Motion planning for a robot and a movable object amidst polygonal obstacles

This paper addresses t h e m o t i o n planning problem for a robot and a movable object amidst polygonal obstacles. M o t i o n planning in this context appears as a constrained instance of t h e coordinated m o t i o n planning problem for t w o robots. Indeed, the object cannot move by itself, at only does when the robot grasps at. W e f irs t show a topological property tha t characterizes t h e existence of solut ions in the subspace of conf igurat ions where the robot “touches” the object. T h i s property t h e n provides a general resolution scheme which is applied t o t h e special case of a convex polygonal robot moving in translat ion amidst a convex polygonal object and polygonal obstacles. T h e algorithm i s complete and exact. It extends a first pioneering s tudy provided by Wilfong an [12].