Coordinated Navigation of Multiple Independent Disk-Shaped Robots

This paper addresses the coordinated navigation of multiple independently actuated disk-shaped robots-all placed within the same disk-shaped workspace. Assuming perfect sensing, shared-centralized communications and computation, as well as perfect actuation, we encode complete information about the goal, obstacles, and workspace boundary using an artificial potential function over the configuration space of the robots' simultaneous nonoverlapping positions. The closed-loop dynamics governing the motion of each (velocity-controlled) robot take the form of the appropriate projection of the gradient of this function. We impose (conservative) restrictions on the allowable goal positions that yield sufficient conditions for convergence: We prove that this construction is an essential navigation function that guarantees collision-free motion of each robot to its destination from almost all initial free placements. The results of an extensive simulation study investigate practical issues such as average resulting trajectory length and robustness against simulated sensor noise.