Lagrangian neural networks for nonholonomic mechanics
This work addresses a specific challenge in physics-informed machine learning for constrained mechanical systems, representing an incremental advancement by extending existing LNN techniques to nonholonomic constraints.
The paper tackled the problem of applying Lagrangian Neural Networks (LNNs) to mechanical systems with nonholonomic constraints, showing that this adaptation improves trajectory estimation accuracy, ensures constraint adherence, and exhibits better energy behavior compared to unconstrained methods.
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.