Learning Nonholonomic Dynamics with Constraint Discovery

Baiyue Wang, Anthony Bloch
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:2123-2137, 2026.

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 for learning the dynamics of a nonholonomic system through Hamel’s formalism, while discovering the system constraints by parameterizing them, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-wang26d, title = {Learning Nonholonomic Dynamics with Constraint Discovery}, author = {Wang, Baiyue and Bloch, Anthony}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {2123--2137}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/wang26d/wang26d.pdf}, url = {https://proceedings.mlr.press/v331/wang26d.html}, 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 for learning the dynamics of a nonholonomic system through Hamel’s formalism, while discovering the system constraints by parameterizing them, 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.} }
Endnote
%0 Conference Paper %T Learning Nonholonomic Dynamics with Constraint Discovery %A Baiyue Wang %A Anthony Bloch %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-wang26d %I PMLR %P 2123--2137 %U https://proceedings.mlr.press/v331/wang26d.html %V 331 %X 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 for learning the dynamics of a nonholonomic system through Hamel’s formalism, while discovering the system constraints by parameterizing them, 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.
APA
Wang, B. & Bloch, A.. (2026). Learning Nonholonomic Dynamics with Constraint Discovery. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:2123-2137 Available from https://proceedings.mlr.press/v331/wang26d.html.

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