基于伪光谱方法月球软着陆轨道快速优化设计

根据软着陆轨道的特征和优化算法的特点,对探月器软着陆轨道状态方程进行合理的转化处理,使其更适合优化数值解法求解。在此基础上,使用伪光谱方法将软着陆轨道优化问题转为一个约束参数优化问题,然后采用乘子法处理约束条件,采用变尺度法求解处理后的参数优化问题,仿真结果表明此方法具有收敛速度快、对初始控制量不敏感、鲁棒性强的优点。

Legendre Pseudospectral Method for Rapid Lunar Soft-Landing Trajectory Optimization

Determining the best soft-landing trajectory of the lunar probe from the lunar satellite orbit involves the solution of an optimal control problem.This problem,which was considered to be difficult,was traditionally solved on the ground prior to flight.First,a new hypothesis was introduced according to the distinguished features of the lunar and soft-landing trajectory.Then,a set of dynamics and kinematics equations of motion was simplified,and this simplification reduced the computation load greatly.Next,the optimal control problem of soft-landing trajectory was transformed into a constrained parameter problem by using Legendre pseudospectral method,and nonlinearprogramming method(methods of multipliers and BFGS) was applied to solve the transformed problem.The simulation results show that the algorithm can generate a feasible soft-landing trajectory of about 300 seconds flight time in 30 seconds on the desktop computer.