{"paper":{"title":"Invariants for Homology Classes with Application to Optimal Search and Planning Problem in Robotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.RO"],"primary_cat":"math.AT","authors_text":"David Lipsky, Robert Ghrist, Subhrajit Bhattacharya, Vijay Kumar","submitted_at":"2012-08-02T18:46:26Z","abstract_excerpt":"We consider planning problems on a punctured Euclidean spaces, $\\mathbb{R}^D - \\widetilde{\\mathcal{O}}$, where $\\widetilde{\\mathcal{O}}$ is a collection of obstacles. Such spaces are of frequent occurrence as configuration spaces of robots, where $\\widetilde{\\mathcal{O}}$ represent either physical obstacles that the robots need to avoid (e.g., walls, other robots, etc.) or illegal states (e.g., all legs off-the-ground). As state-planning is translated to path-planning on a configuration space, we collate equivalent plannings via topologically-equivalent paths. This prompts finding or exploring"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0573","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}