Geometry-Aware Sampling-Based Motion Planning on Riemannian Manifolds
arXiv:2602.00992v1 Announce Type: new Abstract: In many robot motion planning problems, task objectives and physical constraints induce non-Euclidean geometry on the configuration space, yet many planners operate using Euclidean distances that ignore this structure. We address the problem of planning collision-free motions that minimize length under configuration-dependent Riemannian metrics, corresponding to geodesics on the configuration manifold. Conventional numerical methods for computing such paths do not scale well to high-dimensional systems, while sampling-based planners trade scalability for geometric fidelity. […]