Randomized path planning on foliated configuration spaces

This paper presents a randomized planning algorithm for manipulation tasks that require the robot to release an object in different robot configurations. Such problems arise, for example, in robotic suturing and knot tying, and in certain assembly tasks where parts must be guided through cluttered environments. We show that the problem can be posed as one of planning on a foliated manifold. A randomized algorithm that involves sampling and tree propagation in both the robot's task and joint configuration space manifolds is developed. A key component of the algorithm is a path refining phase, in which the topological structure of the foliated manifold is first learned via a sampling and clustering procedure using Gaussian mixtures, and the number of release-regrasp sequences reduced. Comparative case studies evaluating the performance of our algorithm are presented.