Path planning using a Jacobian-based freespace generation algorithm

A simple and efficient algorithm is developed to generate a 2"-tree (generalized quad-tree) representation of the free configuration space for a manipulator moving in a workspace with obstacles. The algorithm is based on the existence of uniform bounds on the Jacobians relating the differential motions of points on the manipulator to differential joint motions. This representation can be searched to generate a collision-free path and optimized with dynamic constraints to produce an executable trajectory.