Multiple-Robot Motion Planning = Parallel Processing + Geometry

We present two problems in multiple-robot motion planning that can be quite naturally solved using techniques from the parallel processing community to dictate how the robots interact with each other and techniques from computational geometry to apply these techniques in the geometric environment in which the robots operate. The first problem we consider is a load-balancing problem in which a pool of work must be divided among a set of processors in order to minimize the amount of time required to complete all the work. We describe a simple polygon partitioning algorithm that allows techniques from parallel processor scheduling to be applied in the multiple-robot setting in order to achieve a good balance of the work. The second problem is that of collision avoidance, where one must avoid that two (or more) processors occupy the same resource at the same time. For this problem, we describe a procedure for robot interaction that is derived from procedures used in shared-memory computers along with a geometric data structure that can efficiently determine when there are potential robot collisions.