Planning For Closed Chains Without Inverse Kinematics

Motion planning for mechanisms with closed chains has received substantial interest in recent years. Most efforts focus on characterizing the geometry and topology of the closure set and on inverse kinematics. In this paper, we show that efficient sampling-based motion planning is possible without having either of these. In particular, we develop a variant of the RRT that uses a kd-tree to actively maintain a sampling domain around the closure set. The method is implemented and has been tested on a dozen examples.