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