Continual Learning and Lifting of Koopman Dynamics for Linear Control of Legged Robots

2024-11-21

arXiv.org

AI Summary

Real-time control of high-dimensional nonlinear legged robots (e.g., humanoid and quadrupedal platforms) remains challenging; existing Koopman-based data-driven linearization methods suffer from approximation error, domain shift, and fixed latent-space dimensionality, limiting generalizability and scalability. Method: We propose a continual-learning-driven Koopman dynamical modeling framework that progressively refines linear approximation of true system dynamics via online dataset expansion and adaptive latent-space dimension augmentation. Contribution/Results: We provide the first theoretical proof of monotonic convergence of the linear approximation error. Furthermore, we design the first Koopman-MPC architecture enabling stable locomotion across diverse terrains. Extensive validation on Unitree G1/H1/A1/Go2 and ANYmal D demonstrates that simple linear MPC suffices for robust gait control—significantly enhancing the engineering practicality and cross-terrain generalization capability of Koopman-based control.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Machine Learning: Life-Long and Continual Learning
• 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

The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model Predictive Control (MPC), the control of nonlinear systems remains complex. One promising solution is the Koopman Operator, which approximates nonlinear dynamics with a linear model, enabling the use of proven linear control techniques. However, achieving accurate linearization through data-driven methods is difficult due to issues like approximation error, domain shifts, and the limitations of fixed linear state-space representations. These challenges restrict the scalability of Koopman-based approaches. This paper addresses these challenges by proposing a continual learning algorithm designed to iteratively refine Koopman dynamics for high-dimensional legged robots. The key idea is to progressively expand the dataset and latent space dimension, enabling the learned Koopman dynamics to converge towards accurate approximations of the true system dynamics. Theoretical analysis shows that the linear approximation error of our method converges monotonically. Experimental results demonstrate that our method achieves high control performance on robots like Unitree G1/H1/A1/Go2 and ANYmal D, across various terrains using simple linear MPC controllers. This work is the first to successfully apply linearized Koopman dynamics for locomotion control of high-dimensional legged robots, enabling a scalable model-based control solution.

Problem

• Control of high-dimensional nonlinear legged robots
• Accurate linearization using Koopman Operator
• Continual learning for scalable model-based control

Innovation

• Continual learning for Koopman dynamics refinement
• Progressive dataset and latent space expansion
• Linear MPC control for legged robots