Learning Nonholonomic Dynamics with Constraint Discovery
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 8 of its 17 references that are in the map. First posted on arXiv 19 Oct 2024.
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References · 8
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
- 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
- 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
- 2023Leveraging Symmetries in Pick and Placecited by 18
- 2023Lie-Poisson Neural Networks (LPNets): Data-Based Computing of Hamiltonian Systems with Symmetriescited by 9
- 2024SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classificationcited by 4
- 2024CLPNets: Coupled Lie-Poisson Neural Networks for Multi-Part Hamiltonian Systems with Symmetriescited by 3
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