Learning Nonholonomic Dynamics with Constraint Discovery

TL;DR

This paper presents a method for learning the dynamics of nonholonomic systems, like a rolling disk, while simultaneously discovering the underlying constraints using neural networks and geometric formalism.

Contribution

It introduces a general procedure to learn nonholonomic dynamics and constraints from trajectory data, leveraging Hamel's formalism and symmetry reduction.

Findings

Proves local convergence of the neural network training process.

Demonstrates the preservation of system symmetry through Lie algebra reduction.

Provides a framework applicable to systems like the rolling disk.

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.