Fast solution to the free return orbit’s reachable domain of the manned lunar mission by deep neural network

doi:10.23919/JSEE.2023.000117

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (2): 495-508.doi: 10.23919/JSEE.2023.000117

• CONTROL THEORY AND APPLICATION • Previous Articles

Fast solution to the free return orbit’s reachable domain of the manned lunar mission by deep neural network

Luyi YANG¹^,²(), Haiyang LI¹^,³(), Jin ZHANG¹^,³^,*(), Yuehe ZHU¹^,³()

¹ College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
² China Astronauts Research and Training Center, Beijing 100094, China
³ Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions, Changsha 410073, China

Received:2021-09-16 Online:2024-04-18 Published:2024-04-18
Contact: Jin ZHANG E-mail:yangluyi@nudt.edu.cn;lihaiyang@nudt.edu.cn;zhangjin@nudt.edu.cn;zhuyuehe@nudt.edu.cn
About author:
YANG Luyi was born in 1995. He received his bachelor degree in aerospace engineering from National University of Defense Technology, in 2017. Then he was enrolled in a combined “Master+PhD” program and he is a doctoral candidate in the College of Aerospace Science and Engineering, National University of Defense Technology since 2019. His research interests are trajectory design and optimization of the manned lunar mission, and combining deep learning with trajectory design method. E-mail: yangluyi@nudt.edu.cn

LI Haiyang was born in 1972. He received his Ph.D. degree from the School of Aerospace Science and Engineering, National University of Defense Technology, in 2000. Currently he is a professor in National University of Defense Technology. His research interests include aircraft design, mission scheduling, and analysis of the manned spacecraft system. E-mail: lihaiyang@nudt.edu.cn

ZHANG Jin was born in 1983. He received his Ph.D. degree from the School of Aerospace Science and Engineering, National University of Defense Technology, in 2013. Currently he is an associate professor in National University of Defense Technology. His research interests include astrodynamics and space mission planning. E-mail: zhangjin@nudt.edu.cn

ZHU Yuehe was born in 1990. He received his Ph.D. degree from the School of Aerospace Science and Engineering, National University of Defense Technology, in 2020. Currently he is a lecturer in National University of Defense Technology. His research interest is space mission planning for large-scale object visiting. E-mail: zhuyuehe@nudt.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (12072365) and the Natural Science Foundation of Hunan Province of China (2020JJ4657).

Abstract

Abstract:

It is important to calculate the reachable domain (RD) of the manned lunar mission to evaluate whether a lunar landing site could be reached by the spacecraft. In this paper, the RD of free return orbits is quickly evaluated and calculated via the classification and regression neural networks. An efficient database-generation method is developed for obtaining eight types of free return orbits and then the RD is defined by the orbit’s inclination and right ascension of ascending node (RAAN) at the perilune. A classify neural network and a regression network are trained respectively. The former is built for classifying the type of the RD, and the latter is built for calculating the inclination and RAAN of the RD. The simulation results show that two neural networks are well trained. The classification model has an accuracy of more than 99% and the mean square error of the regression model is less than ${0.01^ \circ }$ on the test set. Moreover, a serial strategy is proposed to combine the two surrogate models and a recognition tool is built to evaluate whether a lunar site could be reached. The proposed deep learning method shows the superiority in computation efficiency compared with the traditional double two-body model.

Key words: manned lunar mission, free return orbit, reachable domain (RD), deep neural network, computation efficiency

Luyi YANG, Haiyang LI, Jin ZHANG, Yuehe ZHU. Fast solution to the free return orbit’s reachable domain of the manned lunar mission by deep neural network[J]. Journal of Systems Engineering and Electronics, 2024, 35(2): 495-508.

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Type	Name	TLI phase	VCP phase	PRL phase
I	I-0	Ascending	Ascending	Ascending
I	I-1	Ascending	Ascending	Descending
II	II-0	Ascending	Descending	Ascending
II	II-1	Ascending	Descending	Descending
III	III-0	Descending	Ascending	Ascending
III	III-1	Descending	Ascending	Descending
IV	IV-0	Descending	Descending	Ascending
IV	IV-1	Descending	Descending	Descending

Parameter	Range
${i_{ {\text{LEO} } } }/(^ \circ)$	26−30
${i_{ {\text{VCP} } } }/(^ \circ)$	40−44
${h_{ {\text{LEO} } } }/{\text{km} }$	$170$
${h_{ {\text{VCP} } } }/{\text{km} }$	$50$
${T_{ {\text{Transfer} } } }/{\text{day} }$	5.5−6.0
${t_{ {\text{PRL} } } }$	2029-04-01 00:00:00−2029-07-01 00:00:00
TLI phase	Ascending, Descending
PRL phase	Ascending, Descending
VCP phase	Ascending, Descending

Name	Variable
Semi-major axis	${a_{\rm{M}}}$
Eccentricity	${e_{\rm{M}}}$
Inclination	${i_{\rm{M}}}$
RAAN	${\varOmega _{\rm{M} } }$
Argument of latitude	${u_{\rm{M}}}$

Name	Variable
Semi-major axis	${a_{\text{m}}}$
Eccentricity	${e_{\text{m}}}$
Inclination	${i_{\text{m}}}$
RAAN	${\varOmega _{\text{m} } }$
Argument of latitude	${u_{\rm{M}}}$
LTO height	${h_{{\text{LEO}}}}$
LTO inclination	${i_{{\text{LEO}}}}$
PRL height	$ {h_{{\text{PRL}}}} $
VCP inclination	${i_{{\text{VCP}}}}$
VCP height	${h_{{\text{VCP}}}}$

Hyperparameter	Search range
Optimizer	SGD, Adam, Nadam, LM
Activation function	sigmoid, softsign, tanh, ReLU
Number of layers	[1,4]
Number of nodes	[8, 128]
Learning rate	[0.00001, 0.1]

Fast solution to the free return orbit’s reachable domain of the manned lunar mission by deep neural network

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References 31

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Hyperparameter	CL model	RG model
Optimizer	Adam	LM
Activation	tanh	ReLU
Number of layers	2	2
Number of nodes	[8,16]	[16, 32]
Learning rate	0.005	0.005

Orbit type	MSE	Accurate number	Total number	Accuracy rate/%	Training time/s
I	$4.510\;8 \times {10^{ - 4} }$	21797	21803	99.97	306
II	0.0022	21810	21822	99.95	355
III	$4.085\;6 \times {10^{ - 4} }$	21808	21812	99.98	327
IV	0.001831	21813	21824	99.95	317

Orbit type	Inclination MSE/(°)	RAAN MSE/(°)	Inclination MAE/(°)	RAAN MAE/(°)	Training time/s
I-0	$ 1.635 \times {10^{ - 5}} $	$ 2.858 \times {10^{ - 4}} $	$ 5.665 \times {10^{ - 4}} $	$ 1.518 \times {10^{ - 3}} $	553
I-1	$ 9.178 \times {10^{ - 5}} $	$ 1.103 \times {10^{ - 4}} $	$ 6.532 \times {10^{ - 3}} $	$ 7.504 \times {10^{ - 3}} $	373
II-0	$ 1.646 \times {10^{ - 6}} $	$ 1.848 \times {10^{ - 4}} $	$ 7.052 \times {10^{ - 4}} $	$ 1.439 \times {10^{ - 3}} $	523
II-1	$ 2.524 \times {10^{ - 5}} $	$ 3.586 \times {10^{ - 4}} $	$ 2.888 \times {10^{ - 3}} $	$ 4.880 \times {10^{ - 3}} $	461
III-0	$ 1.939 \times {10^{ - 5}} $	$ 3.733 \times {10^{ - 3}} $	$ 3.093 \times {10^{ - 3}} $	$ 7.864 \times {10^{ - 3}} $	528
III-1	$ 4.845 \times {10^{ - 6}} $	$ 4.850 \times {10^{ - 4}} $	$ 1.394 \times {10^{ - 3}} $	$ 2.708 \times {10^{ - 3}} $	545
IV-0	$ 4.024 \times {10^{ - 5}} $	$ 1.930 \times {10^{ - 4}} $	$ 5.102 \times {10^{ - 3}} $	$ 8.275 \times {10^{ - 3}} $	542
IV-1	$ 8.532 \times {10^{ - 5}} $	$ 1.277 \times {10^{ - 4}} $	$ 7.337 \times {10^{ - 3}} $	$ 6.591 \times {10^{ - 3}} $	535
Average	$ 3.560 \times {10^{ - 5}} $	$ 6.848 \times {10^{ - 4}} $	$ 3.452 \times {10^{ - 3}} $	$ 5.128 \times {10^{ - 3}} $	507.5

Computation time	Deep learning model	Double two-body model
Total time	0.1532	4322.5
Computation time per orbit	$ 1.7509 \times {10^{ - 4}} $	4.94

Number	Method
	Monte Carlo data		PRL method		DNN method
	${\varOmega _{ {\text{LCF} } } }$	${i_{ {\text{LCF} } } }$	${\varOmega _{ {\text{LCF} } } }$	${i_{ {\text{LCF} } } }$	${\varOmega _{ {\text{LCF} } } }$	${i_{ {\text{LCF} } } }$
1	176.71	157.96	176.71	157.95	176.71	157.95
2	174.99	79.42	174.98	79.41	174.98	79.41
3	165.33	353.87	165.34	353.87	165.35	353.87
4	170.44	12.82	170.44	12.81	170.44	12.84
5	170.86	15.49	170.85	15.49	170.85	15.49
6	176.24	224.62	176.25	224.64	176.24	224.64
7	171.35	20.92	171.35	20.94	171.36	20.94
8	175.54	97.67	175.57	97.65	175.57	97.65
9	174.02	55.67	173.98	55.69	173.98	55.69
10	176.23	119.92	176.22	119.97	176.22	119.97

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