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This paper introduces the RDG algorithm, a novel kinodynamic motion planning method that achieves asymptotically near-optimal solutions with constant-time complexity per node. By leveraging state space grid decomposition, it significantly outperforms existing sparse planning algorithms in high-dimensional environments up to 10 degrees of freedom while maintaining probabilistic completeness. The advancement represents a substantive improvement in the efficiency and reliability of motion planning for complex robotic systems.
Rapidly-Iterating Grid-Based Near-Optimal Kinodynamic Motion Planning
arXiv:2609.22733v1 Announce Type: new Abstract: This paper develops the Rapidly-iterating kinoDynamic Grid (RDG) algorithm, an asymptotically near-optimal kinodynamic motion planning algorithm that produces high quality solutions through rapid iteration. The algorithm leverages a state space grid decomposition to perform node selection, dynamics propagation, and graph revision in constant time complexity with respect to the number of nodes in the trajectory tree. Through a covering ball sequence induction proof, the algorithm is shown to be asymptotically near-optimal and probabilistically complete. Different subsystems of the algorithm are evaluated against common nearest-neighbor search-based methods at generating exploration bias. The RDG algorithm is evaluated through simulated trials in complex, kinodynamic motion planning problem environments up to 10 DOF relative to similar sparse, kinodynamic planning algorithms with optimality guarantees, SST and DIRT. The RDG algorithm outperforms both SST and DIRT in mean final solution quality by up to 104% and 40% respectively. Additionally, RDG maintained a 100% success rate, even on a 10-DOF test case where both SST and DIRT did not.
Abstract:This paper develops the Rapidly-iterating kinoDynamic Grid (RDG) algorithm, an asymptotically near-optimal kinodynamic motion planning algorithm that produces high quality solutions through rapid iteration. The algorithm leverages a state space grid decomposition to perform node selection, dynamics propagation, and graph revision in constant time complexity with respect to the number of nodes in the trajectory tree. Through a covering ball sequence induction proof, the algorithm is shown to be asymptotically near-optimal and probabilistically complete. Different subsystems of the algorithm are evaluated against common nearest-neighbor search-based methods at generating exploration bias. The RDG algorithm is evaluated through simulated trials in complex, kinodynamic motion planning problem environments up to 10 DOF relative to similar sparse, kinodynamic planning algorithms with optimality guarantees, SST and DIRT. The RDG algorithm outperforms both SST and DIRT in mean final solution quality by up to 104% and 40% respectively. Additionally, RDG maintained a 100% success rate, even on a 10-DOF test case where both SST and DIRT did not.
Robotics (cs.RO)
arXiv:2609.22733 [cs.RO]
(or arXiv:2609.22733v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2609.22733 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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