Adapting Rigid-Body Dynamics Derivatives for Constraint Embedding Closed-Chain Models

Abstract:This paper extends an existing algorithm for the first-order derivatives of rigid-body dynamics to the case of closed-chain kinematic systems modeled using constraint embed- ding. Many standard dynamics algorithms apply to both open- chain and constraint-embedded models, but existing efficient derivative methods assume joint velocity effects are locally config- uration invariant. We remove this assumption and derive adapted algorithms that extend dynamics derivatives to more general joint types, including those arising in constraint-embedded closed- chain models. Our results compare conventional pin-joint robot models with more complete actuation models that capture local closed chains. We show that the additional terms introduced by these generalizations have low computational impact when mod- eling actuation kinematics alone, but can incur higher cost when additional rigid bodies, such as motor rotors, are included in the actuation chain, or when considering non-local loops. Overall, these results enable more accurate dynamics computations for constraint-embedded actuation submechanisms to be adopted in model-predictive control and differentiable simulation.

Robotics (cs.RO)

arXiv:2609.21024 [cs.RO]

(or arXiv:2609.21024v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2609.21024 arXiv-issued DOI via DataCite (pending registration)

D. J. Volpi and P. M. Wensing, "Adapting Rigid-Body Dynamics Derivatives for Constraint Embedding Closed-Chain Models," in IEEE Robotics and Automation Letters, vol. 11, no. 9, pp. 10784-10791, Sept. 2026

https://doi.org/10.1109/LRA.2026.3709575 DOI(s) linking to related resources