一种燃料最省的火星精确着陆动力下降段快速轨迹优化方法

针对火星精确着陆问题，给出一种燃料最省的火星着陆动力下降段快速轨迹优化方法。首先以燃料最省为指标建立了着陆器动力下降段轨迹优化问题模型，然后利用极大值原理对该模型的推力大小、推力方向与协状态变量之间的关系进行分析，得出着陆器推力只能以最大或最小推力工作、推力方向和与速度对应的协状态矢量方向相同的结论。并以此为基础，将原问题的状态微分方程和协状态微分方程转换为有限个推力为常值的分段函数，推导每段内微分方程的解析表达式，给出了动力下降段轨迹优化方法的算法流程；最后通过数学仿真将所提出的方法与凸规划、多项式制导方法进行比较。结果表明该方法不仅避免了多项式方法没有考虑推力约束及燃料消耗的缺陷，而且在计算效率方面较凸规划方法有大幅度提高。

A Rapid Power Descent Phase Trajectory Optimization Method with Minimum Fuel Consumption for Mars Pinpoint Landing

Aiming at the Mars Pinpoint landing problem, a rapid trajectory optimization method with minimum fuel consumption during power descent phase is presented. Firstly, a trajectory optimization model with minimum fuel for Mars power descent phase is established; Secondly, the relationship between thrust magnitude and direction and costate variables is analyzed based on the maximum principle, and a conclusion that the lander should work at max or min thrust magnitude and the thrust direction should be in the direction of the costate vectors corresponding to the velocity states is obtained，on the basis of the conclusion the state and costate differential equations are converted to corresponding piecewise functions with constant thrust. Then, the analytical formulas of the piecewise functions are derived when the terminal time is given. Further, the algorithm flow chart of trajectory optimization for Mars powed descent phase is given. And last, mathematical simulation is conducted to compare the method to convex optimization method and polynomial method. Results show that the proposed method avoids the flaws of polynomial method and has more computational efficiency than convex optimization method.