Trajectory Tracking Control for Autonomous Vehicles based on Gaussian Process Regression and Adaptive Control Increment Constraint Adjustment

Under high-speed and extreme conditions, model mismatch of autonomous vehicles leads to degraded tracking accuracy and reduced lateral stability performance. To solve this problem, a Model Predictive Control (MPC) method using Gaussian Process Regression (GPR) is proposed in this paper. Based on this, an adaptive strategy for adjusting control increment constraints based on steering angle variation is developed using the prediction variance of GPR. This method employs GPR to learn the single-step residuals between the nominal 3-Degree-of-Freedom (3-DOF) vehicle model and its high-fidelity counterpart in Carsim, and then compensates for these residuals recursively within the MPC prediction horizon. Meanwhile, this method uses the prediction variance of GPR as the uncertainty indicator of the GPR model, and establishes an adaptive mapping relationship between the uncertainty parameters and the control increment constraints. When the uncertainty of the GPR model is high, the system actively reduces the control increment constraint. On the Carsim/Simulink platform, the proposed framework is validated under double lane change maneuvers. Simulation results show that, for high-speed dry-road scenarios, the GPR-MPC method lowers the lateral error peak by 16.2% and the heading error peak by 12.7%, compared to the baseline MPC. The A-GPR-MPC method with an adaptive control increment constraint adjustment strategy can, while maintaining the tracking accuracy, further reduce the peak yaw rate by 9.2% and the peak sideslip angle by 8.4%. Under the medium-speed wet road conditions, the A-GPR-MPC can further reduce the peak yaw rate by 9.0%, the peak sideslip angle by 19.0%, and the peak front wheel steering angle by 24.1%. These results demonstrate the proposed method's ability to enhance both tracking accuracy and lateral stability.