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The problem of optimal feedback planning among obstacles in d-dimensionalconfiguration spaces is considered. We present a sampling-based, asymptoticallyoptimal feedback planning method. Our method combines an incrementalconstruction of the Delaunay triangulation, volumetric collision-detectionmodule, and a modified Fast Marching Method to compute a converging sequence offeedback functions. The convergence and asymptotic runtime are proventheoretically and investigated during numerical experiments, in which theproposed method is compared with the state-of-the-art asymptotically optimalpath planners. The results show that our method is competitive with theprevious algorithms. Unlike the shortest trajectory computed by many pathplanning algorithms, the resulting feedback functions can be used directly forrobot navigation in our case. Finally, we present a straightforward extensionof our method that handles dynamic environments where obstacles can appear,disappear, or move.

Planning for Optimal Feedback Control in the Volume of Free Space