K-color multi-robot motion planning

We present a simple and natural extension of the multi-robot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target placement that is assigned to its group. We call this problem k-color multirobot motion planning and provide a sampling-based algorithm specifically designed for solving it. At the heart of the algorithm is a novel technique where the k-color problem is reduced to several discrete multi-robot motion planning problems. These reductions amplify basic samples into massive collections of free placements and paths for the robots. We demonstrate the performance of the algorithm by an implementation for the case of disc robots in the plane and show that it successfully and efficiently copes with a variety of challenging scenarios, involving many robots, while a straightforward extension of prevalent sampling-based algorithms for the k-color case, fails even on simple scenarios. Interestingly, our algorithm outperforms a state-ofthe- art implementation for the standard multi-robot problem, in which each robot has a distinct color.