We propose the formulation of forward and differentiable rigid-body dynamics using Lie-algebra rotation derivatives. In particular, we show how this approach can easily be applied to incremental-potential formulations of forward dymamics, and we introduce a novel definition of adjoints for differentiable dynamics. In contrast to other parameterizations of rotations (notably the popular rotation-vector parameterization), our approach leads to painlessly simple and compact derivatives, better conditioning, and higher runtime efficiency. We demonstrate our approach on fundamental rigid-body problems, but also on Cosserat rods as an example of multi-rigid-body dynamics.
@article{resolvingcollisions2024,
author = {Romanyà-Serrasolsas, Magí and Casafranca, Juan J. and Otaduy, Miguel A.},
title = {Painless Differentiable Rotation Dynamics},
year = {2025},
doi = {10.1145/3730944},
journal = {Volume 44, Issue No. 4 of ACM Transactions on Graphics}
}
