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Learning Nonholonomic Dynamics with Constraint Discovery

Dynamical Systems 2025-11-04 v3 Machine Learning Mathematical Physics math.MP

Abstract

We consider learning nonholonomic dynamical systems while discovering the constraints, and describe in detail the case of the rolling disk. A nonholonomic system is a system subject to nonholonomic constraints. Unlike holonomic constraints, nonholonomic constraints do not define a sub-manifold on the configuration space. Therefore, the inverse problem of finding the constraints has to involve the tangent bundle. This paper discusses a general procedure to learn the dynamics of a nonholonomic system through Hamel's formalism, while discovering the system constraint by parameterizing it, given the data set of discrete trajectories on the tangent bundle TQTQ. We prove that there is a local minimum for convergence of the network. We also preserve symmetry of the system by reducing the Lagrangian to the Lie algebra of the selected group.

Keywords

Cite

@article{arxiv.2410.15201,
  title  = {Learning Nonholonomic Dynamics with Constraint Discovery},
  author = {Baiyue Wang and Anthony Bloch},
  journal= {arXiv preprint arXiv:2410.15201},
  year   = {2025}
}
R2 v1 2026-06-28T19:28:25.569Z