{"paper":{"title":"Novel Algorithms for Smoothly Differentiable and Efficiently Vectorizable Contact Manifold Construction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Analytical signed distance function primitives and a novel manifold routine make collision detection smoothly differentiable and massively vectorizable.","cross_cats":[],"primary_cat":"cs.RO","authors_text":"Andreas Ren\\'e Geist, Anselm Paulus, Georg Martius, Onur Beker","submitted_at":"2026-04-19T16:58:09Z","abstract_excerpt":"Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about rigid-body dynamics in the presence of contact holds great promise in terms of increasing the solution speed and computational efficiency. The main bottleneck in this research direction is the difficulty in obtaining gradients and Hessians that are actually useful for numerical optimization, due to pathologies in all three steps of a common simulation pipeline: i) collision detection, ii) cont"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"a method that can address the collision detection part of the puzzle in a manner that is smoothly differentiable and massively vectorizable. This is achieved via two contributions: i) a highly expressive class of analytical SDF primitives that can efficiently represent complex 3D surfaces, ii) a novel contact manifold generation routine that makes use of this geometry representation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the new SDF primitives and manifold routine can be composed with existing contact dynamics and time-integration modules without reintroducing non-differentiability or prohibitive computational cost.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New analytical SDF primitives and contact manifold generation enable smoothly differentiable and vectorizable collision detection for robot dynamics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Analytical signed distance function primitives and a novel manifold routine make collision detection smoothly differentiable and massively vectorizable.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"aa67a12b11c6d0575ae0453f4e85e836b6bcc3b9e48d75992aa0770512aeff5b"},"source":{"id":"2604.17538","kind":"arxiv","version":2},"verdict":{"id":"ac5a084a-bca0-4343-aa0f-5c2a41609060","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T05:17:00.475976Z","strongest_claim":"a method that can address the collision detection part of the puzzle in a manner that is smoothly differentiable and massively vectorizable. This is achieved via two contributions: i) a highly expressive class of analytical SDF primitives that can efficiently represent complex 3D surfaces, ii) a novel contact manifold generation routine that makes use of this geometry representation.","one_line_summary":"New analytical SDF primitives and contact manifold generation enable smoothly differentiable and vectorizable collision detection for robot dynamics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the new SDF primitives and manifold routine can be composed with existing contact dynamics and time-integration modules without reintroducing non-differentiability or prohibitive computational cost.","pith_extraction_headline":"Analytical signed distance function primitives and a novel manifold routine make collision detection smoothly differentiable and massively vectorizable."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.17538/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"}