通过轨迹数据同时学习非完整系统的动力学与约束，适用于滚动盘等复杂系统。
Learning Nonholonomic Dynamics with Constraint Discovery
- 基于哈梅尔形式化，从切丛轨迹中联合学习动力学与约束
- 证明了网络收敛存在局部极小值，保证学习稳定性
- 保留系统对称性，适合物理建模与机器人控制场景
我们研究在发现约束的同时学习非完整动力系统，并以滚动盘为例进行详细分析。非完整系统受非完整约束限制，这类约束不定义配置空间上的子流形，因此反问题需涉及切丛。本文提出一种通用方法，通过哈梅尔形式化，利用切丛 $TQ$ 上的离散轨迹数据，参数化并学习系统的动力学与约束。我们证明了神经网络存在局部最小值以保证收敛。此外，通过将拉格朗日量约化到选定群的李代数，保持系统的对称性。
原文摘要 · Abstract (English)
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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