Speed-Adaptive Horizon Model Predictive Control for Autonomous Vehicle Lateral Path Tracking Under Varying Speeds

This paper addresses the lateral path tracking problem for autonomous vehicles operating over a wide speed range by proposing a speed-adaptive horizon model predictive control (SAH-MPC) strategy. Unlike conventional fixed-horizon MPC, the proposed approach schedules both the prediction horizon Np and the control horizon Nc as explicit functions of the longitudinal speed. This design maintains high tracking accuracy at low speeds while enhancing stability and suppressing oscillations at high speeds. The controller is formulated using a bicycle-model representation of the lateral-yaw dynamics, with online linearization, forward-Euler discretization, and a quadratic programming solver enforcing hard constraints on steering angle and its increment, as well as soft stability constraints on sideslip angle, lateral acceleration, and tire slip angles. A co-simulation framework is established in MATLAB/Simulink and CarSim, and the algorithm is evaluated under double lane-change and slalom maneuvers at speeds from 36 to 90 km/h, with a fixed-horizon MPC (Np=20, Nc=5) as the baseline. Quantitative comparisons show that at 90 km/h, SAH-MPC reduces the peak lateral error by 33% (from 0.42 m to 0.28 m) and lowers the peak yaw-rate oscillation by 18%. Moreover, it helps maintain the sideslip angle within the prescribed ±4° safety bound, whereas the baseline exceeds this limit with a peak of 5.2°. These results demonstrate that SAH-MPC effectively improves the tracking-stability trade-off across a wide speed range without altering the core MPC structure, offering a simple yet practical enhancement for speed-varying autonomous driving.