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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. Video: https://youtu.be/VU1SZYzeaXw Transcript: This animation shows colored tiles moved by a global signal so they all move in the same direction unless blocked. This simple example is solved using the Greatest Distance heuristic, which finds the shortest path in 21 steps. Each tile has glue on the four sides that only stick to compatible glues. Glue type is denoted by color. The objective is to manipulate the tiles to bond in the shape of the connected polyomino target outlined in red. The Polyomino Assembly Problem is PSPACE-hard, so optimal solutions are difficult to find. This more complicated workspace was solved using the Minimum Move to Polyomino or Target. This approach is not optimal, but is a best-first search that attempts to keep tiles not involved in the present construction step separated from each other. This is done by pruning configurations with undesired subassemblies from the search tree. The solution requires 473 steps. 

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. 

Magnetic induction localization is an inverse problem that determines the relative position and orientation (pose) between transmitting and receiving coils by analyzing the received signals. Related work has established methods to resolve the localization into two candidate poses. However, these methods require having signed signals, or periodic signals whose starting point is unambiguously determined with respect to an absolute reference (the transmitted signal). For distributed systems, the signal signs are difficult to resolve. This paper presents a method to extract partial information about the signs from unsigned signals. The method is tested in a hardware experiment. 

Reconfigurable modular robots can dynamically assemble/disassemble to accomplish the desired task better. Magnetic modular cubes are scalable modular subunits with embedded permanent magnets in a 3D-printed cubic body and can be wirelessly controlled by an external, uniform, timevarying magnetic field. This paper considers the problem of self-assembling these modules into desired 2D polyomino shapes using such magnetic fields. Although the applied magnetic field is the same for each magnetic modular cube, we use collisions with workspace boundaries to rearrange the cubes. We present a closed-loop control method for self-assembling the magnetic modular cubes into polyomino shapes, using computer vision-based feedback with re-planning. Experimental results demonstrate that the proposed closed-loop control improves the success rate of forming 2D user-specified polyominoes compared to an open-loop baseline. We also demonstrate the validity of the approach over changes in length scales, testing with both 10mm edge length cubes and 2.8mm edge length cubes. 

This paper investigates the scheduling problem related to engaging a swarm of attacking drones with a single defensive turret. The defending turret must turn, with a limited slew rate, and remain facing a drone for a dwell time to eliminate it. The turret must eliminate all the drones in the swarm before any drone reaches the turret. In 2D, this is an example of a Traveling Salesman Problem with Time Windows (TSPTW) where the turret must visit each target during the window. In 2D, the targets and turret are restricted to a plane and the turret rotates with one degree of freedom. In 3D, the turret can pan and tilt, while the drones attempt to reach a safe zone anywhere along the vertical axis above the turret. This 3D movement makes the problem more challenging, since the azimuth angles of the turret to the drones vary as a function of time. This paper investigates the theoretical optimal solution for simple swarm configurations. It compares heuristic approaches for the path scheduling problem in 2D and 3D using a simulation of the swarm behavior. It provides results for an improved heuristic approach, the Threat-Aware Nearest Neighbor. 

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 

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 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.