A new approach to motion planning for disc-shaped robots manipulating a polygonal object in the plane

This paper addresses the problem of using three disc-shaped robots to manipulate a polygonal object in the plane in the presence of obstacles. The proposed approach is based on the characterization of the maximal discs (maximum independent capture discs, or MICaDS) where the robots can move independently while preventing the object from escaping their grasp. It is shown that, in the absence of obstacles, it is always possible to bring a polygonal object from any configuration to any other one with robot motions constrained to lie in a set of overlapping MICaDS. A strategy for computing these motions is used in conjunction with an exact motion planner to devise an algorithm guaranteed to find a motion plan avoiding collisions with obstacles as long as a collision-free path exists for the object grown by the diameter of the robots plus some arbitrary positive number ε