and Automation Letters}, title={Magnetic Hammer Actuation for Tissue Penetration Using a Millirobot}, year={2018}, volume={3}, number={1}, pages={403-410}, abstract={Untethered magnetic navigation of millirobots within a human body using a magnetic resonance imaging (MRI) scanner is a promising technology for minimally invasive surgery or drug delivery. Because MRI scanners have a large static magnetic field, they cannot generate torque on magnetic millirobots and must instead use gradient-based pulling. However, gradient values are too small to produce forces large enough to penetrate tissue. This letter presents a method to produce large pulsed forces on millirobots. A ferromagnetic sphere is placed inside a hollow robot body and can move back and forth. This movement is created by alternating the magnetic gradient direction. On the posterior side, a spring allows the sphere to change direction smoothly. On the anterior side, a hard rod creates a surface for the sphere to impact. This impact results in a large pulsed force. The purpose of this study was to understand the functioning of magnetic hammer actuation and control, as well as demonstrate the viability of this mechanism for tissue penetration. This letter begins with modeling and simulating this system. Next, different control strategies are presented and tested. The system successfully penetrated lamb brain samples. Finally, preliminary tests inside a clinical MRI scanner demonstrate the potential of this actuation system.}, keywords={biological tissues;biomedical MRI;brain;drug delivery systems;magnetic actuators;medical robotics;microrobots;surgery;lamb brain samples;gradient-based pulling;drug delivery;gradient values;magnetic millirobots;static magnetic field;MRI scanners;minimally invasive surgery;magnetic resonance imaging scanner;human body;untethered magnetic navigation;actuation system;clinical MRI scanner;tissue penetration;magnetic hammer actuation;magnetic gradient direction;hollow robot body;ferromagnetic sphere;pulsed force;Magnetic resonance imaging;Springs;Mathematical model;Magnetic separation;Robots;Force;Coils;Mechanism design;medical robots and systems;surgical robotics: Steerable catheters/needles}, doi={10.1109/LRA.2017.2739805}, ISSN={2377-3774}, month={Jan},}`

- S. Shahrokhi, L. Lin, C. Ertel, M. Wan, and A. T. Becker, “Steering a swarm of particles using global inputs and swarm statistics,” Ieee transactions on robotics, vol. 34, iss. 1, pp. 207-219, 2018.

[Bibtex]`@ARTICLE{2018_shahrokhi-steering-particle-swarm, author={S. {Shahrokhi} and L. {Lin} and C. {Ertel} and M. {Wan} and A. T. {Becker}}, journal={IEEE Transactions on Robotics}, title={Steering a Swarm of Particles Using Global Inputs and Swarm Statistics}, year={2018}, volume={34}, number={1}, pages={207-219}, abstract={Microrobotics has the potential to revolutionize many applications including targeted material delivery, assembly, and surgery. The same properties that promise breakthrough solutions-small size and large populations-present unique challenges for controlling motion. Robotic manipulation usually assumes intelligent agents, not particle systems manipulated by a global signal. To identify the key parameters for particle manipulation, we used a collection of online games in which players steer swarms of up to 500 particles to complete manipulation challenges. We recorded statistics from more than 10 000 players. Inspired by techniques in which human operators performed well, we investigate controllers that use only the mean and variance of the swarm. We prove that mean position is controllable and provide conditions under which variance is controllable. We next derive automatic controllers for these and a hysteresis-based switching control to regulate the first two moments of the particle distribution. Finally, we employ these controllers as primitives for an object manipulation task and implement all controllers on 100 kilobots controlled by the direction of a global light source.}, keywords={computer games;control engineering computing;manipulators;microrobots;motion control;multi-robot systems;statistics;robotic manipulation;intelligent agents;particle systems;global signal;particle manipulation;online games;manipulation challenges;derive automatic controllers;particle distribution;object manipulation task;global light source;global inputs;material delivery;particle swarm;motion controlling;microrobotics;swarm statistics;Robot kinematics;Robot sensing systems;Sociology;Statistics;Control systems;Human-swarm interaction;manipulation planning;swarm;underactuated robots}, doi={10.1109/TRO.2017.2769094}, ISSN={1941-0468}, month={Feb},}`

### 2017

- S. Manzoor, S. Sheckman, J. Lonsford, H. Kim, M. J. Kim, and A. T. Becker, “Parallel self-assembly of polyominoes under uniform control inputs,” Ieee robotics and automation letters, vol. 2, iss. 4, pp. 2040-2047, 2017.

[Bibtex]`@ARTICLE{2017-manzoor-parallel-self-assembly, author={S. {Manzoor} and S. {Sheckman} and J. {Lonsford} and H. {Kim} and M. J. {Kim} and A. T. {Becker}}, journal={IEEE Robotics and Automation Letters}, title={Parallel Self-Assembly of Polyominoes Under Uniform Control Inputs}, year={2017}, volume={2}, number={4}, pages={2040-2047}, abstract={We present fundamental progress on parallel self-assembly using large swarms of microscale particles in complex environments, controlled not by individual navigation, but by a uniform, global, external force with the same effect on each particle. Consider a 2-D grid world, in which all obstacles and particles are unit squares, and for each actuation, particles move maximally until they collide with an obstacle or another particle. We present algorithms that, given an arbitrary 2-D structure, design an obstacle layout. When actuated, this layout generates copies of the input 2-D structure. We analyze the movement and spatial complexity of the factory layouts. We present hardware results on both a macroscale, gravity-based system, and a microscale, magnetically actuated system.}, keywords={geometry;industrial robots;microassembling;microrobots;self-assembly;magnetically actuated system;gravity-based system;factory layouts;spatial complexity;obstacle layout;arbitrary 2D structure;2D grid world;microscale particles;uniform control inputs;polyominoes;parallel self-assembly;Robots;Two dimensional displays;Production facilities;Shape;Spirals;Algorithm design and analysis;Layout;Automation at micro-nano scales;additive manufacturing;underactuated robots}, doi={10.1109/LRA.2017.2715402}, ISSN={2377-3774}, month={Oct},}`

- H. Nguyen, M. M. P. Arnob, A. T. Becker, J. C. Wolfe, M. K. Hogan, P. J. Horner, and W. Shih, “Fabrication of multipoint side-firing optical fiber by laser micro-ablation,” Opt. lett., vol. 42, iss. 9, p. 1808–1811, 2017.

[Bibtex][Interactive Demo]`@article{Nguyen:17, Abstract = {A multipoint, side-firing design enables an optical fiber to output light at multiple desired locations along the fiber body. This provides advantages over traditional end-to-end fibers, especially in applications requiring fiber bundles such as brain stimulation or remote sensing. This Letter demonstrates that continuous wave (CW) laser micro-ablation can controllably create conical-shaped cavities, or side windows, for outputting light. The dimensions of these cavities determine the amount of firing light and their firing angle. Experimental data show that a single side window on a 730 \&\#x03BC;m fiber can deliver more than 8\% of the input light. This can be increased to more than 19\% on a 65 \&\#x03BC;m fiber with side windows created using femtosecond laser ablation and chemical etching. Fine control of light distribution along an optical fiber is critical for various biomedical applications such as light-activated drug-release and optogenetics studies.}, Author = {Hoang Nguyen and Md Masud Parvez Arnob and Aaron T. Becker and John C. Wolfe and Matthew K. Hogan and Philip J. Horner and Wei-Chuan Shih}, Doi = {10.1364/OL.42.001808}, Journal = {Opt. Lett.}, Keywords = {Laser materials processing; Medical optics and biotechnology; Microstructure fabrication; Microstructured fibers ; High power lasers; Laser beams; Laser light; Laser systems; Plastic optical fibers; Tilted fiber Bragg gratings}, Month = {May}, Number = {9}, Pages = {1808--1811}, Publisher = {OSA}, Title = {Fabrication of multipoint side-firing optical fiber by laser micro-ablation}, Url = {http://ol.osa.org/abstract.cfm?URI=ol-42-9-1808}, Volume = {42}, Year = {2017}, demo = {https://demonstrations.wolfram.com/DefectsInAnOpticalFiber/}, Bdsk-Url-1 = {http://ol.osa.org/abstract.cfm?URI=ol-42-9-1808}, Bdsk-Url-2 = {https://doi.org/10.1364/OL.42.001808}}`

- S. K. V. Sudarshan, V. Montano, A. Nguyen, M. McClimans, L. Chang, R. R. Stewart, and A. T. Becker, “A heterogeneous robotics team for large-scale seismic sensing,” Ieee robotics and automation letters, vol. 2, iss. 3, pp. 1328-1335, 2017.

[Bibtex][Video]`@ARTICLE{2017-sudarshan-heterogeneous-robotics-team, author={S. K. V. {Sudarshan} and V. {Montano} and A. {Nguyen} and M. {McClimans} and L. {Chang} and R. R. {Stewart} and A. T. {Becker}}, journal={IEEE Robotics and Automation Letters}, title={A Heterogeneous Robotics Team for Large-Scale Seismic Sensing}, year={2017}, volume={2}, number={3}, pages={1328-1335}, abstract={Seismic surveying requires placing a large number of sensors (geophones) in a grid pattern, triggering a seismic event, and recording vibration readings. The goal of the surveying is often to locate subsurface resources. Traditional seismic surveying employs human laborers for sensor placement and retrieval. The major drawbacks of surveying with human deployment are the high costs and time, and risks to humans due to explosives, terrain, and climatic conditions. We propose an autonomous, heterogeneous sensor deployment system using unmanned aerial vehicles to deploy mobile and immobile sensors. The proposed system begins to overcome some of the problems associated with traditional systems. This paper provides detailed analysis and comparison with traditional survey techniques. Hardware experiments and simulations show promise for automation reducing cost and time. Autonomous aerial systems will have a substantial contribution to make in future seismic surveys.}, keywords={autonomous aerial vehicles;earthquake engineering;seismology;sensors;vibrations;heterogeneous robotics team;large-scale seismic sensing;seismic surveying;grid pattern;seismic event;vibration readings;subsurface resources;human laborers;sensor placement;human deployment;heterogeneous sensor deployment system;unmanned aerial vehicles;mobile sensors;immobile sensors;Soil;Robot sensing systems;Sensor systems;Soil measurements;Seismic measurements;Aerial robotics;distributed robot systems;robotics in hazardous fields}, doi={10.1109/LRA.2017.2666300}, ISSN={2377-3774}, month={July}, video={https://youtu.be/LHUQ6QmEpQI},}`

### 2016

- O. Felfoul, A. T. Becker, G. Fagogenis, and P. E. Dupont, “Simultaneous steering and imaging of magnetic particles using MRI toward delivery of therapeutics,” , vol. 6, iss. 1, p. 33567, 2016.

[Bibtex][Video]`@Article{ref25, author={Felfoul, Ouajdi and Becker, Aaron T. and Fagogenis, Georgios and Dupont, Pierre E.}, title={Simultaneous steering and imaging of magnetic particles using {MRI} toward delivery of therapeutics}, year={2016}, volume={6}, number={1}, pages={33567}, abstract={Magnetic resonance navigation (MRN) offers the potential for real-time steering of drug particles and cells to targets throughout the body. In this technique, the magnetic gradients of an MRI scanner perform image-based steering of magnetically-labelled therapeutics through the vasculature and into tumours. A major challenge of current techniques for MRN is that they alternate between pulse sequences for particle imaging and propulsion. Since no propulsion occurs while imaging the particles, this results in a significant reduction in imaging frequency and propulsive force. We report a new approach in which an imaging sequence is designed to simultaneously image and propel particles. This sequence provides a tradeoff between maximum propulsive force and imaging frequency. In our reported example, the sequence can image at 27 Hz while still generating 95\% of the force produced by a purely propulsive pulse sequence. We implemented our pulse sequence on a standard clinical scanner using millimetre-scale particles and demonstrated high-speed (74 mm/s) navigation of a multi-branched vascular network phantom. Our study suggests that the magnetic gradient magnitudes previously demonstrated to be sufficient for pure propulsion of micron-scale therapeutics in magnetic resonance targeting (MRT) could also be sufficient for real-time steering of these particles.}, issn={2045-2322}, doi={10.1038/srep33567}, url={https://doi.org/10.1038/srep33567 https://www.nature.com/articles/srep33567.pdf}, file={:internal-pdf://3829176425/Felfoul-2016-Simultaneous steering and imaging.pdf:PDF}, video = {https://youtu.be/3xhVBzjYZSs}, }`

### 2015

- P. S. S. Kim, A. Becker, Y. Ou, A. A. Julius, and M. J. Kim, “Imparting magnetic dipole heterogeneity to internalized iron oxide nanoparticles for microorganism swarm control,” Journal of nanoparticle research, vol. 17, iss. 3, p. 144, 2015.

[Bibtex]`@article{2015-kim-article-imparting-magnetic-dipole-heterog, title={Imparting magnetic dipole heterogeneity to internalized iron oxide nanoparticles for microorganism swarm control}, author={Kim, Paul Seung Soo and Becker, Aaron and Ou, Yan and Julius, Anak Agung and Kim, Min Jun}, journal={Journal of Nanoparticle Research}, volume={17}, number={3}, pages={144}, year={2015}, publisher={Springer}, doi={https://doi.org/10.1007/s11051-014-2746-y}, ISSN={1388-0764}, url={https://link.springer.com/article/10.1007/s11051-014-2746-y}, abstract={Tetrahymena pyriformis is a single cell eukaryote that can be modified to respond to magnetic fields, a response called magnetotaxis. Naturally, this microorganism cannot respond to magnetic fields, but after modification using iron oxide nanoparticles, cells are magnetized and exhibit a constant magnetic dipole strength. In experiments, a rotating field is applied to cells using a two-dimensional approximate Helmholtz coil system. Using rotating magnetic fields, we characterize discrete cells’ swarm swimming which is affected by several factors. The behavior of the cells under these fields is explained in detail. After the field is removed, relatively straight swimming is observed. We also generate increased heterogeneity within a population of cells to improve controllability of a swarm, which is explored in a cell model. By exploiting this straight swimming behavior, we propose a method to control discrete cells utilizing a single global magnetic input. Successful implementation of this swarm control method would enable teams of microrobots to perform a variety of in vitro microscale tasks impossible for single microrobots, such as pushing objects or simultaneous micromanipulation of discrete entities.} }`

- O. Felfoul, A. Becker, C. Bergeles, and P. E. Dupont, “Achieving commutation control of an MRI-powered robot actuator,” Ieee transactions on robotics, vol. 31, iss. 2, pp. 387-399, 2015.

[Bibtex]`@ARTICLE{2015-felfoul-achieving-commutation-control, author={O. {Felfoul} and A. {Becker} and C. {Bergeles} and P. E. {Dupont}}, journal={IEEE Transactions on Robotics}, title={Achieving Commutation Control of an {MRI}-Powered Robot Actuator}, year={2015}, volume={31}, number={2}, pages={387-399}, abstract={Actuators that are powered, imaged, and controlled by magnetic resonance (MR) scanners could inexpensively provide wireless control of MR-guided robots. Similar to traditional electric motors, the MR scanner acts as the stator and generates propulsive torques on an actuator rotor containing one or more ferrous particles. Generating maximum motor torque while avoiding instabilities and slippage requires closed-loop control of the electromagnetic field gradients, i.e., commutation. Accurately estimating the position and velocity of the rotor is essential for high-speed control, which is a challenge due to the low refresh rate and high latency associated with MR signal acquisition. This paper proposes and demonstrates a method for closed-loop commutation based on interleaving pulse sequences for rotor imaging and rotor propulsion. This approach is shown to increase motor torque and velocity, eliminate rotor slip, and enable regulation of rotor angle. Experiments with a closed-loop MR imaging actuator produced a maximum force of 9.4 N.}, keywords={actuators;biomedical MRI;closed loop systems;medical robotics;rotors;stators;torque control;velocity control;commutation control;MRI-powered robot actuator;magnetic resonance scanner;MR scanner;stator;propulsive torque;actuator rotor;ferrous particle;motor torque;closed-loop control;electromagnetic field gradient;rotor angle;rotor slip;rotor propulsion;rotor imaging;MR signal acquisition;high-speed control;Rotors;Magnetic resonance imaging;Actuators;Radio frequency;Commutation;Torque;Magnetic actuation;medical robots and systems;MRI;Magnetic actuation;medical robots and systems;MRI}, doi={10.1109/TRO.2015.2407795}, ISSN={1941-0468}, month={April},}`

### 2014

- A. Becker, C. Onyuksel, T. Bretl, and J. McLurkin, “Controlling many differential-drive robots with uniform control inputs,” The international journal of robotics research, vol. 33, iss. 13, p. 1626–1644, 2014.

[Bibtex]`@article{2014-becker-controlling-many-differential-drive, title={Controlling many differential-drive robots with uniform control inputs}, author={Becker, Aaron and Onyuksel, Cem and Bretl, Timothy and McLurkin, James}, journal={The international journal of Robotics Research}, volume={33}, number={13}, pages={1626--1644}, year={2014}, publisher={SAGE Publications Sage UK: London, England}, url = {https://journals.sagepub.com/doi/pdf/10.1177/0278364914543481?casa_token=3DKux5q0IzcAAAAA:Z_UkhSodQM8Qj4PcUmTkbD2JAbMpFPh7gLnLh4PmOESwgWlnt76VoU34_s50-ir5B1N_BKXWkA}, abstract={This paper derives both open-loop and closed-loop control policies that steer a finite set of differential-drive robots to desired positions in a two-dimensional workspace, when all robots receive the same control inputs but each robot turns at a slightly different rate. In the absence of perturbation, the open-loop policy achieves zero error in finite time. In the presence of perturbation, the closed-loop policy is globally asymptotically stabilizing with state feedback. Both policies were validated with hardware experiments using up to 15 robots. These experimental results suggest that similar policies might be applied to control micro- and nanoscale robotic systems, which are often subject to similar constraints.}, keywords={Ensemble control, micro/nano robots, path planning for multiple mobile robot systems, nonholonomic motion planning, underactuated robots, telerobotics, multi-agent control, uniform inputs}, doi={https://doi.org/10.1177/0278364914543481}, }`

### 2012

- A. Becker and T. Bretl, “Approximate steering of a unicycle under bounded model perturbation using ensemble control,” Ieee transactions on robotics, vol. 28, iss. 3, pp. 580-591, 2012.

[Bibtex]`@ARTICLE{2012-becker-approximate-steering-unicycle, author={A. {Becker} and T. {Bretl}}, journal={IEEE Transactions on Robotics}, title={Approximate Steering of a Unicycle Under Bounded Model Perturbation Using Ensemble Control}, year={2012}, volume={28}, number={3}, pages={580-591}, abstract={This paper considers the problem of steering a nonholonomic unicycle despite model perturbation that scales both the forward speed and the turning rate by an unknown but bounded constant. We model the unicycle as an ensemble control system, show that this system is ensemble controllable, and derive an approximate steering algorithm that brings the unicycle to within an arbitrarily small neighborhood of any given Cartesian position. We apply our work to a differential-drive robot with unknown but bounded wheel radius and validate our approach with hardware experiments.}, keywords={approximation theory;controllability;mobile robots;path planning;robot kinematics;steering systems;approximate steering algorithm;nonholonomic unicycle;bounded model perturbation;ensemble control theory;forward speed;turning rate;ensemble control system;Cartesian position;differential-drive robot;bounded wheel radius;nonholonomic motion planning;Robot sensing systems;Mobile robots;Approximation methods;Control systems;Vectors;Approximation algorithms;Ensemble control theory;model perturbation;nonholonomic motion planning}, doi={10.1109/TRO.2011.2182117}, ISSN={1941-0468}, month={June},}`

### 2011

- D. Y. Li, A. Becker, K. A. Shorter, T. Bretl, and E. T. Hsiao-Wecksler, “Estimating system state during human walking with a powered ankle-foot orthosis,” Ieee/asme transactions on mechatronics, vol. 16, iss. 5, pp. 835-844, 2011.

[Bibtex]`@ARTICLE{2011-li-estimating-system-state-during-human-walking, author={D. Y. {Li} and A. {Becker} and K. A. {Shorter} and T. {Bretl} and E. T. {Hsiao-Wecksler}}, journal={IEEE/ASME Transactions on Mechatronics}, title={Estimating System State During Human Walking With a Powered Ankle-Foot Orthosis}, year={2011}, volume={16}, number={5}, pages={835-844}, abstract={This paper presents a state estimator that reliably detects gait events during human walking with a portable powered ankle-foot orthosis (AFO), based only on measurements of the ankle angle and of contact forces at the toe and heel. Effective control of the AFO critically depends on detecting these gait events. A common approach detects gait events simply by checking if each measurement exceeds a given threshold. Our approach uses cross correlation between a window of past measurements and a learned model to estimate the configuration of the human walker, and detects gait events based on this estimate. We tested our approach in experiments with five healthy subjects and with one subject that had neuromuscular impairment. Using motion capture data for reference, we compared our approach to one based on thresholding and to another common one based on k-nearest neighbors. The results showed that our approach reduced the RMS error by up to 40% for the impaired subject and up to 49% for the healthy subjects. Moreover, our approach was robust to perturbations due to changes in walking speed and to control actuation.}, keywords={gait analysis;mean square error methods;neurophysiology;orthotics;state estimation;state estimator;gait events;human walking;portable powered ankle-foot orthosis;ankle angle measurements;contact forces;toe;heel;AFO;neuromuscular impairment;motion capture data;k-nearest neighbors;RMS error;walking speed;Sensors;Legged locomotion;Torque;Data models;State estimation;Event detection;Ankle-foot orthosis (AFO);cross correlation (CC);event detection;gait;state estimation}, doi={10.1109/TMECH.2011.2161769}, ISSN={1941-014X}, month={Oct},}`

## Conference Papers

##### (**bold face **for lab members)

### 2020

- J. Leclerc, H. Zhao, D. Bao, A. Becker, M. Ghosn, and D. J. Shah, “Agile 3d-navigation of a helical magnetic swimmer,” in Ieee international conference on robotics and automation (icra 2020, paris france), 2020, p. tbd.

[Bibtex][Video]`@inproceedings{leclerc_2020_icra_aggregation, author = {Julien Leclerc and Haoran Zhao and Daniel Bao and Aaron Becker and Mohamad Ghosn and Dipan J. Shah}, title = {Agile 3D-Navigation of a Helical Magnetic Swimmer}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA 2020, Paris France)}, pages = {tbd}, year = {2020}, video = {https://youtu.be/U79idzMZn9Y}, month = {May}, abstract = {Rotating miniature magnetic swimmers are devices that could navigate within the bloodstream to access remote locations of the body and perform minimally invasive procedures. The rotational movement could be used, for example, to abrade a pulmonary embolus. Some regions, such as the heart, are challenging to navigate. Cardiac and respiratory motions of the heart combined with a fast and variable blood flow necessitate a highly agile swimmer. This swimmer should minimize contact with the walls of the blood vessels and the cardiac structures to mitigate the risk of complications. This paper presents experimental tests of a millimeter-scale magnetic helical swimmer navigating in a blood-mimicking solution and describes its turning capabilities. The step-out frequency and the position error were measured for different values of turn radius. The paper also introduces rapid movements that increase the swimmer's agility and demonstrates these experimentally on a complex 3D trajectory.}, }`

- R. A. Moan, V. M. Baez, A. T. Becker, and J. M. O’Kane, “Aggregation and localization of simple robots in curved environments,” in Ieee international conference on robotics and automation (icra 2020, paris france), 2020, p. tbd.

[Bibtex][Video]`@inproceedings{moan_2020_icra_aggregation, author = {Rachel A. Moan and Victor M. Baez and Aaron T. Becker and Jason M. O'Kane}, title = {Aggregation and localization of simple robots in curved environments}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA 2020, Paris France)}, pages = {tbd}, year = {2020}, video = {https://youtu.be/fVhFc41T88I}, month = {May}, abstract = {This paper is about the closely-related problems of localization and aggregation for extremely simple robots, for which the only available action is to move in a given direction as far as the geometry of the environment allows. Such problems may arise, for example, in biomedical applications, wherein a large group of tiny robots moves in response to a shared external stimulus. Specifically, we extend the prior work on these kinds of problems presenting two algorithms for localization in environments with curved (rather than polygonal) boundaries and under low-friction models of interaction with the environment boundaries. We present both simulations and physical demonstrations to validate the approach.}, }`

- A. T. Becker, S. P. Fekete, L. Huang, P. Keldenich, L. Kleist, D. Krupke, C. Rieck, and A. Schmidt, “Targeted drug delivery: advanced algorithmic methods for collecting a swarm of particles with uniform, external forces,” in Ieee international conference on robotics and automation (icra 2020, paris france), 2020, p. tbd.

[Bibtex]`@inproceedings{becker_2020_icra_targeted, author = {Aaron T. Becker and S{\'a}ndor P. Fekete and Li Huang and Phillip Keldenich and Linda Kleist and Dominik Krupke and Christian Rieck and Arne Schmidt}, title = {Targeted Drug Delivery: Advanced Algorithmic Methods for Collecting a Swarm of Particles with Uniform, External Forces}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA 2020, Paris France)}, pages = {tbd}, year = {2020}, month = {May}, abstract = { We investigate algorithmic approaches for targeted drug delivery in a complex, maze-like environment, such as a vascular system. The basic scenario is given by a large swarm of micro-scale particles (``agents'') and a particular target region (``tumor'') within a system of passageways. Agents are too small to contain on-board power or computation and are instead controlled by a global {external} force that acts uniformly on all particles, such as an applied fluidic flow or electromagnetic field. The challenge is to deliver all agents to the target region with a minimum number of actuation steps. We provide a number of results for this challenge. We show that the underlying problem is NP-hard, which explains why previous work did not provide provably efficient algorithms. We also develop a number of algorithmic approaches that greatly improve the worst-case guarantees for the number of required actuation steps. We evaluate our algorithmic approaches by a number of simulations, both for deterministic algorithms and searches supported by deep learning, which show that the performance is practically promising.}, }`

- E. Niehs, A. Schmidt, C. Scheffer, D. E. Biediger, M. Yannuzzi, B. Jenett, A. Abdel-Rahman, K. C. Cheung, A. T. Becker, and S. P. Fekete, “Recognition and reconfiguration of lattice-based cellular structures by simple robots,” in Ieee international conference on robotics and automation (icra 2020, paris france), 2020, p. tbd.

[Bibtex][Video]`@inproceedings{niehs_2020_icra, author = {Eike Niehs and Arne Schmidt and Christian Scheffer and Daniel E. Biediger and Mike Yannuzzi and Benjamin Jenett and Amira Abdel-Rahman and Kenneth C. Cheung and Aaron T. Becker and S{\'a}ndor P. Fekete}, title = {Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA 2020, Paris France)}, pages = {tbd}, year = {2020}, month = {May}, video = {https://youtu.be/K80sV5Xf7v4}, abstract = {We consider recognition and reconfiguration of lattice-based cellular structures by very simple robots with only basic functionality. The underlying motivation is the construction and modification of space facilities of enormous dimensions, where the combination of new materials with extremely simple robots promises structures of previously unthinkable size and flexibility; this is also closely related to the newly emerging field of programmable matter. Aiming for large-scale scalability, both in terms of the number of the cellular components of a structure, as well as the number of robots that are being deployed for construction requires simple yet robust robots and mechanisms, while also dealing with various basic constraints, such as connectivity of a structure during reconfiguration. To this end, we propose an approach that combines ultra-light, cellular building materials with extremely simple robots. We develop basic algorithmic methods that are able to detect and reconfigure arbitrary cellular structures, based on robots that have only constant-sized memory. As a proof of concept, we demonstrate the feasibility of this approach for specific cellular materials and robots that have been developed at NASA.}, }`

- A. T. Becker, S. P. Fekete, L. Huang, P. Keldenich, L. Kleist, D. Krupke, C. Rieck, and A. Schmidt, “Targeted drug delivery: algorithmic methods for collecting a swarm of particles with uniform, external forces,” in 36th european workshop on computational geometry (eurocg), 2020, p. 8:1-8:8.

[Bibtex]`@inproceedings{eurocg20_8, author = {Aaron T. Becker and S{\'a}ndor P. Fekete and Li Huang and Phillip Keldenich and Linda Kleist and Dominik Krupke and Christian Rieck and Arne Schmidt}, title = {Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform, External Forces}, booktitle = {36th European Workshop on Computational Geometry (EuroCG)}, pages = {8:1-8:8}, year = {2020}, }`

- V. Baez, A. T. Becker, S. P. Fekete, and A. Schmidt, “Coordinated particle relocation with global signals and local friction,” in 36th european workshop on computational geometry (eurocg), 2020, p. 9:1-9:8.

[Bibtex][Video]`@inproceedings{eurocg20_9, author = {Victor Baez and Aaron T. Becker and S{\'a}ndor P. Fekete and Arne Schmidt}, title = {Coordinated Particle Relocation with Global Signals and Local Friction}, video = {https://youtu.be/G-t6KYWGHow}, booktitle = {36th European Workshop on Computational Geometry (EuroCG)}, pages = {9:1-9:8}, year = {2020}, }`

- A. Abdel-Rahman, A. T. Becker, D. E. Biediger, K. C. Cheung, S. P. Fekete, B. Jenett, E. Niehs, C. Scheffer, A. Schmidt, and M. Yanuzzi, “Recognition and reconfiguration of lattice-based cellular structures by simple robots,” in 36th european workshop on computational geometry (eurocg), 2020, p. 7:1-7:7.

[Bibtex]`@inproceedings{eurocg20_7, author = {Amira Abdel-Rahman and Aaron T. Becker and Daniel E. Biediger and Kenneth C. Cheung and S{\'a}ndor P. Fekete and Benjamin Jenett and Eike Niehs and Christian Scheffer and Aarne Schmidt and Michael Yanuzzi}, title = {Recognition and Reconfiguration of Lattice-Based Cellular Structures by Simple Robots}, booktitle = {36th European Workshop on Computational Geometry (EuroCG)}, pages = {7:1-7:7}, year = {2020}, }`

- A. T. Becker, S. P. Fekete, L. Huang, P. Keldenich, L. Kleist, D. Krupke, C. Rieck, and A. Schmidt, “Targeted drug delivery: algorithmic methods for collecting a swarm of particles with uniform, external forces,” in 36th european workshop on computational geometry (eurocg), 2020, p. 8:1-8:8.

[Bibtex]`@inproceedings{eurocg20_8, author = {Aaron T. Becker and S{\'a}ndor P. Fekete and Li Huang and Phillip Keldenich and Linda Kleist and Dominik Krupke and Christian Rieck and Arne Schmidt}, title = {Targeted Drug Delivery: Algorithmic Methods for Collecting a Swarm of Particles with Uniform, External Forces}, booktitle = {36th European Workshop on Computational Geometry (EuroCG)}, pages = {8:1-8:8}, year = {2020}, }`

- V. Baez, A. T. Becker, S. P. Fekete, and A. Schmidt, “Packing squares into a disk with optimal worst-case density,” in 36th european workshop on computational geometry (eurocg), 2020, p. 9:1-9:8.

[Bibtex]`@inproceedings{eurocg20_9, author = {Victor Baez and Aaron T. Becker and S{\'a}ndor P. Fekete and Arne Schmidt}, title = {Packing Squares into a Disk with Optimal Worst-Case Density}, booktitle = {36th European Workshop on Computational Geometry (EuroCG)}, pages = {9:1-9:8}, year = {2020}, }`

### 2019

- G. Molina, J. D. Velazco-Garcia, D. Shah, A. T. Becker, I. Seimenis, P. Tsiamyrtzis, and N. V. Tsekos, “Automated segmentation and 4d reconstruction of the heart left ventricle from CINE MRI,” in 2019 ieee 19th international conference on bioinformatics and bioengineering (bibe), 2019, pp. 1019-1023.

[Bibtex]`@INPROCEEDINGS{8941813, author={G. {Molina} and J. D. {Velazco-Garcia} and D. {Shah} and A. T. {Becker} and I. {Seimenis} and P. {Tsiamyrtzis} and N. V. {Tsekos}}, booktitle={2019 IEEE 19th International Conference on Bioinformatics and Bioengineering (BIBE)}, title={Automated Segmentation and 4D Reconstruction of the Heart Left Ventricle from {CINE MRI}}, year={2019}, volume={}, number={}, url={https://ieeexplore.ieee.org/document/8941813}, pages={1019-1023}, abstract={Heart disease is highly prevalent in developed countries, causing 1 in 4 deaths. In this work we propose a method for a fully automated 4D reconstruction of the left ventricle of the heart. This can provide accurate information regarding the heart wall motion and in particular the hemodynamics of the ventricles. Such metrics are crucial for detecting heart function anomalies that can be an indication of heart disease. Our approach is fast, modular and extensible. In our testing, we found that generating the 4D reconstruction from a set of 250 MRI images takes less than a minute. The amount of time saved as a result of our work could greatly benefit physicians and cardiologist as they diagnose and treat patients.}, keywords={biomedical MRI;cardiology;diseases;haemodynamics;image reconstruction;image segmentation;medical image processing;fully automated 4D reconstruction;heart left ventricle;heart wall motion;hemodynamics;heart function anomalies;heart disease;MRI images;CINE MRI;automated segmentation;Magnetic Resonance Imaging;segmentation;reconstruction;cardiac;machine learning;ventricle;heart}, doi={10.1109/BIBE.2019.00189}, ISSN={2159-5410}, month={Oct},}`

- W. Chu, G. Molina, N. V. Navkar, C. F. Eick, A. T. Becker, P. Tsiamyrtzis, and N. V. Tsekos, “BNU-Net: a novel deep learning approach for LV MRI analysis in short-axis MRI,” in 2019 ieee 19th international conference on bioinformatics and bioengineering (bibe), 2019, pp. 731-736.

[Bibtex]`@INPROCEEDINGS{8941959, author={W. {Chu} and G. {Molina} and N. V. {Navkar} and C. F. {Eick} and A. T. {Becker} and P. {Tsiamyrtzis} and N. V. {Tsekos}}, booktitle={2019 IEEE 19th International Conference on Bioinformatics and Bioengineering (BIBE)}, title={{BNU-Net}: A Novel Deep Learning Approach for {LV MRI} Analysis in Short-Axis {MRI}}, year={2019}, volume={}, number={}, pages={731-736}, abstract={This work presents a novel deep learning architecture called BNU-Net for the purpose of cardiac segmentation based on short-axis MRI images. Its name is derived from the Batch Normalized (BN) U-Net architecture for medical image segmentation. New generations of deep neural networks (NN) are called convolutional NN (CNN). CNNs like U-Net have been widely used for image classification tasks. CNNs are supervised training models which are trained to learn hierarchies of features automatically and robustly perform classification. Our architecture consists of an encoding path for feature extraction and a decoding path that enables precise localization. We compare this approach with a parallel approach named U-Net. Both BNU-Net and U-Net are cardiac segmentation approaches: while BNU-Net employs batch normalization to the results of each convolutional layer and applies an exponential linear unit (ELU) approach that operates as activation function, U-Net does not apply batch normalization and is based on Rectified Linear Units (ReLU). The presented work (i) facilitates various image preprocessing techniques, which includes affine transformations and elastic deformations, and (ii) segments the preprocessed images using the new deep learning architecture. We evaluate our approach on a dataset containing 805 MRI images from 45 patients. The experimental results reveal that our approach accomplishes comparable or better performance than other state-of-the-art approaches in terms of the Dice coefficient and the average perpendicular distance.}, keywords={biomedical MRI;cardiology;feature extraction;image classification;image segmentation;learning (artificial intelligence);medical image processing;neural nets;novel deep learning approach;LV MRI analysis;deep learning architecture;BNU-Net;short-axis MRI images;Batch Normalized U-Net architecture;medical image segmentation;deep neural networks;image classification tasks;parallel approach;cardiac segmentation approaches;batch normalization;exponential linear unit approach;image preprocessing techniques;preprocessed images;MRI images;Magnetic Resonance Imaging;Batch Normalization;Exponential Linear Units}, doi={10.1109/BIBE.2019.00137}, ISSN={2159-5410}, month={Oct},}`

- C. M. Morales Mojica, J. D. Velazco-Garcia, H. Zhao, I. Seimenis, E. L. Leiss, D. Shah, A. Webb, A. T. Becker, P. Tsiamyrtzis, and N. V. Tsekos, “Interactive and immersive image-guided control of interventional manipulators with a prototype holographic interface,” in 2019 ieee 19th international conference on bioinformatics and bioengineering (bibe), 2019, pp. 1002-1005.

[Bibtex]`@INPROCEEDINGS{8942031, author={C. M. {Morales Mojica} and J. D. {Velazco-Garcia} and H. {Zhao} and I. {Seimenis} and E. L. {Leiss} and D. {Shah} and A. {Webb} and A. T. {Becker} and P. {Tsiamyrtzis} and N. V. {Tsekos}}, booktitle={2019 IEEE 19th International Conference on Bioinformatics and Bioengineering (BIBE)}, title={Interactive and Immersive Image-Guided Control of Interventional Manipulators with a Prototype Holographic Interface}, year={2019}, volume={}, number={}, pages={1002-1005}, abstract={The emerging potential of augmented reality (AR) to improve 3D medical image visualization for diagnosis, by immersing the user into 3D morphology is further enhanced with the advent of wireless head-mounted displays (HMD). Such information-immersive capabilities may also enhance planning and visualization of interventional procedures. To this end, we introduce a computational platform to generate an augmented reality holographic scene that fuses pre-operative magnetic resonance imaging (MRI) sets, segmented anatomical structures, and an actuated model of an interventional robot for performing MRI-guided and robot-assisted interventions. The interface enables the operator to manipulate the presented images and rendered structures using voice and gestures, as well as to robot control. The software uses forbidden-region virtual fixtures that alerts the operator of collisions with vital structures. The platform was tested with a HoloLens HMD in silico. To address the limited computational power of the HMD, we deployed the platform on a desktop PC with two-way communication to the HMD. Operation studies demonstrated the functionality and underscored the importance of interface customization to fit a particular operator and/or procedure, as well as the need for on-site studies to assess its merit in the clinical realm.}, keywords={augmented reality;biomedical MRI;helmet mounted displays;human computer interaction;image segmentation;manipulators;medical image processing;medical robotics;two-way communication;interactive immersive image-guided control;interface customization;HoloLens HMD;vital structures;forbidden-region virtual fixtures;robot control;rendered structures;robot-assisted interventions;MRI-guided interventions;interventional robot;actuated model;segmented anatomical structures;preoperative magnetic resonance imaging;augmented reality holographic scene;computational platform;information-immersive capabilities;wireless head-mounted displays;3D medical image visualization;prototype holographic interface;interventional manipulators;immersive image-guided control;augmented reality;robot-assistance;image guided interventions}, doi={10.1109/BIBE.2019.00186}, ISSN={2159-5410}, month={Oct},}`

- A. T. Becker, S. P. Fekete, P. Keldenich, S. Morr, and C. Scheffer, “Packing Geometric Objects with Optimal Worst-Case Density (Multimedia Exposition),” in 35th international symposium on computational geometry (socg 2019), Dagstuhl, Germany, 2019, p. 63:1–63:6.

[Bibtex][Video]`@InProceedings{becker2019packing, author = {Aaron T. Becker and S{\'a}ndor P. Fekete and Phillip Keldenich and Sebastian Morr and Christian Scheffer}, title = {{Packing Geometric Objects with Optimal Worst-Case Density (Multimedia Exposition)}}, booktitle = {35th International Symposium on Computational Geometry (SoCG 2019)}, pages = {63:1--63:6}, video={https://youtu.be/QpyjB8c4Ngk}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-104-7}, ISSN = {1868-8969}, year = {2019}, volume = {129}, editor = {Gill Barequet and Yusu Wang}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10467}, URN = {urn:nbn:de:0030-drops-104678}, doi = {10.4230/LIPIcs.SoCG.2019.63}, annote = {Keywords: Packing, complexity, bounds, packing density}, abstract = {We motivate and visualize problems and methods for packing a set of objects into a given container, in particular a set of {different-size} circles or squares into a square or circular container. Questions of this type have attracted a considerable amount of attention and are known to be notoriously hard. We focus on a particularly simple criterion for deciding whether a set can be packed: comparing the total area A of all objects to the area C of the container. The critical packing density delta^* is the largest value A/C for which any set of area A can be packed into a container of area C. We describe algorithms that establish the critical density of squares in a square (delta^*=0.5), of circles in a square (delta^*=0.5390 ...), regular octagons in a square (delta^*=0.5685 ...), and circles in a circle (delta^*=0.5).} }`

- P. Joshi, J. Leclerc, D. Bao, and A. T. Becker, “Motion-planning using rrts for a swarm of robots controlled by global inputs,” in 2019 ieee 15th international conference on automation science and engineering (case), 2019, pp. 1163-1168.

[Bibtex]`@INPROCEEDINGS{8842916, author={P. {Joshi} and J. {Leclerc} and D. {Bao} and A. T. {Becker}}, booktitle={2019 IEEE 15th International Conference on Automation Science and Engineering (CASE)}, title={Motion-planning Using RRTs for a Swarm of Robots Controlled by Global Inputs}, year={2019}, url={https://ieeexplore.ieee.org/abstract/document/8842916}, volume={}, number={}, pages={1163-1168}, abstract={Small-scale robots have great potential in medicine, micro-assembly and many other areas. For example, robots containing iron can be steered using the magnetic gradient generated by MRI scanners. Since the gradient is approximately the same everywhere inside the scanner, each robot receives the same input and therefore they all are subjected to the same force. A similar technique can be used with rotating magnetic fields. Each robot receives the same inputs, making motion planning challenging. This paper uses a Rapidly Exploring Random Tree (RRT) to plan paths that deliver multiple robots to goal positions by using obstacles to break the actuation symmetry.}, keywords={collision avoidance;magnetic resonance imaging;mobile robots;multi-robot systems;trees (mathematics);swarm robots;RRTs;rapidly exploring random tree;small-scale robots;multiple robots;plan paths;motion planning;magnetic fields;MRI scanners;magnetic gradient;Robots;Collision avoidance;Magnetic separation;Magnetic resonance imaging;Planning;Force;Hardware}, doi={10.1109/COASE.2019.8842916}, ISSN={2161-8070}, month={Aug},}`

- D. Biediger, A. Mahadev, and A. T. Becker, “Investigating the survivability of drone swarms with flocking and swarming flight patterns using virtual reality,” in 2019 ieee 15th international conference on automation science and engineering (case), 2019, pp. 1718-1723.

[Bibtex]`@INPROCEEDINGS{8843173, author={D. {Biediger} and A. {Mahadev} and A. T. {Becker}}, booktitle={2019 IEEE 15th International Conference on Automation Science and Engineering (CASE)}, title={Investigating the survivability of drone swarms with flocking and swarming flight patterns using Virtual Reality}, year={2019}, volume={}, number={}, url={https://ieeexplore.ieee.org/abstract/document/8843173}, pages={1718-1723}, abstract={It is now possible to deploy swarms of drones with populations in the thousands. There is growing interest in using such swarms for defense, and it has been natural to program them with bio-mimetic motion models such as flocking or swarming. However, these motion models evolved to survive against predators, not enemies with modern firearms. This paper presents experimental data that compares the survivability of several motion models for large numbers of drones. This project tests drone swarms in Virtual Reality (VR), because it is prohibitively expensive, technically complex, and potentially dangerous to fly a large swarm of drones in a testing environment. We model the behavior of drone swarms flying along parametric paths in both tight and scattered formations. We add random motion to the general motion plan to confound path prediction and targeting. We describe an implementation of these flight paths as game levels in a VR environment. We then allow players to shoot at the drones and evaluate the difference between flocking and swarming behavior on drone survivability.}, keywords={autonomous aerial vehicles;computer games;mobile robots;multi-robot systems;particle swarm optimisation;path planning;virtual reality;swarming flight patterns;bio-mimetic motion models;general motion plan;VR environment;parametric paths;drone swarms flying;flocking flight patterns;drone swarms survivability;virtual reality;Drones;Solid modeling;Testing;Birds;Virtual reality;Biological system modeling;Games}, doi={10.1109/COASE.2019.8843173}, ISSN={2161-8070}, month={Aug},}`

- S. Bhatnagar, S. Soto, J. Garcia, and A. T. Becker, “Robotic harvesting of a moving swarm represented by a markov process,” in 2019 ieee 15th international conference on automation science and engineering (case), 2019, pp. 1157-1162.

[Bibtex][Video]`@INPROCEEDINGS{8843164, author={S. {Bhatnagar} and S. {Soto} and J. {Garcia} and A. T. {Becker}}, booktitle={2019 IEEE 15th International Conference on Automation Science and Engineering (CASE)}, title={Robotic Harvesting of a Moving Swarm Represented by a Markov Process}, year={2019}, volume={}, url={https://ieeexplore.ieee.org/document/8843164}, video={https://youtu.be/_GUFjmxr8Ak}, number={}, pages={1157-1162}, abstract={This paper investigates motion planning for one or more robot(s) that attempt to harvest agents from a moving swarm. Generating motion paths that maximize the number of agents harvested differs from many traditional coverage problems because the agents move. This movement allows previously cleared areas to become recontaminated. We assume that the swarm agents prefer certain regions over others, and that we can represent the swarm by a Markov Process that encodes the agents' preferred regions and their speed of motion. We exploit this model to design and simulate robotic coverage paths that maximize the number of agents harvested by a fleet of robots in a given time budget.}, keywords={Markov processes;mobile robots;path planning;robotic harvesting;moving swarm;Markov process;motion paths;traditional coverage problems;swarm agents;robotic coverage paths;motion planning;Robot sensing systems;Markov processes;Sociology;Statistics;Task analysis;Probabilistic logic}, doi={10.1109/COASE.2019.8843164}, ISSN={2161-8070}, month={Aug},}`

- S. Shahrokhi, H. Zhao, and A. T. Becker, “Reshaping particle configurations by collisions with rigid objects,” in 2019 international conference on robotics and automation (icra), 2019, pp. 4436-4443.

[Bibtex][Video]`@INPROCEEDINGS{8794405, author={S. {Shahrokhi} and H. {Zhao} and A. T. {Becker}}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, title={Reshaping Particle Configurations by Collisions with Rigid Objects}, year={2019}, volume={}, number={}, url={}, video={https://youtu.be/_GUFjmxr8Ak}, pages={4436-4443}, abstract={Consider many particles actuated by a uniform global external field (e.g. gravitational or magnetic fields). This paper presents analytical results using workspace obstacles and global inputs to reshape such a group of particles. Shape control of many particles is necessary for conveying information, construction, and navigation. First we show how the particles' characteristic angle of repose can be used to reshape the particles by controlling angle of attack and the magnitude of the driving force. These can then be used to control the force and torque applied to a rectangular rigid body. Next, we examine the full set of stable, achievable mean and variance configurations for the shape of a particle group in two canonical environments: a square and a circular workspace. Finally, we show how workspaces with linear boundary layers can be used to achieve a more rich set of mean and variance configurations.}, keywords={actuators;collision avoidance;multi-robot systems;shear modulus;uniform global external field;magnetic fields;workspace obstacles;shape control;navigation;driving force;torque;rectangular rigid body;particle group;circular workspace;mean variance configurations;Shape;Force;Torque;Shape control;Magnetic resonance imaging;Magnetoacoustic effects;Correlation}, doi={10.1109/ICRA.2019.8794405}, ISSN={1050-4729}, month={May},}`

- H. Zhao, X. Liu, R. Korpu, M. J. Heffernan, A. T. Becker, and N. V. Tsekos, “Studies on positioning manipulators actuated by solid media transmissions,” in 2019 international conference on robotics and automation (icra), 2019, pp. 1226-1232.

[Bibtex][Video]`@INPROCEEDINGS{8794356, author={H. {Zhao} and X. {Liu} and R. {Korpu} and M. J. {Heffernan} and A. T. {Becker} and N. V. {Tsekos}}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, title={Studies on Positioning Manipulators Actuated by Solid Media Transmissions}, year={2019}, volume={}, number={}, video={https://youtu.be/Os5KGcmPqcs}, url={https://ieeexplore.ieee.org/document/8794356}, pages={1226-1232}, abstract={Fluidic transmission mechanisms use fluids to transmit force through conduits. We previously presented a transmission mechanism called solid-media transmission (SMT), which uses conduits filled with spheres and spacers for push-only bidirectional transmission. In this paper, we present new designs of SMT-actuated one-degree-of-freedom (DoF) and two-degree-of-freedom positioning manipulators, and report experiment studies to assess their performance. In these studies, closed-loop position control was performed with a PI controller and/or master-slave control. With braided PTFE tubing, SMT exhibited sub-millimeter accuracy, with a tolerance of +/-0.05 mm for the tested transmission lines with lengths up to 4m.}, keywords={actuators;closed loop systems;manipulators;PI control;position control;telerobotics;transmission lines;PI controller;master-slave control;positioning manipulators;PTFE tubing;closed-loop position control;push-only bidirectional transmission;SMT;solid-media transmission;fluidic transmission mechanisms;Manipulators;Kinematics;Robot kinematics;Needles;Strips;Fasteners}, doi={10.1109/ICRA.2019.8794356}, ISSN={1050-4729}, month={May},}`

- J. Leclerc, H. Zhao, and A. T. Becker, “3d control of rotating millimeter-scale swimmers through obstacles,” in 2019 international conference on robotics and automation (icra), 2019, pp. 8890-8896.

[Bibtex][Video]`@INPROCEEDINGS{8794045, author={J. {Leclerc} and H. {Zhao} and A. T. {Becker}}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, title={3D Control of Rotating Millimeter-Scale Swimmers Through Obstacles}, year={2019}, volume={}, number={}, video={https://youtu.be/qMR0tZabKk8}, url={https://ieeexplore.ieee.org/document/8794045}, pages={8890-8896}, abstract={This study investigates the high speed 3D navigation of rotating millimeter-scale swimmers. The swimmers have a spiral-shaped surface to ensure propulsion. The rotational movement is used for propulsion and, in future work, could provide the power needed to remove blood clots. For instance, an abrasive tip could be used to progressively grind a blood clot. An algorithm to perform 3D control of rotating millimeter-scale swimmers was implemented and tested experimentally. The swimmers can follow a trajectory and can navigate without touching the walls inside a tube having a diameter of 15 mm. This diameter is smaller than the average diameter of the distal descending aorta, which is the smallest section of the aorta. Several swimmers designs were built and tested. The maximum velocity recorded for our best swimmer was 103.6 mm/s with a rotational speed of 477.5 rotations per second.}, keywords={biomechanics;biomedical equipment;blood;blood vessels;medical control systems;propulsion;swimmer designs;rotating millimeter-scale swimmers;aorta;blood clot;rotational movement;high speed 3D navigation;Arteries;Electromagnets;Force;Trajectory;Manipulators;Velocity control;Navigation}, doi={10.1109/ICRA.2019.8794045}, ISSN={1050-4729}, month={May},}`

- L. Huang, J. Leclerc, and A. T. Becker, “Analysis of 3d position control for a multi-agent system of self-propelled agents steered by a shared, global control input,” in 2019 international conference on robotics and automation (icra), 2019, pp. 4465-4471.

[Bibtex][Video]`@INPROCEEDINGS{8793800, author={L. {Huang} and J. {Leclerc} and A. T. {Becker}}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, title={Analysis of 3D Position Control for a Multi-Agent System of Self-Propelled Agents Steered by a Shared, Global Control Input}, year={2019}, volume={}, number={}, video={https://youtu.be/sSSQgnmjmJw}, url={https://ieeexplore.ieee.org/document/8793800}, pages={4465-4471}, abstract={This paper investigates strategies for 3D multi-agent position control using a shared control input and self-propelled agents. The only control inputs allowed are rotation commands that rotate all agents by the same rotation matrix. In the 2D case, only two degrees-of-freedom (DOF) in position are controllable. We review controllability results in 2D, and then show that interesting things happen in 3D. We provide control laws for steering up to nine DOF in position, which can be mapped in various ways, including to control the x, y, z position of three agents, make four agents meet, or reduce the spread of n agents.}, keywords={closed loop systems;controllability;matrix algebra;multi-agent systems;multi-robot systems;nonlinear control systems;position control;control laws;multiagent system;self-propelled agents;shared control input;global control input;3D multiagent position control;control inputs;rotation commands;rotation matrix;controllability results;2D case;Three-dimensional displays;Two dimensional displays;Orbits;Position control;Perturbation methods;Aerospace electronics;Robots}, doi={10.1109/ICRA.2019.8793800}, ISSN={1050-4729}, month={May},}`

- L. W. Rogowski, X. Zhang, L. Huang, A. Bhattacharjee, J. S. Lee, A. T. Becker, and M. J. Kim, “Feedback control and 3d motion of heterogeneous janus particles,” in 2019 international conference on robotics and automation (icra), 2019, pp. 1352-1357.

[Bibtex]`@INPROCEEDINGS{8793678, author={L. W. {Rogowski} and X. {Zhang} and L. {Huang} and A. {Bhattacharjee} and J. S. {Lee} and A. T. {Becker} and M. J. {Kim}}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, title={Feedback Control and 3D Motion of Heterogeneous Janus Particles}, year={2019}, volume={}, number={}, url={https://ieeexplore.ieee.org/document/8793678}, pages={1352-1357}, abstract={This paper presents 2D feedback control and open loop 3D trajectories of heterogeneous chemically catalyzing Janus particles. Self-actuated particles have enormous implications for both in vivo and in vitro environments, which make them a diverse resource for a variety of medical and assembly applications. Janus particles, consisting of cobalt and platinum hemispheres, can self-propel in hydrogen peroxide solutions due to platinum's catalyzation properties. These particles are directionally controlled using static magnetic fields produced from a triaxial approximate Helmholtz coil system. Since the magnetization direction of Janus particles is often heterogeneous, and thereby not consistent with the propulsion direction, this creates a unique opportunity to explore the motion effects of these particles under 2D feedback control and open loop 3D control. Using a modified closed loop controller, Janus particles with magnetization both closely aligned and greatly misaligned to the propulsion vectors, were instructed to perform complex trajectories. These trajectories were then compared between trials to measure both consistency and accuracy. The effects of increasing offset between the magnetization and propulsion vectors were also analyzed. The effects this heterogeneity had on 3D motion is also briefly discussed. It is our hope going forward to develop a 3D closed loop control system that can retroactively account for variations in the magnetization vector.}, keywords={chemical engineering;closed loop systems;feedback;open loop systems;position control;propulsion;vectors;3D closed loop control system;3D motion;self-actuated particles;open loop 3D control;2D feedback control;triaxial approximate Helmholtz coil system;propulsion vectors;heterogeneous chemically catalyzing Janus particles;Conferences;Automation}, doi={10.1109/ICRA.2019.8793678}, ISSN={1050-4729}, month={May},}`

- D. A. Shell, L. Huang, A. T. Becker, and J. M. O’Kane, “Planning coordinated event observation for structured narratives,” in 2019 international conference on robotics and automation (icra), 2019, pp. 7632-7638.

[Bibtex][Video]`@INPROCEEDINGS{8794450, author={D. A. {Shell} and L. {Huang} and A. T. {Becker} and J. M. {O'Kane}}, booktitle={2019 International Conference on Robotics and Automation (ICRA)}, title={Planning Coordinated Event Observation for Structured Narratives}, year={2019}, volume={}, video={https://youtu.be/WZzHPwlgHkg}, url={https://ieeexplore.ieee.org/document/8794450}, number={}, pages={7632-7638}, abstract={This paper addresses the problem of using autonomous robots to record events that obey narrative structure. The work is motivated by a vision of robot teams that can, for example, produce individualized highlight videos for each runner in a large-scale road race such as a marathon. We introduce a method for specifying the desired structure as a function that describes how well the captured events can be used to produce an output that meets the specification. This function is specified in a compact, legible form similar to a weighted finite automaton. Then we describe a planner that uses simple predictions of future events to coordinate the robots' efforts to capture the most important events, as determined by the specification. We describe an implementation of this approach, and demonstrate its effectiveness in a simulated race scenario both in simulation and in a hardware testbed.}, keywords={finite automata;mobile robots;multi-robot systems;sport;structured narratives;autonomous robots;robot teams;large-scale road race;marathon;legible form;weighted finite automaton;simulated race scenario;coordinated event observation planning;Videos;Robot kinematics;Cameras;Robot vision systems;Mobile robots;Observers}, doi={10.1109/ICRA.2019.8794450}, ISSN={1050-4729}, month={May},}`

### 2018

- D. Wei, S. S. Soto, J. Garcia, A. T. Becker, L. Wang, and M. Pan, “ROV assisted magnetic induction communication field tests in underwater environments,” in Proceedings of the thirteenth acm international conference on underwater networks & systems, New York, NY, USA, 2018.

[Bibtex]`@inproceedings{10082515, author = {Wei, Debing and Soto, Steban S. and Garcia, Javier and Becker, Aaron T. and Wang, Li and Pan, Miao}, title = {{ROV} Assisted Magnetic Induction Communication Field Tests in Underwater Environments}, year = {2018}, isbn = {9781450361934}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, url = {https://doi.org/10.1145/3291940.3291988}, doi = {10.1145/3291940.3291988}, booktitle = {Proceedings of the Thirteenth ACM International Conference on Underwater Networks & Systems}, articleno = {Article 20}, numpages = {5}, keywords = {subsea environment, underwater wireless communications, magnetic induction, ROV}, location = {Shenzhen, China}, series = {WUWNet 18}, abstract={Magnetic Induction (MI) is a promising technique for near-field wireless underwater communications. Although the literature has some theoretical analyses and lab experiments for underwater MI communication, there is a lack of field tests in underwater environments, especially in subsea environments. In this paper, we leverage the remotely operated vehicle (ROV) and the remotely controlled boat (RCB) to develop an MI wireless communication system, and conduct field tests for MI communication performance in both fresh water and sea water. The experiment results show that even in the most challenging subsea environment, the MI communication has very good near-field transmission performance with a small coil antenna and low power consumption.}, }`

- S. Kalantari, A. T. Becker, and R. Ike, “Designing for digital assembly with a construction team of mobile robots.” 2018.

[Bibtex][Video]`@inproceedings{kalantari2018designing, title={Designing for digital assembly with a construction team of mobile robots}, author={Kalantari, Salah and Becker, Aaron T and Ike, Rhema}, year={2018}, organization={ACADIA}, video={https://youtu.be/2f_eN6wMiR0}, anstract={Advances in construction automation have primarily focused on creating heavy machines to accomplish repetitive tasks. While this approach is valuable in an assembly-line context, it does not always translate well for the diverse terrain and dynamic nature of construction sites. As a result, the use of automation in the architectural assembly has lagged far behind other industries. To address the challenges of construction site assembly, this project suggests an alternative technique that uses a fleet of smaller robots working in parallel. The proposed method, which is inspired by the construction techniques of insect colonies, has several advantages over the use of larger machines. It allows for much greater on-site flexibility and portability. It is also easy to scale the operation, by adding or removing additional units as needed. The use of multiple small robots provides operational redundancy that can adapt to the loss of any particular machine. These advantages make the technology particularly suitable for construction in hazardous or inaccessible areas. The use of assembly robots also opens new horizons for design creativity, allowing architects to explore new ideas that would be unwieldy and expensive to construct using traditional techniques. In our tests, we used a team of small mobile robots to fold 2D laser-cut stock into 3D curved structures, and then assemble these units into larger interlocked forms.}, url={https://www.semanticscholar.org/paper/Designing-for-Digital-Assembly-with-a-Construction-Kalantari/d564691fff4469398a79a96c519b183fd69df183}, }`

- P. Keldenich, S. Manzoor, L. Huang, D. Krupke, A. Schmidt, S. P. Fekete, and A. T. Becker, “On designing 2d discrete workspaces to sort or classify polyominoes,” in 2018 ieee/rsj international conference on intelligent robots and systems (iros), 2018, pp. 1-9.

[Bibtex][Video]`@INPROCEEDINGS{8594150, author={P. {Keldenich} and S. {Manzoor} and L. {Huang} and D. {Krupke} and A. {Schmidt} and S. P. {Fekete} and A. T. {Becker}}, booktitle={2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, title={On Designing 2D Discrete Workspaces to Sort or Classify Polyominoes}, year={2018}, volume={}, number={}, video={https://youtu.be/ZeBur5F7sIo}, url={https://ieeexplore.ieee.org/document/8594150}, pages={1-9}, abstract={This paper studies the general problem of physically sorting polyominoes according to shape using a 2D, rigid, grid-based workspace. The workspace is designed for sensorless operation, using a fixed set of open-loop force-field inputs that move a polyomino from an inlet port to an outlet port that corresponds to the polyomino's shape, and reset the workspace to classify the next polyomino. This paper proves that static workspaces can classify all orthoconvex polyominoes of width w and height h, and provides a motion sequence and required size of workspace as a function of wand h. By allowing moving polyomino cams that assist in the sorting, we can design dynamic works paces that can sort all polyominoes that are ``completely filled'' using a constant number of force-field inputs. Hardware experiments using magnetic and gravity-based actuation demonstrate these static and dynamic sensorless classifiers at the millimeter scale.}, keywords={materials handling;robotic assembly;polyominoes sorting;2D discrete workspace design;dynamic sensorless classifiers;orthoconvex polyominoes;grid-based workspace;Sorting;Shape;Robot sensing systems;Two dimensional displays;Machine vision;Cams;Dynamics}, doi={10.1109/IROS.2018.8594150}, ISSN={2153-0858}, month={Oct},}`

- A. T. Becker, S. P. Fekete, P. Keldenich, M. Konitzny, L. Lin, and C. Scheffer, “Coordinated Motion Planning: The Video (Multimedia Exposition),” in 34th international symposium on computational geometry (socg 2018), Dagstuhl, Germany, 2018, p. 74:1–74:6.

[Bibtex][Video]`@InProceedings{beckercoordinatedmotion2018, author = {Aaron T. Becker and S{\'a}ndor P. Fekete and Phillip Keldenich and Matthias Konitzny and Lillian Lin and Christian Scheffer}, title = {{Coordinated Motion Planning: The Video (Multimedia Exposition)}}, booktitle = {34th International Symposium on Computational Geometry (SoCG 2018)}, pages = {74:1--74:6}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-066-8}, ISSN = {1868-8969}, year = {2018}, volume = {99}, video = {https://youtu.be/_2CsL_vaQTo}, editor = {Bettina Speckmann and Csaba D. T{\'o}th}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8787}, URN = {urn:nbn:de:0030-drops-87872}, doi = {10.4230/LIPIcs.SoCG.2018.74}, annote = {Keywords: Motion planning, robot swarms, complexity, stretch, approximation}, abstract = {We motivate, visualize and demonstrate recent work for minimizing the total execution time of a coordinated, parallel motion plan for a swarm of N robots in the absence of obstacles. Under relatively mild assumptions on the separability of robots, the algorithm achieves constant stretch: If all robots want to move at most d units from their respective starting positions, then the total duration of the overall schedule (and hence the distance traveled by each robot) is O(d) steps; this implies constant-factor approximation for the optimization problem. Also mentioned is an NP-hardness result for finding an optimal schedule, even in the case in which robot positions are restricted to a regular grid. On the other hand, we show that for densely packed disks that cannot be well separated, a stretch factor Omega(N^{1/4}) is required in the worst case; we establish an achievable stretch factor of O(N^{1/2}) even in this case. We also sketch geometric difficulties of computing optimal trajectories, even for just two unit disks.}, }`

- A. Nguyen, D. Krupke, M. Burbage, S. Bhatnagar, S. P. Fekete, and A. T. Becker, “Using a uav for destructive surveys of mosquito population,” in 2018 ieee international conference on robotics and automation (icra), 2018, pp. 7812-7819.

[Bibtex][Video]`@INPROCEEDINGS{8463184, author={A. {Nguyen} and D. {Krupke} and M. {Burbage} and S. {Bhatnagar} and S. P. {Fekete} and A. T. {Becker}}, booktitle={2018 IEEE International Conference on Robotics and Automation (ICRA)}, title={Using a UAV for Destructive Surveys of Mosquito Population}, year={2018}, volume={}, video={https://youtu.be/OTQSR03Bv5g}, url={https://ieeexplore.ieee.org/document/8463184}, number={}, pages={7812-7819}, abstract={This paper introduces techniques for mosquito population surveys in the field using electrified screens (bug zappers) mounted to a UAV. Instrumentation on the UAV logs the UAV path and the GPS location, altitude, and time of each mosquito elimination. Hardware experiments with a UAV equipped with an electrified screen provide real-time measurements of (former) mosquito locations and mosquito-free volumes. Planning a trajectory for the UAV that maximizes the number of mosquito kills is related to the Traveling Salesman Problem, the Lawn Mower Problem and, most closely, Milling with Turn Cost. We reduce this problem to considering variants of covering a grid graph with minimum turn cost, corresponding to optimized energy consumption. We describe an exact method based on Integer Programming that is able to compute provably optimal instances with over 1,500 pixels. These solutions are then implemented on the UAV.}, keywords={autonomous aerial vehicles;diseases;graph theory;integer programming;path planning;travelling salesman problems;destructive surveys;mosquito population;electrified screen;UAV path;mosquito elimination;trajectory planning;traveling salesman problem;milling with turn cost;lawn mower problem;grid graph;optimized energy consumption;Integer Programming;mosquito-borne diseases;mosquito-killing UAV;Unmanned aerial vehicles;Sociology;Statistics;Global Positioning System;Robots;Monitoring;Wind tunnels}, doi={10.1109/ICRA.2018.8463184}, ISSN={2577-087X}, month={May},}`

### 2017

- A. T. Becker, S. P. Fekete, P. Keldenich, D. Krupke, C. Rieck, C. Scheffer, and A. Schmidt, “Tilt Assembly: Algorithms for Micro-Factories that Build Objects with Uniform External Forces,” in 28th international symposium on algorithms and computation (isaac 2017), Dagstuhl, Germany, 2017, p. 11:1–11:13.

[Bibtex]`@InProceedings{becker_et_al2017:8221, author = {Aaron T. Becker and S{\'a}ndor P. Fekete and Phillip Keldenich and Dominik Krupke and Christian Rieck and Christian Scheffer and Arne Schmidt}, title = {{Tilt Assembly: Algorithms for Micro-Factories that Build Objects with Uniform External Forces}}, booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)}, pages = {11:1--11:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-054-5}, ISSN = {1868-8969}, year = {2017}, volume = {92}, editor = {Yoshio Okamoto and Takeshi Tokuyama}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8221}, URN = {urn:nbn:de:0030-drops-82214}, doi = {10.4230/LIPIcs.ISAAC.2017.11}, annote = {Keywords: Programmable matter, micro-factories, tile assembly, tilt, approximation, hardness}, abstract = {We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield micro-factories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles can bond when being forced together with another appropriate particle. Due to the physical and geometric constraints, not all shapes can be built in this manner; this gives rise to the Tilt Assembly Problem (TAP) of deciding constructibility. For simply-connected polyominoes P in 2D consisting of N unit-squares (``tiles''), we prove that TAP can be decided in O(N log N) time. For the optimization variant MaxTAP (in which the objective is to construct a subshape of maximum possible size), we show polyAPX-hardness: unless P=NP, MaxTAP cannot be approximated within a factor of N^(1/3); for tree-shaped structures, we give an N^(1/2)-approximation algorithm. For the efficiency of the assembly process itself, we show that any constructible shape allows pipelined assembly, which produces copies of P in O(1) amortized time, i.e., N copies of P in O(N) time steps. These considerations can be extended to three-dimensional objects: For the class of polycubes P we prove that it is NP-hard to decide whether it is possible to construct a path between two points of P; it is also NP-hard to decide constructibility of a polycube P. Moreover, it is expAPX-hard to maximize a path from a given start point.}, }`

- H. Zhao, X. Liu, H. M. Zaid, D. J. Shah, M. J. Heffernan, A. T. Becker, and N. V. Tsekos, “Early studies of a transmission mechanism for mr-guided interventions,” in 2017 ieee 17th international conference on bioinformatics and bioengineering (bibe), 2017, pp. 450-456.

[Bibtex]`@INPROCEEDINGS{8251331, author={H. {Zhao} and X. {Liu} and H. M. {Zaid} and D. J. {Shah} and M. J. {Heffernan} and A. T. {Becker} and N. V. {Tsekos}}, booktitle={2017 IEEE 17th International Conference on Bioinformatics and Bioengineering (BIBE)}, title={Early Studies of a Transmission Mechanism for MR-Guided Interventions}, year={2017}, volume={}, number={}, pages={450-456}, abstract={Magnetic resonance imaging (MRI)-guided, manipulator-assisted interventions have the potential to improve patient outcomes. This work presents a force transmission mechanism, called solid-media transmission (SMT), for actuating manipulators inside MRI scanners. The SMT mechanism is based on conduits filled with spheres and spacers made of a nonmagnetic, nonconductive material that forms a backbone for bidirectional transmission. Early modeling and experimental studies assessed SMT and identified limitations and improvements. Simulations demonstrated the detrimental role of friction, which can be alleviated with a choice of low friction material and long spacers. However, the length of the spacer is limited by the desired bending of the conduit. A closed-loop control law was implemented to drive the SMT. The 3rd order system fit ratio is 92.3%. A 1-m long SMT was experimentally tested under this closed-loop controller with heuristically set parameters using a customized benchtop setup. For commanded displacements of 1 to 50 mm, the SMT-actuated 1 degree of freedom stage exhibited sub-millimeter accuracy, which ranged from 0.109 +/- 0:057 mm to 0.045 +/- 0.029 mm depending on the commanded displacement. However, such accuracy required long control times inversely proportional to displacement ranging from 7.56 +/- 1.85s to 2.53 +/- 0.11s. This was attributed to friction as well as backlash which is due to suboptimal packing of the media. In MR studies, a 4-m long SMT-actuated 1 DoF manipulator was powered by a servo motor located inside the scanner room but outside the 5 Gauss line of the magnet. With shielding and filtering, the SNR of MR images during the operation of the servo motor and SMT- actuation was found to be 89 +/- 9% of the control case.}, keywords={biomedical MRI;closed loop systems;friction;image filtering;manipulators;medical image processing;medical robotics;surgery;MR-guided interventions;magnetic resonance imaging;manipulator-assisted interventions;force transmission mechanism;MRI scanners;SMT mechanism;nonmagnetic material;nonconductive material;bidirectional transmission;low friction material;long spacers;closed-loop control law;closed-loop controller;DoF manipulator;solid-media transmission;servo motor;Gauss line;Force;Friction;Media;Manipulators;Electromagnetic interference;Solids;Solid media transmission;MR compatible;Robotic Actuator}, doi={10.1109/BIBE.2017.00-13}, ISSN={2471-7819}, month={Oct},}`

- L. Huang, L. Rogowski, M. J. Kim, and A. T. Becker, “Path planning and aggregation for a microrobot swarm in vascular networks using a global input,” in 2017 ieee/rsj international conference on intelligent robots and systems (iros), 2017, pp. 414-420.

[Bibtex][Video]`@INPROCEEDINGS{8202188, author={L. {Huang} and L. {Rogowski} and M. J. {Kim} and A. T. {Becker}}, booktitle={2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, title={Path planning and aggregation for a microrobot swarm in vascular networks using a global input}, year={2017}, volume={}, number={}, pages={414-420}, abstract={Microrobots have great potential for microassembly and non-invasive surgery applications. Motivated by studies proposing MRI-guided drug delivery to tumor cells using magnetic micro carriers, this paper studies two major challenges of this problem: (i) microrobot swarm trajectory generation, and (ii) swarm aggregation using a global input. We propose an augmented RRT for trajectory generation to reduce environment interference, and a divide-and-conquer algorithm for swarm aggregation to improve performance. Simulations demonstrate the utility of these approaches in comparison to alternate heuristics. Our trajectory generation and aggregation strategies are implemented on a swarm of ferromagnetic microparticles in oil using a 6-coil electromagnetic system with image feedback.}, keywords={biomedical MRI;drug delivery systems;drugs;magnetic particles;medical robotics;microrobots;path planning;swarm intelligence;tumours;divide-and-conquer algorithm;path planning;MRI-guided drug delivery;microrobot swarm;ferromagnetic microparticles;6-coil electromagnetic system;image feedback;augmented RRT;microrobot swarm trajectory generation;magnetic microcarriers;tumor cells;vascular networks;swarm aggregation;Trajectory;Robots;Drug delivery;Aerospace electronics;Collision avoidance}, doi={10.1109/IROS.2017.8202188}, ISSN={2153-0866}, video = {https://youtu.be/9gQLpYTyg_E}, url = {https://ieeexplore.ieee.org/document/8202188}, month={Sep.},}`

- S. Shahrokhi, A. Mahadev, and A. T. Becker, “Algorithms for shaping a particle swarm with a shared input by exploiting non-slip wall contacts,” in 2017 ieee/rsj international conference on intelligent robots and systems (iros), 2017, pp. 4304-4311.

[Bibtex][Video]`@INPROCEEDINGS{8206294, author={S. {Shahrokhi} and A. {Mahadev} and A. T. {Becker}}, booktitle={2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, title={Algorithms for shaping a particle swarm with a shared input by exploiting non-slip wall contacts}, year={2017}, volume={}, number={}, pages={4304-4311}, abstract={There are driving applications for large populations of tiny robots in robotics, biology, and chemistry. These robots often lack onboard computation, actuation, and communication. Instead, these ``robots'' are particles carrying some payload and the particle swarm is controlled by a shared control input such as a uniform magnetic gradient or electric field. In previous works, we showed that the 2D position of each particle in such a swarm is controllable if the workspace contains a single obstacle the size of one particle. Requiring a small, rigid obstacle suspended in the middle of the workspace is a strong constraint, especially in 3D. This paper relaxes that constraint, and provides position control algorithms that only require non-slip wall contact in 2D. Both in vivo and artificial environments often have such boundaries. We assume that particles in contact with the boundaries have zero velocity if the shared control input pushes the particle into the wall. This paper provides a shortest-path algorithm for positioning a two-particle swarm, and a generalization to positioning an n-particle swarm. Results are validated with simulations and a hardware demonstration.}, keywords={collision avoidance;graph theory;microrobots;mobile robots;velocity control;nonslip wall contact;tiny robots;onboard computation;uniform magnetic gradient;rigid obstacle;position control algorithms;shortest-path algorithm;two-particle swarm;n-particle swarm;zero velocity;Robot kinematics;Robot sensing systems;Particle swarm optimization;Force;Two dimensional displays;Position control}, url={https://ieeexplore.ieee.org/document/8206294}, video = {https://youtu.be/MxudWbNZdC4}, doi={10.1109/IROS.2017.8206294}, ISSN={2153-0866}, month={Sep.},}`

- A. Mahadev, D. Krupke, S. P. Fekete, and A. T. Becker, “Mapping and coverage with a particle swarm controlled by uniform inputs,” in 2017 ieee/rsj international conference on intelligent robots and systems (iros), 2017, pp. 1097-1104.

[Bibtex][Video]`@INPROCEEDINGS{8202280, author={A. {Mahadev} and D. {Krupke} and S. P. {Fekete} and A. T. {Becker}}, booktitle={2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, title={Mapping and coverage with a particle swarm controlled by uniform inputs}, year={2017}, volume={}, number={}, pages={1097-1104}, abstract={We propose an approach to mapping tissue and vascular systems without the use of contrast agents, based on moving and measuring magnetic particles. To this end, we consider a swarm of particles in a 1D or 2D grid that can be tracked and controlled by an external agent. Control inputs are applied uniformly so that each particle experiences the same applied forces. We present algorithms for three tasks: (1) Mapping, i.e., building a representation of the free and obstacle regions of the workspace; (2) Subset Coverage, i.e., ensuring that at least one particle reaches each of a set of desired locations; and (3) Coverage, i.e., ensuring that every free region on the map is visited by at least one particle. These tasks relate to a large body of previous work from robot navigation, both from theory and practice, which is based on individual control. We provide theoretical insights that have potential relevance for fast MRI scans with magnetically controlled contrast media. In particular, we develop a fundamentally new approach for searching for an object at an unknown distance D, where the search is subject to two different and independent cost parameters for moving and for measuring. We show that regardless of the relative cost of these two operations, there is a simple O(log D/log log D)-competitive strategy, which is the best possible. Also, we provide practically useful and computationally efficient strategies for higher-dimensional settings. These algorithms extend to any number of particles and show that additional particles tend to reduce the mean and the standard deviation of the time required for each task.}, keywords={biomedical MRI;collision avoidance;medical image processing;mobile robots;multi-robot systems;particle swarm optimisation;particle swarm;uniform inputs;contrast agents;external agent;control inputs;robot navigation;individual control;fast MRI scans;magnetically controlled contrast media;magnetic particles;Robots;Search problems;Two dimensional displays;Manganese;Atmospheric measurements;Particle measurements}, doi={10.1109/IROS.2017.8202280}, ISSN={2153-0866}, url = {https://ieeexplore.ieee.org/document/8202280}, video = {https://youtu.be/77AaoEnd5b4}, month={Sep.},}`

- T. Kensicher, J. Leclerc, D. Biediger, D. J. Shah, I. Seimenis, A. T. Becker, and N. V. Tsekos, “Towards MRI-guided and actuated tetherless milli-robots: preoperative planning and modeling of control,” in 2017 ieee/rsj international conference on intelligent robots and systems (iros), 2017, pp. 6440-6447.

[Bibtex]`@INPROCEEDINGS{8206550, author={T. {Kensicher} and J. {Leclerc} and D. {Biediger} and D. J. {Shah} and I. {Seimenis} and A. T. {Becker} and N. V. {Tsekos}}, booktitle={2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, title={Towards {MRI}-guided and actuated tetherless milli-robots: Preoperative planning and modeling of control}, year={2017}, volume={}, number={}, pages={6440-6447}, abstract={Image-guided and robot-assisted surgical procedures are rapidly evolving due to their potential to improve patient management and cost effectiveness. Magnetic Resonance Imaging (MRI) is used for pre-operative planning and is also investigated for real-time intra-operative guidance. A new type of technology is emerging that uses the magnetic field gradients of the MR scanner to maneuver ferromagnetic agents for local delivery of therapeutics. With this approach, MRI is both a sensor and forms a closed-loop controlled entity that behaves as a robot (we refer to them as MRbots). The objective of this paper is to introduce a computational framework for preoperative planning using MRI and modeling of MRbot maneuvering inside tortuous blood vessels. This platform generates a virtual corridor that represents a safety zone inside the vessel that is then used to access the safety of the MRbot maneuvering. In addition, to improve safety we introduce a control that sets speed based on the local curvature of the vessel. The functionality of the framework was then tested on a realistic operational scenario of accessing a neurological lesion, a meningioma. This virtual case study demonstrated the functionality and potential of MRbots as well as revealed two primary challenges: real-time MRI (during propulsion) and the need of very strong gradients for maneuvering small MRbots inside narrow cerebral vessels. Our ongoing research focuses on further developing the computational core, MR tracking methods, and on-line interfacing to the MR scanner.}, keywords={biomedical MRI;blood vessels;brain;closed loop systems;medical image processing;medical robotics;neurophysiology;surgery;preoperative planning;surgical procedures;patient management;magnetic field gradients;ferromagnetic agents;sensor;closed-loop controlled entity;tortuous blood vessels;magnetic resonance imaging;cerebral vessels;actuated tetherless milli-robots;MRI-guided millirobots;real-time intraoperative guidance;therapeutic delivery;MRbot;neurological lesion;meningioma;MR tracking methods;Propulsion;Safety;Robots;Arteries;Tumors}, doi={10.1109/IROS.2017.8206550}, ISSN={2153-0866}, month={Sep.},}`

- S. Sheckman, H. Kim, S. Manzoor, L. W. Rogowski, L. Huang, X. Zhang, A. T. Becker, and M. J. Kim, “Manipulation and control of microrobots using a novel permanent magnet stage,” in 2017 14th international conference on ubiquitous robots and ambient intelligence (urai), 2017, pp. 692-696.

[Bibtex]`@INPROCEEDINGS{7992801, author={S. {Sheckman} and H. {Kim} and S. {Manzoor} and L. W. {Rogowski} and L. {Huang} and X. {Zhang} and A. T. {Becker} and M. J. {Kim}}, booktitle={2017 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI)}, title={Manipulation and control of microrobots using a novel permanent magnet stage}, year={2017}, volume={}, url={https://ieeexplore.ieee.org/abstract/document/7992801}, number={}, pages={692-696}, abstract={Controlling microrobots in the past have required the used of heavy coil systems and large power supply units, in this paper we show that a strong permanent magnet is sufficient for the control scheme. The development of a controlling stage was deemed to be a priority and allowed for the manipulation of microrobots, otherwise known as alginate particles or artificial cells, in the xy-plane. We show that the permanent magnet stage can manipulation both single microrobots and swarms. The permanent magnet stage, has the dimensions of 22.86 ? 35.56 cm2, by 15.26 cm in height. This allows for a permanent magnet to move in the xy-plane a total area of 12 ? 24 cm2. Additionally, the permanent magnet to be interchangeable introduces the possibility to investigate different type of magnetic fields. Our experiments were performed using a NdFeB, Grade N52 permanent magnet which provides a maximum magnet flied of 14.8 T.}, keywords={magnetic fields;microrobots;motion control;permanent magnets;magnetic manipulation;microrobots control;permanent magnet;alginate particles;artificial cells;magnetic fields;motion control;Permanent magnets;Magnetic flux;Microscopy;Permanent magnet motors;Magnetic separation;Force;Cell based microrobot;Magnetic field;Motion Control;Magnetic manipulation}, doi={10.1109/URAI.2017.7992801}, ISSN={null}, month={June},}`

- A. T. Becker, M. Debboun, S. P. Fekete, D. Krupke, and A. Nguyen, “Zapping Zika with a Mosquito-Managing Drone: Computing Optimal Flight Patterns with Minimum Turn Cost (Multimedia Contribution),” in 33rd international symposium on computational geometry (socg 2017), Dagstuhl, Germany, 2017, p. 62:1–62:5.

[Bibtex][Video]`@InProceedings{becker_et_al2018zapping, author = {Aaron T. Becker and Mustapha Debboun and S{\'a}ndor P. Fekete and Dominik Krupke and An Nguyen}, title = {{Zapping Zika with a Mosquito-Managing Drone: Computing Optimal Flight Patterns with Minimum Turn Cost (Multimedia Contribution)}}, booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)}, pages = {62:1--62:5}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-038-5}, ISSN = {1868-8969}, year = {2017}, volume = {77}, abstract = {We present results arising from the problem of sweeping a mosquito-infested area with an Un-manned Aerial Vehicle (UAV) equipped with an electrified metal grid. This is related to the Traveling Salesman Problem, the Lawn Mower Problem and, most closely, Milling with TurnCost. Planning a good trajectory can be reduced to considering penalty and budget variants of covering a grid graph with minimum turn cost. On the theoretical side, we show the solution of a problem from The Open Problems Project that had been open for more than 15 years, and hint at approximation algorithms. On the practical side, we describe an exact method based on Integer Programming that is able to compute provably optimal instances with over 500 pixels. These solutions are actually used for practical trajectories, as demonstrated in the video.}, video={https://youtu.be/SFyOMDgdNao}, editor = {Boris Aronov and Matthew J. Katz}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7239}, URN = {urn:nbn:de:0030-drops-72394}, doi = {10.4230/LIPIcs.SoCG.2017.62}, annote = {Keywords: Covering tours, turn cost, complexity, exact optimization} }`

- S. Sheckman, H. Kim, S. Manzoor, L. W. Rogowski, L. Huang, X. Zhang, A. T. Becker, and M. J. Kim, “Manipulation and control of microrobots using a novel permanent magnet stage,” in International conference on manipulation, automation and robotics at small scales (marss 2017), 2017.

[Bibtex]`@INPROCEEDINGS{sheckman2017marss, author={S. {Sheckman} and H. {Kim} and S. {Manzoor} and L. W. {Rogowski} and L. {Huang} and X. {Zhang} and A. T. {Becker} and M. J. {Kim}}, booktitle={International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS 2017)}, title={Manipulation and control of microrobots using a novel permanent magnet stage}, year={2017}, volume={}, number={}, pages={}, abstract={This paper explores the implementation of a permanent magnet control stage for single particle and swarm control applications. The stage was designed to interact with alginate microparticles encapsulated with iron ferrite. We show that the permanent magnet stage can manipulate both single microrobots and swarms effectively.}, keywords={magnetic fields;microrobots;motion control;permanent magnets;magnetic manipulation;microrobots control;permanent magnet;alginate particles;artificial cells;magnetic fields;motion control;Permanent magnets;Magnetic flux;Microscopy;Permanent magnet motors;Magnetic separation;Force;Cell based microrobot;Magnetic field;Motion Control;Magnetic manipulation}, ISSN={null}, month={July},}`

- J. Leclerc, A. Becker, N. Tsekos, K. Berger, and J. Lévêque, “Design and simulation of a superconducting magnetic system for milli/microrobotics applications,” in MARSS 2017, Montréal, Canada, 2017.

[Bibtex]`@inproceedings{leclerc2017design, TITLE = {{Design and simulation of a superconducting magnetic system for milli/microrobotics applications}}, AUTHOR = {Leclerc, Julien and Becker, Aaron and Tsekos, Nikolaos and Berger, K{\'e}vin and L{\'e}v{\^e}que, Jean}, URL = {https://hal.univ-lorraine.fr/hal-01490553}, BOOKTITLE = {{MARSS 2017}}, ADDRESS = {Montr{\'e}al, Canada}, SERIES = {Proceedings of the International Conference on Manipulation, Automation and Robotics at Small Scales}, YEAR = {2017}, MONTH = Jul, abstract={Magnetically actuated robots are currently being studied as a potential technology for navigation within a human body to deliver drugs or perform minimally invasive surgery. Ex vivo applications like microconstruction or micro sensing are also considered. Superconducting materials offer the advantages of being able to carry large current densities with low losses compared to regular conductors. This drastically increases the energy efficiency of the system while reducing its size. It also allows producing higher magnetic field. This paper presents the different elements that need to be taken into consideration when designing a superconducting system for milli/microrobotics applications.}, url={https://hal.univ-lorraine.fr/hal-01490553}, KEYWORDS = {superconducting applications ; microrobotics}, PDF = {https://hal.univ-lorraine.fr/hal-01490553/file/Paper%20MARSS2017%20Superconductivity.pdf}, HAL_ID = {hal-01490553}, HAL_VERSION = {v1}, }`

### 2016

- R. Stewart, L. Chang, S. Sudarshan, A. Becker, and L. Huang, “An unmanned aerial vehicle with vibration sensing ability (seismic drone),” in Seg technical program expanded abstracts 2016, 2016, pp. 225-229.

[Bibtex][Video]`@inproceedings{139734072E1, author = {Robert Stewart and Li Chang and Srikanth Sudarshan and Aaron Becker and Li Huang}, title = {An unmanned aerial vehicle with vibration sensing ability (seismic drone)}, booktitle = {SEG Technical Program Expanded Abstracts 2016}, chapter = {}, video = {https://youtu.be/yxdUEX0SPyw}, pages = {225-229}, year = {2016}, doi = {10.1190/segam2016-13973407.1}, URL = {https://library.seg.org/doi/abs/10.1190/segam2016-13973407.1}, eprint = {https://library.seg.org/doi/pdf/10.1190/segam2016-13973407.1}, abstract = { We describe the design, testing, and potential of an unmanned aerial vehicle (UAV or drone) with seismic sensing capabilities. The seismic or vibration sensing platform (four 100 Hz geophones plus recording electronics) is attached to a 3DR Solo Quadcopter drone. The geophone spikes become the drone’s landing legs. The drone and its geophone payload have been successfully flown a number of times with take-off, programmed or remotely controlled navigation, landing, and recording. We have conducted tests (using hammer and weight drop sources) to compare the response of the landed seismic-drone system to planted geophones and a conventional cabled seismic system. The seismic traces from the drone are quite similar to those of the planted geophones. To test the spike penetration on landing, we created three different scenarios (dropping the drone on sand, grass and dry clay) and measuring the depth of penetration (up to 20 mm). We conducted a walk-away survey with the drone versus a planted geophone line. Again the drone and planted geophone responses are very similar. We conclude that the drone-mounted geophone platform can fly to a site, land, and record seismic vibrations with similar quality as planted geophones. Detachable and roving seismic platforms may further increase the drone’s seismic reach. Drones show considerable promise for various kinds of seismic measurements and surveys. Presentation Date: Monday, October 17, 2016 Start Time: 3:20:00 PM Location: 148 Presentation Type: ORAL } }`

- S. Shahrokhi and A. T. Becker, “Object manipulation and position control using a swarm with global inputs,” in 2016 ieee international conference on automation science and engineering (case), 2016, pp. 561-566.

[Bibtex]`@INPROCEEDINGS{7743453, author={S. {Shahrokhi} and A. T. {Becker}}, booktitle={2016 IEEE International Conference on Automation Science and Engineering (CASE)}, title={Object manipulation and position control using a swarm with global inputs}, year={2016}, volume={}, number={}, pages={561-566}, abstract={Micro robots are suited for targeted drug delivery and micro scale manufacturing because they are small enough to navigate the passageways of the body. However, due to their small size, micro robots cannot contain onboard processing for autonomy nor onboard power. Instead they are controlled by an external signal such as a magnetic field. Because each robot can only provide a small amount of force or transport a small amount of material, large swarms of robots are required, all controlled by the same external field.}, keywords={microrobots;position control;torque control;object manipulation;position control;microrobots;convex polygonal objects;swarm torque control;Force;Torque;Torque control;Robot sensing systems;Position control}, doi={10.1109/COASE.2016.7743453}, ISSN={2161-8089}, month={Aug},}`

- L. Huang, X. Liu, N. V. Tsekos, and A. T. Becker, “Two missing components for solid media transmission: amplifiers and manifolds,” in 2016 ieee international conference on automation science and engineering (case), 2016, pp. 207-212.

[Bibtex][Video]`@INPROCEEDINGS{7743382, author={L. {Huang} and X. {Liu} and N. V. {Tsekos} and A. T. {Becker}}, booktitle={2016 IEEE International Conference on Automation Science and Engineering (CASE)}, title={Two missing components for Solid Media Transmission: Amplifiers and manifolds}, year={2016}, volume={}, number={}, pages={207-212}, abstract={Solid Media Transmission (SMT) is a new technology for transmitting robot actuation. SMT is similar to pneumatic or hydraulic transmissions, but uses solid balls and spacers rather than fluids to transmit force and displacement. SMT has been developed recently as a promising solution for specialized robot applications, including the challenges of confined space and strong magnetic field in Magnetic Resonance (MRI) scanners. Until now, SMT has lacked two capabilities compared to hydraulic and pneumatic devices: (1) manifolds, which can balance force among multiple inputs, and (2) amplifiers, which enable displacement scaling by trading force for displacement resolution. This paper introduces an SMT implementation for each of these missing components, provides scalable designs, parametric optimizations, hardware verifications, and ends with suggestions for future work.}, keywords={actuators;robots;solid media transmission;SMT technology;robot actuation;pneumatic transmission;hydraulic transmission;specialized robot applications;magnetic resonance imaging;MRI scanners;Force;Electron tubes;Manifolds;Magnetic resonance imaging;Solids;Media;Robots}, doi={10.1109/COASE.2016.7743382}, video={https://youtu.be/d5lcDELhmLY}, ISSN={2161-8089}, month={Aug},}`

- A. V. Mahadev, D. Krupke, J. Reinhardt, S. P. Fekete, and A. T. Becker, “Collecting a swarm in a grid environment using shared, global inputs,” in 2016 ieee international conference on automation science and engineering (case), 2016, pp. 1231-1236.

[Bibtex][Video]`@INPROCEEDINGS{7743547, author={A. V. {Mahadev} and D. {Krupke} and J. {Reinhardt} and S. P. {Fekete} and A. T. {Becker}}, booktitle={2016 IEEE International Conference on Automation Science and Engineering (CASE)}, title={Collecting a swarm in a grid environment using shared, global inputs}, year={2016}, volume={}, number={}, video={https://youtu.be/rY7Br4l4SHY}, pages={1231-1236}, abstract={This paper investigates efficient techniques to collect and concentrate an under-actuated particle swarm despite obstacles. Concentrating a swarm of particles is of critical importance in health-care for targeted drug delivery, where micro-scale particles must be steered to a goal location. Individual particles must be small in order to navigate through micro-vasculature, but decreasing size brings new challenges. Individual particles are too small to contain on-board power or computation and are instead controlled by a global input, such as an applied fluidic flow or electric field. To make progress, this paper considers a swarm of robots initialized in a grid world in which each position is either free-space or obstacle. This paper provides algorithms that collect all the robots to one position and compares these algorithms on the basis of efficiency and implementation time.}, keywords={drug delivery systems;health care;medical robotics;microrobots;grid environment;shared global inputs;under-actuated particle swarm;healthcare;targeted drug delivery;on-board power;robot swarm;Robot kinematics;Robot sensing systems;Magnetic resonance imaging;Planning;Medical treatment;Geometry}, doi={10.1109/COASE.2016.7743547}, ISSN={2161-8089}, month={Aug},}`

- S. K. V. Sudarshan, Li Huang, Chang Li, R. Stewart, and A. T. Becker, “Seismic surveying with drone-mounted geophones,” in 2016 ieee international conference on automation science and engineering (case), 2016, pp. 1354-1359.

[Bibtex][Video]`@INPROCEEDINGS{7743566, author={S. K. V. {Sudarshan} and {Li Huang} and {Chang Li} and R. {Stewart} and A. T. {Becker}}, booktitle={2016 IEEE International Conference on Automation Science and Engineering (CASE)}, title={Seismic surveying with drone-mounted geophones}, year={2016}, volume={}, video = {https://youtu.be/yxdUEX0SPyw}, number={}, pages={1354-1359}, abstract={Seismic imaging is the primary technique for subsurface exploration. Traditional seismic imaging techniques rely heavily on manual labor to plant sensors, lay miles of cabling, and then recover the sensors. Often sites of resource or rescue interest may be difficult or hazardous to access. Thus, there is a substantial need for unmanned sensors that can be deployed by air and potentially in large numbers. This paper presents working prototypes of autonomous drones equipped with geophones (vibration sensors) that can fly to a site, land, listen for echoes and vibrations, store the information on-board, and subsequently return to home base. The design uses four geophone sensors (with spikes) in place of the landing gear. This provides a stable landing attitude, redundancy in sensing, and ensures the geophones are oriented perpendicular to the ground. The paper describes hardware experiments demonstrating the efficacy of this technique and a comparison with traditional manual techniques. The performance of the seismic drone was comparable to a well planted geophone, proving the drone mount system is a feasible alternative to traditional seismic sensors.}, keywords={geophysical techniques;seismology;seismometers;seismic surveying;drone-mounted geophones;primary technique;subsurface exploration;seismic imaging techniques;manual labor;plant sensors;unmanned sensors;autonomous drones prototypes;vibration sensors;geophone sensors;hardware experiments;traditional manual techniques;seismic drone;drone mount system;Sensors;Drones;Batteries;Manuals;Vibrations;Prototypes;Hydrocarbons}, doi={10.1109/COASE.2016.7743566}, ISSN={2161-8089}, month={Aug},}`

### 2015

- A. T. Becker, O. Felfoul, L. Huang, and P. E. Dupont, “MRI-powered robotics,” in International symposium on robotics research 2015, 2015.

[Bibtex]`@inproceedings{becker2015mripoweredrobotics, author={Aaron T. Becker and Ouajdi Felfoul and Li Huang and Pierre E. Dupont}, booktitle={International Symposium on Robotics Research 2015}, year={2015}, title={{MRI}-Powered Robotics}, abstract={Magnetic Resonance (MR) scanners provide high-resolution imaging of soft tissue. An unexploited capability of these systems is that they can also wirelessly power, track, and control robots placed inside their bore. Such robots can be fabricated from inexpensive materials and their control can be accomplished entirely through scanner programming. This technology may enable new MR-guided interventions as well as facilitate current procedures. This paper reviews recent developments in MRI-powered robots, and investigates three case studies: (1) high-speed control of an actuator rotor, (2) independent, simultaneous control of n rotors, and (3) MRI-based navigation and propulsion of millirobots that self-assemble into a tool for penetrating tissue. These approaches are illustrated through analytical modeling and experiments in a clinical MRI scanner} }`

- S. Shahrokhi and A. T. Becker, “Stochastic swarm control with global inputs,” in 2015 ieee/rsj international conference on intelligent robots and systems (iros), 2015, pp. 421-427.

[Bibtex][Video]`@INPROCEEDINGS{7353407, author={S. {Shahrokhi} and A. T. {Becker}}, booktitle={2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, title={Stochastic swarm control with global inputs}, year={2015}, volume={}, number={}, pages={421-427}, abstract={Micro- and nanorobots can be built in large numbers, but generating independent control inputs for each robot is prohibitively difficult. Instead, micro- and nanorobots are often controlled by a global field. In previous work we conducted large-scale human-user experiments where humans played games that steered large swarms of simple robots to complete tasks such as manipulating blocks. One surprising result was that humans completed a block-pushing task faster when provided with only the mean and variance of the robot swarm than with full-state feedback. Inspired by human operators, this paper investigates controllers that use only the mean and variance of a robot swarm. We prove that the mean position is controllable, and show how an obstacle can make the variance controllable. We next derive automatic controllers for these and a hybrid, hysteresis-based switching control to regulate the first two moments of the robot distribution. Finally, we employ these controllers as primitives for a block-pushing task.}, keywords={feedback;microrobots;multi-robot systems;stochastic swarm control;global inputs;microrobots;nanorobots;independent control inputs;large-scale human-user experiments;block-pushing task;robot swarm;full-state feedback;human operators;hysteresis-based switching control;robot distribution;Robot kinematics;Control systems;Sociology;Statistics;Robot sensing systems;Games}, doi={10.1109/IROS.2015.7353407}, ISSN={null}, video={https://youtu.be/tCej-9e6-4o}, month={Sep.},}`

- A. T. Becker, E. D. Demaine, S. P. Fekete, H. M. Shad, and R. Morris-Wright, “Tilt: The Video – Designing Worlds to Control Robot Swarms with Only Global Signals,” in 31st international symposium on computational geometry (socg 2015), Dagstuhl, Germany, 2015, p. 16–18.

[Bibtex][Video]`@InProceedings{becker_et_al2015tiltvideo, author = {Aaron T. Becker and Erik D. Demaine and S{\'a}ndor P. Fekete and Hamed Mohtasham Shad and Rose Morris-Wright}, title = {{Tilt: The Video - Designing Worlds to Control Robot Swarms with Only Global Signals}}, booktitle = {31st International Symposium on Computational Geometry (SoCG 2015)}, pages = {16--18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-83-5}, ISSN = {1868-8969}, year = {2015}, volume = {34}, editor = {Lars Arge and J{\'a}nos Pach}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5087}, URN = {urn:nbn:de:0030-drops-50870}, doi = {10.4230/LIPIcs.SOCG.2015.16}, abstract = {We present fundamental progress on the computational universality of swarms of micro- or nano-scale robots in complex environments, controlled not by individual navigation, but by a uniform global, external force. More specifically, we consider a 2D grid world, in which all obstacles and robots are unit squares, and for each actuation, robots move maximally until they collide with an obstacle or another robot. The objective is to control robot motion within obstacles, design obstacles in order to achieve desired permutation of robots, and establish controlled interaction that is complex enough to allow arbitrary computations. In this video, we illustrate progress on all these challenges: we demonstrate NP-hardness of parallel navigation, we describe how to construct obstacles that allow arbitrary permutations, and we establish the necessary logic gates for performing arbitrary in-system computations.}, video = {https://youtu.be/H6o9DTIfkn0}, annote = {Keywords: Particle swarms, global control, complexity, geometric computation} }`

- A. T. Becker, E. D. Demaine, and S. P. Fekete, “Controlling distributed particle swarms with only global signals,” in 3rd workshop on biological distributed algorithms (bda), MIT, Cambridge, MA, USA, 2015.

[Bibtex][Video]`@InProceedings{becker_et_al2015controllingdistributed, author = {Aaron T. Becker and Erik D. Demaine and S{\'a}ndor P. Fekete}, title = {Controlling Distributed Particle Swarms with only Global Signals}, booktitle = {3rd Workshop on Biological Distributed Algorithms (BDA)}, year = {2015}, volume = {34}, address = {MIT, Cambridge, MA, USA}, URL = {https://snl.salk.edu/~navlakha/BDA2015/Material/sandor_slides.pdf}, abstract = {We present fundamental progress on the computational universality of swarms of micro- or nanoscale particles in complex environments such as the vascular system of a biological organism. Components of the swarm are controlled not by individual navigation, but by a uniform global, external force. More specifically, we consider a 2D grid world, in which all obstacles and particles are unit squares, and for each actuation, particles move maximally until they collide with an obstacle or another particle. The objective is to control particle motion within obstacles, design obstacles in order to achieve desired permutation of particles, and establish controlled interaction that is complex enough to allow arbitrary computations. In this short paper, we summarize progress on all these challenges: we demonstrate NP-hardness of parallel navigation, we describe how to construct obstacles that allow arbitrary permutations, and we establish the necessary logic gates for performing arbitrary in-system computations.}, video = {https://youtu.be/H6o9DTIfkn0}, annote = {Keywords: Particle swarms, global control, complexity, geometric computation} }`

- A. T. Becker, O. Felfoul, and P. E. Dupont, “Toward tissue penetration by MRI-powered millirobots using a self-assembled gauss gun,” in 2015 ieee international conference on robotics and automation (icra), 2015, pp. 1184-1189.

[Bibtex][Video]`@INPROCEEDINGS{7139341, author={A. T. {Becker} and O. {Felfoul} and P. E. {Dupont}}, booktitle={2015 IEEE International Conference on Robotics and Automation (ICRA)}, title={Toward tissue penetration by {MRI}-powered millirobots using a self-assembled Gauss gun}, year={2015}, volume={}, number={}, pages={1184-1189}, abstract={MRI-based navigation and propulsion of millirobots is a new and promising approach for minimally invasive therapies. The strong central field inside the scanner, however, precludes torque-based control. Consequently, prior propulsion techniques have been limited to gradient-based pulling through fluid-filled body lumens. This paper introduces a technique for generating large impulsive forces that can be used to penetrate tissue. The approach is based on navigating multiple robots to a desired location and using self-assembly to trigger the conversion of magnetic potential energy into sufficient kinetic energy to achieve penetration. The approach is illustrated through analytical modeling and experiments in a clinical MRI scanner.}, keywords={biomedical MRI;gradient methods;medical robotics;propulsion;torque control;tissue penetration;millirobots;self-assembled Gauss gun;MRI-based navigation;minimally invasive therapies;torque-based control;propulsion techniques;gradient-based pulling;fluid-filled body lumens;impulsive forces;self-assembly;magnetic potential energy;kinetic energy;analytical modeling;clinical MRI scanner;Magnetic resonance imaging;Magnetic separation;Force;Magnetic levitation;Saturation magnetization;Steel;Needles}, doi={10.1109/ICRA.2015.7139341}, ISSN={1050-4729}, video={https://youtu.be/KgNT7aVejuA}, month={May},}`

- H. M. Shad, R. Morris-Wright, E. D. Demaine, S. P. Fekete, and A. T. Becker, “Particle computation: device fan-out and binary memory,” in 2015 ieee international conference on robotics and automation (icra), 2015, pp. 5384-5389.

[Bibtex][Video]`@INPROCEEDINGS{7139951, author={H. M. {Shad} and R. {Morris-Wright} and E. D. {Demaine} and S. P. {Fekete} and A. T. {Becker}}, booktitle={2015 IEEE International Conference on Robotics and Automation (ICRA)}, title={Particle computation: Device fan-out and binary memory}, year={2015}, volume={}, number={}, pages={5384-5389}, abstract={We present fundamental progress on the computational universality of swarms of micro- or nano-scale robots in complex environments, controlled not by individual navigation, but by a uniform global, external force. Consider a 2D grid world, in which all obstacles and robots are unit squares, and for each actuation, robots move maximally until they collide with an obstacle or another robot. In previous work, we demonstrated components of particle computation in this world, designing obstacle configurations that implement AND and OR logic gates: by using dual-rail logic, we designed NOT, NOR, NAND, XOR, XNOR logic gates. However, we were unable to design a FAN-OUT gate, which is necessary for simulating the full range of complex interactions that are present in arbitrary digital circuits. In this work we resolve this problem by proving unit-sized robots cannot generate a FAN-OUT gate. On the positive side, we resolve the missing component with the help of 2?1 robots, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we are able to establish the full range of computational universality as presented by complex digital circuits. As an example we connect our logic elements to produce a 3-bit counter. We also demonstrate how to implement a data storage element.}, keywords={collision avoidance;logic gates;multi-robot systems;particle computation;device fan out;binary memory;computational universality;nano scale robots;micro scale robots;complex environments;obstacles;OR logic gates;AND logic gates;NOT;NOR;NAND;XOR;XNOR logic gates;arbitrary digital circuits;unit sized robots;digital circuits;data storage element;Logic gates;Computers;Clocks;Robot kinematics;Radiation detectors;Wiring}, doi={10.1109/ICRA.2015.7139951}, ISSN={1050-4729}, video={http://youtu.be/EJSv8ny31r8}, month={May},}`

- S. K. V. Sudarshan and A. T. Becker, “Using gradient descent to optimize paths for sustaining wireless sensor networks,” in 2015 texas symposium on wireless and microwave circuits and systems (wmcs), 2015, pp. 1-6.

[Bibtex][Video] [Code]`@INPROCEEDINGS{7233200, author={S. K. V. {Sudarshan} and A. T. {Becker}}, booktitle={2015 Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS)}, title={Using gradient descent to optimize paths for sustaining wireless sensor networks}, year={2015}, volume={}, number={}, url={https://ieeexplore.ieee.org/document/7233200}, video={https://youtu.be/_KFsggUGK08}, code={http://www.mathworks.com/matlabcentral/fileexchange/49863-decentralized-path-planning-for-coverage-using-gradient-descent}, pages={1-6}, abstract={A structural-health wireless sensor network (WSN) should last for decades, but traditional disposable batteries cannot sustain such a network. Energy is the major impediment to sustainability of WSNs. Most energy is consumed by (i) wireless transmissions of perceived data, and (ii) long-distance multi-hop transmissions from the source sensors to the sink. This paper explores how to exploit emerging wireless power transfer technology by using robotic unmanned vehicles (UVs) to service the WSNs. These UVs cut data transmissions from long to short-distances, collect sensed information, and replenish WSN's energy. This paper presents path-planning and path optimization algorithms for sustaining WSNs.}, keywords={autonomous aerial vehicles;gradient methods;inductive power transmission;mobile robots;optimisation;path planning;telecommunication computing;telecommunication power management;wireless sensor networks;gradient descent;structural-health wireless sensor network;disposable batteries;wireless transmissions;perceived data;long-distance multihop transmissions;source sensors;wireless power transfer technology;robotic unmanned vehicles;data transmissions;sensed information;path-planning;path optimization;Wireless sensor networks;Cost function;Wireless communication;Robot sensing systems;Wireless sensor networks;wireless recharge;robot;unmanned vehicles}, doi={10.1109/WMCaS.2015.7233200}, ISSN={null}, month={April},}`

### 2014

- A. Becker, O. Felfoul, and P. E. Dupont, “Simultaneously powering and controlling many actuators with a clinical MRI scanner,” in 2014 ieee/rsj international conference on intelligent robots and systems, 2014, pp. 2017-2023.

[Bibtex][Video] [Code]`@INPROCEEDINGS{6942831, author={A. {Becker} and O. {Felfoul} and P. E. {Dupont}}, booktitle={2014 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={Simultaneously powering and controlling many actuators with a clinical {MRI} scanner}, year={2014}, volume={}, number={}, pages={2017-2023}, abstract={Actuators that are powered, imaged, and controlled by Magnetic Resonance (MR) scanners offer the potential of inexpensively providing wireless control of MR-guided robots. Similar to traditional electric motors, the MR scanner acts as the stator and generates propulsive torques on an actuator rotor containing one or more ferrous particles. The MR scanner can control three orthogonal gradient fields. Prior work demonstrated control of a single actuator rotor. This paper proposes and demonstrates independent, simultaneous control of n rotors. The controller relies on inhomogeneity between rotors, such as ensuring no rotor axes are parallel. This paper provides easily-implemented velocity and position controllers with global asymptotic convergence, and optimization techniques for implementation. Code for simulations and control laws is available online.}, keywords={actuators;biomedical MRI;machine control;magnetic resonance;medical robotics;optimisation;position control;rotors;velocity control;clinical MRI scanner;magnetic resonance scanners;wireless control;MR-guided robots;electric motors;actuator rotor;velocity controllers;position controllers;optimization;Rotors;Magnetic resonance imaging;Torque;Actuators;Robots;Force;Saturation magnetization}, doi={10.1109/IROS.2014.6942831}, ISSN={2153-0866}, video={https://www.youtube.com/watch?v=w6vWSw53ztA&list=UUcWH3VEhJ-f4jnoOLyU_YCg}, code = {http://www.mathworks.com/matlabcentral/fileexchange/45331}, month={Sep.},}`

- J. McLurkin, A. McMullen, N. Robbins, G. Habibi, A. T. Becker, A. Chou, H. Li, M. John, N. Okeke, J. Rykowski, S. Kim, W. Xie, T. Vaughn, Y. Zhou, J. Shen, N. Chen, Q. Kaseman, L. Langford, J. Hunt, A. Boone, and K. Koch, “A robot system design for low-cost multi-robot manipulation,” in 2014 ieee/rsj international conference on intelligent robots and systems, 2014, pp. 912-918.

[Bibtex][Video]`@INPROCEEDINGS{6942668, author={J. {McLurkin} and A. {McMullen} and N. {Robbins} and G. {Habibi} and Aaron T. {Becker} and A. {Chou} and H. {Li} and M. {John} and N. {Okeke} and J. {Rykowski} and S. {Kim} and W. {Xie} and T. {Vaughn} and Y. {Zhou} and J. {Shen} and N. {Chen} and Q. {Kaseman} and L. {Langford} and J. {Hunt} and A. {Boone} and K. {Koch}}, booktitle={2014 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={A robot system design for low-cost multi-robot manipulation}, year={2014}, volume={}, number={}, pages={912-918}, abstract={Multi-robot manipulation allows for scalable environmental interaction, which is critical for multi-robot systems to have an impact on our world. A successful manipulation model requires cost-effective robots, robust hardware, and proper system feedback and control. This paper details key sensing and manipulator capabilities of the r-one robot. The r-one robot is an advanced, open source, low-cost platform for multi-robot manipulation and sensing that meets all of these requirements. The parts cost is around $250 per robot. The r-one has a rich sensor suite, including a flexible IR communication/localization/obstacle detection system, high-precision quadrature encoders, gyroscope, accelerometer, integrated bump sensor, and light sensors. Two years of working with these robots inspired the development of an external manipulator that gives the robots the ability to interact with their environment. This paper presents an overview of the r-one, the r-one manipulator, and basic manipulation experiments to illustrate the efficacy our design. The advanced design, low cost, and small size can support university research with large populations of robots and multi-robot curriculum in computer science, electrical engineering, and mechanical engineering. We conclude with remarks on the future implementation of the manipulators and expected work to follow.}, keywords={manipulators;multi-robot systems;sensors;robot system design;low-cost multirobot manipulation;manipulator capabilities;r-one robot;flexible IR communication-localization-obstacle detection system;high-precision quadrature encoders;gyroscope;accelerometer;integrated bump sensor;light sensors;external manipulator;r-one manipulator;Robot sensing systems;Collision avoidance;Grippers;Receivers;Educational robots;Mobile robots}, doi={10.1109/IROS.2014.6942668}, ISSN={2153-0866}, video={https://youtu.be/FHlSOYLSe2E}, month={Sep.},}`

- A. Becker, E. D. Demaine, S. P. Fekete, and J. McLurkin, “Particle computation: designing worlds to control robot swarms with only global signals,” in 2014 ieee international conference on robotics and automation (icra), 2014, pp. 6751-6756.

[Bibtex][Video] [Code]`@INPROCEEDINGS{6907856, author={A. {Becker} and E. D. {Demaine} and S. P. {Fekete} and J. {McLurkin}}, booktitle={2014 IEEE International Conference on Robotics and Automation (ICRA)}, title={Particle computation: Designing worlds to control robot swarms with only global signals}, year={2014}, volume={}, number={}, pages={6751-6756}, abstract={Micro- and nanorobots are often controlled by global input signals, such as an electromagnetic or gravitational field. These fields move each robot maximally until it hits a stationary obstacle or another stationary robot. This paper investigates 2D motion-planning complexity for large swarms of simple mobile robots (such as bacteria, sensors, or smart building material). In previous work we proved it is NP-hard to decide whether a given initial configuration can be transformed into a desired target configuration; in this paper we prove a stronger result: the problem of finding an optimal control sequence is PSPACE-complete. On the positive side, we show we can build useful systems by designing obstacles. We present a reconfigurable hardware platform and demonstrate how to form arbitrary permutations and build a compact absolute encoder. We then take the same platform and use dual-rail logic to build a universal logic gate that concurrently evaluates AND, NAND, NOR and OR operations. Using many of these gates and appropriate interconnects we can evaluate any logical expression.}, keywords={collision avoidance;computational complexity;control system synthesis;logic gates;microrobots;multi-robot systems;optimal control;particle computation;robot swarms control;global input signals;microrobots;nanorobots;electromagnetic field;gravitational field;stationary obstacle;stationary robot;2D motion planning complexity;NP-hard problem;PSPACE-complete problem;optimal control sequence;obstacle design;reconfigurable hardware platform;dual-rail logic;universal logic gate;AND operation;NAND operation;NOR operation;OR operation;logical expression;Logic gates;Prototypes;Robot sensing systems;Complexity theory;Hardware;Clocks}, doi={10.1109/ICRA.2014.6907856}, ISSN={1050-4729}, video={http://www.youtube.com/watch?v=eExZO0HrWRQ}, code={http://www.mathworks.com/matlabcentral/fileexchange/42892}, month={May},}`

- A. Becker, C. Ertel, and J. McLurkin, “Crowdsourcing swarm manipulation experiments: a massive online user study with large swarms of simple robots,” in 2014 ieee international conference on robotics and automation (icra), 2014, pp. 2825-2830.

[Bibtex][Video] [Code]`@INPROCEEDINGS{6907264, author={A. {Becker} and C. {Ertel} and J. {McLurkin}}, booktitle={2014 IEEE International Conference on Robotics and Automation (ICRA)}, title={Crowdsourcing swarm manipulation experiments: A massive online user study with large swarms of simple robots}, year={2014}, volume={}, number={}, pages={2825-2830}, abstract={Micro- and nanorobotics have the potential to revolutionize many applications including targeted material delivery, assembly, and surgery. The same properties that promise breakthrough solutions - small size and large populations - present unique challenges to generating controlled motion. We want to use large swarms of robots to perform manipulation tasks; unfortunately, human-swarm interaction studies as conducted today are limited in sample size, are difficult to reproduce, and are prone to hardware failures. We present an alternative. This paper examines the perils, pitfalls, and possibilities we discovered by launching SwarmControl.net, an online game where players steer swarms of up to 500 robots to complete manipulation challenges. We record statistics from thousands of players, and use the game to explore aspects of large-population robot control. We present the game framework as a new, open-source tool for large-scale user experiments. Our results have potential applications in human control of micro- and nanorobots, supply insight for automatic controllers, and provide a template for large online robotic research experiments.}, keywords={Internet;microrobots;multi-robot systems;online robotic research experiments;automatic controllers;nanorobots;microrobots;human control;open source tool;game framework;large population robot control;online game;SwarmControl.net;hardware failures;human swarm interaction;manipulation tasks;nanorobotics;microrobotics;massive online user study;crowdsourcing swarm manipulation;Robot sensing systems;Servers;Noise;Sociology;Statistics;Browsers}, doi={10.1109/ICRA.2014.6907264}, ISSN={1050-4729}, video={http://www.youtube.com/watch?v=HgNENj3hvEg}, code={https://github.com/crertel/swarmmanipulate.git}, month={May},}`

- S. K. Lee, A. Becker, S. P. Fekete, A. Kröller, and J. McLurkin, “Exploration via structured triangulation by a multi-robot system with bearing-only low-resolution sensors,” in 2014 ieee international conference on robotics and automation (icra), 2014, pp. 2150-2157.

[Bibtex][Video]`@INPROCEEDINGS{6907155, author={S. K. {Lee} and A. {Becker} and S. P. {Fekete} and A. {Kr\"oller} and J. {McLurkin}}, booktitle={2014 IEEE International Conference on Robotics and Automation (ICRA)}, title={Exploration via structured triangulation by a multi-robot system with bearing-only low-resolution sensors}, year={2014}, volume={}, number={}, pages={2150-2157}, abstract={This paper presents a distributed approach for exploring and triangulating an unknown region using a multirobot system. The resulting triangulation is a physical data structure that is a: compact representation of the workspace, contains distributed knowledge of each triangle, builds the dual graph of the triangulation, and supports reads and writes of auxiliary data. Our algorithm builds a triangulation in a closed two-dimensional Euclidean environment, starting from a single location. It provides coverage with a breadth-first search pattern and completeness guarantees. We show that the computational and communication requirements to build and maintain the triangulation and its dual graph are small. We then present a physical navigation algorithm that uses the dual graph, and show that the resulting path lengths are within a constant factor of the shortest-path Euclidean distance. Finally, we validate our theoretical results with experiments on triangulating a region with a system of low-cost robots. Analysis of the resulting triangulation shows that most of the triangles are of high quality, and cover a large area. Implementation of the triangulation, dual graph, and navigation all use communication messages of fixed size, and are a practical solution for large populations of low-cost robots.}, keywords={graph theory;mobile robots;multi-robot systems;path planning;tree searching;structured triangulation;multirobot system;bearing-only low-resolution sensors;physical data structure;2D Euclidean environment;breadth-first search pattern;dual graph;physical navigation algorithm;shortest-path Euclidean distance;low-cost robots;Robot kinematics;Navigation;Robot sensing systems;Collision avoidance;Geometry}, doi={10.1109/ICRA.2014.6907155}, ISSN={1050-4729}, video={https://youtu.be/V5vpwVFMPqs}, month={May},}`

### 2013

- P. S. Soo Kim, A. Becker, Y. Ou, A. A. Julius, and M. J. Kim, “Swarm control of cell-based microrobots using a single global magnetic field,” in 2013 10th international conference on ubiquitous robots and ambient intelligence (urai), 2013, pp. 21-26.

[Bibtex]`@INPROCEEDINGS{6677461, author={P. S. {Soo Kim} and A. {Becker} and Y. {Ou} and A. A. {Julius} and M. J. {Kim}}, booktitle={2013 10th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI)}, title={Swarm control of cell-based microrobots using a single global magnetic field}, year={2013}, volume={}, number={}, pages={21-26}, abstract={Tetrahymena pyriformis is a single cell eukaryote that can be modified to respond to magnetic fields, a response called magnetotaxis. In experiments, a rotating field is applied to cells using a two dimensional approximate Helmholtz system. Using rotating magnetic fields, we characterize discrete cells' swarm swimming which is affected by several factors. The behavior of the cells under these fields is explained in detail. After the field is removed, relatively straight swimming is observed. By exploiting this straight swimming behavior, we propose a method to control discrete cells utilizing a single global input. Successful implementation of this swarm control method would enable teams of microrobots to perform a variety of microscale tasks impossible for single microrobots, such as pushing objects or simultaneous micromanipulation of discrete entities.}, keywords={discrete systems;Helmholtz equations;magnetic fields;micromanipulators;multi-robot systems;swarm control;cell-based microrobots;single global magnetic field;tetrahymena pyriformis;magnetic fields;magnetotaxis;two dimensional approximate Helmholtz system;micromanipulation;discrete entities;Trajectory;Saturation magnetization;Magnetic separation;Iron;Robot sensing systems;Magnetic flux;Tetrahymena pyriformis;magnetotaxis;swarm control;microrobot}, doi={10.1109/URAI.2013.6677461}, ISSN={null}, month={Oct},}`

- A. Becker, E. D. Demaine, S. P. Fekete, G. Habibi, and J. McLurkin, “Reconfiguring massive particle swarms with limited, global control,” in International symposium on algorithms and experiments for sensor systems, wireless networks and distributed robotics, 2013, p. 51–66.

[Bibtex][Video] [Code]`@inproceedings{becker2013reconfiguring, title={Reconfiguring massive particle swarms with limited, global control}, author={Becker, Aaron and Demaine, Erik D and Fekete, S{\'a}ndor P and Habibi, Golnaz and McLurkin, James}, booktitle={International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics}, pages={51--66}, year={2013}, organization={Springer}, video={http://www.youtube.com/watch?v=eExZO0HrWRQ}, code={http://www.mathworks.com/matlabcentral/fileexchange/42892}, }`

- A. Becker, G. Habibi, J. Werfel, M. Rubenstein, and J. McLurkin, “Massive uniform manipulation: controlling large populations of simple robots with a common input signal,” in 2013 ieee/rsj international conference on intelligent robots and systems, 2013, pp. 520-527.

[Bibtex][Video] [Code]`@INPROCEEDINGS{6696401, author={A. {Becker} and G. {Habibi} and J. {Werfel} and M. {Rubenstein} and J. {McLurkin}}, booktitle={2013 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={Massive uniform manipulation: Controlling large populations of simple robots with a common input signal}, year={2013}, volume={}, number={}, pages={520-527}, abstract={Roboticists, biologists, and chemists are now producing large populations of simple robots, but controlling large populations of robots with limited capabilities is difficult, due to communication and onboard-computation constraints. Direct human control of large populations seems even more challenging. In this paper we investigate control of mobile robots that move in a 2D workspace using three different system models. We focus on a model that uses broadcast control inputs specified in the global reference frame. In an obstacle-free workspace this system model is uncontrollable because it has only two controllable degrees of freedom - all robots receive the same inputs and move uniformly. We prove that adding a single obstacle can make the system controllable, for any number of robots. We provide a position control algorithm, and demonstrate through extensive testing with human subjects that many manipulation tasks can be reliably completed, even by novice users, under this system model, with performance benefits compared to the alternate models. We compare the sensing, computation, communication, time, and bandwidth costs for all three system models. Results are validated with extensive simulations and hardware experiments using over 100 robots.}, keywords={manipulators;mobile robots;position control;massive uniform manipulation;large robot population control;roboticists;biologists;onboard-computation constraints;direct human control;mobile robot control;2D workspace;broadcast control inputs;global reference frame;obstacle-free workspace;system model;degree of freedom;position control algorithm;bandwidth costs;Robot kinematics;Robot sensing systems;Sociology;Statistics;Turning;Hardware}, doi={10.1109/IROS.2013.6696401}, ISSN={2153-0866}, video={http://www.youtube.com/watch?v=px5RdSvGD2Q}, code={http://www.mathworks.com/matlabcentral/fileexchange/42889}, month={Nov},}`

- A. Becker, Y. Ou, P. Kim, M. J. Kim, and A. Julius, “Feedback control of many magnetized tetrahymena pyriformis cells by exploiting phase inhomogeneity,” in 2013 ieee/rsj international conference on intelligent robots and systems, 2013, pp. 3317-3323.

[Bibtex][Video] [Code]`@INPROCEEDINGS{6696828, author={A. {Becker} and Y. {Ou} and P. {Kim} and M. J. {Kim} and A. {Julius}}, booktitle={2013 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={Feedback control of many magnetized Tetrahymena pyriformis cells by exploiting phase inhomogeneity}, year={2013}, volume={}, number={}, pages={3317-3323}, abstract={Biological robots can be produced in large numbers, but are often controlled by uniform inputs. This makes position control of multiple robots inherently challenging. This paper uses magnetically-steered ciliate eukaryon (Tetrahymena pyriformis) as a case study. These cells swim at a constant speed, and can be turned by changing the orientation of an external magnetic field. We show that it is possible to steer multiple T. pyriformis to independent goals if their turning - modeled as a first-order system - has unique time constants. We provide system identification tools to parameterize multiple cells in parallel. We construct feedback control-Lyapunov methods that exploit differing phase-lags under a rotating magnetic field to steer multiple cells to independent target positions. We prove that these techniques scale to any number of cells with unique first-order responses to the global magnetic field. We provide simulations steering hundreds of cells and validate our procedure in hardware experiments with multiple cells.}, keywords={cellular biophysics;feedback;Lyapunov methods;magnetic fields;medical robotics;mobile robots;multi-robot systems;position control;magnetized Tetrahymena pyriformis cells;phase inhomogeneity;biological robots;multiple robot position control;magnetically-steered ciliate eukaryon;external magnetic field;first-order system;system identification tools;feedback control-Lyapunov methods;phase-lags;rotating magnetic field;global magnetic field;Magnetic fields;Robot kinematics;Turning;Lyapunov methods;Orbits;Feedback control}, doi={10.1109/IROS.2013.6696828}, ISSN={2153-0866}, video={http://www.youtube.com/watch?v=MLr2YvghPns}, code={http://www.mathworks.com/matlabcentral/fileexchange/42890}, month={Nov},}`

- A. Becker, S. P. Fekete, A. Kröller, S. K. Lee, J. McLurkin, and C. Schmidt, “Triangulating unknown environments using robot swarms,” in Proceedings of the twenty-ninth annual symposium on computational geometry, New York, NY, USA, 2013, pp. 345-346.

[Bibtex][Video]`@INPROCEEDINGS{beckeretal_2013_triangulating, author = {Becker, Aaron and Fekete, S\'{a}ndor P. and Kr\"{o}ller, Alexander and Lee, Seoung Kyou and McLurkin, James and Schmidt, Christiane}, title = {Triangulating Unknown Environments Using Robot Swarms}, year = {2013}, isbn = {9781450320313}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, url = {https://doi.org/10.1145/2462356.2462360}, doi = {10.1145/2462356.2462360}, booktitle = {Proceedings of the Twenty-Ninth Annual Symposium on Computational Geometry}, pages = {345-346}, numpages = {2}, keywords = {robot swarms, exploration and searching, triangulation, online optimization, r-one robots, robot navigation}, location = {Rio de Janeiro, Brazil}, series = {SoCG 13}, video={http://www.youtube.com/watch?v=V5vpwVFMPqs}, abstract={In recent years, the field of robotics has seen two diverging trends. One has been to achieve progress by increasing the capabilities of individual robots, keeping the cost of state-of-art machines relatively high. An opposite direction has been to develop simpler and cheaper platforms, at the expense of reducing the capabilities per robot. The latter raises new challenges for developing new principles and algorithms, such as coordinating many robots with limited capabilities into a swarm that can carry out difficult tasks, for example, exploration, surveillance, and guidance. In this video, we show a recent collaboration between theory and practice of swarm robotics. We consider online problems related to exploring and surveying a region by a swarm of robots with limited communication range. The minimum relay triangulation problem (MRTP) asks for placing a minimum number of robots, such that their communication graph is a triangulated cover of the region. The maximum area triangulation problem (MATP) aims at finding a placement of n robots such that their communication graph contains a root and forms a triangulated cover of a maximum possible amount of area. We demonstrate the practical relevance of our methods by showing how they can be used on the novel real-world platform r-one.}, }`

### 2012

- A. Becker and T. Bretl, “Approximate steering of a plate-ball system under bounded model perturbation using ensemble control,” in 2012 ieee/rsj international conference on intelligent robots and systems, 2012, pp. 5353-5359.

[Bibtex][Video] [Code]`@INPROCEEDINGS{6385722, author={A. {Becker} and T. {Bretl}}, booktitle={2012 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={Approximate steering of a plate-ball system under bounded model perturbation using ensemble control}, year={2012}, volume={}, number={}, pages={5353-5359}, abstract={In this paper we revisit the classical plate-ball system and prove this system remains controllable under model perturbation that scales the ball radius by an unknown but bounded constant. We present an algorithm for approximate steering and validate the algorithm with hardware experiments. To perform these experiments, we introduce a new version of the plate-ball system based on magnetic actuation. This system is easy to implement and, with our steering algorithm, enables simultaneous manipulation of multiple balls with different radii.}, keywords={approximation theory;magnetic actuators;manipulator kinematics;perturbation techniques;plates (structures);steering systems;approximate plate-ball system steering algorithm;bounded model perturbation;ensemble control;ball radius;magnetic actuation;ball manipulation;bounded constant;Approximation methods;Approximation algorithms;Arrays;Magnetic separation;Magnetic resonance imaging;Control systems;Robot sensing systems}, doi={10.1109/IROS.2012.6385722}, ISSN={2153-0858}, code={http://www.mathworks.com/matlabcentral/fileexchange/38369}, url={https://ieeexplore.ieee.org/abstract/document/6385722}, video={https://youtu.be/nPGz0Nd3QzE}, month={Oct},}`

- C. Orduño, A. Becker, and T. Bretl, “Motion primitives for path following with a self-assembled robotic swimmer,” in 2012 ieee/rsj international conference on intelligent robots and systems, 2012, pp. 1440-1446.

[Bibtex][Video]`@INPROCEEDINGS{6385734, author={C. {Ordu\~no} and A. {Becker} and T. {Bretl}}, booktitle={2012 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={Motion primitives for path following with a self-assembled robotic swimmer}, year={2012}, volume={}, number={}, pages={1440-1446}, abstract={This paper presents a control strategy based on model learning for a self-assembled robotic ``swimmer''. The swimmer forms when a liquid suspension of ferro-magnetic micro-particles and a non-magnetic bead are exposed to an alternating magnetic field that is oriented perpendicular to the liquid surface. It can be steered by modulating the frequency of the alternating field. We model the swimmer as a unicycle and learn a mapping from frequency to forward speed and turning rate using locally-weighted projection regression. We apply iterative linear quadratic regulation with a receding horizon to track motion primitives that could be used for path following. Hardware experiments validate our approach.}, keywords={ferromagnetic materials;iterative methods;linear quadratic control;magnetic fields;mobile robots;path planning;regression analysis;robotic assembly;self-assembly;suspensions;model learning;self-assembled robotic swimmer;liquid suspension;ferromagnetic microparticle;nonmagnetic bead;magnetic field;liquid surface;projection regression;iterative linear quadratic regulation;motion tracking;path following;frequency modulation;Computational modeling;Magnetosphere;Magnetic separation;Self-assembly;Robot kinematics;Data models}, doi={10.1109/IROS.2012.6385734}, ISSN={2153-0858}, video={http://www.youtube.com/watch?v=dMqPhriLXnA}, month={Oct},}`

### 2011

- C. Das, A. Becker, and T. Bretl, “Probably approximately correct coverage for robots with uncertainty,” in 2011 ieee/rsj international conference on intelligent robots and systems, 2011, pp. 1160-1166.

[Bibtex][Video]`@INPROCEEDINGS{6094695, author={C. {Das} and A. {Becker} and T. {Bretl}}, booktitle={2011 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={Probably approximately correct coverage for robots with uncertainty}, year={2011}, volume={}, number={}, pages={1160-1166}, abstract={The classical problem of robot coverage is to plan a path that brings a point on the robot within a fixed distance of every point in the free space. In the presence of significant uncertainty in sensing and actuation, it may no longer be possible to guarantee that the robot covers all of the free space all the time, and so it becomes unclear what problem we are trying to solve. We will restore clarity by adopting a ``probably approximately correct'' measure of performance that captures the probability 1-\epsilon of covering a fraction 1-\delta of the free space. The problem of coverage for a robot with uncertainty is then to plan a feedback policy that achieves a given value of \epsilon and \delta. Just as solutions to the classical problem are judged by the resulting path length, solutions to our problem are judged by the required execution time. We will show the practical utility of our performance measure by applying it to several examples in simulation.}, keywords={mobile robots;path planning;uncertainty;robot coverage;path planning;fixed distance;sensing;actuation;Robot sensing systems;Uncertainty;Shape;Trajectory;Noise}, doi={10.1109/IROS.2011.6094695}, ISSN={2153-0858}, video={https://youtu.be/5e3zz8ezxXo}, month={Sep.},}`

### 2010

- A. Becker and T. Bretl, “Motion planning under bounded uncertainty using ensemble control,” in Robotics: science and systems, Zaragoza, Spain, 2010.

[Bibtex][Video]`@inproceedings{becker2010motion, title={Motion planning under bounded uncertainty using ensemble control}, author={Becker, Aaron and Bretl, Timothy}, booktitle={Robotics: Science and Systems}, year={2010}, video={https://youtu.be/8yYD_KMwfaM}, address={Zaragoza, Spain}, abstract={This paper considers the problem of motion planning for a nonholonomic unicycle despite uncertainty that scales both the forward speed and the turning rate by an unknown but bounded constant. We model the unicycle as an ensemble control system, show that the position of this ensemble is controllable, and derive motion planning algorithms to steer this position between a given start and goal. We apply our work to a differential-drive robot with unknown but bounded wheel radius, and validate our approach with hardware experiments.}, }`

- I. Ruano De Pablo, A. Becker, and T. Bretl, “An optimal solution to the linear search problem for a robot with dynamics,” in 2010 ieee/rsj international conference on intelligent robots and systems, 2010, pp. 652-657.

[Bibtex][Video]`@INPROCEEDINGS{5653185, author={I. {Ruano De Pablo} and A. {Becker} and T. {Bretl}}, booktitle={2010 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={An optimal solution to the linear search problem for a robot with dynamics}, year={2010}, volume={}, number={}, pages={652-657}, abstract={In this paper we derive the control policy that minimizes the total expected time for a point mass with bounded acceleration, starting from the origin at rest, to find and return to an unknown target that is distributed uniformly on the unit interval. We apply our result to proof-of-concept hardware experiments with a planar robot arm searching for a metal object using an inductive proximity sensor. In particular, we show that our approach easily extends to optimal search along arbitrary curves, such as raster-scan patterns that might be useful in other applications like robot search-and-rescue.}, keywords={emergency services;robot dynamics;search problems;sensors;service robots;linear search problem;point mass;proof-of-concept hardware experiments;planar robot arm;inductive proximity sensor;arbitrary curves;raster-scan patterns;robot search-and-rescue;Search problems;Robot sensing systems;Trajectory;Acceleration;Optimal control;Switches}, doi={10.1109/IROS.2010.5653185}, ISSN={2153-0858}, video={https://youtu.be/HVxfTqSy1RA}, month={Oct},}`

### 2009

- A. Becker, R. Sandheinrich, and T. Bretl, “Automated manipulation of spherical objects in three dimensions using a gimbaled air jet,” in 2009 ieee/rsj international conference on intelligent robots and systems, 2009, pp. 781-786.

[Bibtex][Video]`@INPROCEEDINGS{5354427, author={A. {Becker} and R. {Sandheinrich} and T. {Bretl}}, booktitle={2009 IEEE/RSJ International Conference on Intelligent Robots and Systems}, title={Automated manipulation of spherical objects in three dimensions using a gimbaled air jet}, year={2009}, volume={}, number={}, pages={781-786}, abstract={This paper presents a mechanism and a control strategy that enables automated non-contact manipulation of spherical objects in three dimensions using air flow, and demonstrates several tasks that can be performed with such a system. The mechanism is a 2-DOF gimbaled air jet with a variable flow rate. The control strategy is feedback linearization based on a classical fluid dynamics model with state estimates from stereo vision data. The tasks include palletizing, sorting, and ballistics. All results are verified with hardware experiments.}, keywords={feedback;fluid dynamics;manipulator dynamics;state estimation;spherical objects;automated noncontact manipulation;air flow;2-DOF gimbaled air jet;variable flow rate;feedback linearization;classical fluid dynamics model;state estimation;stereo vision data;palletizing;sorting;ballistics;Automatic control;Control systems;Fluid flow control;Linear feedback control systems;State feedback;Fluid dynamics;State estimation;Stereo vision;Sorting;Hardware}, doi={10.1109/IROS.2009.5354427}, ISSN={2153-0866}, video={https://youtu.be/HkhMCCOHFmM}, month={Oct},}`

### 2007

- T. T. Dang, T. D. Vu, and A. Becker, “A lossless coding scheme for images using cross-point regions for modeling,” in 2007 ieee international conference on electro/information technology, 2007, pp. 96-101.

[Bibtex]`@INPROCEEDINGS{4374440, author={T. T. {Dang} and T. D. {Vu} and A. {Becker}}, booktitle={2007 IEEE International Conference on Electro/Information Technology}, title={A lossless coding scheme for images using cross-point regions for modeling}, year={2007}, volume={}, number={}, pages={96-101}, abstract={This paper presents CRIC (cross-point regions for lossless image compression), a scheme for losslessly encoding and decoding images, especially medical images, by optimizing on the probability of cross points that neighbor points of grey levels 2n. The base of this statement is the effect of Gray coding on cross points. At first, the effect of Gray codes is determined on an adjacent data set because images characteristically contain data that does not change much in a specific area; then this effect is generalized for real data without losing generality for their statistical properties. This is especially true for medical images that have many regions with the same grey levels. The Gray code transformation makes the bit states of cross points change from the original data bits, so first the probabilities of data bits on specific bit planes in cross point regions and then the entropies of the messages are changed. These probabilities are estimated and compared with the probabilities of the original data bits. This change of probability has important effects on the encoding and decoding processes in lossless medical image compression.}, keywords={data compression;image coding;lossless coding scheme;cross-point regions;lossless image compression;grey levels;Gray coding;medical image compression;Image coding;Reflective binary codes;Biomedical imaging;Decoding;Probability;Entropy;Tomography;Tin;cross point;entire cross point region;ideal cross point region;probability of bits}, doi={10.1109/EIT.2007.4374440}, ISSN={2154-0373}, month={May},}`

## Peer-Reviewed Educational Software

##### (**bold face **for lab members)

### 2020

- Y. Lu and A. T. Becker, Probabilistic roadmap method with seven-link articulated robot, Wolfram demonstrations project, 2020.

[Bibtex][Interactive Demo]`@misc{2020-yitong-seven-link, Title = {Probabilistic Roadmap Method with Seven-Link Articulated Robot}, url = {https://demonstrations.wolfram.com/ProbabilisticRoadmapMethodWithSevenLinkArticulatedRobot/}, demo = {https://demonstrations.wolfram.com/ProbabilisticRoadmapMethodWithSevenLinkArticulatedRobot/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Yitong Lu and Aaron T. Becker}, year = {2020}, month = {April}, abstract = {This Demonstration challenges you to move the seven-link robot (in brown) to match a goal configuration (in green) with the minimum number of collisions. Drag the locators to move the robot while avoiding collisions with the blue obstacles. This example was used in 1995 to introduce the probabilistic roadmap method (PRM), a robot motion-planning technique. Selecting "relative" movement changes the angle of one robot link at a time, and "absolute" rotates all subsequent links.}, }`

- S. Poyrekar and A. T. Becker, Base conversions from base 2 through 100 using radix points, Wolfram demonstrations project, 2020.

[Bibtex][Interactive Demo]`@misc{2020-shreyas-base-conversion, Title = {Base Conversions from Base 2 through 100 Using Radix Points}, url = {http://demonstrations.wolfram.com/BaseConversionsFromBase2Through100UsingRadixPoints/}, demo = {http://demonstrations.wolfram.com/BaseConversionsFromBase2Through100UsingRadixPoints/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Shreyas Poyrekar and Aaron T. Becker}, year = {2020}, month = {Feb}, abstract = {This Demonstration converts a given number in some base from 2 to 100 into all bases from 2 to 100. Use the buttons to input the number, which may contain the characters '.', 0 through 9, and both lower- and uppercase English and Greek letters. Move the slider to change the input base, output base and the output resolution. This is similar to the Wolfram Language function BaseForm, but handles a larger range of bases and handles numbers with a radix point ('.').}, }`

- A. T. Becker and Y. Lu, Probabilistic roadmap method in 3d, Wolfram demonstrations project, 2020.

[Bibtex][Interactive Demo]`@misc{2020-becker-prm-3D, Title = {Probabilistic Roadmap Method in 3D}, url = {http://demonstrations.wolfram.com/ProbabilisticRoadmapMethodIn3D/}, demo = {http://demonstrations.wolfram.com/ProbabilisticRoadmapMethodIn3D/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Yitong Lu}, year = {2020}, month = {Feb}, abstract = {This Demonstration uses the probabilistic roadmap method (PRM) to plan a motion path for a three-link robot in a 3D configuration space that avoids collisions with a blue and a yellow sphere. If a path from the initial configuration to the goal configuration is found, it can be traversed by moving the ``progress'' slider. To generate a new roadmap, click ``restart'' and then click ``add 100 vertices'' to randomly sample configurations and calculate if they collide with obstacles (red points) or are safe (green points). If no path is found, continue adding vertices or increase the ``radius'' value to try to connect safe vertices less than radius distance apart into a roadmap. Although the PRM does not need to calculate the configuration space obstacles, you can make them visible with a checkbox.}, }`

- A. T. Becker and Y. Lu, Probabilistic roadmap method for robot arm, Wolfram demonstrations project, 2020.

[Bibtex][Interactive Demo]`@misc{2020-becker-prm-robot-arm, Title = {Probabilistic Roadmap Method for Robot Arm}, url = {http://demonstrations.wolfram.com/ProbabilisticRoadmapMethodForRobotArm/}, demo = {http://demonstrations.wolfram.com/ProbabilisticRoadmapMethodForRobotArm/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Yitong Lu}, year = {2020}, month = {Jan}, abstract = {This Demonstration uses the Probabilistic Roadmap Method (PRM) to plan a motion path for a two-link robot that avoids collisions with a blue sphere and an orange sphere. First, click (add 100 vertices) to randomly sample configurations and calculate if they collide with obstacles (red points) or are safe (green points). Next, select (radius) value to try to connect safe vertices less than radius distance apart into a roadmap. If a path from the initial to goal configuration is found, it can be traversed with the (progress) slider. Although the PRM does not need to calculate the configuration space obstacles, you can make them visible with a checkbox.}, }`

- A. T. Becker and Y. Lu, Probabilistic roadmap method, Wolfram demonstrations project, 2020.

[Bibtex][Interactive Demo]`@misc{2020-becker-prm, Title = {Probabilistic Roadmap Method}, url = {http://demonstrations.wolfram.com/ProbabilisticRoadmapMethod/}, demo = {http://demonstrations.wolfram.com/ProbabilisticRoadmapMethod/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Yitong Lu}, year = {2020}, month = {Jan}, abstract = {This Demonstration uses the probabilistic roadmap method (PRM) to connect configurations from an initial configuration (shown by a Locator) to a goal configuration. First, click the button (add 50 vertices) to randomly sample configurations and calculate if they collide with obstacles (red) or are safe (green). Next, select a (radius) value to try and connect safe vertices less than the radius distance into a roadmap. If a path from the initial to the goal configuration is found, it can be traversed using the ``progress'' slider. Although the PRM does not need to calculate the configuration space obstacles, you can make them visible by clicking the checkbox.}, }`

### 2019

- M. Sultan and A. T. Becker, Reachable set for a drone, Wolfram demonstrations project, 2019.

[Bibtex][Interactive Demo]`@misc{2019-sultan-reachable-set-drone, Title = {Reachable Set for a Drone}, url = {http://demonstrations.wolfram.com/ReachableSetForADrone/}, demo = {http://demonstrations.wolfram.com/ReachableSetForADrone/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Mohammad Sultan and Aaron T. Becker}, year = {2019}, month = {Dec}, abstract = {This Demonstration shows the set of all positions (x,z) a drone can reach in time Overscript[T, ^]. To ensure applicability to many different kinds of drones, this Demonstration uses a nondimensionalized two-dimensional model with two parameters: minimum/maximum thrust values Subscript[U, min/max]. The plot shows the reachable set of positions in blue and the path of a particular drone with a dashed line. The optimal control inputs are all functions of two switching times, Subscript[Overscript[t, ^], R] and Subscript[Overscript[t, ^], T], which are controlled by the locator. The drone rotates at maximum angular speed for time less than Subscript[Overscript[t, ^], R] and flies with no rotation afterward. The drone moves with minimum thrust for time less than Subscript[Overscript[t, ^], T], and maximum thrust afterward.}, }`

- M. Sultan and A. T. Becker, Smallest circle problem, Wolfram demonstrations project, 2019.

[Bibtex][Interactive Demo]`@misc{2019-sultan-smallest-circle, Title = {Smallest Circle Problem}, url = {http://demonstrations.wolfram.com/SmallestCircleProblem/}, demo = {http://demonstrations.wolfram.com/SmallestCircleProblem/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Mohammad Sultan and Aaron T. Becker}, year = {2019}, month = {Dec}, abstract = {The smallest circle problem for a set of two-dimensional points seeks to find the smallest-radius circle that contains all the points. This Demonstration uses the Matoušek, Sharir and Welzl (MSW) algorithm [1] that computes the circle for n points in expected O(n) time. Move the locators to interact with the solution and use the slider to change the number of points. The built-in Wolfram Language function BoundingRegion uses a similar method.}, }`

- S. Poyrekar, A. Sultana, and A. T. Becker, Art gallery problem, Wolfram demonstrations project, 2019.

[Bibtex][Video] [Interactive Demo]`@misc{2019-poyrekar-art-gallery-problem, Title = {Art Gallery Problem}, url = {http://demonstrations.wolfram.com/ArtGalleryProblem/}, demo = {http://demonstrations.wolfram.com/ArtGalleryProblem/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Shreyas Poyrekar and Arifa Sultana and Aaron T. Becker}, year = {2019}, month = {Sept}, abstract = {How many omnidirectional cameras are needed to fully observe every part of a polygonal art gallery? Move the cameras by dragging the colored locators (guards) to try to cover the polygon with the fewest guards.}, video = {https://youtu.be/WMvlHk_6guY}, }`

- S. Poyrekar, A. Sultana, and A. T. Becker, Visibility region of a polygon, Wolfram demonstrations project, 2019.

[Bibtex][Interactive Demo]`@misc{2019-poyrekar-visibility-region-of-polygon, Title = {Visibility Region of a Polygon}, url = {http://demonstrations.wolfram.com/VisibilityRegionOfAPolygon/}, demo = {http://demonstrations.wolfram.com/VisibilityRegionOfAPolygon/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Shreyas Poyrekar and Arifa Sultana and Aaron T. Becker}, year = {2019}, month = {Sept}, abstract = {The parts of a polygon reachable by straight lines from a point without hitting a wall are called the visibility region. The visibility region is useful for finding accessible paths. This Demonstration allows you to drag the reference point (or source), shown as a blue disk, to construct a visibility region.}, }`

- S. Poyrekar, A. Sultana, and A. T. Becker, Minkowski sum of convex robot and obstacle, Wolfram demonstrations project, 2019.

[Bibtex][Interactive Demo]`@misc{2019-poyrekar-minkowskit-sum-convex, Title = {Minkowski Sum of Convex Robot and Obstacle}, url = {http://demonstrations.wolfram.com/MinkowskiSumOfConvexRobotAndObstacle/}, demo = {http://demonstrations.wolfram.com/MinkowskiSumOfConvexRobotAndObstacle/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Shreyas Poyrekar and Arifa Sultana and Aaron T. Becker}, year = {2019}, month = {Apr}, abstract = {The Minkowski sum of a convex obstacle and a robot delineates the region where an obstacle and a robot might collide. Knowing this region simplifies robot motion planning. Set ``view'' to (static) and drag the locators to make arbitrary two-dimensional robots and obstacles. The region of the Minkowski sum can be traced out by choosing (move around Minkowski) to animate the robot moving around the edge of the obstacle.}, }`

### 2018

- M. Sultan and A. T. Becker, Maximizing apparent velocity in a camera’s frame, Wolfram demonstrations project, 2018.

[Bibtex][Interactive Demo]`@misc{2018-sultan-maximizing-apparent-velocity, Title = {Maximizing Apparent Velocity in a Camera’s Frame}, url = {http://demonstrations.wolfram.com/MaximizingApparentVelocityInACamerasFrame/}, demo = {http://demonstrations.wolfram.com/MaximizingApparentVelocityInACamerasFrame/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Mohammad Sultan and Aaron T. Becker}, year = {2018}, month = {Nov}, abstract = {How should a drone move to maximize its apparent velocity in the frame of a camera? This Demonstration solves this problem for a drone that can move a distance r in any direction.}, }`

- A. T. Becker and J. Garcia, Steering multiple radio control (rc) cars with one joystick, Wolfram demonstrations project, 2018.

[Bibtex][Video] [Interactive Demo]`@misc{2018-garcia-steering-mulitple-radio-control-cars, Title = {Steering Multiple Radio Control (RC) Cars with One Joystick}, url = {https://demonstrations.wolfram.com/SteeringMultipleRadioControlRCCarsWithOneJoystick/}, demo = {https://demonstrations.wolfram.com/SteeringMultipleRadioControlRCCarsWithOneJoystick/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Javier Garcia}, year = {2018}, month = {Nov}, abstract = {Imagine n radio control (RC) cars all controlled using the same radio frequency. When you command one car to move along a certain trajectory, all other cars follow a trajectory of the same shape, starting from their initial positions and rotated according to their initial heading. Each pair of cars can collide only in the regions shown by gray disks. During setup, gray disks determine where two cars can collide. This collision area is a function of the position and orientation of the cars, so changing these changes the positions of the disks. The car used as reference for commands is car 1, so during (running) the gray disks show where car 1 must be positioned to make any two cars collide. The paths of the robots are drawn in different colors. Change n to generate new robots.}, video = {https://youtu.be/sSSQgnmjmJw}, }`

- A. T. Becker and J. Garcia, The homicidal chauffeur problem, Wolfram demonstrations project, 2018.

[Bibtex][Video] [Interactive Demo]`@misc{2018-garcia-homicidal-chauffer, Title = {The Homicidal Chauffeur Problem}, url = {http://demonstrations.wolfram.com/TheHomicidalChauffeurProblem/}, demo = {http://demonstrations.wolfram.com/TheHomicidalChauffeurProblem/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Javier Garcia}, year = {2018}, month = {Jan}, abstract = {In this Demonstration, a chauffeur driving a car with a minimum turning radius r_min pursues a slower pedestrian with an unrestricted turning radius. The car is red and the evading pedestrian is blue. Click setup to set values for r_min and the velocity ratio v_car/v_pedestrian, and drag the locators to set the initial positions of the car and pedestrian and the orientation of the car. Then click ``running'' and move the locator to control the goal position of the pedestrian; after three seconds, the car attempts to run over the pedestrian. Avoid the car as long as possible!}, video = {https://youtu.be/pbSCsGh_OBo}, }`

- A. T. Becker and L. Huang, Rapidly exploring random tree (rrt) and rrt*, Wolfram demonstrations project, 2018.

[Bibtex][Video] [Interactive Demo]`@misc{2018-li-rrt, Title = {Rapidly Exploring Random Tree (RRT) and RRT*}, url = {http://demonstrations.wolfram.com/RapidlyExploringRandomTreeRRTAndRRT/}, demo = {http://demonstrations.wolfram.com/RapidlyExploringRandomTreeRRTAndRRT/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Li Huang}, year = {2018}, month = {Jan}, abstract = {A rapidly exploring random tree (RRT) grows a tree rooted at a start node. RRTs are designed to efficiently explore paths in a high-dimensional space. This Demonstration lets you compare random trees (RTs), RRTs and RRT*. An RT selects a node at random from the tree and adds an edge in a random direction, but an RRT first selects a goal point, then tries to add an edge from the closest node in the tree toward the goal point. RRT* improves on this by rewiring the tree to form shortest paths. Drag the goal locator to search for a path.}, video = {https://youtu.be/Ob3BIJkQJEw}, }`

- A. T. Becker and S. Shahrokhi, Configuration space for four-bar linkage, Wolfram demonstrations project, 2018.

[Bibtex][Interactive Demo]`@misc{2018-shahrokhi-4-bar, Title = {Configuration Space for Four-Bar Linkage}, url = {http://demonstrations.wolfram.com/ConfigurationSpaceForFourBarLinkage/}, demo = {http://demonstrations.wolfram.com/ConfigurationSpaceForFourBarLinkage/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Shiva Shahrokhi}, year = {2018}, month = {Jan}, abstract = {A planar four-bar linkage has four joints, so its configuration is described by four numbers. However, because the linkage is a closed chain, the resulting constraints make most configurations unattainable. The linkage's configuration space is a one-dimensional curve embedded in a four-dimensional space. The plot at left projects the configuration space onto the joint angles (theta, phi) of the first and third links. You can drag the locator to explore the set of reachable configurations. Because theta and phi are angles, this configuration space wraps around from pi to -pi. If any link is greater than the sum of the other three links, no valid configurations exist.}, }`

### 2017

- A. T. Becker and S. Shahrokhi, Isochrons for a dubins car, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-isochrons-dubins, Title = {Isochrons for a Dubins Car}, url = {http://demonstrations.wolfram.com/IsochronsForADubinsCar/}, demo = {http://demonstrations.wolfram.com/IsochronsForADubinsCar/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Shiva Shahrokhi}, year = {2017}, month = {Dec}, abstract = {This Demonstration shows the set of (x,y), positions reachable at time t by a car with a minimum turning radius r. This set is bounded by four isochrons. An isochron is a line on a diagram or map connecting points relating to the same or equal times. You can choose whether to show areas reachable at time t or less than or equal to t. The boundary of this set is defined by turning at the maximum rate in either direction for seconds and then either switching directions or moving straight ahead. The percent of the path traveled is denoted by p.}, }`

- A. T. Becker and S. Shahrokhi, Shortest path for the dubins car, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-shortest-path-dubins, Title = {Shortest Path for the Dubins Car}, url = {http://demonstrations.wolfram.com/ShortestPathForTheDubinsCar/}, demo = {http://demonstrations.wolfram.com/ShortestPathForTheDubinsCar/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Shiva Shahrokhi}, year = {2017}, month = {Dec}, abstract = {In 1957, Lester Eli Dubins proved that the shortest path between two (x,y,theta) coordinates for a forward-moving vehicle with a minimum turning radius r_min is composed entirely of no more than three circular arcs of radius r_min or straight lines.}, }`

- A. T. Becker and B. Isichei, Distance norms in robot workspace and phase space, Wolfram demonstrations project, 2017.

[Bibtex][Video] [Interactive Demo]`@misc{2017-isichei-distance-norm-robot, Title = {Distance Norms in Robot Workspace and Phase Space}, url = {https://demonstrations.wolfram.com/DistanceNormsInRobotWorkspaceAndPhaseSpace/}, demo = {https://demonstrations.wolfram.com/DistanceNormsInRobotWorkspaceAndPhaseSpace/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Benedict Isichei}, year = {2017}, month = {Dec}, abstract = {This Demonstration shows the area within the distance d of a two-link planar-arm robot with configuration (theta_1,theta_2). The distance is measured in the L_1, L_2, L_3 or L_infinity norm, with the norm applied either in the workspace or the phase space of the robot. You can change the norm type, the length of the first arm joint and the angles of the two arm joints.}, video = {https://youtu.be/B8I43AEerUU}, }`

- A. T. Becker, B. Isichei, M. Sultan, and M. S. Chemudupati, Distance norms in robot workspace and phase space, Wolfram demonstrations project, 2017.

[Bibtex][Video] [Interactive Demo]`@misc{2017-isichei-robot-manipulator-workspaces, Title = {Distance Norms in Robot Workspace and Phase Space}, url = {http://demonstrations.wolfram.com/RobotManipulatorWorkspaces/}, demo = {http://demonstrations.wolfram.com/RobotManipulatorWorkspaces/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Benedict Isichei and Muhammad Sultan and Maruthi S. Chemudupati}, year = {2017}, month = {Dec}, abstract = {A robot's workspace is the total volume swept out by the end effector as the manipulator executes all possible motions. The shape of the workspace dictates the applications for which each design can be used. This Demonstration lets you load several robot designs to compare their workspaces. You can set the position and range for each joint using sliders.}, video = {https://youtu.be/hIRZeYgcG5E}, }`

- A. T. Becker, B. Isichei, and P. R. Padala, Breadth-first search robot mo- tion planning, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-isichei-breadth-first-search-robot, Title = {Breadth-First Search Robot Mo- tion Planning}, url = {http://demonstrations.wolfram.com/RobotManipulatorWorkspaces/}, demo = {http://demonstrations.wolfram.com/RobotManipulatorWorkspaces/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Benedict Isichei and Praveen Reddy Padala}, year = {2017}, month = {Dec}, abstract = {This Demonstration shows a resolution-complete planner that finds the shortest path between an initial and final configuration of a two-link, planar-arm robot by using a breadth-first search. The robot operates in the workspace on the left that contains two small circular obstacles. The corresponding robot phase space on the right shows the configurations (theta_1,theta_2), for which an arm intersects an obstacle. You can relocate obstacles in the workspace and change the initial and final positions. You can improve the resolution of the search grid by increasing Q and move the robot along the shortest path by increasing P.}, }`

- B. Isichei and A. T. Becker, Breadth-first search robot motion planning, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-isichei-three-parameterizations-rotation, Title = {Breadth-First Search Robot Motion Planning}, url = {http://demonstrations.wolfram.com/ThreeParametrizationsOfRotations/}, demo = {http://demonstrations.wolfram.com/ThreeParametrizationsOfRotations/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Benedict Isichei and Aaron T. Becker}, year = {2017}, month = {Sept}, abstract = {A rotation can be parameterized in several ways. This Demonstration compares three popular parametrizations: * Euler angles about the axes XYZ, * the angle of rotation about an arbitrary axis, * the roll, pitch and yaw about the world XYZ axes. The progress slider rotates a teapot shape through these rotations, from an initial orientation in green to a final orientation in red. The intermediate configurations of the teapot depend on the parametrization chosen, but the final configuration is always the same.}, }`

- J. Shi and A. T. Becker, Shortest path between two points in the unit disk reflecting off the circumference, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-shi-shortest-path-unit-disk, Title = {Shortest Path between Two Points in the Unit Disk Reflecting off the Circumference}, url = {https://demonstrations.wolfram.com/ShortestPathBetweenTwoPointsInTheUnitDiskReflectingOffTheCir/}, demo = {https://demonstrations.wolfram.com/ShortestPathBetweenTwoPointsInTheUnitDiskReflectingOffTheCir/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Jingang Shi and Aaron T. Becker}, year = {2017}, month = {Sept}, abstract = {Given two points within the unit disk labeled S (in green) and E (in red), what is the shortest path between the two points that reflects off the unit circle? You can drag the two points. The central angle between the two points is beta. The angle from the x axis to S is \phi. The shortest path that touches the unit circle is at angle theta*.}, }`

- D. Bao, T. Song, and A. T. Becker, Spreading particles in a disk, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-bao-spread-particles, Title = {Spreading Particles in a Disk}, url = {http://demonstrations.wolfram.com/SpreadingParticlesInADisk/}, demo = {http://demonstrations.wolfram.com/SpreadingParticlesInADisk/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Daniel Bao and Tate Song and Aaron T. Becker}, year = {2017}, month = {Sept}, abstract = {This Demonstration shows particles spreading inside a disk workspace. These might, for example, be magnetized particles inside a Petri dish pushed by an external magnetic field. The particles start along the green arc, bounded by red and blue locators. The propagated particles are pushed in the direction of theta and are incident along the arc drawn in blue. Often particles cannot be controlled perfectly, which is modeled by specifying an angular spread +/-delta to either side of theta. This Demonstration shows the maximum and minimum particle spread (arc length) into which the particles can be manipulated.}, }`

- M. Sultan and A. T. Becker, Common robot arm configurations, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-sultan-common-arm-configurations, Title = {Common Robot Arm Configurations}, url = {http://demonstrations.wolfram.com/CommonRobotArmConfigurations/}, demo = {http://demonstrations.wolfram.com/CommonRobotArmConfigurations/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Mohammad Sultan and Aaron T. Becker}, year = {2017}, month = {Jul}, abstract = {Robot manipulators can be concisely described by a convention called the Denavit–Hartenberg parameters (DH parameters) to assign one variable and three parameters to describe the distance and angular offset between each joint. This Demonstration allows you to choose an arbitrary robot specified by DH parameters and animate the degrees of freedom.}, }`

- A. T. Becker, H. Zhao, and L. Huang, Compression ratio of spheres in a curved tube, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-becker-compression-ratio-spheres, Title = {Compression Ratio of Spheres in a Curved Tube}, url = {http://demonstrations.wolfram.com/CompressionRatioOfSpheresInACurvedTube/}, demo = {http://demonstrations.wolfram.com/CompressionRatioOfSpheresInACurvedTube/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Haoran Zhao and Li Huang}, year = {2017}, month = {March}, abstract = {This Demonstration determines the optimal packing for spheres in a curved tube. Spheres of radius s are packed in a tube of radius t, where t>=s, with a 180 degree bend of radius b. We seek the minimum value of the compression ratio. For small ratios t/s, the spheres are in contact with the outside wall. For larger t/s, optimal compression is attained by arranging the spheres in a zigzag pattern parallel to the axis of curvature along the tube centerline.}, }`

- H. Zhao and A. T. Becker, Transmitting force through a tube filled with spheres and spacers, Wolfram demonstrations project, 2017.

[Bibtex][Interactive Demo]`@misc{2017-zhao-transmitting-force-through-a-tube, Title = {Transmitting Force through a Tube Filled with Spheres and Spacers}, url = {https://demonstrations.wolfram.com/TransmittingForceThroughATubeFilledWithSpheresAndSpacers/}, demo = {https://demonstrations.wolfram.com/TransmittingForceThroughATubeFilledWithSpheresAndSpacers/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Haoran Zhao and Aaron T. Becker}, year = {2017}, month = {March}, abstract = {This Demonstration examines a model for force transmitted through a cylindrical tube filled with an arrangement of spheres and cylindrical spacers. We consider the densest packing of spheres with unit diameter in a linear tubing of inner diameter D_tube>D_sphere.}, }`

### 2016

- A. T. Becker and H. Nguyen, Defects in an optical fiber, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-defects-optical-fiber, Title = {Defects in an Optical Fiber}, url = {http://demonstrations.wolfram.com/DefectsInAnOpticalFiber/}, demo = {http://demonstrations.wolfram.com/DefectsInAnOpticalFiber/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Hoang Nguyen}, year = {2016}, month = {Nov}, abstract = {Light can propagate in an optical fiber by total internal reflection (TIR) when the outside medium has a lower refractive index than the core. However, light can still be refracted through the boundary if the angle between the light and boundary is greater than the critical angle. Optical fibers are usually cladded with another material to increase the critical angle and to protect the core. This Demonstration shows the effect of a triangular defect in the core. The origins of two light rays can be set with locators.}, }`

- A. T. Becker, Poles and zeros of time-domain response functions, Wolfram demonstrations project, 2016.

[Bibtex][Video] [Interactive Demo]`@misc{2016-becker-poles-and-zeros, Title = {Poles and Zeros of Time-Domain Response Functions}, url = {http://demonstrations.wolfram.com/PolesAndZerosOfTimeDomainResponseFunctions/}, demo = {http://demonstrations.wolfram.com/PolesAndZerosOfTimeDomainResponseFunctions/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2016}, month = {Nov}, abstract = {This Demonstration displays the response of a system with s domain representation H(s) to an impulse, step or sinusoidal input. H(s) is a transfer function generated by multiplying the poles and zeros together. Poles are at locations p_i marked with a red X and have the form 1/(s-p_i). Zeros are at locations z_i marked with a blue O and have the form (s-z_i). You can drag the poles and zeros, but because the generating differential equation is assumed to have real coefficients, all complex poles and zeros occur as complex conjugates.}, video = {https://youtu.be/PybGMXKTp7c}, }`

- A. T. Becker, Synthesis with even and odd functions, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-synthesis-odd-even, Title = {Synthesis with Even and Odd Functions}, url = {http://demonstrations.wolfram.com/SynthesisWithEvenAndOddFunctions/}, demo = {http://demonstrations.wolfram.com/SynthesisWithEvenAndOddFunctions/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2016}, month = {Aug}, abstract = {A signal x(t) has even symmetry if x(t)=x(-t), which means the signal is symmetric about the vertical axis. A signal x(t) has odd symmetry if x(t)=-x(-t), which means the signal to the left of the vertical axis is the inverted mirror image of the signal to the right of the vertical axis. This Demonstration shows that any arbitrary signal x(t) can be synthesized by adding an even and an odd signal. Slide the time offset T to change the input signal to x(t-T).}, }`

- A. T. Becker and S. Shahrokhi, Measuring distance and orientation using camera and lasers, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-measure-distance-using-camera-and-lasers, Title = {Measuring Distance and Orientation Using Camera and Lasers}, url = {http://demonstrations.wolfram.com/MeasuringDistanceAndOrientationUsingCameraAndLasers/}, demo = {http://demonstrations.wolfram.com/MeasuringDistanceAndOrientationUsingCameraAndLasers/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Shiva Shahrokhi}, year = {2016}, month = {Jul}, abstract = {Distance to an object can be measured with a single camera and a laser, if the laser position relative to the camera is known. Usually the laser is pointed in the same direction as the camera and mounted a known distance from the camera. By dragging the locator, you can choose the orientation of the brown cuboid and two red lasers mounted s units to the left and right of a camera, which has a focal length lambda. These lasers can measure the distance to the cuboid, as shown by the reticule on the camera image. The cuboid's angle can be computed from two distance measurements.}, }`

- A. T. Becker and M. Wan, Time shifting and time scaling in signal processing, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-time-shifting-and-scaling-signal-processing, Title = {Time Shifting and Time Scaling in Signal Processing}, url = {http://demonstrations.wolfram.com/TimeShiftingAndTimeScalingInSignalProcessing/}, demo = {http://demonstrations.wolfram.com/TimeShiftingAndTimeScalingInSignalProcessing/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Mable Wan}, year = {2016}, month = {June}, abstract = {Transforming an input signal by time scaling and time shifting is a fundamental concept in signal processing. Drag the sliders to scale the time and time shift the signal.}, }`

- A. T. Becker and L. Lin, Forward and inverse kinematics for two-link arm, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-forward-and-inverse-kinematics-two-link, Title = {Forward and Inverse Kinematics for Two-Link Arm}, url = {http://demonstrations.wolfram.com/ForwardAndInverseKinematicsForTwoLinkArm/}, demo = {http://demonstrations.wolfram.com/ForwardAndInverseKinematicsForTwoLinkArm/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Lillian Lin}, year = {2016}, month = {June}, abstract = {Transforming an input signal by time scaling and time shifting is a fundamental concept in signal processing. Drag the sliders to scale the time and time shift the signal.}, }`

- A. T. Becker and M. Burbage, Forward and inverse kinematics for two-link arm, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-dh-parameters-three-link, Title = {Forward and Inverse Kinematics for Two-Link Arm}, url = {https://demonstrations.wolfram.com/DenavitHartenbergParametersForAThreeLinkRobot/}, demo = {https://demonstrations.wolfram.com/DenavitHartenbergParametersForAThreeLinkRobot/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Mary Burbage}, year = {2016}, month = {June}, abstract = {The Denavit–Hartenberg (DH) convention for assigning coordinate frames uses four variables to define the reference coordinate frame for each link in a robotic arm. This Demonstration lets you select a three-link combination of revolute (rotating) and prismatic (sliding) joints. You can then vary their DH parameters to create a variety of robot arms in different configurations.}, }`

- L. Huang and A. T. Becker, Packing spheres into a thin cylinder, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-huang-packing-spheres, Title = {Packing Spheres into a Thin Cylinder}, url = {http://demonstrations.wolfram.com/PackingSpheresIntoAThinCylinder/}, demo = {http://demonstrations.wolfram.com/PackingSpheresIntoAThinCylinder/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Li Huang and Aaron T. Becker}, year = {2016}, month = {May}, abstract = {The densest packing of spheres with radius r in a cylinder of radius R, where R>=r, is a challenging problem. This Demonstration provides the optimal packing for small ratios of R/r and upper bounds that show dense packings up to R/r=3.}, }`

- H. Zhao and A. T. Becker, Chart for a torus, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-zhao-chart-for-torus, Title = {Chart for a Torus}, url = {http://demonstrations.wolfram.com/ChartForATorus/}, demo = {http://demonstrations.wolfram.com/ChartForATorus/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Haoran Zhao and Aaron T. Becker}, year = {2016}, month = {May}, abstract = {A torus (more precisely, a 2-torus) has the shape of the outer surface of a donut. A torus can be parametrized by two angular variables (theta,phi), each in [0,2pi). A dissected torus can be pictured as equivalent to a rectangle in the two-dimensional Euclidean plane R^2, with opposite pairs of edges glued together. Locally, the 2-torus resembles R^2, but there is no global continuous mapping since the Euclidean plane extends to infinity. This Demonstration shows possible mappings from a 2-torus to R^2. The operation necessarily introduces discontinuities, where small changes of theta or phi create large jumps in the planar configuration. Two rotary dials determine a point (theta,phi) (highlighted in green) in the course of a transformation.}, }`

- H. Zhao and A. T. Becker, Robot motion with obstacles, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-zhao-robot-motion-with-osbtacles, Title = {Robot Motion with Obstacles}, url = {http://demonstrations.wolfram.com/RobotMotionWithObstacles/}, demo = {http://demonstrations.wolfram.com/RobotMotionWithObstacles/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Haoran Zhao and Aaron T. Becker}, year = {2016}, month = {Apr}, abstract = {This Demonstration shows a two-link planar arm robot operating in the workspace on the left, containing two small circular obstacles. The corresponding robot phase space on the right shows the configurations q=(theta_1,theta_2) for which an arm intersects an obstacle. You can relocate an obstacle in the workspace and see the corresponding change in phase space. Move the locator in phase space vertically or horizontally to rotate the robot arms. The angles theta_1 and theta_2 are expressed modulo 2 pi. The obstacle regions are computed using 32Q unit squares. You can improve the quality of the computation by increasing Q.}, }`

- H. Zhao and A. T. Becker, Distribution of a swarm of robots in a circular workplace under gravity, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-zhao-distribution-swarm-circle-undergravity, Title = {Distribution of a Swarm of Robots in a Circular Workplace under Gravity}, url = {https://demonstrations.wolfram.com/DistributionOfASwarmOfRobotsInACircularWorkplaceUnderGravity/}, demo = {https://demonstrations.wolfram.com/DistributionOfASwarmOfRobotsInACircularWorkplaceUnderGravity/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Haoran Zhao and Aaron T. Becker}, year = {2016}, month = {Feb}, abstract = {This Demonstration examines the mean, variance, correlation, and covariance of a very large swarm of robots as they move inside a circular workplace under the influence of gravity pointing in the direction beta. The swarm is large, whereas the robots are much smaller by comparison. Under gravity, the swarm flows like a liquid, moving to a side of the workplace and filling the area under a chord to height h.}, }`

- A. T. Becker and R. Pakeetharan, Probabilistic models for robot motion, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-probabilistic-models-for-robot-motion, Title = {Probabilistic Models for Robot Motion}, url = {http://demonstrations.wolfram.com/ProbabilisticModelsForRobotMotion/}, demo = {http://demonstrations.wolfram.com/ProbabilisticModelsForRobotMotion/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker and Renuka Pakeetharan}, year = {2016}, month = {Jan}, abstract = {A mobile robot, repeatedly commanded to move for one second with linear velocity v and angular velocity omega, will travel approximately the same distance each time. However, small random errors due to wheel slip, terrain interactions, and unmodeled dynamics mean that the robot's expected final position is better described as a probability density function (PDF). This Demonstration implements four probabilistic motion models [1], allowing you to modify noise parameters and see their effect. The initial pose is shown in green and the final pose in red; the position and the heading of the robot are indicated by a circle and a line, respectively.}, }`

- H. Zhao and A. T. Becker, Distribution of a robot swarm in a square under gravity, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-zhao-distribution-robot-swarm-in-square, Title = {Distribution of a Robot Swarm in a Square under Gravity}, url = {https://demonstrations.wolfram.com/DistributionOfARobotSwarmInASquareUnderGravity/}, demo = {https://demonstrations.wolfram.com/DistributionOfARobotSwarmInASquareUnderGravity/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Haoran Zhao and Aaron T. Becker}, year = {2016}, month = {Jan}, abstract = {This Demonstration determines the mean, variance, and covariance for a very large swarm of robots as they move inside a square workplace under the influence of gravity, pointing in the direction beta. The swarm is large, but the robots are comparatively small and together cover a constant area A. Under gravity, they flow like a liquid, moving to one side of the workplace to form a polygonal shape.}, }`

- A. T. Becker, Lowpass filter design by pole placement, Wolfram demonstrations project, 2016.

[Bibtex][Interactive Demo]`@misc{2016-becker-lowpass-filter, Title = {Lowpass Filter Design by Pole Placement}, url = {http://demonstrations.wolfram.com/LowpassFilterDesignByPolePlacement/}, demo = {http://demonstrations.wolfram.com/LowpassFilterDesignByPolePlacement/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2016}, month = {Jan}, abstract = {An ideal lowpass filter, drawn in blue, passes all frequencies less than omega_c and rejects all frequencies greater than omega_c. Such a filter cannot be implemented physically because it is non-causal. However, we can design causal filters, drawn in orange, that approximate the ideal lowpass filter. This Demonstration lets you design such a filter by locating poles (of the transfer function), drawn with red Xs, in different arrangements.}, }`

### 2015

- S. Shahrokhi and A. T. Becker, Moving two particles with shared control inputs using wall friction, Wolfram demonstrations project, 2015.

[Bibtex][Interactive Demo]`@misc{2015-shahrokhi-two-particles-wall-friction, Title = {Moving Two Particles with Shared Control Inputs Using Wall Friction}, url = {http://demonstrations.wolfram.com/MovingTwoParticlesWithSharedControlInputsUsingWallFriction/}, demo = {http://demonstrations.wolfram.com/MovingTwoParticlesWithSharedControlInputsUsingWallFriction/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Shiva Shahrokhi and Aaron T. Becker}, year = {2015}, month = {Nov}, abstract = {How can two particles in a two-dimensional workspace, steered by the same global control signal, be moved to arbitrary final positions? This is difficult because the control input is symmetrical. This Demonstration provides an algorithm to move the particles from starting positions (denoted by squares) to the desired final positions (denoted by circles) with the shortest path, making use of boundary interactions (dark red boundaries) to break this control symmetry. The parameter epsilon controls how the particles approach the boundaries.}, }`

- A. T. Becker, Maximize the number of vertices in an equilateral triangular lattice, Wolfram demonstrations project, 2015.

[Bibtex][Interactive Demo]`@misc{2015-becker-maximize-number-vertices-lattice, Title = {Maximize the Number of Vertices in an Equilateral Triangular Lattice}, url = {https://demonstrations.wolfram.com/MaximizeTheNumberOfVerticesInAnEquilateralTriangularLattice/}, demo = {https://demonstrations.wolfram.com/MaximizeTheNumberOfVerticesInAnEquilateralTriangularLattice/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2015}, month = {July}, abstract = {An equilateral triangular lattice is parameterized by four variables: an x and y offset for the initial vertex, the angle theta of the grid with respect to the horizontal, and a scale parameter for the edge lengths. In this Demonstration, you can vary these parameters and see how many vertices and edges fit in the open workspace (white). Drag the locator to create a ``narrow passage,'' while keeping the area of the workspace constant.}, }`

- A. T. Becker, Sensor fusion with normally distributed noise, Wolfram demonstrations project, 2015.

[Bibtex][Video] [Interactive Demo]`@misc{2015-becker-sensor-fusion, Title = {Sensor Fusion With Normally Distributed Noise}, url = {https://demonstrations.wolfram.com/SensorFusionWithNormallyDistributedNoise/}, demo = {https://demonstrations.wolfram.com/SensorFusionWithNormallyDistributedNoise/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2015}, month = {July}, abstract = {Given n unbiased sensor measurements of a scalar quantity, each corrupted by independent, normally distributed noise with variance sigma_n^2, the likelihood function for the true value (purple, dashed) is also a normal density.}, video = {https://youtu.be/-zOmHUENLJE}, }`

### 2014

- A. T. Becker, Ensemble control of robots with unicycle kinematics, Wolfram demonstrations project, 2014.

[Bibtex][Interactive Demo]`@misc{2014-becker-ensemble-control-robots-unicycle, Title = {Ensemble Control of Robots with Unicycle Kinematics}, url = {https://demonstrations.wolfram.com/EnsembleControlOfRobotsWithUnicycleKinematics/}, demo = {https://demonstrations.wolfram.com/EnsembleControlOfRobotsWithUnicycleKinematics/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2014}, month = {Oct}, abstract = {What can you do with multiple remote-control robots all slaved to one remote control? This Demonstration shows you can steer all the robots (represented by colored circles with a line indicating heading) to any desired final position (colored disks). This is possible because of noise: each time the robots are commanded to turn, every robot turns a slightly different amount. You can use these differences to slowly push the robots to goal positions, using the plot on the right for guidance. Research in this area is motivated by real-world challenges in micro- and nanorobotics, where often all the robots are steered by the same control signal.}, }`

- A. T. Becker, Optimizing a gauss gun, Wolfram demonstrations project, 2014.

[Bibtex][Interactive Demo]`@misc{2014-becker-optimize-gauss-gun, Title = {Optimizing a Gauss Gun}, url = {http://demonstrations.wolfram.com/OptimizingAGaussGun/}, demo = {http://demonstrations.wolfram.com/OptimizingAGaussGun/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2014}, month = {Oct}, abstract = {A Gauss gun is a type of linear magnetic accelerator in which projectiles (here ball bearings) interact with an array of magnets. The magnets are shown as red/green spheres, fixed in position. A ball bearing introduced on the left is attracted to the first magnet and undergoes a rapid acceleration that increases its kinetic energy. Upon colliding with the magnet, this energy is transferred through the magnet and a chain of stationary ball bearings, releasing the rightmost bearing. See how the final velocity varies as you change the ball radius, air gap, number of stages, and balls per stage.}, }`

- A. T. Becker, Weber points and multifocal ellipse, Wolfram demonstrations project, 2014.

[Bibtex][Interactive Demo]`@misc{2014-becker-weber-points, Title = {Weber Points and Multifocal Ellipse}, url = {https://demonstrations.wolfram.com/WeberPointsAndMultifocalEllipse/}, demo = {https://demonstrations.wolfram.com/WeberPointsAndMultifocalEllipse/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2014}, month = {Aug}, abstract = {Where should a fire station be placed to minimize the total distance to houses? This type of minimizing location is called the Weber point, and is shown in green for the red locations. Add or move the locators and notice the Weber point is often different than the mean location, shown in blue.}, }`

- A. T. Becker, The marching chinese, Wolfram demonstrations project, 2014.

[Bibtex][Video] [Interactive Demo]`@misc{2014-becker-marching-chinese, Title = {The Marching Chinese}, url = {http://demonstrations.wolfram.com/TheMarchingChinese/}, demo = {http://demonstrations.wolfram.com/TheMarchingChinese/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2014}, month = {Aug}, abstract = {In 1910, Ripley's Believe It or Not claimed, ``If all the Chinese in the world were to march four abreast past a given point they would never finish passing, though they marched forever and ever.'' Try for yourself to see if this is true, adjusting country, rank size and spacing, and marching speed.}, video = {https://youtu.be/f_OrWJTcssA}, }`

- A. T. Becker, Coverage probability with the occupancy problem, Wolfram demonstrations project, 2014.

[Bibtex][Interactive Demo]`@misc{2014-becker-coverage-occupancy, Title = {Coverage Probability with the Occupancy Problem}, url = {https://demonstrations.wolfram.com/CoverageProbabilityWithTheOccupancyProblem/}, demo = {https://demonstrations.wolfram.com/CoverageProbabilityWithTheOccupancyProblem/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2014}, month = {Jan}, abstract = {In probability theory, the ``occupancy problem'' considers throwing k stones into n buckets. If each stone has equal probability of entering any bucket, what is the probability there are j empty buckets?}, }`

- A. T. Becker, Parametric equation of a circle in 3d, Wolfram demonstrations project, 2014.

[Bibtex][Interactive Demo]`@misc{2014-becker-parametric-equation-circle-3d, Title = {Parametric Equation of a Circle in 3D}, url = {http://demonstrations.wolfram.com/ParametricEquationOfACircleIn3D/}, demo = {http://demonstrations.wolfram.com/ParametricEquationOfACircleIn3D/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2014}, month = {Feb}, abstract = {A circle in 3D is parameterized by six numbers: two for the orientation of its unit normal vector, one for the radius, and three for the circle center.}, }`

### 2012

- A. T. Becker, Gridiron pendulum, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-gridiron-pendulum, Title = {Gridiron Pendulum}, url = {http://demonstrations.wolfram.com/GridironPendulum/}, demo = {http://demonstrations.wolfram.com/GridironPendulum/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Dec}, abstract = {The gridiron pendulum was designed by John Harrison in 1726 to make the swing period insensitive to changes in temperature. It consists of alternating brass and iron rods with lengths selected so that the effects of thermal expansion counteract. In this Demonstration, you can explore the effects of the temperature and the length of the gridiron pendulum on the clock error.}, }`

- A. T. Becker, Roll any point on the sphere to any desired latitude-longitude coordinates with one straight-line roll, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-roll-sphere-point-to-let-long, Title = {Roll Any Point on the Sphere to Any Desired Latitude-Longitude Coordinates with One Straight-Line Roll}, url = {http://demonstrations.wolfram.com/RollAnyPointOnTheSphereToAnyDesiredLatitudeLongitudeCoordina/}, demo = {http://demonstrations.wolfram.com/RollAnyPointOnTheSphereToAnyDesiredLatitudeLongitudeCoordina/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Oct}, abstract = {Pick a point on a sphere (in green). This point has certain latitude-longitude coordinates. In one straight-line roll, we can move this point to any desired latitude-longitude coordinates (in red). This Demonstration shows the shortest such roll.}, }`

- A. T. Becker, Roll a sphere without changing orientation to a new location in two straight rolls, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-roll-sphere-without-changing-orientation, Title = {Roll a Sphere without Changing Orientation to a New Location in Two Straight Rolls}, url = {https://demonstrations.wolfram.com/RollASphereWithoutChangingOrientationToANewLocationInTwoStra/}, demo = {https://demonstrations.wolfram.com/RollASphereWithoutChangingOrientationToANewLocationInTwoStra/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Aug}, abstract = {A sphere can be moved to any location with no net change in orientation by rolling without slipping in two straight-line rolls. Rolling a sphere in a straight line a distance of , where is any integer, returns the sphere to its initial orientation. By combining two such rolls, the sphere can be moved to any location.}, }`

- R. Morris-Wright and A. T. Becker, Kinematics of planar elastic chains, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-morris-wright-kinematics-planar, Title = {Kinematics of Planar Elastic Chains}, url = {https://demonstrations.wolfram.com/KinematicsOfPlanarElasticChains/}, demo = {https://demonstrations.wolfram.com/KinematicsOfPlanarElasticChains/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Rose Morris-Wright and Aaron T. Becker}, year = {2012}, month = {Aug}, abstract = {This Demonstration shows an n-link planar kinematic chain with a fixed base in which each joint is a linearly elastic torsional spring. The shape of this chain in static equilibrium can be represented as the solution of a discrete-time optimal control problem, with boundary conditions that vary with the position and orientation of the last link. McCarthy and Bretl proved that the set of all solutions to this problem is a smooth manifold that can be parameterized by a single chart. We have added gravitational force to this model.}, }`

- A. T. Becker, Rolling a sphere around a circle without slipping, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-roll-sphere-circle, Title = {Rolling a Sphere around a Circle without Slipping}, url = {https://demonstrations.wolfram.com/RollingASphereAroundACircleWithoutSlipping/}, demo = {https://demonstrations.wolfram.com/RollingASphereAroundACircleWithoutSlipping/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Jan}, abstract = {Consider a sphere of unit radius rolling (without spinning or slipping) around a circle of radius R in the plane. The sphere's orientation can be described by a rotation theta about the circle center and a rotation phi about an axis from the sphere center to the circle center. For what angles theta along the circle is phi=0? For what values of R will the sphere periodically return to its initial configuration (position and orientation)?}, }`

- A. T. Becker, Sampling a uniformly random rotation, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-sampling-uniformly-random-rotation, Title = {Sampling a Uniformly Random Rotation}, url = {https://demonstrations.wolfram.com/SamplingAUniformlyRandomRotation/}, demo = {https://demonstrations.wolfram.com/SamplingAUniformlyRandomRotation/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = { Aaron T. Becker}, year = {2012}, month = {Jan}, abstract = {The orientation of a sphere is an element of SO(3) and can be represented by three Euler angles. However, uniformly sampling three Euler angles does not result in a uniform sampling of SO(3). To generate a uniformly distributed random rotation in SO(3), first perform a random rotation about the z axis, then rotate the z axis to a random position on the sphere.}, }`

- A. T. Becker, Re-orient a sphere with two straight rolls, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-re-orient-sphere-two-rolls, Title = {Re-Orient a Sphere with Two Straight Rolls}, url = {https://demonstrations.wolfram.com/ReOrientASphereWithTwoStraightRolls/}, demo = {https://demonstrations.wolfram.com/ReOrientASphereWithTwoStraightRolls/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = { Aaron T. Becker}, year = {2012}, month = {Jun}, abstract = {It is well-known that a sphere can be rolled in the horizontal plane to any orientation by three sequentially orthogonal rolls. This Demonstration shows that only two straight rolls are necessary. The desired orientation, shown in red, is specified by moving the north pole to a desired latitude and longitude , then twisting about this pole by . Rolling from the initial orientation, shown in green, along the blue and red lines brings the sphere to the desired orientation.}, }`

- A. T. Becker, Morph sphere to disc, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-morph-sphere-to-disc, Title = {Morph Sphere to Disc}, url = {https://demonstrations.wolfram.com/MorphSphereToDisc/}, demo = {https://demonstrations.wolfram.com/MorphSphereToDisc/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Feb}, abstract = {By removing a single point from the sphere (here, the south pole), we can smoothly deform the sphere into a disc. The transformation shown here preserves the distance from any point on the sphere to the north pole.}, }`

- A. T. Becker, Curvature of the projection of a trefoil knot, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-curvature-trefoil, Title = {Curvature of the Projection of a Trefoil Knot}, url = {https://demonstrations.wolfram.com/CurvatureOfTheProjectionOfATrefoilKnot/}, demo = {https://demonstrations.wolfram.com/CurvatureOfTheProjectionOfATrefoilKnot/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Feb}, abstract = {The trefoil knot is the simplest example of a nontrivial knot. This Demonstration shows the projection of a two-parameter version of the trefoil knot and plots the minimum (in blue) and maximum (in red) curvature points along the knot. The maximum and minimum osculating circles (also known as the kissing circles or the circles of curvature) are drawn as well.}, }`

- A. T. Becker, Dark fraction of the moon, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-dark-fraction-of-moon, Title = {Dark Fraction of the Moon}, url = {https://demonstrations.wolfram.com/DarkFractionOfTheMoon/}, demo = {https://demonstrations.wolfram.com/DarkFractionOfTheMoon/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Mar}, abstract = {The fraction of the Moon that is dark is a function of the phase angle phi. This function is cos(phi/2)^2 and can be found by taking an area integral over the circle. A sphere with one hemisphere black, the other hemisphere white, and rotated by phi is shown in the top-left corner. The area integral being performed is shown in the top-right corner.}, }`

- A. T. Becker, Tangent plane to a sphere, Wolfram demonstrations project, 2012.

[Bibtex][Interactive Demo]`@misc{2012-becker-tangent-plane-to-sphere, Title = {Tangent Plane to a Sphere}, url = {https://demonstrations.wolfram.com/TangentPlaneToASphere/}, demo = {https://demonstrations.wolfram.com/TangentPlaneToASphere/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2012}, month = {Mar}, abstract = {The equation of the tangent plane to a sphere of radius r and center at the origin at latitude theta and longitude phi is x cos(theta) sin(phi) + y sin(theta)sin(phi) + z cos(phi) = r^2.}, }`

### 2011

- A. T. Becker, Fraction of a circle covered by arcs of a given length, Wolfram demonstrations project, 2011.

[Bibtex][Interactive Demo]`@misc{2011-becker-fraction-circle-covered-by-arcs, Title = {Fraction of a Circle Covered by Arcs of a Given Length}, url = {https://demonstrations.wolfram.com/FractionOfACircleCoveredByArcsOfAGivenLength/}, demo = {https://demonstrations.wolfram.com/FractionOfACircleCoveredByArcsOfAGivenLength/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2011}, month = {Mar}, abstract = {This Demonstration shows the probability density function for the fraction of a circle with unit circumference covered by n random arcs, each of length a. This probability distribution is a mixed distribution. The discrete probability mass p is shown and captioned in red, and the continuous probability density is shown in blue (scaled by a). mu and sigma^2 are the mean and variance of the fraction covered.}, }`

- A. T. Becker, Coverage of a unit square by random discs, Wolfram demonstrations project, 2011.

[Bibtex][Interactive Demo]`@misc{2011-becker-coverage-unit-square-random-discs, Title = {Coverage of a Unit Square by Random Discs}, url = {https://demonstrations.wolfram.com/CoverageOfAUnitSquareByRandomDiscs/}, demo = {https://demonstrations.wolfram.com/CoverageOfAUnitSquareByRandomDiscs/}, journal = {Wolfram Demonstrations Project}, publisher = { Wolfram Demonstrations Project}, author = {Aaron T. Becker}, year = {2011}, month = {Mar}, abstract = {If n discs of radius r have centers randomly distributed over the unit square, how much of the square will be covered? What is the underlying probability distribution function?}, }`

## PhD Dissertations

### 2019

- L. Huang, “Towards microrobot swarm path planning,” PhD Thesis, Houston, Texas, 2019.

[Bibtex]`@phdthesis{2019-li-phdthesis, author = {Li Huang}, title = {Towards Microrobot Swarm Path Planning}, school = {The University of Houston}, year = 2019, address = { Houston, Texas}, month = 8, url = {https://hdl.handle.net/10657/5289}, note = {Advisor: Aaron Becker Committee: Frank J. ‘Fritz’ Claydon, Professor Department of Electrical and Computer Engineering David Mayerich, Assistant Professor Department of Electrical and Computer Engineering Hien Nguyen Van, Assistant Professor Department of Electrical and Computer Engineering Peggy Lindner}, abstract = {Tiny robots have many promising applications in medical treatment including targeted drug delivery, non-invasive diagnosis, and minimally invasive surgery; and in micro-assembly/-fabrication for Micro-Electro-Mechanical-Systems (MEMS). Microrobots are often deployed in large populations, and typically steered by uniform driving signals, including magnetic, electromagnetic, electrostatic, optical, gravitational, thermal, and chemical. The homogeneity of the microrobots and the uniformity of the control input make microrobot swarm manipulation difficult in constrained workspaces such as human vascular networks. The control laws and path-planning algorithms designed for macro-size robotics do not scale well to a microrobot swarm, so new methodology must be developed to address more efficient planning with constraints for a multi-agent problem in microscale. This thesis addresses the path-planning problem of a swarm of microrobots using a global control input. It begins with an introduction to state-of-the-art research and applications in microrobots. Chapter 2 gives an analysis of 2D and 3D position control of heterogeneous microrobots in the free space, together with demonstrations in simulations and hardware experiments. Motivated by the need for higher computational efficiency and capability of swarm manipulation with spatial constraints, chapter 3 discusses strategies of planning in 2D vascular networks for a swarm of homogeneous microrobots given a shared, global control input. Multiple path-planning methods and control algorithms are proposed, and their performance is compared in multiple vascular networks with different scale and complexity. The algorithms are validated with simulations and hardware experiments. Chapter 4 investigates reinforcement learning strategies to further improve path-planning efficiency, and to overcome local minima dilemmas in online algorithms. Chapter 5 reports automatic steering methods in multi-bifurcation vessels with flow, and reinforcement learning algorithms are implemented for improvement in microrobot delivery rate.}, }`

### 2018

- S. Shahrokhi, “Controlling a swarm of simple robots using global inputs,” PhD Thesis, Houston, Texas, 2018.

[Bibtex]`@phdthesis{2018-shahrokhi-phdthesis, author = {Shiva Shahrokhi}, title = {Controlling a Swarm of Simple Robots Using Global Inputs}, school = {The University of Houston}, year = 2018, url = {https://hdl.handle.net/10657/4012}, address = { Houston, Texas}, month = 8, note = {Advisor: Aaron Becker Committee: Lydia Kavraki, Noah Harding Professor Department of Computer Science, Rice University Stanko Brankovic, Associate Professor Department of Electrical and Computer Engineering David Mayerich, Assistant Professor Department of Electrical and Computer Engineering Rose Faghih, Assistant Professor}, abstract = {Microrobotics has the potential to revolutionize many applications, including targeted material delivery, assembly, and surgery. The same properties that promise breakthrough solutions---small size and large populations---present unique challenges for controlling motion. When there are more particles than control inputs, the system is underactuated and requires new control techniques. Rather than focusing on a specific microrobotic system, this dissertation designs control laws and algorithms for steering many particles controlled by global fields. First, we identify key parameters for particle manipulation by using a collection of online games where players steer swarms of up to 500 particles to complete manipulation challenges. Inspired by techniques where human operators performed well, we investigate controllers that only use the mean and variance of the swarm. We next derive automatic controllers for these and a hysteresis-based switching control to regulate the first two moments of the particle distribution. Torque control is also necessary for manipulating objects as well as for aligning sensors, emitters, or redirecting an incoming signal. Second, this dissertation proves that swarm torque control is possible, then presents algorithms to automate the task. Torque control enables us to control the position and orientation of an object. Finally, this dissertation investigates particle control with uniform magnetic gradients (the same force is applied everywhere in the workspace). We provide position control algorithms that only require non-slip wall contact in 2D. The walls of in vivo and artificial environments often have surface roughness such that the particles do not move unless actuation pulls them away from the wall. We assume that particles in contact with the boundaries have zero velocity if the shared control input pushes the particle into the wall. All the results are validated with simulations and hardware implementations.}, keywords = {Swarm Control; Global Control; Shared Input; Object Manipulation} }`

### 2012

- A. T. Becker, “Ensemble control of robotic systems,” PhD Thesis, Urbana-Champaign, Illinois, 2012.

[Bibtex][Video]`@phdthesis{2012-becker-phdthesis, author = {Aaron T. Becker}, title = {Ensemble Control of Robotic Systems}, school = {University of Illinois at Urbana-Champaign}, year = 2012, address = { Urbana-Champaign, Illinois}, month = 8, note = {Advisor: Timothy Bretl Committee: Seth Hutchinson, Daniel Liberzon, Alejandro Dom\'inguez-Garc\'ia}, abstract = {In this dissertation, we apply the framework of ensemble control theory to derive an approximate steering algorithm for two classical robotic systems---the nonholonomic unicycle and the plate-ball manipulator---in the presence of model perturbation that scales all inputs by an unknown but bounded constant. The basic idea is to maintain the set of all possible configurations and to select inputs that reduce the size of this set and drive it toward some goal configuration. The key insight is that the evolution of this set can be described by a family of control systems that depend continuously on the unknown constant. Ensemble control theory provides conditions under which it is possible to steer this entire family to a neighborhood of the goal configuration with a single open-loop input trajectory. For both the nonholonomic unicycle and the plate-ball manipulator, we show how to construct this trajectory using piecewise-constant inputs. We also validate our approach with hardware experiments, where the nonholonomic unicycle is a differential-drive robot with unknown wheel size, and the plate-ball manipulator is a planar motion stage that uses magnetic actuation to orient a sphere of unknown radius. We conclude by showing how the same framework can be applied to feedback control of multi-robot systems under the constraint that every robot receives exactly the same control input. We focus on the nonholonomic unicycle, instantiated in experiment by a collection of differential-drive robots. Assuming that each robot has a unique wheel size, we derive a globally asymptotically stabilizing feedback control policy. We show that this policy is robust to standard models of noise and scales to an arbitrary number of robots. These results suggest that our approach may have possible future application to control of micro- and nano-scale robotic systems, which are often subject to similar constraints.}, video = {https://youtu.be/_v4KUBfzbv0}, url = {http://hdl.handle.net/2142/34221}, }`

## MS Thesis

### 2019

- J. Lonsford, “Innovative robotics for liquid environs: mri gauss guns and drift nodes,” Master Thesis, Houston, TX, 2019.

[Bibtex]`@mastersthesis{2019-lonsford-msthesis, author = {Jarrett Lonsford}, title = {Innovative Robotics for Liquid Environs: MRI Gauss Guns and Drift Nodes}, school = {The University of Houston}, year = 2019, address = {Houston, TX}, url = {https://hdl.handle.net/10657/5636}, month = 12, note = {Advisor: Aaron T. Becker}, abstract = {This thesis covers the following two projects: MRI Compatible Gauss Guns (sections I-VI) and Biodegradable Drift Nodes (VII-XI). Project 1: Millirobots propelled and imaged by MRI are a promising approach for minimally invasive therapies. The strong constant magnetic field inside the MRI precludes torque-based control. Consequently, prior propulsion techniques have been limited to gradient-based pulling through fluid-filled body lumens using the weaker magnetic gradient coils. One mechanism to generate additional force to pierce tissue is an MRI Gauss gun, a device that stores magnetic potential energy in an internal arrangement of components. This potential energy can be released through a self-assembly operation. This report presents a new design for an underwater MRI Gauss gun with numerical analysis and results for optimizing the kinetic energy generated. Experiments performed both inside and outside the MRI, in air and underwater validate the optimization analysis. Project 2: As Earth faces environmental changes such as rising sea levels, melting ice caps and increasingly severe tropical storm systems, monitoring of our oceans has become increasingly important. Many of the oceanic environments that require monitoring are vast and dangerous, making the successful deployment and subsequent retrieval of these devices challenging. Ideally, monitoring devices for harsh climates would not require retrieval if they are inexpensive, environmentally benign, and fully degradable. This report describes the design, fabrication and testing of a network of cheap monitoring devices known as Drift Nodes and the ongoing process to make them fully biodegradable, from the 3d-printed housing to the electronics, sensors and batteries.}, }`

- S. Bhatnagar, “Swarm robotics: harvesting of moving swarms represented by a markov process,” Master Thesis, Houston, TX, 2019.

[Bibtex]`@mastersthesis{2019-bhatnagar-msthesis, author = {Shriya Bhatnagar}, title = {Swarm Robotics: Harvesting of Moving Swarms Represented by a Markov Process}, url = {https://hdl.handle.net/10657/5749}, school = {The University of Houston}, year = 2019, address = {Houston, TX}, month = 5, note = {Advisor: Aaron T. Becker, Committee: Radford, Nicolaus and Jackson, David}, abstract = {This project presents methods of harvesting moving swarm agents, with two different experimental applications. We investigated motion planning for one or more robot(s). These methods differ from traditional motion planning problems because the agents move. This allows areas that were previously cleared to become recontaminated. The movement of agents is represented by a Markov process that encodes the agents' preferred regions and their speed of motion. There are two different categories of controllers presented in this project, one for single robot applications and a second for multi-robot applications. We conducted experiments using the single robot controllers. For the first application we studied a destructive survey of mosquitoes. We researched behavior and other characteristic of mosquitoes to design an electrified screen that can be carried on a UAV. For the second application we studied the harvesting of moving swarms using an autonomous robotic boat with an acoustic larvicide unit in a body of water.}, }`

### 2018

- P. Joshi, “Motion-planning using rrts for a swarm of robots controlled by global inputs,” Master Thesis, Houston, TX, 2018.

[Bibtex]`@mastersthesis{2018-joshi-msthesis, author = {Parth Joshi}, title = {Motion-planning using RRTs for a swarm of robots controlled by global inputs}, school = {The University of Houston}, year = 2018, address = {Houston, TX}, month = 12, url = {https://hdl.handle.net/10657/4443}, note = {Advisor: Aaron T. Becker, Committee: Faghih, Dr. Rose and Tsekos, Dr. Nikolaos and Leclerc, Julien}, abstract = {Small-scale robots have great potential to bring transformation in the field of medical applications, defense systems, security, micro-assembly and many other areas. Imagine a group of milli, micro or nano-robots that can navigate inside the body to solve medical problems, or a swarm of robots that can paint a beautiful painting. Robots containing iron can be steered using a magnetic field generated by an MRI scanner, but all the robots will move in the same direction because the magnetic effect is global and not local. This thesis uses a customized version of the motion-planning technique called Rapidly Exploring Random Tree (RRT) to solve this problem for multiple robots by using obstacles. This thesis project solves instances of this motion-planning problem for more than one robot when steered using a magnetic field, and develops a motion planner that searches for sequences of control inputs to simulations steer the robots to desired goal positions.}, }`

- P. R. Padala, “Sensing technologies for mosquito control: deafening mosquitoes and underwater ranging,” Master Thesis, Houston, TX, 2018.

[Bibtex]`@mastersthesis{2018-padala-msthesis, author = {Praveen Reddy Padala}, title = {Sensing Technologies for Mosquito Control: Deafening Mosquitoes and Underwater Ranging}, school = {The University of Houston}, year = {2018}, address = {Houston, TX}, month = {12}, url = {https://hdl.handle.net/10657/5807}, note = {Advisor: Aaron T. Becker, Committee: Jackson, David and Lent, Ricardo}, abstract = {This thesis is comprised of two projects related to mosquito sensing technologies. In the first project, a novel method is proposed in which sound waves with high particle velocities are used to potentially disrupt the mating process in mosquitoes. The experimental setup and the results are elucidated in this thesis. The second project is about the design of an underwater depth finding sensor module which is used in an autonomous remote operated vehicle developed by the Robotic Swarm Control Lab to kill mosquito larvae in water bodies. The analog circuit design and the embedded programming are shown in this thesis.}, }`

- S. Manzoor, “Parallel self-assembly and sorting of polyominoes under uniform control inputs,” Master Thesis, Houston, TX, 2018.

[Bibtex]`@mastersthesis{2018-manzoor-msthesis, author = {Sheryl Manzoor}, title = {Parallel Self-assembly and Sorting of Polyominoes Under Uniform Control Inputs}, url = {https://hdl.handle.net/10657/4438}, school = {The University of Houston}, year = {2018}, address = {Houston, TX}, month = {12}, note = {Advisor: Aaron T. Becker, Committee: Ruchhoeft, Paul and Faghih, Rose}, abstract = {Automated assembly at micro and nano-scale is essential for manufacturing smaller and inexpensive products at faster rates. Traditional micro-assembly and manipulation techniques involve micro-grippers and manipulators that have limited degrees of freedom when compared to their macro-scale counterparts. A major disadvantage of these techniques is that only one part can be manufactured at a time. Thus, it would be a significant progress if control algorithms are devised that can automatically assemble a huge quantity of small scale components. We present a novel approach towards micro-assembly which employs a large swarm of micro-particles, controlled by a global signal to assemble arbitrary 2D structures. The algorithm automatically generates a micro-factory layout for a given structure, and when this layout is actuated, it manufactures the required number of copies of the shape. We have analyzed the size and time complexity of the micro-factories and present several simulation and hardware results for the assembly task. Since the assembly process is performed in open-loop, the assembled parts could have errors, and in order to detect these errors, we sort them based on their shape.}, }`

- A. Nguyen, “Applications of unmanned vehicles with wireless sensor networks and surveying,” Master Thesis, Houston, TX, 2018.

[Bibtex]`@mastersthesis{2018-nguyen-msthesis, author = {An Nguyen}, title = {Applications of Unmanned Vehicles with Wireless Sensor Networks and Surveying}, url = {https://hdl.handle.net/10657/5857}, school = {The University of Houston}, year = 2018, address = {Houston, TX}, month = 11, note = {Advisor: Aaron T. Becker, Committee: Franchek, Matthew and Pan, Miao}, abstract = {An unmanned vehicle, such as a flying multi-copter, an unmanned rover, a remote-controlled boat, can be used to cover a large area of land, to perform repetitive, tedious yet strenuous tasks for people. We can have an unmanned aerial vehicle (UAV) distribute a network of seismic microphone, used during seismic surveying, in treacherous terrain, free of heavy signal wiring, without risking injury to human workers. A UAV can sweep a large area with a mosquito-zapping net, destructively sampling mosquito population in the area, giving entomology researcher better data about their distribution and behavior through time and space. An unmanned boat, or a UAV, can distribute a drifting wireless sensor network (WSN) into a body of water. The same, or several unmanned vehicles, can then monitor, recharge and finally recollect them. The following thesis presents hardware for all of the above applications, as well as software and algorithms for the unmanned vehicles, and sensor nodes.}, }`

- B. Isichei, “Robotic manipulators: cryogenic magnetic manipulation system, two-body magnetic manipulation, and low-cost robotic manipulators,” Master Thesis, Houston, TX, 2018.

[Bibtex]`@mastersthesis{2018-isichei-msthesis, author = {Benedict Isichei}, title = {Robotic Manipulators: Cryogenic Magnetic Manipulation System, Two-body Magnetic Manipulation, and Low-cost Robotic Manipulators}, school = {The University of Houston}, year = 2018, url = {https://hdl.handle.net/10657/4023}, address = {Houston, TX}, month = 8, note = {Advisor: Aaron T. Becker, Committee: Mayerich, David and Faghih, Rose a nd Leclerc, Julien}, abstract = {This project presents three different robotic manipulators, and then compares their control systems. The first system is a cryogenically-cooled manipulation system. In this system, the robotic system implements 3-dimensional control on the robots position and orientation. To obtain accurate control without a solid iron core, this system has all of its coils cooled with liquid nitrogen to drive more current into the coils without damaging them. The second system is created to test an algorithm for navigation in a cavity using global inputs, while taking advantage of the cavity's geometry and frictional wall contacts. The last system is a robotic manipulator created out of a toy robotic arm kit. The aim here was to increase the robots accuracy and augment its functionality, while making it user friendly to students new to robotics.}, }`

- S. Shahrokhi, “Shaping a swarm using a shared control input,” Master Thesis, Houston, TX, 2018.

[Bibtex]`@mastersthesis{2018-shahrokhi-msthesis, author = {Shahrokhi, Shiva}, title = {Shaping a Swarm Using a Shared Control Input}, school = {The University of Houston}, year = 2018, address = {Houston, TX}, month = 8, url = {https://hdl.handle.net/10657/4014}, note = {Advisor: Aaron T. Becker, Committee: Mayerich, David and Faghih, Rose}, abstract = {Micro-robots are small enough to move through the passageways of the body, therefore they are suited for targeted drug delivery and micro-scale manufacturing. Due to their small size, a single robot does not have enough force to deliver payloads, and it is prohibitively difficult to have onboard computation. Therefore, these robots are usually controlled by global inputs such as a uniform external magnetic field. This thesis presents controllers and algorithms for steering such an under-actuated swarm. This work first proves that the mean position of the swarm is controllable, and shows how an obstacle can make the variance controllable. Then it derives automatic controllers for these and a hysteresis-based switching control to regulate the first two moments of the swarm distribution. Finally, this work uses friction with boundary walls to break the symmetry caused by the global input and uses it to steer two particles to arbitrary positions.}, }`

### 2017

- M. Sultan, “Optimize an MRI Gauss gun,” Master Thesis, Houston, TX, 2017.

[Bibtex]`@mastersthesis{2017-sultan-msthesis, author = {Mohammad Sultan}, title = {Optimize an {MRI} {G}auss Gun}, url = {http://hdl.handle.net/10657/2959}, school = {The University of Houston}, year = 2017, address = {Houston, TX}, month = 10, note = {Advisor: Aaron T. Becker, Committee: Wolfe, Jack and Tsekos, Nikolaos and Contreras-Vidal, Jose}, abstract = {MRI-based navigation and propulsion of millirobots is a new and promising approach for minimally invasive therapies. The strong constant magnetic field inside the scanner precludes torque-based control. Consequently, prior propulsion techniques have been limited to gradient-based pulling through fluid-filled body lumens using the weaker gradient magnetic coils. Performing interventions requires techniques or mechanism to increase this weak magnetic pulling force. One technique is a self-assembling robotic tool designed by our lab called a Gauss gun. This thesis shows numerical analysis and results for optimizing the kinetic energy generated by a Gauss gun to penetrate tissue, deliver a drug or remove a clot. This analysis based on the equations of energy for an MRI Gauss gun. The numerical method used for this optimization is Nelder Mead, implemented in Mathematica software.}, }`

- A. Ramakrishnan, “Design and control of magnetically actuated millirobots for tissue penetration,” Master Thesis, Houston, TX, 2017.

[Bibtex]`@mastersthesis{2017-ramakrishnan-msthesis, author = {Ashwin Ramakrishnan}, title = {Design and Control of Magnetically Actuated Millirobots for Tissue Penetration}, school = {The University of Houston}, year = 2017, address = {Houston, TX}, month = 5, url = {https://hdl.handle.net/10657/4911}, note = {Advisor: Aaron T. Becker}, abstract = {Millirobots propelled by magnetic fields show promise for minimally invasive surgery or drug delivery. MRI scanners can generate magnetic gradients to apply propulsive forces on ferromagnetic objects. However, MRI gradient forces are insufficient for tissue penetration. This project presents a millirobot design and control methods to produce pulsed forces. A ferromagnetic sphere inside a hollow robot body can move back and forth between a spring and an impact rod. Repeated impacts convert the kinetic energy of the sphere into large pulsed forces that can penetrate tissue. An estimator helps achieve the maximum possible average impact velocity with minimal sensing, for a given set of material and geometric parameters, and input magnetic gradient force. Prototypes were 3D printed and tested on a custom magnetic test bed. Analytical, numerical and experimental results are presented.}, }`

- A. Mahadev, “Algorithms for particle swarms using global control: aggregation, mapping, coverage, foraging and shape control,” Master Thesis, Houston, TX, 2017.

[Bibtex]`@mastersthesis{2017-mahadev-msthesis, author = {Arun Mahadev}, title = {Algorithms For Particle Swarms Using Global Control: Aggregation, Mapping, Coverage, Foraging And Shape Control}, school = {The University of Houston}, year = 2017, url = {https://hdl.handle.net/10657/4610}, address = {Houston, TX}, month = 5, note = {Advisor: Aaron T. Becker}, abstract = {Targeted drug delivery is a promising technique to reduce the side effects of drugs by delivering them in concentrated doses using large swarms (10^16) of controllable microbots only targeting bad or infected tissue. A promising way to control small steerable microbots is by using a global control field such as the magnetic gradient of an MRI machine. In this work we develop benchmark algorithms for performing aggregation of microbots using global control. Using our findings we develop algorithms for a novel approach of mapping tissue and vascular systems without the use of harmful contrast agents in an MRI. In our work we consider a swarm of particles in a 1D, 2D, and 3D grids that can be tracked and controlled by an external agent thus building a map. We present algorithms for controlling particles using global inputs to perform: (1) Mapping, i.e., building a representation of the free and obstacle regions of the workspace; (2) Foraging, i.e., ensuring that at least one particle reaches each target location;and (3) Coverage, i.e., ensuring that every free region on the map is visited by at least one particle. Finally we also demonstrate shape control of large swarms using global control by developing an algorithm for position control.}, }`

- M. Burbage, “Maximizing swarm coverage: hunting for members of a moving population,” Master Thesis, Houston, TX, 2017.

[Bibtex]`@mastersthesis{2017-burbage-msthesis, author = {Mary Burbage}, title = {Maximizing Swarm Coverage: Hunting for Members of a Moving Population}, school = {The University of Houston}, year = 2017, address = {Houston, TX}, month = 5, url = {https://hdl.handle.net/10657/4561}, note = {Advisor: Aaron T. Becker, Mayerich, David and Tsekos, Nikolaos}, abstract = {We explore search methods for finding and removing members of a large population of mobile particles in different environments. We begin by simulating the movement of individual swarm members biased by a map image with four search patterns and find that simulation duration affects the results. We then treat particle motion as a Markov process in an environment bounded with walls that retain a portion of the swarm and in an environment that attracts the particles into a normal distribution at the center of the space. We test six search patterns with several parameter variations. We show that a two-step greedy algorithm has the best performance in all cases but second best performance varies with the parameters of the swarm and the search.}, }`

### 2016

- S. K. V. Sudarshan, “Automating a seismic survey using heterogeneous sensor teams and uavs,” Master Thesis, Houston, TX, 2016.

[Bibtex]`@mastersthesis{2016-sudarshan-msthesis, author = {Srikanth Kandanuru Venkata Sudarshan}, title = {Automating a Seismic Survey using Heterogeneous Sensor Teams and UAVs}, school = {The University of Houston}, year = 2016, address = {Houston, TX}, month = 12, url = {http://hdl.handle.net/10657/3684}, Keywords = {Seismic Survey, UAVs, Automation, Field Robotics, Heterogeneous Sensors}, note = {Advisor: Aaron T. Becker, committee Stewart, Robert and Pan, Miao and Han, Zhu}, abstract = {Seismic imaging is the primary technique for subsurface exploration. It requires placing a large number of sensors (geophones) in a grid pattern, triggering a seismic event, and recording the propagating waves. The location of hydrocarbons is inferred from these readings. Traditional seismic surveying for hydrocarbons employs human laborers for sensor placement, lays miles of cabling, and then recovers the sensors. Often sites of resource or rescue interest may be difficult or hazardous to access. The major drawbacks of surveying with human deployment are the high costs and time, and risks to humans due to explosives and harsh climatic conditions. Thus, there is a substantial need to automate the process of seismic sensor placement and retrievals using robots. We propose an autonomous, heterogeneous sensor deployment system using UAVs to plant immobile sensors and deploy mobile sensors. Detailed analysis and comparison with traditional surveying were conducted. Hardware experiments and simulations prove the effectiveness of automation regarding cost and time. The proposed system overcame the drawbacks and displayed higher efficiency. The deployed sensors essentially became a wireless sensor network (WSN). Thus traditional batteries cannot sustain a WSN. Energy is the major impediment to the sustainability of WSNs. Most energy is consumed by (i) wireless transmissions of sensed data and (ii) long-distance multi-hop transmissions from the source sensors to the sink. This research also presents an optimal path-planning algorithm for sustaining WSNs and validates the claim with simulations. The research in the future aims at exploring methods to exploit emerging wireless power transfer technology by using UAVs to service the WSNs. These UAVs cut data transmissions from long to short distances by collecting sensed information and replenishing WSN’s energy.}, }`

- Y. Wei, “Metrics on crowd control with overhead video and vocal commands,” Master Thesis, Houston, TX, 2016.

[Bibtex]`@mastersthesis{2016-wei-msthesis, author = {Yao Wei}, title = {Metrics on Crowd Control with Overhead Video and Vocal Commands}, school = {The University of Houston}, year = 2016, address = {Houston, TX}, month = {5}, identifier = {OCLC : (OCoLC)1082522152}, url = {http://hdl.handle.net/10657/3212}, note = {Advisor: Aaron T. Becker}, abstract = {This thesis presents an agent-tracking framework for semi-structured, crowded video. This framework is used to investigate how large numbers of people respond to vocal commands with local feedback and an overhead camera video. We analyze a video showing an overhead view of more than 200 people, each holding an umbrella equipped with red, blue, and green LED lights. The crowd's motion under the vocal command formed a variety of patterns. We use k-means clustering to separate umbrella from each other. Kalman filtering is used to estimate how each umbrella moves and track their motion path. In particular, we present results on: (1) Automatic segmentation and classification of each umbrella. (2) Swarm's response time to a simple command. (3) Time constant for a harder command. (4) Comparing accuracy. (5) ``Shape-matching'' ability. (6) Documenting the position memory. (7) Distribution consensus simulation.}, }`

### 2008

- A. T. Becker, “Mobile robot motion-planning using wireless signals for localization,” Master Thesis, Urbana-Champaign, Illinois, 2008.

[Bibtex][Video]`@mastersthesis{2008-becker-msthesis, author = {Aaron T. Becker}, title = {Mobile Robot Motion-Planning Using Wireless Signals for Localization}, school = {University of Illinois at Urbana-Champaign}, year = 2008, address = { Urbana-Champaign, Illinois}, month = 5, note = {Advisor: Mark Spong}, abstract = {Many applications for autonomous agents require the agent to have accurate position data. Signal-strength based localization attempts to determine an agent’s location in Rn from a scalar sensor reading z. This is a nontrivial problem because the mapping from Rn to z is noninvertible. Indoor Localization attempts to solve this problem in an indoor environment. This adds challenges. Among these are the effects of signal interference; signal dropout due to walls, doors, and humans; and the expense of data collection. This project implements a localization system on an autonomous system, the Seg-Monster. The SegMonster is a human-sized robot that rides a commercial Segway personal transporter. Local data from wheel-mounted encoders are combined with signal-strength based localization that interprets wireless signal strength using Gaussian processes to calculate a global position estimate.}, video = {https://youtu.be/TTtliHC7siY}, }`