MPC-Based Trajectory Tracking Controller for Autonomous Vehicles

Trajectory tracking control is a critical component of the autopilot system, essential for achieving high-performance autonomous driving. This paper presents the design of a stable, reliable, accurate, fast, and robust trajectory tracking controller. Specifically, a lateral and longitudinal trajectory tracking controller based on a linear parameter time-varying model predictive control (LPV-MPC) framework is designed. Firstly, a three-degree-of-freedom vehicle dynamics model and a tracking error model are established. Secondly, a multi-objective function and constraints considering tracking accuracy and lateral stability are formulated, and the quadratic programming (QP) method is employed to solve the optimization problem. Finally, PID speed tracking control is introduced in the longitudinal control scheme for comparison with the proposed MPC longitudinal speed control. A step velocity tracking test validates the effectiveness of the MPC speed tracking controller. In the lateral control scheme, double lane change and circumferential tests are designed to assess the comprehensive performance of the controller under medium-low adhesion road conditions. Additionally, the trajectory tracking performance of the proposed MPC controller is evaluated by comparing it with traditional Sliding Mode Control (SMC) and Linear Quadratic Regulator (LQR) trajectory tracking controllers. The simulation results indicate that the maximum heading error of the MPC controller is less than 0.09 rad, the heading error remains within 0.05 rad, and the front wheel angle stabilizes within 7.5 degrees under both operating conditions. Furthermore, the MPC controller ensures tracking accuracy and smoothness without any obvious jitter while minimizing control inputs to achieve optimal control, thereby significantly enhancing the accuracy and stability of the vehicle's trajectory tracking.