Recursive Rigid-Body Dynamics Algorithms for Systems with Kinematic Loops.
CoRR(2023)
摘要
We propose a novel approach for generalizing the following rigid-body
dynamics algorithms: Recursive Newton-Euler Algorithm, Articulated-Body
Algorithm, and Extended-Force-Propagator Algorithm. The classic versions of
these recursive algorithms require systems to have an open chain structure.
Dealing with closed-chains has, conventionally, required different algorithms.
In this paper, we demonstrate that the classic recursive algorithms can be
modified to work for closed-chain mechanisms. The critical insight of our
generalized algorithms is the clustering of bodies involved in local loop
constraints. Clustering bodies enables loop constraints to be resolved locally,
i.e., only when that group of bodies is encountered during a forward or
backward pass. This local treatment avoids the need for large-scale matrix
factorization. We provide self-contained derivations of the algorithms using
familiar, physically meaningful concepts. Overall, our approach provides a
foundation for simulating robotic systems with traditionally
difficult-to-simulate designs, such as geared motors, differential drives, and
four-bar mechanisms. The performance of our library of algorithms is validated
numerically in C++ on various modern legged robots: the MIT Mini Cheetah, the
MIT Humanoid, the UIUC Tello Humanoid, and a modified version of the JVRC-1
Humanoid. Our algorithms are shown to outperform state-of-the-art algorithms
for computing constrained rigid-body dynamics.
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