Reproduce “Lie Group Formulation of Recursive Dynamics Algorithms of Higher Order for Floating-Base Robots” on OpenResearch
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About this paper
Ahmed Ali, Chiara Gabellieri, Antonio Franchi
Researchers at the University of Twente developed recursive algorithms to compute higher-order time derivatives of inverse, forward, and hybrid dynamics for floating-base robots with an SE(3) base. These algorithms scale linearly with the number of bodies and quadratically with derivative order, offering improved computational efficiency compared to automatic differentiation.
Key insights
- The articulated body inertia tensor remains invariant across all higher-order time derivatives of the dynamics, simplifying computations by allowing reuse of 0th-order results.
- The recursive outputs can be systematically collected into closed-form Lagrangian equations of motion and their first-time derivatives, demonstrating theoretical consistency.
- The approach maintains established Lie-group advantages, including coordinate-invariant expressions, singularity-free SE(3) base representation, and compact recursions, even for higher derivative orders.
Summary by alphaXiv.
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