Sampling-based Volumetric Methods for Optimal Feedback Planning

We present a sampling-based, asymptotically optimal feedback planning method for the shortest path problem among obstacles in R. Our method combines an incremental sampling-based Delaunay triangulation with the newly introduced Repairing Fast Marching Method for computing a converging sequence of control policies. The convergence rate and asymptotic computational complexity of the algorithm are proven theoretically. In addition, the proposed method is compared with the state-of-the-art asymptotically optimal path planners in numerical simulation of a realistic planning problem. Finally, we present a straightforward extension of our method that handles dynamic environments where obstacles can appear, disappear, or move.