SE(2) Assembly Planning for Magnetic Modular Cubes

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.