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

2026-04-05

AI Summary

This work addresses model mismatch in quadrupedal robots operating in unstructured off-road environments, where contact variations and terrain disturbances degrade control performance. To this end, the authors propose the RK-MPC framework, which integrates a nominal template model with a data-driven linear residual predictor in the Koopman lifting space to correct model errors, embedded within a convex quadratic programming-based model predictive controller for efficient real-time execution. A key innovation is the introduction of a residual correction mechanism with provable multi-step prediction error bounds, which significantly reduces sensitivity to the choice of observable function dictionary while preserving the structural advantages and constraint-handling capabilities of MPC. Experiments demonstrate 500 Hz real-time performance in both Gazebo simulations and on the Unitree Go1 hardware, achieving robust blind locomotion across challenging terrains including grass, gravel, snow, and ice.

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.

Problem

• quadruped locomotion
• model mismatch
• offroad environments
• contact variability
• terrain disturbances

Innovation

• Residual Koopman
• Model Predictive Control
• Quadruped Locomotion
• Data-driven Control
• Lifted Coordinates