求解最优月球软着陆轨道的隐式打靶法

doi:10.7527/S1000-6893.2018.22641

电子电气工程与控制

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求解最优月球软着陆轨道的隐式打靶法

彭坤¹, 彭睿², 黄震¹, 张柏楠¹

1. 中国空间技术研究院载人航天总体部, 北京 100094;
2. 北京航空航天大学, 北京 100083

收稿日期:2018-09-03 修回日期:2018-11-21 出版日期:2019-07-15 发布日期:2018-12-17
通讯作者: 彭坤 E-mail:bhkpeng@126.com
基金资助:
载人航天预先研究项目（010201）

Implicit shooting method to solve optimal Lunar soft landing trajectory

PENG Kun¹, PENG Rui², HUANG Zhen¹, ZHANG Bainan¹

1. Institute of Manned Space System Engineering, China Academy of Space Technology, Beijing 100094, China;
2. Beihang University, Beijing 100083, China

Received:2018-09-03 Revised:2018-11-21 Online:2019-07-15 Published:2018-12-17
Supported by:
Manned Space Pre-research Projects (010201)

摘要/Abstract

摘要： 基于间接法思想推导出一种隐式打靶法对月球软着陆轨道优化问题进行了研究。建立月球软着陆轨道归一化系统模型，利用庞特亚金极大值原理将月球软着陆轨道优化问题转化为满足最优必要条件的两点边值问题（TPBVP），采用一种新的时间变量使两点边值问题的终端时刻固定，同时将终端时刻看作状态变量并引入终端时刻的哈密尔顿函数值作为隐式终端条件，提出一种隐式打靶法对含有隐式终端条件的两点边值问题进行迭代求解，从而得出燃料消耗最优的月球软着陆轨道。仿真结果表明，与直接法和混合法相比，隐式打靶法优化精度高，收敛速度快，实现了月球软着陆过程燃料消耗最优。同时应用隐式打靶法求解不同发动机推力值的最优月球软着陆问题，得到燃料消耗最小的最优推重比，可为月面着陆器下降级发动机选型提供参考。

关键词: 月球软着陆, 最优轨迹, 两点边值问题, 隐式打靶法, 最优控制

Abstract: Based on the idea of indirect method, an implicit shooting method is derived to solve the optimal Lunar soft landing trajectory. Firstly, a normalization system model of Lunar soft landing trajectory is established. Secondly, based on the Pontryagin's maximum principle, the optimization of Lunar soft landing trajectory is converted into a Two-Point Boundary Value Problem (TPBVP) of satisfying the necessary conditions for optimality. A new time variable is adopted, and then the terminal time-free TPBVP is changed into terminal time-fixed TPBVP. Moreover, the terminal time is considered as state variable and the value of the Hamiltonian function in terminal time is introduced as an implicit terminal condition. Finally, an implicit shooting method is proposed to solve the TPBVP with implicit terminal condition. The simulation results show that the proposed method has better convergence speed and higher optimization precision than the direct method and the hybrid method, achieving the goal of optimal fuel consumption in Lunar soft landing process. Meanwhile, the optimal Lunar soft landing trajectory with different engine thrusts is studied by this method, obtaining the optimal thrust-weight ratio with lowest fuel consumption. This can provide references for the engine selection of Lunar lander descent stage.

Key words: Lunar soft landing, optimal trajectory, two-point boundary value problem, implicit shooting method, optimal control

中图分类号:

V412.4

彭坤, 彭睿, 黄震, 张柏楠. 求解最优月球软着陆轨道的隐式打靶法[J]. 航空学报, 2019, 40(7): 322641-322641.

PENG Kun, PENG Rui, HUANG Zhen, ZHANG Bainan. Implicit shooting method to solve optimal Lunar soft landing trajectory[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(7): 322641-322641.

参考文献

[1] MAKUSHENKO Y, MURTAZIN R, DERECHIN A,et al. The cislunar spaceport:An effective approach for the crew delivery to the lunar surface[C]//68th International Astronautical Congress (IAC), 2017.
[2] LI C L, LIU J J, REN X, et al. The Chang'e 3 mission overview[J]. Space Science Reviews, 2015, 190(1-4):85-101.
[3] LEE A Y.Fuel-efficient descent and landing guidance logic for a safe lunar touchdown[C]//AIAA Guidance,Navigation, and Control Conference. Reston, VA:AIAA, 2011.
[4] NASA. NASA's exploration systems architecture study:NASA-TM-2005-214062[R]. Washington, D.C.:NASA,2005.
[5] LI Z Y, LI H J. Lunar soft landing trajectory optimization methods[C]//International Conference on Cyberspace Technology, 2014.
[6] 张建辉, 张峰. 月球软着陆轨道优化方法比较研究[J]. 工程数学学报, 2012, 29(3):355-365. ZHANG J H, ZHANG F. Research on trajectory optimization of lunar soft landing[J]. Chinese Journal of Engineering Mathematics, 2012, 29(3):355-365(in Chinese).
[7] 王大轶, 李铁寿, 马兴瑞. 月球最优软着陆两点边值问题的数值解法[J]. 航天控制, 2000(3):44-49. WANG D Y, LI T S, MA X R. Numerical solution of TPBVP in optimal lunar soft landing[J]. Aerospace Control, 2000(3):44-49(in Chinese).
[8] 孙军伟, 乔栋, 崔平远. 基于SQP方法的常推力月球软着陆轨道优化方法[J]. 宇航学报, 2006, 27(1):99-102. SUN J W, QIAO D, CUI P Y. Study on the optimal trajectories of lunar soft landing with fixed-thrust using SQP method[J]. Journal of Astronautics, 2006, 27(1):99-102(in Chinese).
[9] TU L H, YUAN J P, LUO J J, et al. Lunar soft landing rapid trajectory optimization using direct collocation method and nonlinear programming[C]//The Second International Conference on Space Information Technology, 2007.
[10] 朱建丰, 徐世杰. 基于自适应模拟退火遗传算法的月球软着陆轨道优化[J]. 航空学报, 2007, 28(4):806-812. ZHU J F, XU S J. Optimization of lunar soft landing trajectory based on adaptive simulated annealing genetic algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28(4):806-812(in Chinese).
[11] 段佳佳, 徐世杰, 朱建丰. 基于蚁群算法的月球软着陆轨迹优化[J]. 宇航学报, 2008, 29(2):476-481. DUAN J J, XU S J, ZHU J F. Optimization of lunar soft landing trajectory based on ant colony algorithm[J]. Journal of Astronautics, 2008, 29(2):476-481(in Chinese).
[12] 彭祺擘, 李海阳, 沈红新. 基于高斯-伪谱法的月球定点着陆轨道快速优化设计[J]. 宇航学报, 2010, 31(4):1012-1016. PENG Q B, LI H Y, SHEN H X. Rapid lunar exact-landing trajectory optimization via gauss pseudospectral method[J]. Journal of Astronautics, 2010, 31(4):1012-1016(in Chinese).
[13] PARK B G, TAHK M J. Three-dimensional trajectory optimization of soft lunar landings from the parking orbit wIth consideratIons of the landing site[J]. International JournaI of Control, Automation and Systems, 2011, 9(6):1164-1172.
[14] ZHANG J H, PENG Q B. Lunar soft landing trajectory optimization by a chebyshev pseudospectral method[C]//IEEE InternationaI Conference on Computer Science and Automation Engjneering. Piscataway, NJ:IEEE Press, 2011.
[15] 单永正, 段广仁, 吕世良. 月球探测器软着陆的最优控制[J]. 光学精密工程, 2009, 17(9):2153-2158. SHAN Y Z, DUAN G R, LV S L. Optimal control for soft landing of lunar probe[J]. Optics and Precision Engineering, 2009, 17(9):2153-2158(in Chinese).
[16] 曹涛, 董长虹. 基于组合优化策略的月球软着陆最优轨道设计[J]. 北京航空航天大学学报, 2012, 38(11):1537-1541. CAO T, DONG C H. Optimization of lunar soft landing trajectory based on combinational algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, 38(11):1537-1541(in Chinese).
[17] 彭坤, 果琳丽, 向开恒, 等. 基于混合法的月球软着陆轨迹优化[J]. 北京航空航天大学学报, 2014, 40(7):910-915. PENG K, GUO L L, XIANG K H, et al. Optimization of lunar soft landing trajectory based on hybrid method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2014, 40(7):910-915(in Chinese).
[18] 赵吉松, 谷良贤, 潘雷. 月球最优软着陆两点边值问题的数值解法[J]. 中国空间科学技术, 2009, 29(4):21-27. ZHAO J S, GU L X, PAN L. Numerical solution of TPBVP for optimal lunar soft landing[J]. Chinese Space Science and Technology, 2009, 29(4):21-27(in Chinese).
[19] TAPLEY B D,WILLIAMSON W E.Comparison of linear and riccati equations used to solve optimal control problems[J]. AIAA Journal, 1972, 10(9):1154-1159.
[20] 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, 2017, 51(6):734-740. XIAO Y, RUAN X G, WEI R Y. An optimal fuel guidance law for lunar soft-landing based on three-dimensional dynamic model[J]. Journal of Shanghai Jiao Tong University, 2017, 51(6):734-740(in Chinese).
[21] ASCHER U, RUSSELL R D. Reformulation of boundary value problems into "standard" form[J]. SIAM Review, 1981, 23(2):238-254.
[22] 张光澄. 最优控制计算方法[M]. 成都:成都科技大学出版社, 1991:113-117. ZHANG G C. Computational method of optimal control problems[M]. Chengdu:Chengdu University of Science and Technology Press, 1991:113-117(in Chinese).

E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

求解最优月球软着陆轨道的隐式打靶法

Implicit shooting method to solve optimal Lunar soft landing trajectory

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