Motion planning in the presence of movable obstacles

Abstract

Motion planning algorithms have generally dealt with motion in a static environment, or more recently, with motion in an environment that changes in a known manner. We consider the problem of finding collision-free motions in a changeable environment. That is, we wish to find a motion for an object where the object is permitted to move some of the obstacles. In such an environment the final positions of the movable obstacles may or may not be part of the goal. In the case where the final positions of the obstacles are unspecified, the motion planning problem is shown to be NP-hard. An algorithm that runs in O(n2logn) time after O(n3log2n) preprocessing time is presented when the object to be moved is polygonal and there is only one movable polygonal obstacle in a polygonal environment of complexity O(n). In the case where the final positions of the obstacles are specified the general problem is shown to be PSPACE-hard and an algorithm is given when there is one movable obstacle with the same preprocessing time as the previous algorithm but with O(n2) query time.