用数据驱动的残差模型提升四足机器人复杂地形的运动预测与控制精度。
RK-MPC: Residual Koopman Model Predictive Control for Quadruped Locomotion in Offroad Environments
- 在升维空间中学习线性残差项，修正接触与地形扰动带来的模型偏差。
- 在500Hz下实时运行，实现雪地、冰面等复杂地形上的稳定行走。
- 对观测变量选择不敏感，适合实际硬件部署的鲁棒控制。
本文提出基于数据驱动的残差柯普曼模型预测控制（RK-MPC），用于四足机器人在非结构化地形下的运动控制。该方法在基准模板模型基础上，引入一个从数据中学习的紧凑线性残差预测器，该预测器位于升维坐标系中，可系统性纠正因接触变化和地形扰动引起的模型失配，并对多步预测误差提供可证明的上界。残差模型嵌入凸二次规划型MPC框架，生成可在机载设备以500 Hz频率运行的滚动时域控制器，同时保持优化控制的约束处理优势。我们在Gazebo仿真和Unitree Go1硬件平台上进行了评估，验证了其在草地、碎石、雪地、冰面等多种挑战性地形下的可靠盲行能力，涵盖多种步态调度和接触扰动场景。相比基于柯普曼/EDMD的基线方法（使用单项式及$SE(3)$结构基函数），本方法显著提升了多步预测精度与闭环性能，且对观测变量选择不敏感。总体而言，RK-MPC为非结构化环境中四足机器人的数据驱动预测控制提供了可落地、经硬件验证的技术路径。
原文摘要 · Abstract (English)
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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