基于3维模型的月球表面软着陆燃耗最优制导方法

摘要/Abstract

摘要： 为了解决月球探测器软着陆燃耗最优制导问题，基于变分法设计了最优制导律.首先，基于变分法，将问题转换为终端时间自由且带有条件约束的两点边值问题；其次，引入了时间尺度变换方法，将终端时间自由的两点边值转换成终点时间固定的两点边值问题；最后，为了确保两点边值的求解迭代算法收敛，提出了一种终端时间和共轭变量初始值猜测方法，并通过数值方法取得终端时间和共轭变量精确的初始值以及着陆过程中最优制导律和3维最优轨迹.仿真实验结果表明，所提方法有效，算法可收敛，并且实现了燃耗最优制导.

关键词: , 月球软着陆, 3维动力学模型, 燃耗最优, 制导律, 两点边值问题

Abstract: Optimal fuel consumption is required in the process of lunar softlanding. An optimal fuel guidance law is designed with the method of variational calculus. The problem is converted into the terminal timefree twopoint boundary value problem (TPBVP) based on variational calculus. Then a timescale method is used to convert the terminal timefree TPBVP into terminal timefixed TPBVP. Finally, an initial adjoint variables guess approach is introduced to assure the convergence of the numerical iteration method for solving TPBVP. The exact terminal time and initial value of adjoint variables are calculated by numerical method, as well as the optimal fuel guidance law and 3D optimal trajectory. The simulation results show that the proposed method is valid and achieve the goal of optimal fuel guidance.

Key words: , lunar softlanding, 3dimensional dynamic model, optimal fuel, guidance law, twopoint boundary value problem (TPBVP)

中图分类号:

V 448.2

肖尧,阮晓钢,魏若岩. 基于3维模型的月球表面软着陆燃耗最优制导方法[J]. 上海交通大学学报（自然版）, 2017, 51(6): 734-740.

XIAO Yao,RUAN Xiaogang,WEI Ruoyan. An Optimal Fuel Guidance Law for Lunar SoftLanding Based on
ThreeDimensional Dynamic Model[J]. Journal of Shanghai Jiaotong University, 2017, 51(6): 734-740.

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