无人机三维追逃问题的半直接法求解

摘要

This paper addresses a novel method to solve the three-dimensional pursuit-evasion game of Unmanned Aerial Vehicles (UAVs).Since this method combines the variational method with the pseudospectral method,it belongs to a semi-direct method.Firstly,the differential equations and its constraint conditions for solving the optimal control law of one player are derived by means of the variational method.Therefore,the differential game problem is transformed into an optimal control problem.Secondly,the optimal control problem is further transformed into a nonlinear programming problem by pseudo-spectral method.Finally,the SNOPT solver is utilized to obtain the numerical solution and simulation is carried out.The simulation results show that both players have adopted the optimal control strategies,which verifies the correctness,validity and rapidity of the method.%提出一种新颖的无人机三维追逃问题的求解方法,该方法结合变分法和伪谱法,是一种半直接法求解思想.求解过程首先应用变分法给出求解一个局中人最优控制律的微分方程组及其约束条件,将微分对策问题转换为最优控制问题,然后通过伪谱法再将最优控制问题转换成非线性规划问题,最后利用SNOPT求解器对其进行数值求解,并进行了数值仿真.对仿真结果的分析表明,追逃双方在博弈过程中都采取了各自最优的控制策略,验证了该方法的正确性、有效性和快速性.