Global Vector Field Computation for Feedback Motion Planning

We present a global vector field computation algorithm in configuration spaces for smooth feedback motion planning. Our algorithm performs approximate cell decomposition in the configuration space and approximates the free space using rectanguloid cells. We compute a smooth local vector field for each cell in the free space and address the issue of the smooth composition of the local vector fields between the non-uniform adjacent cells. We show that the integral curve over the computed vector field is guaranteed to converge to the goal configuration, be collision-free, and maintain C∞ smoothness. As compared to prior approaches, our algorithm works well on non-convex robots and obstacles.We demonstrate its performance on planar robots with 2 or 3 DOFs, articulated robots composed of 3 serial links and multi-robot systems with 6 DOFs.