Learning the Geometric Mechanics of Robot Motion Using Gaussian Mixtures

Ruizhen Hu, Shai Revzen

arXiv preprint, 2025

Abstract

Data-driven models of robot motion constructed using principles from Geometric Mechanics have been shown to produce useful predictions of robot motion for a variety of robots. For robots with a useful number of DoF, these geometric mechanics models can only be constructed in the neighborhood of a gait. Here we show how Gaussian Mixture Models (GMM) can be used as a form of manifold learning that learns the structure of the Geometric Mechanics "motility map" and demonstrate: [i] a sizable improvement in prediction quality when compared to the previously published methods; [ii] a method that can be applied to any motion dataset and not only periodic gait data; [iii] a way to pre-process the data-set to facilitate extrapolation in places where the motility map is known to be linear. Our results can be applied anywhere a data-driven geometric motion model might be useful.

BibTeX

@unpublished{hu2025learning,
  author = {Hu, Ruizhen and Revzen, Shai},
  title = {Learning the Geometric Mechanics of Robot Motion Using Gaussian Mixtures},
  year = {2025},
  eprint = {2502.05309},
  eprinttype = {arxiv},
  journal = {arXiv preprint},
  doi = {10.48550/arXiv.2502.05309}
}