Model Predictive Controller Design Based on Residual Model Trained by Gaussian Process for Robots

Model mismatch is inevitable in robot control due to the presence of unknown dynamics and unknown perturbations. Traditional model predictive control algorithms are usually based on constant value assumptions and are not able to overcome the degradation of controller performance due to model mismatch. In this paper, a model predictive control (MPC) algorithm based on Gaussian process regression (GPR) is proposed. Firstly, the kinematic equations of the mobile robot are established by the mechanistic analysis method; similarly, the dynamics of the mobile robot system are modeled using the second-class Lagrangian equations. Secondly, the problem of stability and reliability degradation due to model mismatch during the operation of mobile robot is considered. This paper uses a MPC algorithm with a main model plus residual model to solve the MPC closed-loop control strategy. The state at each moment is decomposed into a predicted state based on the first-principles model and a residual state. The residual state is learned by GPR in real-time and used to compensate for deviations between the real process model and the predicted model. The proposed method requires fewer data samples, enhancing the technique's practicality. Finally, the simulation results show that the proposed algorithm is more stable and achieves the desired tracking faster. Compared with the MPC algorithm, the arrival time of the system is reduced by 28% and the speed error is controlled within 0.07.