Koopman Operator Based Linear Model Predictive Control for Quadruped Trotting

TL;DR

This paper introduces a novel approach using the Koopman operator to create a high-fidelity linear model for quadruped robot control, enabling real-time adaptive locomotion with improved accuracy over traditional linearization methods.

Contribution

It is the first to apply Koopman operator theory to linear model predictive control for quadrupedal locomotion, enhancing model fidelity and control performance.

Findings

High fidelity tracking achieved on quadrupedal robot

Effective disturbance rejection demonstrated

First application of Koopman-based LMPC in this domain

Abstract

Online optimal control of quadruped robots would enable them to adapt to varying inputs and changing conditions in real time. A common way of achieving this is linear model predictive control (LMPC), where a quadratic programming (QP) problem is formulated over a finite horizon with a quadratic cost and linear constraints obtained by linearizing the equations of motion and solved on the fly. However, the model linearization may lead to model inaccuracies. In this paper, we use the Koopman operator to create a linear model of the quadrupedal system in high dimensional space which preserves the nonlinearity of the equations of motion. Then using LMPC, we demonstrate high fidelity tracking and disturbance rejection on a quadrupedal robot. This is the first work that uses the Koopman operator theory for LMPC of quadrupedal locomotion.