Cooperative game theory-based steering law design of a CMG system

doi:10.23919/JSEE.2023.000024

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (1): 185-196.doi: 10.23919/JSEE.2023.000024

• CONTROL THEORY AND APPLICATION • Previous Articles Next Articles

Cooperative game theory-based steering law design of a CMG system

Bing HUA(), Rui NI(), Mohong ZHENG(), Yunhua WU(), Zhiming CHEN()

¹ School of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210000, China

Received:2021-05-09 Online:2023-02-18 Published:2023-03-03
Contact: Rui NI E-mail:huabing@nuaa.edu.cn;1944135366@qq.com;mohongzheng@nuaa.edu.cn;yunhuawu@nuaa.edu.cn;chenzhiming@nuaa.edu.cn
About author:
HUA Bing was born in 1978. She received her Ph.D. degree in navigation, guidance, and control engineering from Nanjing University of Aeronautics and Astronautics in 2007. Since 2007, she has been an associate professor with Nanjing University of Aeronautics and Astronautics. She was a TX-1 satellite attitude control system designer with the Small Satellite Research Center. Her research interests include navigation, guidance, and control. E-mail: huabing@nuaa.edu.cn

NI Rui was born in 1996. She received her B.S. degree in automation from Yangzhou University in 2019, and she is pursuing her M.S. degree in the School of Aerospace, Nanjing University of Aeronautics and Astronautics. Her research interests include spacecraft attitude determination and control. E-mail: 1944135366@qq.com

ZHENG Mohong was born in 1995. She received her B.S. degree in detection guidance and control technology from Nanjing University of Aeronautics and Astronautics in 2018, and M.S. degree in 2021. Her research interests include spacecraft attitude dynamics and control and microsatellite constellation design. E-mail: mohongzheng@nuaa.edu.cn

WU Yunhua was born in 1981. He received his B.S., M.S., and Ph.D. degrees in aerospace engineering from the Harbin Institute of Technology in 2004, 2006, and 2009, respectively. From 2010 to 2012, he was a research fellow with the Surrey Space Center, University of Surrey. Since 2013, he has been an associate professor with the School of Astronautics, Nanjing University of Aeronautics and Astronautics. His research interests include space vehicle design, mission analysis, space vehicle dynamics and control, and hardware-in-the-loop simulation. E-mail: yunhuawu@nuaa.edu.cn

CHEN Zhiming was born in 1982. He received his B.S, M.S., and Ph.D. degrees in precision instruments and mechanism engineering from Nanjing University of Aeronautics and Astronautics in 2004, 2007, and 2012, respectively. Since 2012, he has been with the School of Astronautics, Nanjing University of Aeronautics and Astronautics. His research interests include satellite formation control, mission planning, and visual navigation. E-mail: chenzhiming@nuaa.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (61973153)

Abstract

Abstract:

Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope (CMG) is employed to provide a strong moment. However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated. When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.

Key words: control moment gyroscopes (CMG), cooperative game theory, steering laws

Bing HUA, Rui NI, Mohong ZHENG, Yunhua WU, Zhiming CHEN. Cooperative game theory-based steering law design of a CMG system[J]. Journal of Systems Engineering and Electronics, 2023, 34(1): 185-196.

Figures/Tables 10

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References 17

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Scenario	Scenario design	Initial state/(°)	Parameter
1	(Null motion) X-channel singularity (nearby)	${\boldsymbol{\alpha}} =\left[-{105},\;{10},\;{95},\;{170}\right]$	${\boldsymbol{W}} ={\rm{ diag} }\left[ {5,5,5,5} \right]$
2	X-channel singularity (nearby)	${\boldsymbol{\alpha}} =\left[-105,\;10,\;95,\;170\right]$	$ {\varepsilon }_{\lambda }=1\times {10}^{-12},\;{\varepsilon }^{*}=1\times {10}^{-10} $
3	Y-channel singularity (nearby)	${\boldsymbol{\alpha}} =\left[20,\;90,\;20,\;100\right]$	$ {\varepsilon }_{\lambda }=1\times {10}^{-12},\;{\varepsilon }^{*}=1\times {10}^{-10} $
4	Z-channel singularity (nearby)	${\boldsymbol{\alpha}} =\left[105,\;115,\;110,\;105\right]$	$ {\varepsilon }_{\lambda }=1\times {10}^{-12},\;{\varepsilon }^{*}=1\times {10}^{-10} $
5	Singularity of X-channel	${\boldsymbol{\alpha}} =\left[90,\;0,\;90,\;0\right]$	$ {\varepsilon }_{\lambda }=1\times {10}^{-12},\;{\varepsilon }^{*}=1\times {10}^{-10} $
6	Singularity of Y-channel	${\boldsymbol{\alpha}} =\left[0,\;90,\;0,\;90\right]$	$ {\varepsilon }_{\lambda }=1\times {10}^{-12},\;{\varepsilon }^{*}=1\times {10}^{-10} $
7	Singularity of Z-channel	${\boldsymbol{\alpha }}=\left[90,\;90,\;90,\;90\right]$	$ {\varepsilon }_{\lambda }=1\times {10}^{-12},\;{\varepsilon }^{*}=1\times {10}^{-10} $

Scenario	Scenario design	Singularity situation	Control torque error/(N·m)	Actuator energy/J
1	(Null motion) Singularity of Z-channel	Singularity	0.6	14×10⁻⁴
2	X-channel singularity (nearby)	No singularity	1×10⁻¹⁶	0.42×10⁻³
3	Y-channel singularity (nearby)	No singularity	1×10⁻¹⁶	1.1×10⁻³
4	Z-channel singularity (nearby)	No singularity	1×10⁻¹⁶	0.3×10⁻³
5	Singularity of X-channel	Escape from singularity	After escaping the singularity 1×10⁻¹⁶	1.5×10⁻³
6	Singularity of Y-channel	Escape from singularity	After escaping the singularity 1×10⁻¹⁶	3×10⁻³
7	Singularity of Z-channel	Escape from singularity	After escaping the singularity 1×10⁻¹⁶	4×10⁻³

Cooperative game theory-based steering law design of a CMG system

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