On-orbit servicing launch dynamics and multi-objective optimization of impulsive rendezvous

doi:10.23919/JSEE.2025.000123

Journal of Systems Engineering and Electronics ›› 2026, Vol. 37 ›› Issue (2): 697-711.doi: 10.23919/JSEE.2025.000123

• CONTROL THEORY AND APPLICATION • Previous Articles

On-orbit servicing launch dynamics and multi-objective optimization of impulsive rendezvous

Weikang LI¹(), Ju JIANG¹(), Yue BIAN²(), Yanhua HAN³^,*()

¹College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
²Aviation Industry Corporation of China Nanjing Electromechanical Technology Co., Ltd, Nanjing 130012, China
³College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2025-03-18 Online:2026-04-18 Published:2026-04-30
Contact: Yanhua HAN E-mail:liweikang@nuaa.edu.cn;jiangju@nuaa.edu.cn;bianyue@nuaa.edu.cn;hanyanhua@nuaa.edu.cn
About author:
LI Weikang was born in 1997. He received his B.S. degree in mechanical engineering from Northeastern University, Shenyang, China, in 2019, and M.S. degree in control science and engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2023. He is pursuing his doctoral degree at NUAA. His current research interests include multi-agent systems and aircraft control. E-mail: liweikang@nuaa.edu.cn

JIANG Ju was born in 1963. He received his B.S. and M.S. degrees from Beihang University, Beijing, China, in 1984 and 1987, respectively, and Ph.D. degree from the University of Waterloo, Canada, in 2007. He is a professor with the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics. His research interests include advanced flight control technology, intelligent decision-making and control, machine learning, and artificial intelligence. E-mail: jiangju@nuaa.edu.cn

BIAN Yue was born in 1998. She received her B.S. and M.S. degrees in electronic information engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2020 and 2023, respectively. She is currently an engineer at Aviation Industry Corporation of China Nanjing Electromechanical Technology Co., Ltd. Her research interests include vehicle navigation, guidance and control. E-mail: bianyue@nuaa.edu.cn

HAN Yanhua was born in 1976. He received his Ph.D. degree in navigation, guidance and control from Northwestern Polytechnical University in 2006. He is currently an associate professor in the College of Astronautics at Nanjing University of Aeronautics and Astronautics. His research interests include multibody coupled dynamics and control in aerospace, flight vehicle guidance and control. E-mail: hanyanhua@nuaa.edu.cn
Supported by:
This work was supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX25_0587).

Abstract

Abstract:

The multi-body dynamics in the launch process of a space platform deploying a server, as well as the optimal double impulse rendezvous guidance law between the server and the target spacecraft, are studied. Firstly, the space platform enters into orbit around the target, keeping its launch tube axis aiming at it. After receiving the launch command, the server shoots out from the launch tube, flying to the target. Due to body coupling, the platform’s attitude is disturbed, preventing the server from accurately aiming at the target during separation. The server uses its small rocket engine to apply two velocity pulses: the first one to adjust its trajectory for rendezvous, and the second near the target to reduce relative velocity to zero for soft docking. A two-body dynamics model is established using the Newton-Euler method, and a virtual prototype is developed in ADAMS for validation. To solve the multi-objective optimization subject to energy consumption and flight time for rendezvous, an improved non-dominated sorting genetic algorithm II (NSGA-II) algorithm is proposed. Simulation results show that launch-induced perturbations are non-negligible, and the proposed algorithm effectively derives the optimal guidance law that balances energy use and flight time.

Key words: multi-body dynamics, virtual prototype, impulse rendezvous, multi-objective optimization, on-orbit servicing

Weikang LI, Ju JIANG, Yue BIAN, Yanhua HAN. On-orbit servicing launch dynamics and multi-objective optimization of impulsive rendezvous[J]. Journal of Systems Engineering and Electronics, 2026, 37(2): 697-711.

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Input parameter	Value
$G/({{\text{m}}^2} \cdot {{\text{s}}^{ - 2}} \cdot {\text{k}}{{\text{g}}^{ - 1}}{\text{)}}$	$6.67 \times {10^{ - 11}}$
${M_{\text{e}}}/{\text{kg}}$	$5.965 \times {10^{24}}$
${R_{\text{e}}}/{\text{m}}$	$6.371 \times {10^6}$
$h/{\text{m}}$	$4 \times {10^5}$
$\mu /({{\text{m}}^3} \cdot {{\text{s}}^{ - 2}}{\text{)}}$	$3.986 \times {10^{14}}$
$n/({\text{rad}} \cdot {{\text{s}}^{ - 1}}{\text{)}}$	$1.132 \times {10^{ - 3}}$
$a/{\text{m}}$	$1\;000$
$b/{\text{m}}$	$500$
${n_{{x}}}$	$3$
${n_{{y}}}$	$2$
${l_{\text{r}}}/{\text{m}}$	$1.2$
${l_{{\text{cg}}}}/{\text{m}}$	$0.6$
${d_{\text{r}}}/{\text{m}}$	$0.3$
${d_{{x}}}/{\text{m}}$	$0.05$
${d_{{y}}}/{\text{m}}$	$0.1$
${m_{\text{p}}}/{\text{kg}}$	$900$
$ {J}_{\text{p}}/(\text{kg}\cdot {m}^{2}) $	$615$
${m_{\text{r}}}/{\text{kg}}$	$300$
$ {J}_{\text{r}}/(\text{kg}\cdot {m}^{2}) $	$36$
${F_{{x}}}/{\text{N}}$	$0$
${F_{{y}}}/{\text{N}}$	$0$
$M/({\text{N}} \cdot {\text{m)}}$	$ 0 $
$f/{\text{N}}$	$300$

Parameter	Value
x/m	+0.01
y/m	−0.13
V_x/(m/s)	+0.03
V_y/(m/s)	−0.19
η/(°)	+3.91
ω/(°/s)	+4.29
$V_{\text{F}}^{\text{P}}$/(m/s)	+1.67

Object	a/m	e	i/(°)	Ω/(°)	w/(°)	f/(°)
Target	${R_{\text{e}}} + 4 \times {10^5}$	0	45	115	60	0
Chaser	${R_{\text{e}}} + 4 \times {10^5}$	$6.7144 \times {10^{ - 5}}$	45	115	60	0

Type	IGD	HV	t/s
MOEA/D	1.25	2.48	0.8
NSGA-II	1.05	2.87	1.3
Improved NSGA-II	0.57	3.64	1.5

Results	J₁/s	J₂/(m/s)²	θ/(°)	t₁/s	t₂/s	Δv_x1/(m/s)	Δv_y1/(m/s)	Δv_x2/(m/s)	Δv_y2/(m/s)
Energy-optimal	2863	0.9632	126.33	606	2257	0.9448	0.1762	0.0021	0.0002
Integrated optimal	511	1.2639	116.915	10	501	0.2061	0.0023	0.9497	0.4676

On-orbit servicing launch dynamics and multi-objective optimization of impulsive rendezvous

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Result	Orbits of different transfer phases	a/m	e	i/(°)	Ω/(°)	w/(°)	f/(°)
Energy-optimal	Free-flying orbit	$ 6.76 \times {10^6} $	$4.09 \times {10^{ - 4}}$	45	115	4.51	166.09
Energy-optimal	Impulsive flight orbit	$ 6.76 \times {10^6} $	$4.09 \times {10^{ - 6}}$	45	115	58.12	151.93
Integrated optimal	Free-flying orbit	$ 6.76 \times {10^6} $	$4.09 \times {10^{ - 4}}$	45	115	357.20	167.42
Integrated optimal	Impulsive flight orbit	$ 6.76 \times {10^6} $	$4.09 \times {10^{ - 4}}$	45	115	1.79	163.47

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