Refined Analysis of Asymptotically-Optimal Kinodynamic Planning in the State-Cost Space
This work addresses the theoretical gap for motion planning with kinodynamic constraints, offering a rigorous foundation for practitioners in robotics and autonomous systems, though it is incremental as it builds on prior algorithm analysis.
The paper provides an optimality proof for the single-tree version of AO-RRT, a kinodynamic motion planner, showing it can approximate any piecewise-constant control trajectory with positive clearance from obstacles under mild Lipschitz-continuity assumptions.
We present a novel analysis of AO-RRT: a tree-based planner for motion planning with kinodynamic constraints, originally described by Hauser and Zhou (AO-X, 2016). AO-RRT explores the state-cost space and has been shown to efficiently obtain high-quality solutions in practice without relying on the availability of a computationally-intensive two-point boundary-value solver. Our main contribution is an optimality proof for the single-tree version of the algorithm---a variant that was not analyzed before. Our proof only requires a mild and easily-verifiable set of assumptions on the problem and system: Lipschitz-continuity of the cost function and the dynamics. In particular, we prove that for any system satisfying these assumptions, any trajectory having a piecewise-constant control function and positive clearance from the obstacles can be approximated arbitrarily well by a trajectory found by AO-RRT. We also discuss practical aspects of AO-RRT and present experimental comparisons of variants of the algorithm.