An Optimal Fuel Guidance Law for Lunar SoftLanding Based on
 ThreeDimensional Dynamic Model

Abstract

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)

CLC Number:

V 448.2

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 Jiao Tong University, 2017, 51(6): 734-740.

References

［1］王劼，崔乃刚，刘暾，等. 定常推力登月飞行器最优软着陆轨道研究［J］. 高技术通讯，2003(4)：3942.
WANG Jie, CUI Naigang, LIU Dun, et al. Study on softlanding trajectories of constantthrustamplitude lunar probe ［J］. High Technology Letters, 2003(4): 3942.
［2］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 Junwei， QIAO Dong, CUI Pingyuan. Study on the optimal trajectories of lunar softlanding with fixedthrust using sqp method ［J］. Journal of Astronautics, 2006, 27(1): 99102.
［3］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 Journal of Control, Automation and Systems, 2011, 9(6): 11641172.
［4］王吉力，李俊峰，崔乃刚，等. 登月飞行器软着陆轨道的遗传算法优化［J］. 清华大学学报（自然科学版），2003，43(8)：10561059.
WANG Jie, LI Junfeng, CUI Naigang, et al. Genetic algorithm optimization of lunar probe softlanding trajectories ［J］. Journal of Tsinghua University (Science and Technology), 2003, 43(8): 10561059.
［5］ZHANG J H, PENG Q B. Lunar soft landing trajectory optimization by a chebyshev pseudospectral method ［J］. IEEE International Conference on Computer Science and Automation Engineering, 2011, 2: 425430.
［6］王明光，裴听国，袁建平. 基于伪光谱方法月球软着陆轨道快速优化设计［J］. 中国空间科学技术，2007(5)：2732.
WANG Mingguang, PEI Tingguo, YUAN Jianping. Legendre pseudospectral method for rapid lunar softlanding trajectory optimization ［J］. Chinese Space Science and Technology, 2007(5): 2732.
［7］CHANG S, WANG Y J, WEI X. Optimal soft lunar landing based on differential evolution［C］∥2013 IEEE International Conference on Industrial Technology. South Africa: IEEE, 2013: 152156.
［8］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 Dayi, LI Tieshou, MA Xingrui. Numerical solution of TPBVP in optimal lunar soft landing ［J］. Aerospace Control, 2000(3): 4449.
［9］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 (4)：2127.
ZHAO Jisong, GU Liangxian, PAN Lei. Numerical solution of tpbvp for optimal lunar soft landing ［J］. Chinese Space Science and Technology, 2009(4), 2127.
［10］UENO S, YAMAGUCHI Y. 3dimensional nearminimum fuel guidance law of a lunar landing module ［C］∥Guidance, Navigation, and Control Conference and Exhibit. Portland, OR, USA: AIAA, 1999: AIAA993983.
［11］D’Souza C. An optimal guidance law for planetary landing ［C］∥Guidance, Navigation, and Control Conference. New Orleans, LA, USA: AIAA, 1997: AIAA973709.
［12］王大轶，李铁寿，严辉，等. 月球软着陆的一种燃耗次优制导方法［J］. 宇航学报，2000，21(4)：5563.
WANG Dayi, LI Tieshou, YAN Hui, et al. A suboptimal fuel guidance law for lunar soft landing ［J］. Journal of Astronautics, 2000, 21(4): 5563.
［13］王鹏基，张熇，曲广吉. 月球软着陆下降轨迹与制导律优化设计研究［J］. 宇航学报，2007，28(5)：11751179.
WANG Pengji, ZHANG He, QU Guangji. Design and optimization of the descending trajectory and guidance of lunar softlanding ［J］. Journal of Astronautics, 2007, 28(5):11731179.
［14］ZHOU J Y, TEO K L, ZHOU D, et al. Optimal guidance for lunar module soft landing ［J］. Nonlinear Dynamics and Systems Theory, 2010, 10(2): 189201.
［15］ASCHER U, RUSSELL R D. Reformulation of boundary value problems into “standard” form ［J］. SIAM Review, 1981, 23(2): 238254.

[1]	ZHAO Ziren1, DU Shichang1, HUANG Delin1, REN Fei2, LIANG Xinguang2. Modelling and Bottleneck Analysis of Product Quality in Transient Phase#br# of MultiStage Manufacturing Systems Based on Markovian Chains [J]. Journal of Shanghai Jiao Tong University, 2017, 51(10): 1166-1173.
[2]	ZHOU Penghui, MA Hongzhan, CHEN Dongping, CHEN Mengyue, CHU Xuening. Identification of Product Redesign Modules Based on#br# Fuzzy Random Failure Mode and Effects Analysis [J]. Journal of Shanghai Jiao Tong University, 2017, 51(10): 1189-1195.
[3]	LI Changxi1, 2, ZHOU Yan1, LIN Han3, LI Lingzhi1, GUO Ge1. TemporalSpatial Sequential Fusion Recognition Method of#br# Ballistic Missile Target Based on MIMOFNN Model [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1138-.
[4]	FENG Mingyue, HE Minghao, HAN Jun, YU Chunlai. High Resolution Direction of Arrival Estimation Based on#br# Covariance Fitting Estimation of Signal Parameters by#br# Rotational Invariance Technique Algorithm [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1145-.
[5]	?YANG Ping1,SHENG Jie1,WANG Yucheng2,LI Zhuyong1,JIN Zhijian1,HONG Zhiyong1. Quench Propagation Characteristics Influenced by NonUniform Properties of YBa2Cu3O7δ High Temperature Superconducting Tape [J]. Journal of Shanghai Jiaotong University, 2017, 51(9): 1090-1096.
[6]	WANG Xing, ZHOU Yipeng, TIAN Yuanrong, CHEN You, ZHOU Dongqing, HE Jiyuan. Sparse Decomposition for Frequency Modulation Radar Signal Based on#br# Advanced Genetic Algorithm and SinChirplet Atom [J]. Journal of Shanghai Jiao Tong University, 2017, 51(9): 1124-1130.
[7]	ZHANG Liangjun1, 2, LI Xiaoci1, WU Jingyi1, CAI Aifeng1. ThermalStructure Coupling Analysis of #br# Microgravity Environment Simulation Suspension Structure for #br# Large Space Deployable Mechanisms [J]. Journal of Shanghai Jiao Tong University, 2017, 51(8): 954-961.
[8]	XIA Hailiang1, 2, LIU Yakun1, 2, LIU Quanzhen3, LIU Baoquan3, FU Zhengcai1, 2. Metal Ablation Affected by Electrode Shapes Under#br# Long Continuing Lightning Current [J]. Journal of Shanghai Jiao Tong University, 2017, 51(8): 903-908.
[9]	GU Jiayang, XIE Yulin, TAO Yanwu, HUANG Xianghong, WU Jie. Numerical Simulation and Experimental Study on VortexInduced#br# Motion of a New Type of Floating Drilling Production Storage Offloading [J]. Journal of Shanghai Jiao Tong University, 2017, 51(7): 878-885.
[10]	LIN Da, ZHU Yijia, WEI Xiaodong, WANG Zhiyu, ZHANG Wugao. Combustion and Particle Emission Characteristics Affected by#br# Fuel Supply Parameters for a Diesel Engine Fuelled with#br# Polyoxymethylene Dimethyl Ethers/Diesel [J]. Journal of Shanghai Jiao Tong University, 2017, 51(7): 787-795.
[11]	MENG Qingyang1, YAN Weiwu1, HU Yong1, CHENG Jianlin1, CHEN Shihe2, ZHANG Xi2. Model Identification Based on Subspace Model Identification of#br# Superheated Steam System in UltraSupercritical CoalFired Power Unit [J]. Journal of Shanghai Jiao Tong University, 2017, 51(6): 672-678.
[12]	JIANG Huajuna, CAI Yana, b, LI Chaohaoa, LI Fanga, b, HUA Xueminga, b. Recognition Method for Gas Pores on XRay Image of Lap Joints#br# Based on the Improved Sobel Algorithm [J]. Journal of Shanghai Jiao Tong University, 2017, 51(6): 665-671.
[13]	DONG Guanhua,YIN Qin,YIN Guofu,XIANG Zhaowei. Identification and Modeling of Coupling Dynamic Stiffness in Joints of Machine Tool [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1263-1434.
[14]	XIE Qijiang,YU Haidong. Coupling Relationship Between Loads on Cutterhead of Tunnel Boring Machine and Contact Stiffness of Gripper Shoes and Rocks [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1269-1275.
[15]	ZHONG Jianlin1,MA Dawei1,REN Jie1,LI Shijun2,WANG Xu3. Static Compression Analysis of Rubber Hollow Cylinder Based on Plane Strain Assumption [J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1276-1280.