Lagrangian Neural Networks for Quadrupedal Locomotion

Abstract

This work investigates Lagrangian Neural Networks (LNNs) for infinite horizon planning in quadrupedal locomotion. Unlike standard neural networks, LNNs learn the Lagrangian of the system preserving physical constraints and energy conservation properties.

Methodology

• Architecture: Lagrangian Neural Network with automatic differentiation
• Training: Supervised learning on trajectory data from full-order physics simulation
• Integration: Symplectic Euler integration for stable long-horizon predictions

Key Findings

LNNs demonstrate better generalization to unseen terrains compared to black-box neural networks, with 40% lower prediction error over 10-second horizons.