Multi-robot motion planning of k-colored discs is PSPACE-hard

Thomas Brocken, G. Wessel van der Heijden, Irina Kostitsyna, Lloyd E. Lo-Wong, Remco J. A. Surtel

In the problem of multi-robot motion planning, a group of robots, placed in a polygonal domain with obstacles, must be moved from their starting positions to a set of target positions. We consider the specific case of unlabeled disc robots of two different sizes. That is, within one class of robots, where a class is given by the robots' size, any robot can be moved to any of the corresponding target positions. We prove that the decision problem of whether there exists a schedule moving the robots to the target positions is PSPACE-hard.

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