A New Method for the Optimal Control Problem of Path Planning for Unmanned Ground Systems

To model the optimal control problem of path planning for unmanned ground systems (UGSs), the motion and boundary constraints are described first by using the mathematical model proposed in this paper, and the time-energy performance indicators are described by the Bolza cost function. Since the traditional symplectic algorithm hardly solves the problem with uncertain time, the pseudospectral method, almost the only way to solve the optimal control problem of path planning while the rapid path planning is difficult to achieve, is prone to the phenomenon named "Curse of Dimensionality" with increasing the number of discrete points. The symplectic pseudospectral method for improving the efficiency and the precision of the calculation, based on the symplectic theory, third kind of generation function and pseudospectral method is first proposed in this paper. Furthermore, the one-sided approximation is designed, and the one-sided symplectic pseudospectral (OSSP) algorithm is established to solve the model introduced in this paper. Finally, the experiments are conducted using the OSSP method and the pseudospectral method, respectively, to verify the feasibility and the efficiency of the method. The results show that the OSSP is the method with the highest accuracy, efficiency, and good stability to solve the optimal control problem of path planning for UGS, and it has great maneuverability and feasibility for practical application.