基于势场法的卫星编队保持及其稳定性分析

doi:10.16182/j.issn1004731x.joss.17-0096

系统仿真学报 ›› 2019, Vol. 31 ›› Issue (2): 332-339.doi: 10.16182/j.issn1004731x.joss.17-0096

基于势场法的卫星编队保持及其稳定性分析

杨盛庆^{1, 2}, 叶文郁³, 何煜斌^{1, 2}, 万亚斌^{1, 2}

1. 上海航天控制技术研究所,上海 201109;
2. 上海市空间智能控制技术重点实验室,上海 201109;
3. 上海航天技术研究院,上海 201109

收稿日期:2017-02-28 修回日期:2017-04-17 出版日期:2019-02-15 发布日期:2019-02-15
作者简介:杨盛庆(1985-),男,浙江绍兴,博士,高工,研究方向为卫星轨道动力学、卫星编队导航;叶文郁(1981-),男,湖南益阳,硕士,高工,研究方向为卫星编队导航。
基金资助:
上海市青年科技启明星计划(17QB1401400),上海市青年科技英才扬帆计划(17YF1408300)

Satellite Formation Keeping and Its Stability Analysis Based on Artificial Potential Field Method

Yang Shengqing^{1, 2}, Ye Wenyu³, He Yubin^{1, 2}, Wan Yabin^{1, 2}

1. Shanghai Institute of Spaceflight Control Technology, Shanghai 201109, China;
2. Shanghai Key Laboratory of Aerospace Intelligent Control Technology, Shanghai 201109, China;
3. Shanghai Academy of Spaceflight Technology, Shanghai 201109, China

Received:2017-02-28 Revised:2017-04-17 Online:2019-02-15 Published:2019-02-15

摘要/Abstract

摘要： 本文研究了基于人工势场法的卫星编队保持的控制方法。由于多体问题无法求其解析解,转而考虑领导-跟随结构的限制性多体问题。其惯性坐标系下的平衡结构对应了无穷多的坐标组合,使得误差动力学系统的平衡点处的雅可比矩阵无法求解。提出了一类由惯性坐标系到特殊参考坐标系的坐标变换,使对误差动力学系统的稳定性分析只取决于编队的构型。通过对参考坐标系下误差动力学系统的约化及其平衡点处雅克比矩阵的特征值的求解,证明了此类控制方法的稳定性。

关键词: 编队保持, 人工势场, 稳定性分析, 小推力卫星, 领导-跟随结构

Abstract: In this paper, a control method of satellite formation keeping is investigated based on artificial potential field. Since the N-body problem doesn’t have analytical solutions, a leader-follower formation is proposed as a restricted N-body problem. The stable structure has infinite possible pairs of coordinates in the inertial frame, therefore the Jacobian matrix of the corresponding error dynamic system at the equilibrium point is unsolvable. By introducing a transformation of coordinates from inertial frame to a specific reference frame, the stability analysis of error dynamic system is only related to the structure of formation. By the reduction of error dynamic system in the reference frame and the solving of eigenvalues of Jacobian matrix at equilibrium point, the stability analysis of the novel control method is given.

Key words: formation keeping, artificial potential field, stability analysis, low-thrust satellite, leader-follower structure

中图分类号:

V412.4+1

杨盛庆, 叶文郁, 何煜斌, 万亚斌. 基于势场法的卫星编队保持及其稳定性分析[J]. 系统仿真学报, 2019, 31(2): 332-339.

Yang Shengqing, Ye Wenyu, He Yubin, Wan Yabin. Satellite Formation Keeping and Its Stability Analysis Based on Artificial Potential Field Method[J]. Journal of System Simulation, 2019, 31(2): 332-339.

参考文献

[1] 杨嘉墀. 航天器轨道动力学与控制[M]. 北京: 宇航出版社, 1995.
Yang J C.The spacecraft orbital dynamics and control[M]. Beijing: China Astronautic Publishing House, 1995.
[2] 陈世明, 方华京. 大规模智能群体的建模及稳定性分析[J]. 控制与决策, 2005, 20(5): 490-494.
Chen S M, Fang H J.Modeling and stability analysis of large-scale intelligent swarm[J]. Control and Decision, 2005, 20(5): 490-494.
[3] Anderson B, Yu C B, Dasgupta S, et al.Control of a Three-coleader formation in the plane[J]. Systems Control Letters (S0167-6911), 2007, 56(9): 573-578.
[4] Cao M, Morse A S, Yu C B, et al.Maintaining a directed, triangular formation of mobile autonomous agents[J]. Communications in Information and Systems (S0916-8532), 2011, 11(1): 1-16.
[5] Gurfil P, Kasdin N J.Stability and control of spacecraft formation flying in trajectories of the restricted three-body problem[J]. Acta Astronautica (S0094-5765), 2004, 54(6): 433-453.
[6] Olfati-Saber R, Murray R M.Distributed cooperative control of multiple vehicle formations using structural potential functions[C]. In IFAC World Congress, Barcelona, Spain, July 21-26, 2002.
[7] Yang S Q, Yu J Q.Stability analysis and variational integrator for real-time formation based on potential field[J]. Mathematical Problems in Engineering (S1024-123X), 2014, 13(3):1-13.
[8] Lechevin N, Rabbath C A, Sicard P.Trajectory tracking of leader-follower formations characterized by constant line-of-sight angles[J]. Automatica (S0005-1098), 2006, 42(12): 2131-2141.
[9] Sastry S.Nonlinear systems: analysis, stability and control[M]. New York: Springer, 1999.
[10] 刘林. 航天器轨道理论[M]. 北京: 国防工业出版社, 2000.
Liu L.Orbit theory of spacecraft[M]. Beijing: National Defense Industry Press, 2000.
[11] 孙炳磊, 贺亮, 韩飞, 等. 静止轨道卫星高精度悬停编队最优滑模控制器设计[J]. 空间控制技术与应用, 2016, 42(6): 9-13.
Sun B L, He L, Han F, et al.Optimal sliding mode control for geostationary satellite high-precision hovering formation flying[J]. Aerospace Control and Application, 2016, 42(6): 9-13.

基于势场法的卫星编队保持及其稳定性分析

Satellite Formation Keeping and Its Stability Analysis Based on Artificial Potential Field Method

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