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We present a heuristic method to construct an optimal communication network in an obstacle-dense environment. A set of immobile terminals must be connected by a network of straight-line edges by adding agents to serve as relays. Obstacles are represented by polygons, unaccessible by the agents of the network or by the edges. The problem with obstacles is reduced to a problem without obstacles by choosing the nodes of the optimal network among the obstacles’ vertices that are in mutual line of sight. A second heuristic method is developed to solve the bicriteria optimization problem with number of agents and length of the network as concurrent costs. 

We present a magnetic camera system developed to detect ferrous or ferromagnetic objects. The main motivation is detection and tracking of underwater pipelines. Many industries, such as oil and gas, must perform inspection and maintenance of pipelines and automation is desirable. An electromagnet generates a static magnetic field which is read by an array of Hall-effect sensors. The presence of ferromagnetic materials distorts this field, which can be detected by the sensors and creates a magnetic image. The grid configuration of the camera allows for quick computation of the center of mass and general orientation of detected pipes, facilitating tracking. This camera is carried by an ROV and tested in a pool environment. 

We present strategies for realizing a swarm of mobile relays to provide a bi-directional wireless network that connects fixed terminals. Neither terminals or relays are permitted to transmit into disk-shaped no-transmission zones. We assume a planar environment and that each transmission area is a disk centered at the transmitter. We seek a strongly connected network between all terminals with minimal total cost, where the cost is the sum area of the transmission disks.Results for networks with increasing levels of complexity are provided. The solutions for local networks containing low numbers of relays and terminals are applied to larger networks. For more complex networks, algorithms for a minimum-spanning tree (MST) based procedure are implemented to reduce the solution cost. 

Many potential medical applications for magnetically controlled tetherless devices inside the human body have been proposed, including procedures such as biopsies, blood clot removal, and targeted drug delivery. These devices are capable of wirelessly navigating through fluid-filled cavities in the body, such as the vascular system, eyes, urinary tract, and ventricular system, to reach areas difficult to access via conventional methods. Once at their target location, these devices could perform various medical interventions. This paper focuses on a special type of magnetic tetherless device called a magnetic rotating swimmer, which has internal magnets and propeller fins with a helical shape. To facilitate the design process, an automated geometry generation program using OpenSCAD was developed to create the swimmer design, while computational fluid dynamics simulations using OpenFOAM were employed to calculate the propulsive force produced by the swimmer. Furthermore, an experimental approach is proposed and demonstrated to validate the model. The results show good agreement between simulations and experiments, indicating that the model could be used to develop an automatic geometry optimization pipeline for rotating swimmers. 

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. 

Given starting and ending positions and velocities, L2 bounds on the acceleration and velocity, and the restriction to no more than two constant control inputs, this paper provides routines to compute the minimal-time path. Closed form solutions are provided for reaching a position in minimum time with and without a velocity bound, and for stopping at the goal position. A numeric solver is used to reach a goal position and velocity with no more than two constant control inputs. If a cruising phase at the terminal velocity is needed, this requires solving a non-linear equation with a single parameter. Code is provided on GitHub 1 , extended paper version at [1]. [1] https://github.com/RoboticSwarmControl/MinTimeL2pathsConstraints/ 

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. 

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.