Pith Number

pith:L7UN5C3H

pith:2026:L7UN5C3HQGCBAOP7WA7AOW3HRL

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Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots

Ahmed Ali, Antonio Franchi, Chiara Gabellieri

Recursive Lie-group algorithms enable higher-order dynamics computation for floating-base robots at quadratic cost.

arxiv:2605.06498 v1 · 2026-05-07 · cs.RO · cs.SY · eess.SY

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Claims

C1strongest claim

their computational cost scales quadratically with the derivative order, whereas the automatic-differentiation baseline exhibits exponential scaling

C2weakest 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.

C3one 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.

References

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[1] and Roth, B., 1990,Theoretical kinematics, Vol 1990

[2] 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 2010

[3] Angeles, J., 2003,Fundamentals of robotic mechanical systems: theory, meth- ods, and algorithms, Springer 2003

[4] A Recursive Lagrangian Formulation of Maniputator Dynamics and a Comparative Study of Dynamics Formulation Complexity, 1980

[5] Dynamics of articulated open- chain active mechanisms, 1976

Receipt and verification

First computed	2026-05-25T02:01:22.214830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fe8de8b6781841039ffb03e075b678aead1e8c1312209b654d4f528910cc806

Aliases

arxiv: 2605.06498 · arxiv_version: 2605.06498v1 · doi: 10.48550/arxiv.2605.06498 · pith_short_12: L7UN5C3HQGCB · pith_short_16: L7UN5C3HQGCBAOP7 · pith_short_8: L7UN5C3H

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/L7UN5C3HQGCBAOP7WA7AOW3HRL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5fe8de8b6781841039ffb03e075b678aead1e8c1312209b654d4f528910cc806

Canonical record JSON

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    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.RO",
    "submitted_at": "2026-05-07T16:17:39Z",
    "title_canon_sha256": "39695d43ad45088424252fad1c7c15db369a0b79e0b8c35de72995c8c91f4b19"
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  "source": {
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