Asymptotically Optimal Kinodynamic Planning Using Bundles of Edges

Using sampling to estimate the connectivity of high-dimensional configuration spaces has been the theoretical underpinning for effective sampling-based motion planners. Typical strategies either build a roadmap, or a tree as the underlying search structure that connects sampled configurations, with a focus on guaranteeing completeness and optimality as the number of samples tends to infinity. Roadmap-based planners allow preprocessing the space, and can solve multiple kinematic motion planning problems, but need a steering function to connect pairwise-states. Such steering functions are difficult to define for kinodynamic systems, and limit the applicability of roadmaps to motion planning problems with dynamical systems. Recent advances in the analysis of single-query tree-based planners has shown that forward search trees based on random propagations are asymptotically optimal. The current work leverages these recent results and proposes a multi-query framework for kinodynamic planning. Bundles of kinodynamic edges can be sampled to cover the state space before the query arrives. Then, given a motion planning query, the connectivity of the state space reachable from the start can be recovered from a forward search tree reasoning about a local neighborhood of the edge bundle from each tree node. The work demonstrates theoretically that considering any constant radial neighborhood during this process is sufficient to guarantee asymptotic optimality. Experimental validation in five and twelve dimensional simulated systems also highlights the ability of the proposed edge bundles to express high-quality kinodynamic solutions. Our approach consistently finds higher quality solutions compared to SST, and RRT, often with faster initial solution times. The strategy of sampling kinodynamic edges is demonstrated to be a promising new paradigm.