End-to-end learning with stability control for autonomous vehicles in maneuvering environments remains a significant challenge. To solve this problem, a framework of dual-layer gated recurrent unit (GRU) and linear quadratic regulator (LQR) is proposed to realize the end-to-end learning of trajectory tracking control in autonomous vehicles. Considering the lateral stability and tracking ability of vehicles, a bicycle model is introduced to convert the coordinate into Frenét frame to realize the lateral and longitudinal motion decoupling. The subsequent analysis of the primary features is facilitated by SHapley Additive exPlanations (SHAP) via the vehicle data, which helps to build the data set for the learning model. In addition, an outer GRU network is used to plan the optimal geometry path and an inner GRU network is established to predict a real-time deviation displacement under various driving conditions. The lateral tracking effect of the steering parameters of the autonomous driving system is analyzed under various road conditions and speeds. The method is designed to eliminate the deviation displacement to realize the stability control. Then, a LQR controller and a feedforward controller are constructed to ensure the stability of the vehicle maneuver. The controller is dynamically adjusted according to the predicted deviation displacement. The double lane change (DLC) scenario has been implemented in the Carsim/Simulink environment for the purpose of verifying the effectiveness of the dual-layer GRU-LQR of the control system. Furthermore, the experimental results show that the lateral deviation of the proposed method is within a centimeter range. The proposed method is subsequently verified and has a satisfactory maneuvering effect.
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