Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotion

2025-06-19

AI Summary

In infinite-horizon motion planning for quadrupedal robots, accumulated modeling errors in dynamics lead to control instability. Method: This paper presents the first systematic evaluation of Lagrangian Neural Networks (LNNs) for quadrupedal locomotion across four dynamical modeling paradigms. We propose a mass matrix diagonalization strategy that preserves partial physical interpretability while significantly accelerating computation for real-time receding-horizon optimization. Our approach integrates physics-constrained LNN training, forward/inverse dynamics modeling, and simplified centroidal dynamics to achieve high-fidelity, low-bias dynamics learning. Results: Experiments demonstrate a 10× improvement in sample efficiency and 2–10× higher prediction accuracy over baselines; control frequency is substantially increased. The method has been successfully deployed on a physical quadruped platform, enabling stable, sustainable gait control.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Learning to Search
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Lagrangian Neural Networks (LNNs) present a principled and interpretable framework for learning the system dynamics by utilizing inductive biases. While traditional dynamics models struggle with compounding errors over long horizons, LNNs intrinsically preserve the physical laws governing any system, enabling accurate and stable predictions essential for sustainable locomotion. This work evaluates LNNs for infinite horizon planning in quadrupedal robots through four dynamics models: (1) full-order forward dynamics (FD) training and inference, (2) diagonalized representation of Mass Matrix in full order FD, (3) full-order inverse dynamics (ID) training with FD inference, (4) reduced-order modeling via torso centre-of-mass (CoM) dynamics. Experiments demonstrate that LNNs bring improvements in sample efficiency (10x) and superior prediction accuracy (up to 2-10x) compared to baseline methods. Notably, the diagonalization approach of LNNs reduces computational complexity while retaining some interpretability, enabling real-time receding horizon control. These findings highlight the advantages of LNNs in capturing the underlying structure of system dynamics in quadrupeds, leading to improved performance and efficiency in locomotion planning and control. Additionally, our approach achieves a higher control frequency than previous LNN methods, demonstrating its potential for real-world deployment on quadrupeds.

Problem

• Evaluating Lagrangian Neural Networks for quadrupedal locomotion planning
• Improving sample efficiency and prediction accuracy in dynamics models
• Reducing computational complexity while retaining interpretability for real-time control

Innovation

• Lagrangian Neural Networks for dynamics learning
• Diagonalized Mass Matrix reduces computation complexity
• Higher control frequency enables real-time deployment