基于Gauss伪谱法和直接打靶法结合的月球定点着陆轨道优化

摘要

Rapid lunar exact-landing trajectory optimization was studied by combining a new optimal control method-Gauss Pseudospectral Method (GPM) with the traditional direct shooting method. Landing dynamics equation in high precision model was educed. Aiming at the characters of optimization method and the difficulties in optimization of lunar soft landing trajectory with many constraints, a serial optimization strategy was proposed. Firstly, control variables and state variables were dispersed, and control variables and flying time were used as optimal variables. By giving fewer Gauss nodes, initial values were obtained using GPM, and a serial optimization framework was adopted to obtain the optimal solution from a feasible solution. Then the control variables were dispersed at Gauss nodes, the precise optimal solution was obtained by direct shooting method. Simulation results show that the methodology and strategy for the optimal trajectory design have good robustness and strong convergence-%将一种求解最优控制问题的新方法—高斯伪谱法( Gauss Pseudospectral Method-GPM)和传统的直接打靶法有效结合,对月球着陆器定点软着陆轨道快速优化问题做出了研究.推导了高精度模型下着陆动力学方程.针对优化方法各自的特点和多约束条件下最优月球软着陆轨道设计的难点,提出了问题求解的串行优化策略:将控制变量和终端时间一同作为优化变量,同时离散控制变量与状态变量,取较少的Gauss节点,利用GPM求解初值,初值的求解采用从可行解到最优解的串行优化策略；在Gauss节点上离散控制变量,利用直接打靶法求解精确最优解.仿真结果表明,本文提出的轨道优化方法具有较强的鲁棒性和快速收敛性.