{"paper":{"title":"Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Recursive Lie-group algorithms enable higher-order dynamics computation for floating-base robots at quadratic cost.","cross_cats":["cs.SY","eess.SY"],"primary_cat":"cs.RO","authors_text":"Ahmed Ali, Antonio Franchi, Chiara Gabellieri","submitted_at":"2026-05-07T16:17:39Z","abstract_excerpt":"In this paper, we describe procedures for computing higher-order time derivatives of the Lie-group Newton-Euler, Articulated-Body Inertia, and hybrid dynamics algorithms for floating-base trees, where the base configuration evolves on SE(3) and the attached mechanism is an open kinematic tree with configuration on the (n1+n2)-dimensional manifold T^{n1} \\times R^{n2}, using spatial representation of twists. After presenting the algorithms, we collect the resulting recursions into closed-form equations of motion, identifying an admissible Coriolis matrix satisfying the passivity property, and s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"their computational cost scales quadratically with the derivative order, whereas the automatic-differentiation baseline exhibits exponential scaling","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The recursive procedures for higher-order derivatives can be collected into closed-form equations while preserving an admissible Coriolis matrix that satisfies passivity and leaving the articulated inertia tensor unchanged across derivatives.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Lie-group recursive dynamics algorithms are extended to higher-order time derivatives for floating-base robots, with quadratic computational scaling shown versus exponential for automatic differentiation on a 12-DoF aerial manipulator.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Recursive Lie-group algorithms enable higher-order dynamics computation for floating-base robots at quadratic cost.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"dc72b622cd20f868dae4c2a7b9f5b1b7da04468ecb071bb27eef057d7f8a1738"},"source":{"id":"2605.06498","kind":"arxiv","version":1},"verdict":{"id":"c338b9ea-d471-4433-9a31-40f40da0669a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T08:42:03.863570Z","strongest_claim":"their computational cost scales quadratically with the derivative order, whereas the automatic-differentiation baseline exhibits exponential scaling","one_line_summary":"Lie-group recursive dynamics algorithms are extended to higher-order time derivatives for floating-base robots, with quadratic computational scaling shown versus exponential for automatic differentiation on a 12-DoF aerial manipulator.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The recursive procedures for higher-order derivatives can be collected into closed-form equations while preserving an admissible Coriolis matrix that satisfies passivity and leaving the articulated inertia tensor unchanged across derivatives.","pith_extraction_headline":"Recursive Lie-group algorithms enable higher-order dynamics computation for floating-base robots at quadratic cost."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06498/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T12:22:03.893672Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T07:41:00.608200Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:01:19.751302Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:37:06.624603Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6c7e99023fe3520ed7d2b2330476c2058259fadf70b77d46e1148ee66444e6ed"},"references":{"count":71,"sample":[{"doi":"","year":1990,"title":"and Roth, B., 1990,Theoretical kinematics, Vol","work_id":"","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Siciliano, B., Sciavicco, L., Villani, L., and Oriolo, G., 2010,Robotics: Mod- elling, Planning and Control, Advanced Textbooks in Control and Signal Pro- cessing, Springer London","work_id":"","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Angeles, J., 2003,Fundamentals of robotic mechanical systems: theory, meth- ods, and algorithms, Springer","work_id":"","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1980,"title":"A Recursive Lagrangian Formulation of Maniputator Dynamics and a Comparative Study of Dynamics Formulation Complexity,","work_id":"","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1976,"title":"Dynamics of articulated open- chain active mechanisms,","work_id":"","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":7,"snapshot_sha256":"4dbbb8fb8e4dd7ed60630d873426cf931c5a4ea39fc79afac24c01d1738c03e0","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"}