Robust Tube-MPC Trajectory Tracking Control for Four-Wheel Independent Steering Vehicles on Intermittent Snowy and Icy Roads

Abstract Four-Wheel Independent Steering (4WIS) Vehicles can independently control the angle of each wheel, demonstrating superior trajectory tracking performance under normal conditions. However, on intermittent icy and snowy roads, the presence of time-varying adhesion coefficients, time-varying cornering stiffness, and the irregularities due to ice and snow accumulation introduce multiple uncertainties into the steering system, significantly degrading the trajectory tracking performance of 4WIS vehicles. In response, this paper proposes a robust Tube Model Predictive Control (Tube-MPC) trajectory tracking control method for 4WIS. In this method, a Bi-directional Long Short-Term Memory neural network is established for online estimation of tire cornering stiffness under different road adhesion coefficients, providing accurate estimation of time-varying cornering stiffness for each wheel to mitigate the uncertainties of time-varying adhesion coefficients and cornering stiffness. Additionally, considering the road irregularities caused by snow accumulation on intermittent icy and snowy roads, a trajectory tracking controller that integrates Tube-MPC and robust Sliding Mode Control is proposed. The nominal MPC model, developed from the estimated tire cornering stiffness, utilizes the sliding surface and the optimal auxiliary control unit law for the tube is derived from the reaching law in Tube-MPC, aiming to minimize the trajectory tracking error while enhancing the controller's robustness against road uncertainties. The experiments show that the proposed method outperforms the Tube-MPC algorithm in terms of trajectory accuracy and robustness. This method demonstrates excellent trajectory tracking accuracy under intermittent icy and snowy road conditions, and it lays a theoretical foundation for future studies on vehicle stability and trajectory tracking under such road conditions.