Asymptotically Optimal Sampling-based Kinodynamic Planning

Sampling-based planning algorithms are efficient practical solutions to motion planning challenges. Existing algorithms such as PRM* and RRT* take advantages of random geometric graph theory to answer motion planning queries. This theory requires solving the two-point boundary value problem (BVP) in the state space, which is generally considered to be difficult and impractical. This work presents a different theory of asymptotic optimality. It fills in the gap between optimal kinodynamic planning problems and sampling-based algorithms. The resulting contributions explain some open problems, e.g., the existence of BVP-free asymptotically optimal sampling-based kinodynamic algorithms, properties of a previously proposed heuristical algorithm RRT-BestNear. This work further presents new algorithms Stable Sparse-RRT (SST) and SST*. Analysis and experimental results show that SST and SST* are efficient, general, BVP-free, sampling-based optimal kinodynamic planning algorithms that are practical for a great variety of physical systems.