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

• URL: http://arxiv.org/abs/2604.04221v2
• Date: Tue, 07 Apr 2026 21:39:59 GMT
• Title: RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments
• Abstract summary: Residual Koopman MPC (RK-MPC) is a data-driven model predictive control framework for quadruped locomotion.<n> RK-MPC augments a nominal template model with a compact linear residual predictor learned from data in lifted coordinates.<n> RK-MPC provides a practical, hardware-validated pathway for data-driven predictive control of quadrupeds in unstructured environments.
• Score: 1.4610038284393168
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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