Optimal maneuver strategy to improve the observability of angles-only rendezvous

doi:10.23919/JSEE.2023.000091

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (4): 1020-1032.doi: 10.23919/JSEE.2023.000091

• CONTROL THEORY AND APPLICATION • Previous Articles

Optimal maneuver strategy to improve the observability of angles-only rendezvous

Ronghua DU(), Wenhe LIAO(), Xiang ZHANG()

¹ School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

Received:2021-11-24 Online:2023-08-18 Published:2023-08-28
Contact: Wenhe LIAO E-mail:Duronghua1995@126.com;cnwho@mail.njust.edu.cn;zhxiang2002@126.com
About author:
DU Ronghua was born in 1995. He received his B.S. degree in mechanical engineering from the School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China, in 2017. He is pursuing his Ph.D. degree in mechanical engineering from the School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China. Since 2017, he has studied in the the Micro Satellite Research Centre and has been a postgraduate with the School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include satellite attitude determination, vision-based relative navigation, guidance navigation and control, and angles-only relative navigation. E-mail: Duronghua1995@126.com

LIAO Wenhe was born in 1965. He received his B.S. degree in aerospace manufacturing engineering from the School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1990 and Ph.D. degree in aerospace manufacturing engineering from the School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1996. He is currently the Vice President of the Nanjing University of Science and Technology, Nanjing, China. He is also the Director of the Micro Satellite Research Centre and a professor with the School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include satellite system design and high-end equipment design. E-mail: cnwho@mail.njust.edu.cn

ZHANG Xiang was born in 1973. He received his B.S. degree in aerospace manufacturing engineering from the School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1998 and Ph.D. degree in aerospace manufacturing engineering from the School of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2007. He is currently the Deputy Director of the Micro Satellite Research Centre and a professor with the School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include satellite system design, satellite attitude control, satellite payloads, and ground stations. E-mail: zhxiang2002@126.com
Supported by:
This work was supported by the China Aerospace Science and Technology Corporation 8th Research Institute Industry-University-Research Cooperation Fund (SAST 2020-019)

Abstract

Abstract:

This paper proposes an optimal maneuver strategy to improve the observability of angles-only rendezvous from the perspective of relative navigation. A set of dimensionless relative orbital elements (ROEs) is used to parameterize the relative motion, and the objective function of the observability of angles-only navigation is established. An analytical solution of the optimal maneuver strategy to improve the observability of angles-only navigation is obtained by means of numerical analysis. A set of dedicated semi-physical simulation system is built to test the performances of the proposed optimal maneuver strategy. Finally, the effectiveness of the method proposed in this paper is verified through the comparative analysis of the objective function of the observability of angles-only navigation and the performances of the angles-only navigation filter under different maneuver schemes. Compared with the cases without orbital maneuver, it is concluded that the tangential filtering accuracy with the optimal orbital maneuver at the terminal time is increased by 35% on average, and the radial and normal filtering accuracy is increased by 30% on average.

Key words: angles-only navigation, observability, optimal maneuver, orbital rendezvous

Ronghua DU, Wenhe LIAO, Xiang ZHANG. Optimal maneuver strategy to improve the observability of angles-only rendezvous[J]. Journal of Systems Engineering and Electronics, 2023, 34(4): 1020-1032.

Figures/Tables 14

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References 32

1	SEARS P J, HO J Impact evaluation of in-space additive manufacturing and recycling technologies for on-orbit servicing. Journal of Spacecraft and Rockets, 2018, 55 (4): 1498- 1508. doi: 10.2514/1.A34135
2	CHIU S W Promoting international cooperation in the age of global space governance: a study on on-orbit servicing operations. Acta Astronautica, 2019, 161, 375- 381. doi: 10.1016/j.actaastro.2018.07.019
3	RAZZAGHI P, KHATIB E A, BAKHTIARI S Sliding mode and SDRE control laws on a tethered satellite system to de-orbit space debris. Advances in Space Research, 2019, 64 (1): 18- 27. doi: 10.1016/j.asr.2019.03.024
4	CHU Z Y, WEI T, SHEN T, et al Optimal commands based multi-stage drag de-orbit design for a tethered system during large space debris removal. Acta Astronautica, 2019, 163, 238- 249. doi: 10.1016/j.actaastro.2018.12.038
5	ZHU Z H, GUO Y Adaptive coordinated attitude control for spacecraft formation with saturating actuators and unknown inertia. Journal of the Franklin Institute, 2019, 356, 1021- 1037. doi: 10.1016/j.jfranklin.2018.02.021
6	IVANOV D, KUSHNIRUK M, OVCHINNIKOV M Study of satellite formation flying control using differential lift and drag. Acta Astronautica, 2018, 152, 88- 100. doi: 10.1016/j.actaastro.2018.07.047
7	MITCHELL A, PIMENTA D, GILL J, et al Cardiovascular effects of space radiation: implications for future human deep space exploration. European Journal of Preventive Cardiology, 2019, 26 (16): 1707- 1714. doi: 10.1177/2047487319831497
8	LI H, ZHANG Q Y, ZHANG N T Autonomous navigation of formation flying spacecrafts in deep space exploration and communication by hybrid navigation utilizing neural network filter. Acta Astronautica, 2009, 65, 1028- 1031. doi: 10.1016/j.actaastro.2009.03.038
9	HAN J, LI W X, FENG K, et al Vision-based aerial image mosaicking algorithm with object detection. Journal of Systems Engineering and Electronics, 2022, 33 (2): 259- 268.
10	GONG B C, LI W D, LI S, et al Angles-only initial relative orbit determination algorithm for non-cooperative spacecraft proximity operations. Astrodynamics, 2018, 2, 217- 231. doi: 10.1007/s42064-018-0022-0
11	GAIAS G, ARDAENS J S Flight demonstration of autonomous non-cooperative rendezvous in low earth orbit. Journal of Guidance, Control and Dynamics, 2018, 41, 1137- 1154.
12	D’AMICO S, PAVONE M, SARAF S, et al. Miniaturized autonomous distributed space systems for future science and exploration. Proc. of the 8th International Workshop of Spacecraft Formation Flying, 2015. https://elib.dlr.de/98200/.
13	GELLER D K, PEREZ A C Initial relative orbit determination for close-in proximity operations. Journal of Guidance, Control and Dynamics, 2015, 38, 1833- 1841. doi: 10.2514/1.G000933
14	GRZYMISCH J, FICHTER W Observability criteria and unobservable maneuvers for in-orbit bearings-only navigation. Journal of Guidance, Control and Dynamics, 2014, 37 (4): 1250- 1259. doi: 10.2514/1.62476
15	GRZYMISCH J, FICHTER W Optimal rendezvous guidance with enhanced bearings-only observability. Journal of Guidance, Control and Dynamics, 2015, 38 (6): 1131- 1139. doi: 10.2514/1.G000822
16	GELLER D K, KLEIN I Angles-only navigation state observability during orbital proximity operations. Journal of Guidance, Control and Dynamics, 2014, 37 (6): 1976- 1983. doi: 10.2514/1.G000133
17	NEWMAN B, LOVELL T A, PRATT E, et al. Quadratic hexa-dimensional solution for relative orbit determination. Proc. of the AIAA/AAS Astrodynamics Specialist Conference, 2014. https://www.webofscience.com/wos/alldb/full-record/wos:00371647200201.
18	PEREZ A C, GELLER D K, LOVELL T A Non-iterative angles-only initial relative orbit determination with J₂ perturbations . Acta Astronautica, 2018, 151, 146- 159. doi: 10.1016/j.actaastro.2018.06.033
19	WOFFINDEN D C, GELLER D K Observability criteria for angles-only navigation. IEEE Trans. on Aerospace and Electronic System, 2009, 45 (3): 1194- 1208.
20	ARDAENS J S, GAIAS G A numerical approach to the problem of angles-only initial relative orbit determination in low earth orbit. Advances in Space Research, 2019, 63 (12): 3884- 3899. doi: 10.1016/j.asr.2019.03.001
21	ROSCOE C, WESTPHAL J, GRIESBACH J, et al Formation establishment and reconfiguration using differential elements in J₂-perturbed orbits . Journal of Guidance, Control and Dynamics, 2015, 38 (9): 1725- 1740. doi: 10.2514/1.G000999
22	GAIAS G, D’AMICO S, ARDAENS J S Generalized multi-impulsive maneuvers for optimum spacecraft rendezvous in near-circular orbit. International Journal of Space Science and Engineering, 2015, 3 (1): 68- 88. doi: 10.1504/IJSPACESE.2015.069361
23	CHERNICK M, D’AMICO S New closed-form solutions for optimal impulsive control of spacecraft relative motion. Journal of Guidance, Control, and Dynamics, 2018, 41 (2): 301- 319. doi: 10.2514/1.G002848
24	KOENIG A, GUFFANTI T, D’AMICO S. New state transition matrices for relative motion of spacecraft formations in perturbed orbits. Proc. of the AIAA/AAS Astrodynamics Specialist Conference, 2016: 1749−1768.
25	GAIAS G, ARDAENS J S, MONTENBRUCK O Model of J₂ perturbed satellite relative motion with time-varying differential drag . Celestial Mechanics and Dynamical Astronomy, 2015, 123 (4): 411- 433. doi: 10.1007/s10569-015-9643-2
26	VADDI S, ALFRIEND K, VADALI S, et al Formation establishment and reconfiguration using impulsive control. Journal of Guidance, Control and Dynamics, 2005, 28 (2): 262- 268. doi: 10.2514/1.6687
27	GRZYMISCH J, FICHTER W Analytic optimal observability maneuvers for in-orbit bearings-only rendezvous. Journal of Guidance, Control and Dynamics, 2014, 37 (5): 1658- 1664. doi: 10.2514/1.G000612
28	DAVIS C Theory of positive linear dependence. American Journal of Mathematics, 1954, 76 (4): 733- 746. doi: 10.2307/2372648
29	BOYD S, VANDENBERGHE L. Convex optimization. Cambridgeshire: Cambridge University Press, 2004.
30	YIN J F, HAN C Elliptical formation control based on relative orbit elements. Chinese Journal of Aeronautics, 2013, 26, 1554- 1567. doi: 10.1016/j.cja.2013.07.014
31	GAIAS G, D’AMICO S, ARDAENS J S Angles-only navigation to a non-cooperative satellite using relative orbital elements. Journal of Guidance, Control and Dynamics, 2014, 37 (2): 439- 451. doi: 10.2514/1.61494
32	BATTIN R H. An introduction to the mathematics and methods of astrodynamics. Reston: American Institute of Aeronautics & Astronsutics, 1999.

Parameter	Value
Absolute orbital elements of the space target (a/km, e, i/(°), Ω/(°), ω/(°), M/(°))	(6878.137, 0, 40, 120, 0, 50)
ROE1 (aδa, aδλ, aδe_x, aδe_y, aδi_x, aδi_y)/km	(0, −30, 0.5, 0, −0.5, 0)
ROE2 (aδa, aδλ, aδe_x, aδe_y, aδi_x, aδi_y)/km	(−0.15, −20, 0.3, 0, −0.3, 0)
ROE3 (aδa, aδλ, aδe_x, aδe_y, aδi_x, aδi_y)/km	(0, −5, 0, 0, 0, 0)
Sample period T/s	10
Simulation time $t_f $ /s	1000
Sensor measurement noise (σ_α = σ_ε)/arcsec	30

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Optimal maneuver strategy to improve the observability of angles-only rendezvous

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