Magnetic modular millibots, capable of deterministic self-assembly and reconfiguration under wireless magnetic fields, offer a promising route toward mesoscale manipulation in structured and confined environments. This work presents a modular chain millibot composed of cubic units with free-to-spin internal magnets that align under external fields. While individual cubes cannot propel independently, their assembly into chains enables controlled locomotion through sliding and tumbling modes. We first demonstrate open-loop operation in confined workspaces, including chain formation, navigation, controlled disassembly, and wall climbing, supported by a dynamic model and parametric analysis that identify the actuation and geometric conditions required for successful climbing. Building on this foundation, we introduce a closed-loop control framework that integrates vision-based feedback. As the millibot’s movement speed increases with chain length, the order of assembly strongly affects task completion time; we therefore formulate the sequence-planning problem as a harmonic traveling salesman problem (HTSP) and solve it to compute deterministic cube-collection sequences that minimize the effective travel cost. The controller applies sliding and tumbling dynamics to realize obstacle-aware navigation and reliable self-assembly. Experiments validate autonomous assembly of four cubes with a two-cube chain into a six-cube chain in free space and collection of three cubes with wall climbing in a confined workspace, both with 100% success. The measured mean unit travel times were 0.67 s/mm in free space and 0.89 s/mm in confined environments. Collectively, these results establish a robust automation framework for reversible mesoscale self-assembly, programmable navigation, and lab-on-chip applications.

A common robotics sensing problem is to place sensors to robustly monitor a set of assets, where robustness is assured by requiring asset$p$to be monitored by at least$\kappa(p)$sen-sors. Given$n$assets that must be observed by$m$sensors, each with a disk-shaped sensing region, where should the sensors be placed to minimize the total area observed? We provide and analyze a fast heuristic for this problem. We then use the heuristic to initialize an exact Integer Program-ming solution. Subsequently, we enforce separation constraints between the sensors by modifying the integer program formulation and by changing the disk candidate set.

Robotic scope assistant systems allow surgeons to adjust the operative field view during surgery by robotically maneuvering laparoscopes. A Human-Robot Interface (HRI) is used for issuing commands to these systems, with an interaction mode mapping these commands to laparoscope movements. Optimizing the HRI and interaction mode can streamline laparoscope positioning as well as reduce cognitive workload, helping the surgeon focus on the surgical procedure. Comparing and assessing various HRIs and interaction modes is essential for efficient laparoscope maneuvering. This study evaluates HRIs based on head-motion, eye-motion, hand-motion, and voice-input operating under three interaction modes (namely: discrete, continuous, and threshold). The participants performed a user study comparing different HRIs under two simulated surgical scenarios (one in a real environment and the other in a virtual environment). The results indicated that head and eye-based HRIs performed well in continuous interaction mode, while the voice-based interface suffered from a delay. Conversely, hand-based HRIs demonstrated superior performance in both scenarios across all evaluation parameters. The study provides a benchmark for the comparison of different HRIs and provides insights into the effectiveness, limitations, and potential advantages of different HRIs.

We present an analytic solution to the 3D Dubins path problem for paths composed of an initial circular arc, a straight component, and a final circular arc. These are commonly called CSC paths. By modeling the start and goal configurations of the path as the base frame and final frame of an RRPRR manipulator, we treat this as an inverse kinematics problem. The kinematic features of the 3D Dubins path are built into the constraints of our manipulator model. Furthermore, we show that the number of solutions is not constant, with up to seven valid CSC path solutions even in non-singular regions. An implementation of solution is available at https: //github.com/aabecker/dubins3D.

We present progress on the problem of reconfiguring a 2D arrangement of building material by a cooperative group of robots. These robots must avoid collisions, deadlocks, and are subjected to the constraint of maintaining connectivity of the structure. We develop two reconfiguration methods, one based on spatio-temporal planning, and one based on target swapping, to increase building efficiency. The first method can significantly reduce planning times compared to other multi-robot planners. The second method helps to reduce the amount of time robots spend waiting for paths to be cleared, and the overall distance traveled by the robots.

Millimeter-scale magnetic rotating swimmers have multiple potential medical applications. They could, for example, navigate inside the bloodstream of a patient toward an occlusion and remove it. Magnetic rotating swimmers have internal magnets and propeller fins with a helical shape. A rotating magnetic field applies torque on the swimmer and makes it rotate. The shape of the swimmer, combined with the rotational movement, generates a propulsive force. Visual feedback is suitable for in-vitro closed-loop control. However, in-vivo procedures will require different feedback modalities due to the opacity of the human body. In this paper, we provide new methods and tools that enable the 3D control of a magnetic swimmer using a 2D ultrasonography device attached to a robotic arm to sense the swimmer’s position. We also provide an algorithm that computes the placement of the robotic arm and a controller that keeps the swimmer within the ultrasound imaging slice. The position measurement and closed-loop control were tested experimentally.

Magnetic modular cubes are cube-shaped bodies with embedded permanent magnets. The cubes are uniformly controlled by a global time-varying magnetic field.A 2D physics simulator is used to simulate global control and the resulting continuous movement of magnetic modular cube structures. We develop local plans, closed-loop control algorithms for planning the connection of two structures at desired faces. The global planner generates a building instruction graph for a target structure that we traverse in a depth-first-search approach by repeatedly applying local plans.We analyze how structure size and shape affect planning time. The planner solves 80% of the randomly created instances with up to 12 cubes in an average time of about 200 seconds.

We investigate motion planning algorithms for the assembly of shapes in the tilt model in which unit-square tiles move in a grid world under the influence of uniform external forces and self-assemble according to certain rules. We provide several heuristics and experimental evaluation of their success rate, solution length, and runtime.

Miniature Magnetic Rotating Swimmers (MMRSs) are untethered machines containing magnetic materials. An external rotating magnetic field produces a torque on the swimmers to make them rotate. MMRSs have propeller fins that convert the rotating motion into forward propulsion. This type of robot has been shown to have potential applications in the medical realm. This paper presents new MMRS designs with (1) an increased permanent magnet volume to increase the available torque and prevent the MMRS from becoming stuck inside a thrombus; (2) new helix designs that produce an increased force to compensate for the weight added by the larger permanent magnet volume; (3) different head drill shape designs that have different interactions with thrombi. The two best MMRS designs were tested experimentally by removing a partially dried 1-hour-old thrombus with flow in a bifurcating artery model. The first MMRS disrupted a large portion of the thrombus. The second MMRS retrieved a small remaining piece of the thrombus. In addition, a tool for inserting, retrieving, and switching MMRSs during an experiment is presented and demonstrated. Finally, this paper shows that the two selected MMRS designs can perform accurate 3D path-following.

This paper presents four data-driven system models for a magnetically controlled swimmer. The models were derived directly from experimental data, and the accuracy of the models was experimentally demonstrated. Our previous study successfully implemented two non-model-based control algorithms for 3D path-following using PID and model reference adaptive controller (MRAC). This paper focuses on system identification using only experimental data and a model-based control strategy. Four system models were derived: (1) a physical estimation model, (2, 3) Sparse Identification of Nonlinear Dynamics (SINDY), linear system and nonlinear system, and (4) multilayer perceptron (MLP). All four system models were implemented as an estimator of a multi-step Kalman filter. The maximum required sensing interval was increased from 180 ms to 420 ms and the respective tracking error decreased from 9 mm to 4.6 mm. Finally, a Model Predictive Controller (MPC) implementing the linear SINDY model was tested for 3D path-following and shown to be computationally efficient and offers performances comparable to other control methods.

This paper investigates using a sampling-based approach, the RRT*, to reconfigure a 2D set of connected tiles in complex environments, where multiple obstacles might be present. Since the target application is automated building of discrete, cellular structures using mobile robots, there are constraints that determine what tiles can be picked up and where they can be dropped off during reconfiguration. We compare our approach to two algorithms as global and local planners, and show that we are able to find more efficient build sequences using a reasonable amount of samples, in environments with varying degrees of obstacle space.

For biomedical applications in targeted therapy delivery and interventions, a large swarm of micro-scale particles (“agents”) has to be moved through a maze-like environment (“vascular system”) to a target region (“tumor”). Due to limited on-board capabilities, these agents cannot move autonomously; instead, they are controlled by an external global force that acts uniformly on all particles. In this work, we demonstrate how to use a time-varying magnetic field to gather particles to a desired location. We use reinforcement learning to train networks to efficiently gather particles. Methods to overcome the simulation-to-reality gap are explained, and the trained networks are deployed on a set of mazes and goal locations. The hardware experiments demonstrate fast convergence, and robustness to both sensor and actuation noise. To encourage extensions and to serve as a benchmark for the reinforcement learning community, the code is available at Github.

This work presents an online trajectory generation algorithm using a sinusoidal jerk profile. The generator takes initial acceleration, velocity and position as input, and plans a multi-segment trajectory to a goal position under jerk, acceleration, and velocity limits. By analyzing the critical constraints and conditions, the corresponding closed-form solution for the time factors and trajectory profiles are derived. The proposed algorithm was first derived in Mathematica and then converted into a C++ implementation. Finally, the algorithm was utilized and demonstrated in ROS & Gazebo using a UR3 robot. Both the Mathematica and C++ implementations can be accessed at https://github.com/Haoran-Zhao/Jerk-continuous-online-trajectory-generator-with-constraints.git

Reconfigurable modular robots, which can actively assemble and disassemble on command, offer the possibility of mesoscale (milliscale and microscale) manufacturing with robustness and controllability. In this study, we present a design of a scalable modular subunit with embedded permanent magnets in a 3-D printed cubic body. The subunit can be wirelessly controlled by an external uniform magnetic field. We also present controlled assembly–disassembly techniques for these subunits. Our modular robotic platform is highly reconfigurable and can create programmable, predetermined patterns based on open-loop control. The 2-D motion planner computes all reachable polyomino shapes from an arbitrary initial configuration and provides the shortest movement sequences to form each shape. Experimental results match computational modeling, demonstrating robust and reproducible behavior of the modular robotic platform that is promising for mesoscale manufacturing applications. Two cube sizes were tested: 10-mm edge lengths and 2.8-mm edge lengths.

We illustrate and animate the classic problem of deciding whether a given graph has an Eulerian path. Starting with a collection of instances of increasing difficulty, we present a set of pictorial instructions, and show how they can be used to solve all instances. These IDEA instructions ("A series of nonverbal algorithm assembly instructions") have proven to be both entertaining for experts and enlightening for novices. We (w)rap up with a song and dance to Euler’s original instance.

Soil strength testing and collecting soil cores from wetlands is currently a slow, manual process that runs the risk of disturbing and contaminating soil samples. This paper describes a method using an instrumented dart deployed and retrieved by a drone for performing core sample tests in soft soils. The instrumented dart can simultaneously conduct free- fall penetrometer tests. A drone-mounted mechanism enables deploying and reeling in the dart for sample return or for multiple soil strength tests. Tests examine the effect of dart tip diameter and drop height on soil retrieval, and the requisite pull force to retrieve the samples. Further tests examine the dart’s ability to measure soil strength and penetration depth. Hardware trials demonstrate that the drone can repeatedly drop and retrieve a dart, and that the soil can be discretely sampled.

We consider a robot tasked with observing its environment and later selectively summarizing what it saw as a vivid, structured narrative. The robot interacts with an uncertain environment, modelled as a stochastic process, and must decide what events to pay attention to (substance), and how to best make its recording (style) for later compilation of its summary. If carrying a video camera, for example, it must decide where to be, what to aim the camera at, and which stylistic selections, like the focus and level of zoom, are most suitable. This paper examines planning algorithms that help the robot predict events that (1)will likely occur; (2)would be useful in telling a tale; and (3)may be hewed to cohere stylistically. The third factor, a time-extended requirement, is entirely neglected in earlier, simpler work. With formulations based on underlying Markov Decision Processes, we compare two algorithms: a monolithic planner that jointly plans over events and style pairs and a decoupled approach that prescribes style conditioned on events. The decoupled approach is seen to be effective and much faster to compute, suggesting that computational expediency justifies the separation of substance from style. Finally, we also report on our hardware implementation.

Quadcopters are increasingly popular for robotics applications. Being able to efficiently calculate the set of positions reachable by a quadcopter within a time budget enables collision avoidance and pursuit-evasion strategies.This paper examines the set of positions reachable by a quadcopter within a specified time limit using a simplified 2D model for quadcopter dynamics. This popular model is used to determine the set of candidate optimal control sequences to build the full 3D reachable set. We calculate the analytic equations that exactly bound the set of positions reachable in a given time horizon for all initial conditions. To further increase calculation speed, we use these equations to derive tight upper and lower spherical bounds on the reachable set.

This paper investigates the pursuit-evasion problem of a defensive gun turret and one or more attacking drones. The turret must "visit" each attacking drone once, as quickly as possible, to defeat the threat. This constitutes a Shortest Hamiltonian Path (SHP) through the drones. The investigation considers situations with increasing fidelity, starting with a 2D kinematic model and progressing to a 3D dynamic model. In 2D we determine the region from which one or more drones can always reach a turret, or the region close enough to it where they can evade the turret. This provides optimal starting angles for n drones around a turret and the maximum starting radius for one and two drones.We show that safety regions also exist in 3D and provide a controller so that a drone in this region can evade the pan-tilt turret. Through simulations we explore the maximum range n drones can start and still have at least one reach the turret, and analyze the effect of turret behavior and the drones’ number, starting configuration, and behaviors.

This paper examines a family of designs for magnetic cubes and counts how many configurations are possible for each design as a function of the number of modules. Magnetic modular cubes are cubes with magnets arranged on their faces. The magnets are positioned so that each face has either magnetic south or north pole outward. Moreover, we require that the net magnetic moment of the cube passes through the center of opposing faces. These magnetic arrangements enable coupling when cube faces with opposite polarity are brought in close proximity and enable moving the cubes by controlling the orientation of a global magnetic field. This paper investigates the 2D and 3D shapes that can be constructed by magnetic modular cubes, and describes all possible magnet arrangements that obey these rules. We select ten magnetic arrangements and assign a "color" to each of them for ease of visualization and reference. We provide a method to enumerate the number of unique polyominoes and polycubes that can be constructed from a given set of colored cubes. We use this method to enumerate all arrangements for up to 20 modules in 2D and 16 modules in 3D. We provide a motion planner for 2D assembly and through simulations compare which arrangements require fewer movements to generate and which arrangements are more common. Hardware demonstrations explore the self-assembly and disassembly of these modules in 2D and 3D.

In this video, 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. We present algorithmic methods that are able to detect and reconfigure arbitrary polyominoes, based on finite-state robots, while also preserving connectivity of a structure during reconfiguration. Specific results include methods for determining a bounding box, scaling a given arrangement, and adapting more general algorithms for transforming polyominoes.

In this video, 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. This concept can be used for a wide range of applications in which particles do not have their own energy supply or in which they are subject to the same global control commands. A crucial challenge for achieving any desired target configuration is breaking global symmetry in a controlled fashion. Previous work (some of which was presented during SoCG 2015) made use of specifically placed barriers; however, introducing precisely located obstacles into the workspace is impractical for many scenarios. In this paper, 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 theoretical characterizations 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.

In this video we describe why producing a Computational Geometry video is a good idea, what it takes to make one, and how to actually do it. This includes a guide for the overall process, a number of examples, and a variety of tips and tricks.

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.

Rotating miniature magnetic swimmers are de-vices 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.

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.

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.

This paper presents a method for performing free-fall penetrometer tests for soft soils using an instrumented dart deployed by a quadcopter. Tests were performed with three soil types and used to examine the effect of drop height on the penetration depth and the deceleration profile. Further tests analyzed the force required to remove a dart from the soil and the effect of pulling at different speeds and angles. The pull force of a consumer drone was measured, and tests were performed where a drone delivered and removed darts in soil representative of a wetland environment.

There are many design trade-offs when building a magnetic manipulator to control millimeter-scale rotating magnetic swimmers for surgical applications.For example, increasing the magnitude of the flux density generated by the magnetic manipulator increases the torque applied to the swimmer, which could enable performing a wider variety of surgical tasks in the future. However, producing stronger magnetic fields has drawbacks, such as increased active power usage.To produce a quickly rotating field, EMs must be quickly charged and discharged. This results in a low power factor (high reactive power used in comparison with the active power). Adding capacitors in series with the electromagnets improves the power factor because the capacitors can provide reactive power. With this method, larger flux densities can be produced without necessitating an increase of the apparent power delivered by the power supplies.This paper highlights the benefits of using capacitors for the magnetic manipulation of rotating swimmers. Rotating swimmers can be used to remove blood clots. The clot removal rate of resonating magnetic manipulators is measured using a realistic blood clot model. This paper also presents a control method for the currents inside the electromagnets that enable 3D navigation without current sensing.

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 \(O(N\log N)\) 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 \(\Omega (N^{\frac{1}{3}})\) ; for tree-shaped structures, we give an \(\Omega (N^{\frac{1}{2}})\) -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 sequentially constructible path from a given start point.

This article presents a miniature magnetic swimmer and a control apparatus able to perform both 3-D path following and blood clot removal. The robots are 2.5 mm in diameter, 6 mm in length, contain an internal permanent magnet, and have cutting tips coated in diamond powder. The robots are magnetically propelled by an external magnetic system using three coil pairs arranged orthogonally. A range of robot tip designs were tested for abrading human blood clots in vitro. The best design removed a blood clot at a maximum rate of 20.13 mm3/min. A controller for 3-D navigation is presented and tested. The best prototype was used in an experiment that combined both 3-D path following and blood clot removal.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 polyomi-noes 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

No abstract available.

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.

In this paper we investigate controlling many nonholonomic unicycles that each receive exactly the same inputs. The robots are almost homogeneous, but each robot has a unique parameter that scales its turning rate. Previous work showed that such a collection of robots can be approximately steered to arbitrary Cartesian positions, but not to arbitrary heading angles in a global reference frame. We extend this work by proving we can always steer such a collection of robots exactly to arbitrary range and bearing locations relative to targets in R2in a finite number of steps. We also provide existence proofs for controlling the final heading angles of many robots. This work addresses a fundamental challenge in micro-and nanorobotics with possible applications in targeted therapy, sensing, and actuation. Scale hardware experiments validate the control policy. All code is provided online.

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.

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.

In this paper, we derive a globally asymptotically stabilizing feedback control policy for a collection of differential-drive robots under the constraint that every robot receives exactly the same control inputs. We begin by assuming that each robot has a slightly different wheel size, which scales its forward speed and turning rate by a constant that can be found by offline or online calibration. The resulting feedback policy is easy to implement, is robust to standard models of noise, and scales to an arbitrary number (even a continuous ensemble) of robots. We validate this policy with hardware experiments, which additionally reveal that our feedback policy still works when the wheel sizes are unknown and even when the wheel sizes are all approximately identical. These results have possible future application to control of micro- and nano-scale robotic systems, which are often subject to similar constraints.

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.

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.

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-¿ of covering a fraction 1-¿ 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 ¿ and ¿. 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.

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.

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.