Lagrangian neural networks for nonholonomic mechanics

TL;DR

This paper extends Lagrangian Neural Networks to nonholonomic mechanical systems, improving trajectory prediction accuracy and constraint adherence by incorporating nonholonomic restrictions into the learning process.

Contribution

It introduces a novel adaptation of LNNs for nonholonomic systems, enhancing their ability to model constrained mechanical systems accurately.

Findings

Improved trajectory estimation for nonholonomic systems.

Better energy conservation compared to unconstrained models.

Enhanced adherence to nonholonomic constraints.

Abstract

Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart.