  The problem of optimal feedback planning among obstacles in d-dimensional
configuration spaces is considered. We present a sampling-based, asymptotically
optimal feedback planning method. Our method combines an incremental
construction of the Delaunay triangulation, volumetric collision-detection
module, and a modified Fast Marching Method to compute a converging sequence of
feedback functions. The convergence and asymptotic runtime are proven
theoretically and investigated during numerical experiments, in which the
proposed method is compared with the state-of-the-art asymptotically optimal
path planners. The results show that our method is competitive with the
previous algorithms. Unlike the shortest trajectory computed by many path
planning algorithms, the resulting feedback functions can be used directly for
robot navigation in our case. Finally, we present a straightforward extension
of our method that handles dynamic environments where obstacles can appear,
disappear, or move.
