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

TL;DR

This paper introduces a continual learning approach to refine Koopman dynamics for high-dimensional legged robots, enabling effective linear control of complex nonlinear systems across various terrains.

Contribution

It presents the first scalable method to iteratively improve Koopman-based linear models for legged robot control using continual learning.

Findings

High control performance on multiple legged robots.

Monotonic convergence of linear approximation error.

Effective control across diverse terrains.

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.