Model predictive control with residual learning and real-time disturbance rejection: Design and experimentation

Model Predictive Control (MPC) deteriorates with low-quality prediction models and unknown external disturbances. Simply incorporating residual physics learning or uncertainty/disturbance rejection alone as in existing studies often yields limited performance gains for MPC. In this study, we integrate sparse Gaussian Process (GP) and Generalized Extended State Observer (GESO) within MPC, forming the GP-MPC-GESO controller. In this framework, GP learns the residual physics, improving the prediction model while reducing GESO's disturbance estimation load. Meanwhile, GESO estimates the GP's remaining residual uncertainties and external disturbances in real time and is directly incorporated into MPC prediction model. The synergy between GP residual learning and real-time GESO in managing uncertainties and disturbances significantly enhances MPC's tracking control performance with a simplified nominal physical model. Comparative trajectory tracking control experiments on Mecanum Wheel Mobile Robots in both indoor and outdoor environments under various settings demonstrate that the proposed GP-MPC-GESO controller reduces RMSE by 12.4% and 16.2% compared to the state-of-the-art MPC-GESO controller in indoor and outdoor Lemniscate tracking, respectively. The video demonstration of this work is available at https://drive.google.com/file/d/1LC81S093iogWxzyBcHFuWGLth1u-Wwcx/view?usp=drive_link.