A Tube-based MPC Method for Path Tracking of Autonomous Vehicles with Disturbances at Handling Limits

Lateral stability preservation and disturbance rejection, such as crosswind resistance and unmodeled dynamics, remain critical challenges for autonomous vehicles (AVs) operating at handling limits during high-performance path tracking. This paper introduces a novel tube-based model predictive control (MPC) approach to enhance AV lateral stability and robustness. A composite strategy combining the modified lateral stability envelope (mLSE) and the equivalent Lyapunov stability-based yaw rate is proposed, effectively suppressing yaw rate oscillations while maintaining tracking accuracy. Furthermore, a semi-definite programming method is employed to derive a polyhedral robust positive invariant (pRPI) set and its associated feedback compensation measures, aiming to refine the mLSE and counteract disturbance effects. By integrating the mLSE, the equivalent yaw rate, and the pRPI set, the tube-based MPC controller is developed with mathematical proofs provided for the recursive feasibility and the input-to-state stability of the controller. Simulation experiments demonstrate that, in the presence of disturbances at handling limits, the proposed controller reduces yaw rate oscillations and improves tracking accuracy while maintaining robustness.