On the Complexity of Motion Planning for Multiple Independent Objects; PSPACE- Hardness of the “Warehousemans's Problem”

Coordinated motion planning for a large number af three-di mensional objects in the presence of obstacles is a computa tional problem whose complexity is important to calibrate. In this paper we show that even the restricted two-dimensional problem for arbitrarily many rectangles in a rectangular region is PSPACE-hard. This result should be viewed as a guide to the difficulty, of the general problem and should lead researchers to consider more tractable restricted classes of motion problems of practical interest.