Learning Nonholonomic Dynamics with Constraint Discovery
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908623509127168 |
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| author | Wang, Baiyue Bloch, Anthony |
| author_facet | Wang, Baiyue Bloch, Anthony |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning Nonholonomic Dynamics with Constraint Discovery Wang, Baiyue Bloch, Anthony Dynamical Systems Machine Learning Mathematical Physics 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. |
| title | Learning Nonholonomic Dynamics with Constraint Discovery |
| topic | Dynamical Systems Machine Learning Mathematical Physics |
| url | https://arxiv.org/abs/2410.15201 |