{"paper":{"title":"Phasing Through the Flames: Rapid Motion Planning with the AGHF PDE for Arbitrary Objective Functions and Constraints","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.RO","authors_text":"Bohao Zhang, C\\'esar E. Ramos Chuquiure, Challen Enninful Adu, Pearl Lin, Ram Vasudevan, Ruikai Yang, Shubham Singh, Yutong Zhou","submitted_at":"2025-05-02T21:18:47Z","abstract_excerpt":"The generation of optimal trajectories for high-dimensional robotic systems under constraints remains computationally challenging due to the need to simultaneously satisfy dynamic feasibility, input limits, and task-specific objectives while searching over high-dimensional spaces. Recent approaches using the Affine Geometric Heat Flow (AGHF) Partial Differential Equation (PDE) have demonstrated promising results, generating dynamically feasible trajectories for complex systems like the Digit V3 humanoid within seconds. These methods efficiently solve trajectory optimization problems over a two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01589","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.01589/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}