Reduced-order Control and Geometric Structure of Learned Lagrangian Latent Dynamics

2026-02-09

AI Summary

This work addresses the challenge of achieving high-performance, theoretically grounded control for high-dimensional Lagrangian systems—such as soft robots—where accurate dynamical models are often unavailable. The authors propose a structure-preserving latent-variable reduced-order control framework that leverages Riemannian-geometric projection to construct a latent-space dynamics model retaining the intrinsic Lagrangian structure. Within this framework, they derive interpretable stability conditions and a tracking control law, and further extend the approach to underactuated systems by incorporating learned actuation modes. Implemented via structure-preserving neural networks, the method demonstrates both modeling accuracy and theoretical validity in simulation and physical experiments, enabling stable and efficient control of high-dimensional systems.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Machine Learning: Learning with Manifolds
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or soft robots. While neural architectures can learn to approximate complex dynamics, they are either limited to low-dimensional systems or provide only limited formal control guarantees due to a lack of embedded physical structure. This paper introduces a latent control framework based on learned structure-preserving reduced-order dynamics for high-dimensional Lagrangian systems. We derive a reduced tracking law for fully actuated systems and adopt a Riemannian perspective on projection-based model-order reduction to study the resulting latent and projected closed-loop dynamics. By quantifying the sources of modeling error, we derive interpretable conditions for stability and convergence. We extend the proposed controller and analysis to underactuated systems by introducing learned actuation patterns. Experimental results on simulated and real-world systems validate our theoretical investigation and the accuracy of our controllers.

Problem

• reduced-order control
• Lagrangian systems
• model-based control
• high-dimensional dynamics
• physical structure

Innovation

• structure-preserving reduced-order modeling
• learned Lagrangian dynamics
• latent space control
• Riemannian model reduction
• actuation pattern learning