Integrated RBF-EKF observer and MPC for simultaneous trajectory tracking and stability control of 4WID-EVs

Accurate trajectory tracking and stable motion control under extreme operating conditions remain significant challenges for Four-Wheel-Independent-Drive Electric Vehicles (4WID-EVs). To address these issues, this paper focuses on state estimation and trajectory tracking control, proposes novel algorithms and conducts comprehensive simulations and experiments. Firstly, a high-fidelity 7-Degree-of-Freedom (7-DOF) vehicle dynamics model is established and validated against a commercial CarSim model, providing a reliable platform for controller design. Secondly, to tackle the difficulty in directly measuring key states like the sideslip angle, a hybrid observer that fuses a Radial Basis Function Neural Network (RBFNN) with an Extended Kalman Filter (EKF) is proposed. The RBFNN, optimized via the control variates method, generates a "pseudo-sideslip angle," which is then fed as an observation into the EKF, significantly enhancing estimation accuracy. Thirdly, a Linear Time-Varying Model Predictive Control (LTV-MPC) based trajectory tracking controller is designed. The nonlinear vehicle model is linearized at each sampling point, transforming the optimal control problem into a Quadratic Programming (QP) problem. Crucially, explicit mathematical relationships between control variables and stability indices (sideslip angle, tire slip angle) are derived and embedded as stability constraints within the optimization framework, effectively coordinating tracking accuracy with vehicle stability. Finally, co-simulations (CarSim/Simulink) and Hardware-in-the-Loop (HIL) tests on a dSPACE platform are performed. Results demonstrate that the proposed RBF-EKF observer reduces the Root-Mean-Square Error (RMSE) of sideslip angle estimation by up to 30.43% compared to the standard EKF. Furthermore, the proposed Model Predictive Control (MPC) controller outperforms the traditional Preview Driver Model (PDM), reducing the maximum lateral tracking error and yaw angle error by 0.30 m and 3.11°, respectively, in high-speed double-lane-change scenarios, while ensuring all states remain within stability boundaries.