微小卫星编队飞行相关技术研究
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摘要
微小卫星编队飞行及其相关技术集中了目前为止航天技术中所取得的几乎所有的先进技术,早在20世纪90年代,美国宇航局就已经把编队飞行及其相关技术视为下一代可用的关键技术,我国在“九五”期间先后成功发射了北斗一号和北斗二号导航定位卫星,为发展我国自己的卫星编队组网奠定了技术基础。然而,由于微小卫星编队飞行这一技术在国际上的发展不过十几年,许多方面还有待于继续完善,国际国内都在积极寻求新的突破。该文章的研究内容就是在已有成果的基础上,利用数学模型,在相对轨道方程、三维编队队形设计、摄动分析和地面覆盖等方面做出各种简洁的计算方法。
文章在第二部分,首先建立三个坐标系,在参考卫星运行于圆轨道,环绕卫星运行于近圆轨道的假设条件下,通过两次坐标系旋转使得环绕卫星和参考卫星位于同一坐标系空间中,进而依据动力学关系采用作差的方法推导出环绕卫星相对参考卫星的运动方程。
利用第二部分推导出的相对运动方程,通过把小卫星编队中环绕卫星的运动分解为两个方面的分运动,在初始化参考卫星的轨道根数后,文章在第三部分设计出了一种三维螺旋式编队飞行的队形,并给出了一组用以计算各环绕卫星轨道根数的计算公式。
相对运动方程的推导和三维螺旋式编队飞行队形的设计都是在理想状态下获得的,实际中卫星编队运行时会受到各种摄动因素的影响,因此该文在第四部分从相对构型和整体绝对位置两个方面详细分析了摄动对编队的影响,并提出了通过施加冲量的方法来消除J 2项摄动和大气阻力摄动对编队飞行的影响。
卫星编队进行轨道控制以后,文章在第五部分分析了其主要的应用,也即卫星编队的地面覆盖问题。通过合理的概念定义和模型建立,文中给出了一整套用于分析卫星编队覆盖性能的各种参数计算公式,包括:最大地心角、最小地心角,覆盖带宽度、以及南北某纬度范围内全球覆盖所需的总时间和总圈数等。
文章中在相应的章节都给出了计算机仿真,从仿真的结果可以看出,文中提出的一系列方法不仅是可行的,而且计算过程十分简洁。该篇文章中所推导出的各种计算公式和分析出的设计思想可以为深入研究编队飞行小卫星系统提供参考。
Almost all advanced techniques obtained in aerospace domain up to now are being concentrated in the formation flying of micro-satellites and it’s interrelated techniques. As early as 90’s in 20 centuries, NASA has regarded formation flying of micro-satellites and it’s interrelated techniques as the available key technique in the future. China succeeded in launching the navigation and orientation satellites of Beidou No.1 and Beidou No.2 in "95" period, which established the technique foundation for the development of our country’s formation flying of micro-satellites.
However, the researchful time of formation flying of micro-satellites in the world is only more than ten years, many aspects were needed to be consummated. Our country and all the other countries are looking for the new breakthrough actively. Based the obtained achievement, this paper established a mathematics model, obtained many terse computational methods in the equation of relative orbit、the design of formation flying in three-dimensional orbits、the influence of perturbation、the analysis of surface coverage and etc.
In the second section, this paper establishes three reference frames, under the assumptive condition of reference satellite moving in a circle orbit and surrounding satellite moving in a near circle orbit, surrounding satellite and reference satellite were located in the same reference frame by two times circumvolving of reference frame, and then a relative position dynamic equation for surrounding satellite and reference satellite was derived by the method of subtraction according to kinetic relationship.
Utilizing the relative position dynamic equation, and then the surrounding satellite’s motion was separated into two simple parts, after the initialization of the reference satellite’s orbital elements, this paper designs the configuration of formation flying in three-dimensional orbits, and a set of calculated formulas of surrounding satellite’s orbital elements were deduced.
The relative position dynamic equation and the design of the configuration of formation flying in three-dimensional orbits were gained in the perfect situation , however, many kinds of perturbation will affect the structure of formation flying in fact. So this paper analyzes the influence of perturbation from two aspect of the relevant configuration and the integral absolute location of the formation in the fourth section, and then this paper brings forward a method to eliminate the affect of J2 perturbation and atmospheric drag perturbation to the formation flying by put an impulse on satellites.
After controlling of formation flying, this paper analyzes the main application of formation flying in the fifth section. It is the surface coverage for satellites formation flying. A set of calculational formulas were advanced in this section, for example, the maximal coverage angle、the minimal coverage angle、the belt width of coverage and the total time、the total amount of circles needed for global coverage of the satellites formation flying.
This paper gives many simulations at the end of every section, the results of the simulation prove that these technique bring forward in this paper are feasible and compact. These formulas and researchful methods can be served as reference for other kinds of researches about formation flying systems of micro-satellites.
文章在第二部分,首先建立三个坐标系,在参考卫星运行于圆轨道,环绕卫星运行于近圆轨道的假设条件下,通过两次坐标系旋转使得环绕卫星和参考卫星位于同一坐标系空间中,进而依据动力学关系采用作差的方法推导出环绕卫星相对参考卫星的运动方程。
利用第二部分推导出的相对运动方程,通过把小卫星编队中环绕卫星的运动分解为两个方面的分运动,在初始化参考卫星的轨道根数后,文章在第三部分设计出了一种三维螺旋式编队飞行的队形,并给出了一组用以计算各环绕卫星轨道根数的计算公式。
相对运动方程的推导和三维螺旋式编队飞行队形的设计都是在理想状态下获得的,实际中卫星编队运行时会受到各种摄动因素的影响,因此该文在第四部分从相对构型和整体绝对位置两个方面详细分析了摄动对编队的影响,并提出了通过施加冲量的方法来消除J 2项摄动和大气阻力摄动对编队飞行的影响。
卫星编队进行轨道控制以后,文章在第五部分分析了其主要的应用,也即卫星编队的地面覆盖问题。通过合理的概念定义和模型建立,文中给出了一整套用于分析卫星编队覆盖性能的各种参数计算公式,包括:最大地心角、最小地心角,覆盖带宽度、以及南北某纬度范围内全球覆盖所需的总时间和总圈数等。
文章中在相应的章节都给出了计算机仿真,从仿真的结果可以看出,文中提出的一系列方法不仅是可行的,而且计算过程十分简洁。该篇文章中所推导出的各种计算公式和分析出的设计思想可以为深入研究编队飞行小卫星系统提供参考。
Almost all advanced techniques obtained in aerospace domain up to now are being concentrated in the formation flying of micro-satellites and it’s interrelated techniques. As early as 90’s in 20 centuries, NASA has regarded formation flying of micro-satellites and it’s interrelated techniques as the available key technique in the future. China succeeded in launching the navigation and orientation satellites of Beidou No.1 and Beidou No.2 in "95" period, which established the technique foundation for the development of our country’s formation flying of micro-satellites.
However, the researchful time of formation flying of micro-satellites in the world is only more than ten years, many aspects were needed to be consummated. Our country and all the other countries are looking for the new breakthrough actively. Based the obtained achievement, this paper established a mathematics model, obtained many terse computational methods in the equation of relative orbit、the design of formation flying in three-dimensional orbits、the influence of perturbation、the analysis of surface coverage and etc.
In the second section, this paper establishes three reference frames, under the assumptive condition of reference satellite moving in a circle orbit and surrounding satellite moving in a near circle orbit, surrounding satellite and reference satellite were located in the same reference frame by two times circumvolving of reference frame, and then a relative position dynamic equation for surrounding satellite and reference satellite was derived by the method of subtraction according to kinetic relationship.
Utilizing the relative position dynamic equation, and then the surrounding satellite’s motion was separated into two simple parts, after the initialization of the reference satellite’s orbital elements, this paper designs the configuration of formation flying in three-dimensional orbits, and a set of calculated formulas of surrounding satellite’s orbital elements were deduced.
The relative position dynamic equation and the design of the configuration of formation flying in three-dimensional orbits were gained in the perfect situation , however, many kinds of perturbation will affect the structure of formation flying in fact. So this paper analyzes the influence of perturbation from two aspect of the relevant configuration and the integral absolute location of the formation in the fourth section, and then this paper brings forward a method to eliminate the affect of J2 perturbation and atmospheric drag perturbation to the formation flying by put an impulse on satellites.
After controlling of formation flying, this paper analyzes the main application of formation flying in the fifth section. It is the surface coverage for satellites formation flying. A set of calculational formulas were advanced in this section, for example, the maximal coverage angle、the minimal coverage angle、the belt width of coverage and the total time、the total amount of circles needed for global coverage of the satellites formation flying.
This paper gives many simulations at the end of every section, the results of the simulation prove that these technique bring forward in this paper are feasible and compact. These formulas and researchful methods can be served as reference for other kinds of researches about formation flying systems of micro-satellites.
引文
[1] Didier Massonnet. Capabilities and Limitations of the Interferometric Cartwheel. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING,2001,39(3):506-520
[2] S.Ramongassie,L.Phalippou,E.Thouvenot,D.Massonnet. Preliminary Design of the Payload for the Interferometric Cartwheel. IEEE,2000,0-7803-6359-0
[3] Josef Mittermayer,Krieger,Alberto Moreira,Michael Wendler. Interferometric Performance Estimation for the Inerferometric Cartwheel in Combination with a Transmitting SAR-Satellite. IEEE,2001,0-7803-7031-1
[4] 范剑峰. 卫星星座述评. 中国空间科学技术,1986,6(6):22-30
[5] 林来兴. 发展我国小卫星星座和测控技术. 飞行器测控学报,2000,19(3):17-22
[6] 林来兴. 现代小卫星及其关键技术. 中国空间科学技术,1995,8(4):37-43
[7] 朱振才,杨根庆,余金培,张锐. 微小卫星组网与编队技术的发展. 上海航天,2004,6:46-49
[8] 刘林,王海红,胡松杰. 卫星定轨综述. 飞行器测控学报,2005,24(2):28-34
[9] 林来兴,张洪华,车汝才. 编队飞行区域性导航卫星和位置保持. 宇航学报,2004,25(1):82-88
[10] 孟鑫,李俊峰,高云峰. 卫星编队飞行相对轨道的摄动研究综述. 宇航学报,2004,25(4):473-478
[11] 王兆魁,张育林. 分布式卫星群构形初始化控制策略. 宇航学报,2004,25(3):334-337
[12] 陈力,申敬松,胡松杰. 卫星星座的相对几何和区域覆盖重复周期. 宇航学报,2003,24(3):278-281
[13] 李新峰,黄天衣. RKNF 方法和大偏心率轨道数值积分. 紫金山天文台台刊,1999,18(1):1-8
[14] 季江徽,刘林,张伟. 第三体摄动分析解的一种表达式. 天文学报,2000,41(1):79-92
[15] 刘林. 航天器轨道理论[M]. 北京:国防工业出版社,2000
[16] William E,Wiesel. Optimal Impulsive Control of Relative Satellite Motion. Journal of Guidance,Control,and Dynamics,2003,26(1):74278
[17] Hsiao F Y,Scheeres DJ. Design of Spacecraft Formation Orbits Relative to a Stabilized TraJectory. AAS/ AIAA Space Flight Mechanics Meeting,February 2003,Paper No. AAS 032175
[18] Schaub H. Stabilization of Satellite Motion Relative to a Coulomb Spacecraft Formation. AAS/ AIAA Space Flight Mechanics Meeting,Feb,2004
[19] 胡松杰,王歆,刘林. 卫星星座与编队飞行问题综述. 天文学进展,2003,21(3):231～240.
[20] 王五生. 人造卫星在大气中运动的相对论摄动方程的解. 陕西师范大学学报,1996,24(4):21～24.
[21] HU Song-jie,CHEN Li, LIU Lin. Evolution of the Structure Evolution of Satellite Constellations. Chinese Astronomy and Astrophysics , 2003,27 :325～334.
[22] 徐敏,程凤舟,陈士橹. 星座覆盖性能数值仿真. 宇航学报,2000,21(增刊):11-17
[23] 郗晓宁,王威等. 近地航天器轨道基础[M]. 长沙:国防科技大学出版社,2003
[24] Crossley,W.A.,and William,E.A.:’Simulated annealing and genetic algorithm approaches for discontinuous coverage satellite constellation design’, Eng.Optim,2000,32,pp. 353-371
[25] Cho,S.:’Adaptive dynamic channel allocation scheme for spotbeam handover in LEO satellite networks’.Proc.Vehicular Technology Conf.VTC 2000, Boston,MA,USA,September 2000,pp.1925-1929
[26] Alvarez,R.,Tafazolli,R.,and Evans,B.G.:’Mobile terminal positioning methods for dynamic constellations with dual satellite visibility’.Proc.19th AIAAInt.Conf.on Communication satellite systems.Toulouse,France,17-20 April 2001,Vol.2
[27] Qiguo Yan,Vikram.Kapila,and Andrew G.Sparks.:’Pulse-based periodic control for spacecraft formation flying’.Proceedings of the American Control Conference Chicago,lllinois.June 2000,pp.374-378
[28] Kapila,V.,Sparks,A.G.,Buffington,J.M.,and Yan,Q.,”Spacecraft Formation Flying:Dynamics and Control,”Proc.of the American Control Conference,Dan Diego,CA,June1999,pp.4137-4141;see also J.Guidance,Control,and Dynamics,to appear.
[29] Chao,C.C.,Pollard,J.E.,and Janson,S.W.,”dynamics and Control of Cluster Orbits for Distributed Space Missions,”AAS/AIAA Space Flight Mechanics Meeting,1999,Paper No.AAS99-126
[30] Sabol,C.,Burns,R.,and McLaughlin,C.,”Formation Flying Design and Evolution,”AAS/ AIAA Space Flight Mechanice Meeting,1999.
[31] J.Galtier.”Geographical reservation for guaranteed handover and routing in low earth orbit constellations.”In 1 Workshop de Comunicacao sem Fio.Julho,1999.
[32] Ely,T.A.,Crossley,W.A.,and William,E.A.:’Satellite constellation design for zonal coverage using genetic algorithms’,J.Astronaut.Sci,1999,47,(3 and 4),pp.207-228
[33] Alvarez,R.,Tafazolli,R.,and Evans,B.G.:’Mobile terminal positioning methods for dynamic constellations with dual satellite visibility’.Proc.19th AIAA Int.conf.on Communication satellite systems.Toulouse,France,17-20 April 2001,Vol.2
[34] 曾国强,张育林. 编队飞行队形设计一般化方法. 中国空间科学技术,2003,2(1):21～25
[35] 冯初刚,朱元兰,张飞鹏. LAGEOS 卫星精密定轨及残差分析. 天文学报,2003,44(1):55～64
[36] 张传定,柴洪洲,杨强文. 高斯型龙格库塔积分器. 天文学报,2000,41(4):337～346
[37] 杨宇,韩潮. 编队飞行卫星群描述及摄动分析. 中国空间科学技术,2002,4(2):15～23
[38] 张玉锟,戴金海. 卫星编队飞行的地球扁率摄动分析. 宇航学报,2002,23(3):72～76
[39] 杨维廉. 椭圆轨迹编队飞行轨道分析. 中国空间科学技术,2001,10(5):1～6
[40] 肖业伦,张晓敏. 编队飞行卫星群的轨道动力学特性与构形设计. 宇航学报,2001,22(4):7～12
[41] 张洪华,林来兴. 卫星编队飞行相对轨道的确定. 宇航学报,2002,23(6):77～81
[2] S.Ramongassie,L.Phalippou,E.Thouvenot,D.Massonnet. Preliminary Design of the Payload for the Interferometric Cartwheel. IEEE,2000,0-7803-6359-0
[3] Josef Mittermayer,Krieger,Alberto Moreira,Michael Wendler. Interferometric Performance Estimation for the Inerferometric Cartwheel in Combination with a Transmitting SAR-Satellite. IEEE,2001,0-7803-7031-1
[4] 范剑峰. 卫星星座述评. 中国空间科学技术,1986,6(6):22-30
[5] 林来兴. 发展我国小卫星星座和测控技术. 飞行器测控学报,2000,19(3):17-22
[6] 林来兴. 现代小卫星及其关键技术. 中国空间科学技术,1995,8(4):37-43
[7] 朱振才,杨根庆,余金培,张锐. 微小卫星组网与编队技术的发展. 上海航天,2004,6:46-49
[8] 刘林,王海红,胡松杰. 卫星定轨综述. 飞行器测控学报,2005,24(2):28-34
[9] 林来兴,张洪华,车汝才. 编队飞行区域性导航卫星和位置保持. 宇航学报,2004,25(1):82-88
[10] 孟鑫,李俊峰,高云峰. 卫星编队飞行相对轨道的摄动研究综述. 宇航学报,2004,25(4):473-478
[11] 王兆魁,张育林. 分布式卫星群构形初始化控制策略. 宇航学报,2004,25(3):334-337
[12] 陈力,申敬松,胡松杰. 卫星星座的相对几何和区域覆盖重复周期. 宇航学报,2003,24(3):278-281
[13] 李新峰,黄天衣. RKNF 方法和大偏心率轨道数值积分. 紫金山天文台台刊,1999,18(1):1-8
[14] 季江徽,刘林,张伟. 第三体摄动分析解的一种表达式. 天文学报,2000,41(1):79-92
[15] 刘林. 航天器轨道理论[M]. 北京:国防工业出版社,2000
[16] William E,Wiesel. Optimal Impulsive Control of Relative Satellite Motion. Journal of Guidance,Control,and Dynamics,2003,26(1):74278
[17] Hsiao F Y,Scheeres DJ. Design of Spacecraft Formation Orbits Relative to a Stabilized TraJectory. AAS/ AIAA Space Flight Mechanics Meeting,February 2003,Paper No. AAS 032175
[18] Schaub H. Stabilization of Satellite Motion Relative to a Coulomb Spacecraft Formation. AAS/ AIAA Space Flight Mechanics Meeting,Feb,2004
[19] 胡松杰,王歆,刘林. 卫星星座与编队飞行问题综述. 天文学进展,2003,21(3):231～240.
[20] 王五生. 人造卫星在大气中运动的相对论摄动方程的解. 陕西师范大学学报,1996,24(4):21～24.
[21] HU Song-jie,CHEN Li, LIU Lin. Evolution of the Structure Evolution of Satellite Constellations. Chinese Astronomy and Astrophysics , 2003,27 :325～334.
[22] 徐敏,程凤舟,陈士橹. 星座覆盖性能数值仿真. 宇航学报,2000,21(增刊):11-17
[23] 郗晓宁,王威等. 近地航天器轨道基础[M]. 长沙:国防科技大学出版社,2003
[24] Crossley,W.A.,and William,E.A.:’Simulated annealing and genetic algorithm approaches for discontinuous coverage satellite constellation design’, Eng.Optim,2000,32,pp. 353-371
[25] Cho,S.:’Adaptive dynamic channel allocation scheme for spotbeam handover in LEO satellite networks’.Proc.Vehicular Technology Conf.VTC 2000, Boston,MA,USA,September 2000,pp.1925-1929
[26] Alvarez,R.,Tafazolli,R.,and Evans,B.G.:’Mobile terminal positioning methods for dynamic constellations with dual satellite visibility’.Proc.19th AIAAInt.Conf.on Communication satellite systems.Toulouse,France,17-20 April 2001,Vol.2
[27] Qiguo Yan,Vikram.Kapila,and Andrew G.Sparks.:’Pulse-based periodic control for spacecraft formation flying’.Proceedings of the American Control Conference Chicago,lllinois.June 2000,pp.374-378
[28] Kapila,V.,Sparks,A.G.,Buffington,J.M.,and Yan,Q.,”Spacecraft Formation Flying:Dynamics and Control,”Proc.of the American Control Conference,Dan Diego,CA,June1999,pp.4137-4141;see also J.Guidance,Control,and Dynamics,to appear.
[29] Chao,C.C.,Pollard,J.E.,and Janson,S.W.,”dynamics and Control of Cluster Orbits for Distributed Space Missions,”AAS/AIAA Space Flight Mechanics Meeting,1999,Paper No.AAS99-126
[30] Sabol,C.,Burns,R.,and McLaughlin,C.,”Formation Flying Design and Evolution,”AAS/ AIAA Space Flight Mechanice Meeting,1999.
[31] J.Galtier.”Geographical reservation for guaranteed handover and routing in low earth orbit constellations.”In 1 Workshop de Comunicacao sem Fio.Julho,1999.
[32] Ely,T.A.,Crossley,W.A.,and William,E.A.:’Satellite constellation design for zonal coverage using genetic algorithms’,J.Astronaut.Sci,1999,47,(3 and 4),pp.207-228
[33] Alvarez,R.,Tafazolli,R.,and Evans,B.G.:’Mobile terminal positioning methods for dynamic constellations with dual satellite visibility’.Proc.19th AIAA Int.conf.on Communication satellite systems.Toulouse,France,17-20 April 2001,Vol.2
[34] 曾国强,张育林. 编队飞行队形设计一般化方法. 中国空间科学技术,2003,2(1):21～25
[35] 冯初刚,朱元兰,张飞鹏. LAGEOS 卫星精密定轨及残差分析. 天文学报,2003,44(1):55～64
[36] 张传定,柴洪洲,杨强文. 高斯型龙格库塔积分器. 天文学报,2000,41(4):337～346
[37] 杨宇,韩潮. 编队飞行卫星群描述及摄动分析. 中国空间科学技术,2002,4(2):15～23
[38] 张玉锟,戴金海. 卫星编队飞行的地球扁率摄动分析. 宇航学报,2002,23(3):72～76
[39] 杨维廉. 椭圆轨迹编队飞行轨道分析. 中国空间科学技术,2001,10(5):1～6
[40] 肖业伦,张晓敏. 编队飞行卫星群的轨道动力学特性与构形设计. 宇航学报,2001,22(4):7～12
[41] 张洪华,林来兴. 卫星编队飞行相对轨道的确定. 宇航学报,2002,23(6):77～81