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arXiv · 2410.15201

Learning Nonholonomic Dynamics with Constraint Discovery

Baiyue Wang·Anthony Bloch
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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 $TQ$. 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.

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Baiyue Wang, Anthony Bloch. 2024-10-19. Learning Nonholonomic Dynamics with Constraint Discovery. https://arxiv.org/abs/2410.15201

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