{"paper":{"title":"Geometry-Aware Sampling-Based Motion Planning on Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A midpoint-based approximation of Riemannian geodesic distance achieves third-order accuracy for sampling-based robot motion planning.","cross_cats":[],"primary_cat":"cs.RO","authors_text":"Jonathan Kelly, Phone Thiha Kyaw","submitted_at":"2026-02-01T03:14:46Z","abstract_excerpt":"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. To bridge this gap,"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce a computationally efficient midpoint-based approximation of the Riemannian geodesic distance and prove that it matches the true Riemannian distance with third-order accuracy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the third-order midpoint approximation combined with first-order retractions remains accurate enough during sampling in high-dimensional configuration spaces without accumulating unacceptable errors or requiring excessive samples.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A sampling-based planner approximates Riemannian geodesic distances via midpoints with third-order accuracy and uses retractions plus natural gradients for local planning, producing lower-cost trajectories than Euclidean baselines on robotic arms and SE(2) systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A midpoint-based approximation of Riemannian geodesic distance achieves third-order accuracy for sampling-based robot motion planning.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"76bf36b0f36cfe8514c53ce120d006e766063c498eefc2886ef27cf7a33c91e1"},"source":{"id":"2602.00992","kind":"arxiv","version":2},"verdict":{"id":"a4e1c892-3489-411d-a8e1-9cefedd0d7c7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T09:21:24.078616Z","strongest_claim":"We introduce a computationally efficient midpoint-based approximation of the Riemannian geodesic distance and prove that it matches the true Riemannian distance with third-order accuracy.","one_line_summary":"A sampling-based planner approximates Riemannian geodesic distances via midpoints with third-order accuracy and uses retractions plus natural gradients for local planning, producing lower-cost trajectories than Euclidean baselines on robotic arms and SE(2) systems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the third-order midpoint approximation combined with first-order retractions remains accurate enough during sampling in high-dimensional configuration spaces without accumulating unacceptable errors or requiring excessive samples.","pith_extraction_headline":"A midpoint-based approximation of Riemannian geodesic distance achieves third-order accuracy for sampling-based robot motion planning."},"references":{"count":56,"sample":[{"doi":"","year":2025,"title":"Expert Systems with Applications p","work_id":"6d690628-9ef7-4f5a-9bff-3acbe3e1859c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"The International Journal of Robotics Research42(10), 729–754 (2023)","work_id":"727a1288-7d48-43e2-ac69-4ae499f9975d","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"Proceed- ings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science216(1), 47–60 (2002)","work_id":"dcd9ee50-6658-40fb-adaa-7fee9fecb7f6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Physical Review E—Statistical, Nonlinear, and Soft Matter Physics83(3), 031927 (2011)","work_id":"670e669a-280f-4011-926a-235860436d4f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2007,"title":"Journal of Neuroscience 27(48), 13045–13064 (2007)","work_id":"b8e6a072-31ea-4945-8367-184b03d288fe","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":56,"snapshot_sha256":"5c8b2b798607c966624efedb9bc974046ecb05c16cba78e0fed5dd1358a161a2","internal_anchors":1},"formal_canon":{"evidence_count":1,"snapshot_sha256":"a5136f9e2ab33e4d67f8e2bdd5931d1aaee91682b909100b721728556484d456"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}