Adaptive UKF with BKA-optimized Gaussian process regression for lateral stability control of three-axle 6WS vehicles

To improve the lateral stability of a three-axle six-wheel steering (TA-6WS) vehicle under extreme driving conditions, this paper proposes a direct yaw moment control (DYC) strategy that integrates a Gaussian Process Regression (GPR) model optimized by the Black Kite Algorithm (BKA) into an adaptive Unscented Kalman Filter (AUKF). First, a nine degrees of freedom TA vehicle dynamics model with equivalent stiffness is established to capture full-wheel load transfer. Then, a BKA-GPR-based sideslip angle estimator is developed to provide both state estimates and their uncertainty. On this basic, a vehicle state fusion estimation method is designed by further combining the AUKF algorithm and the TA vehicle dynamics model, to improve the estimation accuracy. Finally, a hierarchical DYC scheme is designed, where the upper-level additional yaw moment is regulated by an adaptive nonsingular fast terminal sliding mode (ANFTSM) controller, and the lower-level force allocation is achieved through optimal control. Simulation results show that the proposed BKA-GPR-AUKF method significantly improves sideslip angle estimation accuracy without degrading the estimation of longitudinal velocity and yaw rate, achieving reductions of up to 73% and 76% in root mean square error and absolute error (AE), respectively. Furthermore, compared with the NFTSM controller, the ANFTSM controller achieves higher tracking accuracy for both the reference yaw rate and the reference sideslip angle, with the maximum AE values reduced from 0.1116 rad/s and 0.0695 rad to 0.0691 rad/s and 0.0525 rad, corresponding to reductions of 38% and 24%, respectively.