Learning Forced Multibody Dynamics on Lie Groups

2026-07-14

AI Summary

This work addresses the challenge of modeling multibody system dynamics in scenarios where velocity data are missing or corrupted by noise. We propose a learning framework grounded in discrete forced Euler–Lagrange equations on Lie groups, which directly models dynamics in the manifold configuration space. This approach inherently preserves the system’s geometric structure and conservation laws while explicitly incorporating external control inputs. As the first framework to integrate Lie group geometric mechanics with purely position-based data-driven learning, our method synergistically combines discrete variational mechanics, geometric deep learning, and multibody dynamics modeling. Evaluated on both synthetic and real-world datasets, it demonstrates superior accuracy and robustness, effectively retaining physical priors and geometric invariances.

Abstract

We propose an architecture for learning the dynamics of mechanical systems based on discrete forced Euler-Lagrange equations on Lie groups using only position data. By formulating the dynamics directly on manifold-valued configuration spaces, the method naturally respects the geometric structure of the systems and preserves geometric invariants and conservation laws. The reliance on position measurements alone makes the framework applicable in settings where velocity data are unavailable or noisy. The approach extends naturally to multibody systems, accommodates external control inputs, and demonstrates strong performance on both synthetic and real-world datasets.

Problem

• multibody dynamics
• Lie groups
• position-only data
• forced systems
• geometric structure

Innovation

• Lie groups
• forced Euler-Lagrange equations
• geometric deep learning
• multibody dynamics
• position-only learning