Optimum Path Tracking Control for the Inverse Problem of Vehicle Handling Dynamics Based on the hp-Adaptive Gaussian Pseudospectral Method

We propose a vehicle path-tracking method based on the hp-adaptive Gaussian pseudospectral method (GPM), which tackles the problem of the slow convergence speed of the optimal control of vehicle path tracking. First, we establish a kinematic vehicle model by considering the path constraints and boundary constraints during the process of tracking the described path of a vehicle. Subsequently, finding the minimum error of the lateral distance between the prescribed path and the expected trajectory is set as the performance objective function. Finally, the vehicle path tracking problem is transformed into an optimal control problem. The optimization algorithm is combined with the sequential quadratic programming algorithm to optimize problems related to the control and state variables and the boundary and path constraints. The simulated results show that the hp-adaptive GPM can improve the convergence rate of the optimal control problem for vehicle path tracking. The proposed hp-adaptive pseudospectral method has a higher solving efficiency compared with traditional approaches for the vehicle path-tracking problem. Concurrently, the verification results of a real vehicle test indicate the feasibility of the proposed algorithm for solving the vehicle path tracking problem. This research provides valuable insight into the design work of lane changes and is an important step towards the design of feedback control laws for path tracking.