SOKOBAN and other motion planning problems

We consider a natural family of motion planning problems with movable obstacles and obtain hardness results for them. Some members of the family are shown to be PSPACE-complete thus improving and extending (and also simplifying) a previous NP-hardness result of Wilfong. The family considered includes a motion planning problem which forms the basis of a popular computer game called SOKOBAN. The decision problem corresponding to SOKOBAN is shown to be NP-hard. The motion planning problems considered are related to the “warehouseman's problem” considered by Hopcroft, Schwartz and Sharir, and to geometric versions of the motion planning problem on graphs considered by Papadimitriou, Raghavan, Sudan and Tamaki.