Optimal Design of Stable Configuration of Space Gravitational Wave Detector Based on Dual Quaternion

Abstract

To ensure the stability of the orbital configuration of the space gravitational wave detector, the design and optimization method of stable formation configuration of the large-scale spacecraft in space was studied. Considering the influence of the sun-earth-moon gravitational field on the formation configuration, the earth, the moon, and three spacecraft were regarded as a formation for research in the heliocentric coordinate system. Based on dual quaternion, the natural/artificial celestial body dynamics model was established, and the space gravitational wave detection system model with and without a central celestial body was uniformly described. The parameters to be optimized based on genetic algorithm were given, and the optimization objective function was designed. Simulation results show that the detector meets the stability requirements of the orbit configuration within one year without orbit control.

Keywords

spacecraft formation / orbital configuration / dual quaternion / genetic algorithm

References

[1] STEBBINS R T. Rightsizing LISA[J]. Classical and Quantum Gravity,2009,26(9):094014
[2] SWEETSER T H. An end-to-end trajectory description of the LISA mission[J]. Classical and Quantum Gravity 2005，22（10）：S429.
[3] LUO J，CHEN L S，DUAN H Z，et al. TianQin：a space-borne gravitational wave detector[J]. Class Quantum Gravity 2016; 33（3）：19.
[4] HU W R，WU Y L. The Taiji Program in Space for gravitational wave physics and the nature of gravity[J]. National Science Review, 2017, 4（5）：685-686.
[5] XIA Y,LI G,HEINZEL G,RUEDIGER A,et al. Orbit design for the Laser Interferometer Space Antenna (LISA)[J]. Science China Physics,Mechanics and Astronomy,2010,53(1):179-186
[6] CHIHANG Y，HAO Z. Formation flight design for a LISA-like gravitational wave observatory via Cascade optimization[J]. Astrodynamics 2019，3（2）：155-171.
[7] 万小波，张晓敏，黎明. 天琴计划轨道构型长期漂移特性分析[J]. 中国空间科学技术 2017; 37（3）：110-116.
WAN X B，ZHANG X M，LI M. Analysis of long-period drift characteristics for orbit configuration of the Tianqin Mission[J]. Chinese Space Science and Technology，2017，37（3）：110-116.
[8] YE B B,ZHANG X F,ZHOU M Y,et al. Optimizing orbits for TianQin[J]. International Journal of Modern Physics D,2019,28(9):1950121
[9] CHEN J L,MASDEMONT J J,GOMEZ G,et al. Rotation-translation coupling analysis on perturbed spacecraft relative translational motion[J]. Nonlinear Dynamics,2020,102(4):2549-2561
[10] DANG Q Q,GUI H C,WEN H. Dual-quaternion-based spacecraft pose tracking with a global exponential velocity observer[J]. Journal of Guidance,Control,and Dynamics,2019,42(9):2106-2115
[11] DANG Q Q,GUI H C,XU M,et al. Dual-quaternion immersion and invariance velocity observer for controlling asteroid-hovering spacecraft[J]. Acta Astronautica,2019,161:304-312
[12] DE CASTRO F Z,VALLE M E. A broad class of discrete-time hypercomplex-valued Hopfield neural networks[J]. Neural Networks,2020,122:54-67
[13] TSIOTRAS P,VALVERDE A. Dual quaternions as a tool for modeling,control,and estimation for spacecraft robotic servicing missions[J]. The Journal of the Astronautical Sciences,2020,67(2):595-629
[14] 北京宇航系统工程研究所. GB∕T 32296-2015，航天飞行器常用坐标系[S]. 北京：中国标准出版社，2015.
[15] WANG J Y,LIANG H Z,SUN Z W,et al. Finite-time control for spacecraft formation with dual-number-based description[J]. Journal of Guidance,Control,and Dynamics,2012,35(3):950-962
[16] JOFFE E,WEALTHY D,FERNANDEZ I,et al. LISA:heliocentric formation design for the laser interferometer space antenna mission[J]. Advances in Space Research,2021,67(11):3868-3879