RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments

TL;DR

RK-MPC introduces a data-driven, residual Koopman model predictive control framework for quadruped robots, enhancing prediction accuracy and robustness in off-road environments while maintaining real-time performance.

Contribution

The paper develops RK-MPC, a novel Koopman-based MPC that incorporates a learned residual model for improved prediction and control of quadruped locomotion in complex terrains.

Findings

RK-MPC runs onboard at 500 Hz, enabling real-time control.

Demonstrated reliable locomotion across diverse off-road terrains.

Residual correction improves multi-step prediction and reduces sensitivity to observables.

Abstract

This paper presents Residual Koopman MPC (RK-MPC), a Koopman-based, data-driven model predictive control framework for quadruped locomotion that improves prediction fidelity while preserving real-time tractability. RK-MPC augments a nominal template model with a compact linear residual predictor learned from data in lifted coordinates, enabling systematic correction of model mismatch induced by contact variability and terrain disturbances with provable bounds on multi-step prediction error. The learned residual model is embedded within a convex quadratic-program MPC formulation, yielding a receding-horizon controller that runs onboard at 500 Hz and retains the structure and constraint-handling advantages of optimization-based control. We evaluate RK-MPC in both Gazebo simulation and Unitree Go1 hardware experiments, demonstrating reliable blind locomotion across contact disturbances, multiple gait schedules, and challenging off-road terrains including grass, gravel, snow, and ice. We further compare against Koopman/EDMD baselines using alternative observable dictionaries, including monomial and $SE(3)$-structured bases, and show that the residual correction improves multi-step prediction and closed-loop performance while reducing sensitivity to the choice of observables. Overall, RK-MPC provides a practical, hardware-validated pathway for data-driven predictive control of quadrupeds in unstructured environments. See https://sriram-2502.github.io/rk-mpc for implementation videos.