Learning Forced Multibody Dynamics on Lie Groups

2026-07-14 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, quick

Summary

A new architecture is proposed for learning the dynamics of mechanical systems, utilizing discrete forced Euler-Lagrange equations formulated directly on Lie groups. This method uniquely relies solely on position data, making it highly suitable for scenarios where velocity measurements are either unavailable or noisy. By operating on manifold-valued configuration spaces, the approach inherently respects the geometric structure of the systems, thereby preserving geometric invariants and conservation laws. The framework is designed to extend naturally to complex multibody systems, accommodating external control inputs, and has demonstrated robust performance across both synthetic and real-world datasets, validating its practical applicability.

Key takeaway

For Robotics Engineers developing control systems or Machine Learning Engineers modeling complex physical dynamics, this approach offers a robust solution. If your projects are constrained by noisy or absent velocity sensor data, you should consider implementing Lie group-based dynamics learning from position data. This method ensures geometric consistency and conservation laws, potentially simplifying model development and improving prediction accuracy for multibody systems with external controls.

Key insights

Learning multibody dynamics on Lie groups using only position data preserves geometric structure and conservation laws.

Principles

• Formulate dynamics on manifold-valued spaces.
• Respect geometric structure for invariants.
• Position-only data enables broader applicability.

Method

The method uses discrete forced Euler-Lagrange equations on Lie groups, learning dynamics from position data alone to respect geometric structure and preserve invariants.

In practice

• Apply in systems lacking velocity sensors.
• Integrate external control inputs directly.
• Model complex multibody systems effectively.

Topics

• Lie Group Dynamics
• Multibody Systems
• Euler-Lagrange Equations
• Geometric Mechanics
• Position-Only Learning
• Control Systems

Best for: Research Scientist, AI Scientist, Robotics Engineer, Machine Learning Engineer

Related on AIssential

• CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts — Symplectic learning extends to non-conservative systems by enforcing geometric priors in a structured, lifted phase space.
• Non-intrusive Learning of Physics-Informed Spatio-temporal Surrogate for Accelerating Design — PISTM combines physics constraints and Koopman autoencoders for generalizable spatio-temporal surrogate modeling.
• Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control — Co-learning pH system models and optimal EB-PBC policies via alternating optimization ensures stability and robustness in control.
• MoSA: Motion-constrained Stress Adaptation for Mitigating Real-to-Sim Gap in Continuum Dynamics via Learning Residual Anisotropy — MoSA learns residual anisotropy and heterogeneity using physics priors to close the real-to-sim gap in continuum dynamics.
• The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space — Lie Diffuser Actor corrects geometric errors in VLA policies by operating intrinsically on the SE(3) manifold, ensuring geodesic optimality.
• Riemannian Deep Learning:Modules, Networks, and Geometries — A unified framework for Riemannian deep learning generalizes core components and introduces efficient geometric representations.

See Counsel's argued verdicts on the open AI decisions leaders are weighing →

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.