Stability of high-speed trajectory tracking for four-wheel steering vehicles under time-varying tire cornering stiffness

Current research predominantly focuses on enhancing vehicle driving stability when tires operate in the linear region. Thus, the effect of cornering stiffness on vehicle driving stability under nonlinear region remains an unresolved challenge. To address this issue, this paper proposes a novel nonlinear model predictive control (NMPC)-based four-wheel steering trajectory tracking controller that incorporates time-varying cornering stiffness. First, the longitudinal and lateral axle forces are estimated using a strong tracking unscented Kalman filter (STUKF); these estimated forces are then applied to a cornering stiffness estimator based on the unscented Kalman filter (UKF). Simulation tests under various scenarios are conducted using CarSim and Simulink, with comparisons made against the linear quadratic regulator (LQR) and conventional model predictive control (MPC) strategies. Finally, hardware-in-the-loop (HIL) experimental results verify that the proposed NMPC controller exhibits satisfactory trajectory tracking performance, stability, and real-time performance.