摘要
卫星编队飞行是一种崭新的航天器空间在轨运行模式,凭借其巨大的技术优势和广阔的应用前景,从研究之初就备受关注,是一种能够代表未来航天发展趋势的技术。同时,卫星编队飞行对目前的航天技术提出了巨大挑战,在动力学、相对导航、队形控制等方面还有许多问题有待深入研究。本文以近地轨道卫星编队飞行为研究背景,对卫星编队的动力学、相对导航、队形保持、队形重构以及卫星编队飞行应用于空间轨道的封锁等问题进行了较为深入的研究和探讨。主要研究内容包括:
编队卫星数学模型的建立和队形设计。分别从动力学和运动学角度出发,建立了两种卫星编队飞行的数学模型,推导了这两种数学模型之间的坐标转换关系,在此基础之上,分析了地球非球形引力、大气阻力和太阳光压等轨道摄动力对编队飞行的影响,然后针对主星在圆或椭圆轨道上运动,进行了队形设计。
卫星编队飞行相对导航研究。本文提出了激光测距仪测量、特征光点与CCD相机组合测量、激光测距仪和特征光点组合测量三种不同的卫星编队飞行相对测量方案,利用扩展卡尔曼滤波算法、Unscented卡尔曼滤波算法和粒子滤波算法对星间相对导航问题进行了深入的研究,仿真结果表明无论是估计精度还是收敛速度,Unscented卡尔曼滤波在相对导航应用中都要优于扩展卡尔曼滤波,而粒子滤波对于系统噪声是非高斯白噪声的情况具有较强的适应性。
卫星编队飞行的队形保持和控制研究。根据卫星编队飞行的动力学模型,提出了线性二次型调节器控制和势函数控制两种不同的控制方案。线性二次型调节器控制主要是针对主星在近圆轨道上运动,无摄动的情况,而势函数控制理论可以适用于主星在任意椭圆轨道上运动,有摄动的情况,数学仿真验证了这两种不同控制方法的有效性。
卫星编队飞行队形重构研究。研究了基于多种约束条件下的编队卫星队形重构技术。根据队形重构的特点,推导了防止星间碰撞、燃料消耗均衡和控制力限幅等约束条件,将编队的队形重构问题归结为代数方程求解问题,提出了基于非线性规划和遗传算法的求解思路,数学仿真验证了方法的可行性。
卫星编队飞行轨道封锁研究。文中探讨了轨道封锁机理和本质,研究了主星在椭圆轨道上运动情况下,编队卫星轨道封锁问题,数学仿真显示,利用编队卫星进行空间轨道封锁是可以实现的。
总之,本文以理论分析与仿真计算相结合的方式,对近地轨道航天器编队飞行的动力学、导航、控制以及应用进行了有益的研究和探讨,提出了若干解决编队控制和应用问题的方法,对于其它轨道上的航天器编队飞行的相关研究也具有借鉴意义,将为我国分布式航天器技术的理论研究和实际应用提供参考。
Formation flying is a new paradigm in space mission design, which has been a hot view since it appeared and is regarded as trend about spacecraft technology, at the same time, there are a lot of challenges in dynamics, relative navigation, control and application.
Based on the excellent characteristic and the wide application of low earth orbit, the research on formation flying, including formation dynamics and design analysis with perturbations, relative navigation, formation maintenance and control as well as formation reconfiguration problem which formation orbit transfer and maneuvers in phase, are studied detailed in the dissertation. What’s more, there is a discussion on the method and the ability of local space control with formation flying. The main contents are as follows:
Model building and formation designing on formation flying. From the view of dynamics and kinematics accordingly, the two models of formation flying are built, and transform matrix is also be derived between them, on this condition, the different perturbation from the J 2 perturbation arising from the aspherical nature of the Earth, drag and solar radiation pressure is analyzed, at last formation is designed when master satellite is in circle or elliptical reference orbit. Achieving the objectives of maintenance and control, therefore, understanding and utilizing the dynamics of relative motion is of significant importance.
The research on relative navigation of formation flying. Three different measurement methods are proposed in the dissertation, which are laser range finder, charge coupled device sensor and a combination of laser range finder and charge coupled device sensor, relative navigation is approached respectively by extended kalman filter, unscented kalman filter and particle filter, by comparing the characteristics of extended kalman filter with that of unscented kalman filter , the conclusion can be drawn that unscented kalman filter gets better performance than extended kalman filter in the relative navigation, especially, paticle filter is fit for non-Gaussian noise well.
The research on maintenance and control of formation flying. According to dynamics model of formation flying, two kind of control scheme that is LQRcontroller and potential function controller is studied in the dissertation, LQRcontroller is applied when master satellite is in circle or very small eccentricityreference orbit, and Tperturbations have no effect on formation. TPotential functioncontroller is applied when master satellite is in any reference orbit, andTperturbations have effect on formation. TThe simulation results show that the twocontrol method is effective.
The research on formation reconfiguration. The technique is developed forthe numerical treatment of optimal control problems for formation systems inorder to compute optimal control laws for the reconfiguration of a group offormation flying satellites. In process of formation reconfiguration, the collisionfree,equalization of energy, limited controller and so on are regarded as restrictconditions. Nonlinear program and Genetic Algorithms are applied to satellitesformation reconfiguration, the simulation results validate t the reconfigurationmethod is feasible.
The research on space combat using satellite formation flying. The differentmethod to control local space is discussed in the dissertation. the problem ofcontrolling local space using satellite formation flying is investigated as masterbeing in circle or elliptical reference orbit, the results indicate the research onspace combat using satellite formation flying is significative.In conclusion, by analyzing and simulating, it mainly makes researches onthe problems in dynamics, relative navigation, control, reconfiguration andapplication of satellite formation in the dissertation and proposes some methodson the navigation, control and the application of satellites formation flying,which maybe provide ideas for the research on formation flying in differentorbits and be of some help to the development of distributed spacecraft system.
引文
1美国航天司令部长期规划—2020年设想.国家高级技术航天领域专家委员会
2闻新,马文弟,周露.小卫星编队飞行的应用模式分析及展望.中国航天:2005,8
3 R.Sedwick, D.Miller, and E.Kong.,”Mitigation of Differential Perturbations in Synthetic Apertures Comprised of Formation Flying Satellites,”presented at the 9th AAS/AIAA Space Flight Mechanics Meeting, Brenckenridge, Colorado, February 7-10, 1999
4 Kim Luu, et al.,”University Nanosatellite Distributed Satellite Capabilities to Support TechSat21,”AIAA/USU Small Satellite Conference, Logan UT,23-26 Aug 99
5 Danzmann K.LISA -An ESA Cornerstone Mission for the Detection and Observation of Gravitational Waves[J].Advances in Space Research,2003,32 (7):1233~1242
6 Tien JY,Srinivasan JM,Young JE,“Formation Acquisition Sensor for the Terrestrial Planet Finder(TPF) Mission[C],”2004 IEEE Aerospace Conference Proceedings, IEEE,2004,Vol.6:2680-2690
7 Massonnet D.,”Capabilities and limitations of the interferometric cartwheel[J],”IEEE Trans on Geoscience and Remote Sensing,2001,39(3) :506-520
8 A. Giazotto, D. Passuello, and A. Stefanini,“One-mile equivalent length interferometric pendulum for seismic noise reduction,”Rev. Sci. Instrum. 57, 1145 (1986)
9 TA Moccia, G Rufino, M Aragri.,”TTBISSAT: A Bistatic SAR for Earth Observation,”TTScience Small Missions Program, Second Cycle, Final Report, 2001
10 TR Larsson, S Berge, P Bodin, U J?nsson.,”TFuel Efficient Relative Orbit Control Strategies for Formation Flying Rendezvous within PRISMA,”T 29 thAnnual AAS Guidance and Control Conference. AAS 06-025
11刘林.航天器轨道理论.北京:国防工业出版社,2000
12 Prussing, J. E. and Conway, B. A., Orbital Mechanics. Oxford University Press. New York,1996
13 Battin, R. H., An Introduction to the Mathematics and Methods of Astrodynamics, AIAA Press, New York, 1987
14郗晓宁,王威.近地航天器轨道基础.长沙:国防科学技术大学出版社,2003
15 Clohessy W H, Wilshire R S,“Terminal guidance system for satellite rendezvous[J],”Journal of the aerospace science,1960,27(9):653-674
16 Clohessy,W.H. and Wiltshire,R.S.,”Terminal Guidance System for Satellite Rendezvous,”Journal of the Aerospace Science,Vol.27,No.9,1960,pp,653-658
17 Richard H. Vassar, and Richard B.Sherwood,“Formation keeping for a pair of satellites in a circular orbit,”Journal ofGuidance, Control, and Dynamics, Vol. 8, No. 2, pp. 235-242, March-April 1985
18 David C. Redding, and Neil J. Adams,“Linear-quadratic station keeping for the STS orbiter,”Journal of Guidance, Control, and Dynamics, Vol. 12, No. 2, pp. 248-255, March-April 1989
19 R.J.Sedwick, D.W.Miller, and E.M.C.Kong,“Mitigation of differential perturbations in formation flying satellite clusters,”The Journal of the Astronautical Sciences, Vol. 47, No. 3 and 4, pp.309-331, July-December 1999
20 Qiguo Yan, Vikram Kapila, and Andrew G. Sparks,“Pulse-based periodic control for spacecraft formation flying,”American Control Conference, pp. 374-378, Vol. 1, Chicago, IL, June 28-30, 2000
21 De Queiroz, V.Kapila, and Q.Yan,“Adaptive nonlinear control of satellite formation flying,”AIAA Guidance, Navigation and Control Conference, pp. 1596-1604, Portland, Oregon, August 1999
22 De Queiroz, Yan, Q.; Yang, G.; Kapila, V.,“Global output feedback tracking control of spacecraft formation flying with parametric uncertainty,”Decision and Control, pp. 584 -589, Phoenix, AZ, December 7-10, 1999
23 Kapila V, Sparkss AG, Buffington JM, et al.,”Spacecraft formation flying: dynamics and control[A],”In: Proceedings of the American Control Conference [C]. San Diego, California, 1999,4137– 4141
24 Gkhan Inalhan, Michael Tillerson, and Jonathan P. How,“Relative dynamics and control of spacecraft formations in eccentric orbits,”Journal of Guidance, Control, and Dynamics, Vol. 25, No. 1, pp. 43-60, January-February 2002
25 Schiff, C.; Rohrbaugh, D.; Bristow, J.“Formation flying in elliptical orbits,”IEEE Aerospace Conference, pp. 37-47, Vol. 7, Big Sky, MT, March 18-25, 2000
26 Lawden,D.F. Optimal trajectories for Space Navigation. Butterworths, London, 1963
27 Tschauner,J and Hempel,P.,”Rendezvous. Optimum acceleration program for a rendezvous maneuver,”Astronautica Acta, Vol. 11, No. 5, 1965: 312-321
28 Garrison,J.L gardner,T.G and Axelrad,P.,”Relative Motion in Highly Elliptical Orbits,”AAS Spaceflight Mechanics 1995,Vol.89,1995:1359-1376
29 Melton R G.,”Time explicit representation of relative motion between elliptical orbits[J],”Journal of Guidance,Control,and Dynamics,2000,23(4): 604-610
30 Schaub H,Alfriend K T.,”J2 invariant relative orbits for spacecraft formations[R],”NASA GSFC Flight Center,May 1999
31 TH Schaub, SR Vadali, JL Junkins, KT Alfriend,“TTSpacecraft Formation Flying Control Using Mean Orbit Elements,”TAAS Astrodynamics 1999,Vol,103. 1999:163-182
32 Vadali S R,Schaub H,Alfriend K T,”Initial conditions and fuel-optimal control for formation flying of Statellites,”AIAA GN&C Conference,Paper AIAA 99-4265,Portlan,OR,August 1999
33 KT Alfriend, DW Gim, and SR Vadali,“The characterization of formation flying satellite relative motion orbits,”TAdvances in the Astronautical Sciences, 2002,Vol.112,2002:577-584
34 Dong Woo Gim,Kyle T.Alfriend,”The State Transition Matrix of Relative Motion for the Perturbed Noncircular Reference Orbit,”AAS Spaceflight Mechanics 2001,Vol,108,2001:913-934
35 Dong Woo Gim,Kyle T.Alfriend.,”The state transition matrix for relative motion of formation flying satellites,”AAS Spaceflight Mechanics 2002,Vol,112,2002:1021-1042
36张玉锟,戴金海.编队卫星群的运动分析与轨道设计.微小卫星编队飞行及其应用论文集。北京,2000
37张玉锟.卫星编队飞行的动力学与控制技术研究[工学博士论文].国防科学技术大学,2002
38 James,K.Whiting. Orbital transferr Trajectory Optimization,Master’s thesis, Massachusetts Institute of Technology, February 2004
39 Steven, P.Hughes. Formation Flying Performance Measures for Earth Pointing Missions. Master’s thesis, Virginia Polytechnic Institute and State University, Blackburg, VA, December 1999
40 TS Schweighart, R Sedwick.,”TTA perturbative analysis of geopotential disturbances for satellite cluster formation flying,”TT2001, IEEE Proceedings
41 S. Schweighart and R. Sedwick,“High-Fidelity Linearized J2 Model for Satellite Formation Flight. Journal of Guidance, Control and Dynamics, Vol.25, No.6, Nov-Dec 2002, pp1073-1080
42 D. Izzo,“Formation Flying for MUSTANG,”5th Cranfield Conference on Dynamics and Control of Systems and Structures in Space, Cambridge, 14th-18th July 2002
43 K. T. Alfriend, H. Schaub, and D. Gim,“Gravitational Perturbations, Nonlinearity and Circular Orbit Assumption Effects on Formation Flying Control Strategies,”AAS Rocky Mountain Guidance and Control Conference, Breckenridge, Colorado, February 3-7 2000. Paper AAS 00-012
44 M,E.Campbell, D.Zanon and J.Kulkarni.,“Cluster Planning and Control for Spacecraft Formations”, Proceedings of the 14th AAS/AIAA Space Flight Mechanics Meeting, Maui,Hawaii, February 8-12 2004, AAS 04-254
45 Mitchell, J. W. and Richardson, D. L.,“Maintaining Periodic Trajectories with the First-Order Nonlinear Hill's Equations," Proceedings of the 2001 Astrodynamics Specialist Conference, Quebec City, Canada, July-August 2001
46 C.Sabol, R.Burns and C.A .Mclangblin,“Satellite formation flying design and eveolution,”Journal of spacecraft and rockets,2001,38(2):270-278
47 Queiroz, M. S.d., Kapila, V., and Yan, Q.,“Adaptive Nonlinear Control of Mul tiple Spacecraft Formation Flying," AIAA, Journal of Guidance, Control and Dynamics, Vol. 23, No.3, May-June 2000
48 Naasz, B. J., Karlgaard, C. D., and Hall, C. D.,“Application of SeveralControl Techniques for the Ionospheric Observation Nanosatellite Formation," Proceedings of the 2002 AAS/AIAA Space Flight Mechanics Meeting, San Antonio, TX, January 2002
49 Zhang, F. and Krishnaprasad, P. S.,“Formation Dynamics Under a Class of Control Laws," Proceedings of the American Control Conference, No. ACC02 AIAA1052, Anchorage, AK, July-August 2002
50 David Folta, Francesco Bordi, Christopher Scolese.,”Considerations on formation flying separation for earth observing satellite missions[J],”Advances in the Astronautical Sciences,1992,79(2):803-822
51 Starin, S. R., Yedavalli, R. K., and Sparks, A. G.,“Spacecraft Formation Flying Maneuvers Using Linear Quadratic Regulation with No Radial Axis Inputs," Proceedings of the 2001 AIAA Guidance, Navigation and Control Conference and Exhibit, Montreal, Canada, August 2001
52 Ulybyshev, Y., "Long-Term Formation Keeping of Satellite Constellation Using Linear Quadratic Controller," Journal of Guidance, Control, and Dynamics, Vol. 21, No. 1, 1998, pp. 109-115
53 TH Wong, V Kapila, AG Sparks.,”TAdaptive output feedback tracking control of spacecraft formation,”J. Robust Nonlinear Control 2002; 12:117-139
54 TR Pongvthithum, SM Veres, SB Gabriel, E Rogers.,”TUniversal adaptive control of satellite formation flying,”TInternational Journal of Control. TNo. 1, January 2005, 45-52
55 H H Yeh, E Nelson,A Sparks.,”Nonlinear tracking control for satellite formations,”Journal of Guidance, Control and Dynamics Vol.25,No.2,March-April 2002
56 Smith, R. S. and Hadaegh, F. Y.,“Control of Deep-Space Formation-Flying Scacecraft: Relative Sensing and Switched Information,”Journal of Guidance, Control, and Dynamics, Vol. 28, No. 1, January-February 2005, pp. 106-114
57 Mesbahi, M. and Hadaegh, F. Y,“Formation Flying Control of Multiple Spacecraft via Graphs, Matrix Inequalities, and Switching,”Journal of Guidance, Control, and Dynamics, Vol. 24, No. 2, March-April 2001, pp. 369-377
58 Beard, R. W., Lawton, J. and Hadaegh, F. Y.,“A Coordination Architecturefor Spacecraft Formation Control,”IEEE Trans. on Control Systems Technology, November 2001
59 Gurfil, P., Idan M. and Kasdin, N. J.,“Adaptive Neural Control of Deep-Space Formation Flying,”Journal of Guidance, Control, and Dynamics, Vol.
26, No. 3, May-June 2003, pp. 491-501
60 H.Schaub.,”Spacecraft Relative Orbit Description Through Orbit Element Differences,”14th U.S. National Congress of Theoretical and Applied Mechanics, Blackberg, Virginia, June 23-28, 2002
61 H.Schaub.,”Incorporating Secular Drifts into the Orbit Element Difference Description of Relative Orbits,”in Proceedings of AAS/AIAA Space Flight Mechanics Meeting, Ponce, Puetro Rico, Feb. 9-13,2003, pp. 239-258
62 H.Schaub, and K.T.Alfiend,”Impulsive Spacecraft Formation Flying Control to Establish Specific Mean Orbit Elements,”In AAS Space Mechanics Specialist Meeting, Clearwater, Florida, Jan 23-26,2000,Paper No. AAS-00-113
63 H.Schaub, and K.T.Alfriend.,”Hybrid Cartesian and Orbit Element Feedback Law for Formation Flying Spacecraft,”AIAAGuidance, Navigation and Control Conference, Denver, CO, 2000, Paper No.2000-4131
64 Vadali, S. R., Schaub, H., and Alfriend, K. T.,“Initial Conditions and Fuel Optimal Control for Formation Flying of Satellites," Proceedings of the 1999 AIAA GNC Conference, Portland, OR, July-August 1999
65 J.P.How and M.Tillerson, "Analysis of the impact of sensor noise on formation flying control," Proceedings of the American Control Conference, pp 3986-3991, 2001
66 D.Highsmith, P.Axelrad, "relative state estimation using GPS flight data from coorbiting spacecraft,”Proceedings of the Institute of Navigation GPS conference, Nashville, TN, Sep.1999
67 I.Kawano, M.Mokuno, T.Kasai, T.Suzuki,"First Autonomous rendezvous using relative GPS navigation by ETS-VII," Journal of the Institute of Navigation, Vol.48, No.1, spring 2001
68 C. Park and J.P. How," Precise Relative navigation using augmented CDGPS," Proceedings of the ION-GPS Conference, Sept.2001
69 C.Bourga, C.Mehlen et al., "A formation flying RF subsystem for Darwin andSmart-2," International Symposium Formation Flying: Missions & Technologies. Toulouse, France 29 to 31 October,2002
70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
71 Roberto Alonso,John L.Crassidis and John L.Junkins.,”Vision based relative navigation for formation flying of spacecraft,”AIAA Guidance,Navigation and Control Conference and Exhibit 2000
72 Son Goo Kim, John L. Crassidis, Yang Cheng and Adam M. Fosbury.,”TKalman Filtering for Relative Spacecraft Attitude and Position Estimation,”TTJournal OF Guidance, Control, and Dynamics, 2007
73 TJR. Yim, JL Crassidis, JL Junkins.,”TTAutonomous Orbit Navigation of Interplanetary Spacecraft,”TT Astrodynamics Specialist Conference 2000
74秦永元,张洪钺,汪叔华.卡尔曼滤波与组合导航原理.西安:西北工业大学出版社,1998:205-212
75赵瑞,顾启泰.滤波理论的最新进展及其在导航系统中的应用.清华大学学报(自然科学版),2000,40(5):24-27
76 Julier,S.J., Uhlmann,J.K., and Durrant-Whyte,H.F., "A New Approach for Filtering Nonlinear Systems," Proceedings of the American Control Conference,Seattle,WA,June 1995,pp.1628-1632
77 Gustafsson F,Gunnarsson F,Niclas Bergman,Forssell U,Hansson J,Karlsson R and Nordlund, P.J,“Particle filters for positioning,navigation and tracking[j],”IEEE trans on signal processing.Vol.50.No.2.Feb.2002
78 Wan,E.and van der Merwe, R., Kalman Filtering and Neural Networks, edited by S.Haykin, chap.7, John Wiley & Sons, New York,NY,2001
79 Doucet A,Godsil S.On Sequential Monte Car Sampling Methods for Bayesian Filtering[R].Cambridge:University of Cambridge,1998
80 E.A.Wan and R.Vander Merwe.Kalman Filtering and Neural Networks.Wiley Publishing.Eds.S.Haykin.2001
81 P.K.C. Wang and F.Y. Hadaegh,“Optimal Formation-Reconfiguration for Multiple Spacecraft,”Paper AIAA-98-4226
82 P.K.C. Wang and F.Y. Hadaegh,“Minimum-Fuel Formation Reconfiguration of Multiple Free-Flying Spacecraft,”J. Astronautical Sciences,Vol.47, Nos.1 and 2, Jan.-Jun. 1999, pp.77-102
83 R.W. Beard, J. Lawton and F.Y. Hadaegh,“A Coordination Architecture forSpacecraft Formation Control,”IEEE Transactions on Control SystemsTechnology, Vol.9, No.6, Nov.2001, pp.777-790
84 Michael.Tillerson., Coordination and Control of Multiple Spacecraft usingConvex Optimization Techniques. Master’s thesis, Massachusetts Institute ofTechnology,June 2002
85 Tillerson, M., Inalhan, G., and How, J. P.,“Coordination and Control ofDistributed Spacecraft Systems Using Convex Optimization Techniques,”International Journal on Nonlinear and Robust Control , Vol. 12, No. 2-3, Feb2002, pp. 207–242
86 TT Schetter, M Campbell, D Surka.,“T TMultiple agent-based autonomy forsatellite constellations,”T TArtificial Intelligence, 2001
87 Inalhan G, Tillerson M,How J P.,“Relative dynamics and control ofspacecraft formations in Tin eccentric orbits,”T TJournal of Guidance, Control,and Dynamics, 2002
88 TME Campbell, D Zanon, J Kulkarni.,”T TCluster Planning And Control ForSpacecraft Formations,”T TAdvances in the Astronautical Sciences, 2005
89 TDJ Zanon, ME Campbell.,“TOptimal Planner for Spacecraft Formations Tineccentric orbits,”T TJournal of Guidance, Control, and Dynamics, 2006
90 C.Y. Xia and P.K.C. Wang,“Optimal Formation Reconfiguration of MultipleSpacecraft with Docking and Undocking Capability,”AIAA Guidance,Navigation and Control Conference and Exhibit 15-18 August 2005, SanFrancisco, California
91 TP Sengupta, SR Vadali.,“TA Lyapunov-Based Controller For SatelliteFormation Reconfiguration In The Presence Of J2 Perturbations,”Advancesin the Astronautical Sciences 119, 2371-2393, 2005
92 Armellin R., Massari M., Ercoli Finzi A,“Optimal Formation FlyingReconfiguration and Station Keeping Maneuvers Using Low ThrustPropulsion,”18th International Symposium on Space Flight Dynamics, 11-15October 2004, Munich, Germany
93 TH.C Lim, H.C Bang, K.D Park, W.K Lee.,”TOptimal Formation TrajectoryPlanning Using Parameter Optimization Technique,”J. Astron. Space Sci.21(3), 209–220 (2004)
94 C. Sultan, S. Seereeram, R. Mehra, and F. Hadaegh,“Energy Optimal Reconfiguration for Large Scale Formation Flying,”In Proceedings of the American Control Conference, p. 2986–2991, July 2004
95 C. Sultan, S. seereeram, R. K. Mehra, "Minimization and Equalization of Energy for Formation Flying Reconfiguration", in Proceedings of Intl .Conference of Robotic and Automation.2004
96 Cornel Sultan, Sanjeev Seereeram, and Raman K. Mehra,“Energy optimal multi-spacecraft relative reconfiguration of deep space formation flying,”43rd IEEE Conference on Decision and Control , December 14-17, 2004
97 TD Dumitriu, S Marques, P Lima, B Udrea,”TDecentralized Low Communication State Estimation and Optimal Guidance of Formation Flying Spacecraft,”16th AAS/AIAA spacecraft flight mechanics conference, Tampa, Florida. January 22-26, 2006
98 TMB Milam, N Petit, RM Murray.,”TTConstrained trajectory generation for microsatellite formation flying,”TTAIAA Guidance, Navigation and Control Conference, 2001
99 Tsuda, Y.,“Global Optimization of Maneuver Schedule for Multiple Spacecrafts Flying in Formation,”55th International Astronautical Congress, Vancouver, Canada, IAC-04-A.2.01, 2004
100 TO Junge, S Ober-Blobaum.,”TOptimal Reconfiguration of Formation Flying Satellites,”TDecision and Control, TSpain, December 12-15, 2005
101 Mailhe L, Jose Guzman J.,”Initialization and Resizing of Formation Flying using Global and Local Optimization Methods,”IEEE Aerospace Conference Proceedings.2004:547-556
102 Guzman, Jose J.“Tetrahedron Formation Control,”Journal of the Astronautical Sciences, Vol. 51,No. 4, pp. 419-431, 2003
103 Yuichi Tsuda, Shinichi Nakasuka.,”Impulsive optimal guidance algorithm for formation flying spacecraft,”Proceedings of the 23th international symposium on space technology and science, vol. I, 2002: 917-923
104 Battin, R. H., An Introduction to the Mathematics and Methods of Astrodynamics, AIAA Press, New York, 1987
105 Chobotov, V. A., Ed., Orbital Mechanics, AIAA Press, New York, 1991
106杨家墀.航天器轨道动力学与控制.北京:宇航出版社,2002
107章仁为.卫星轨道姿态动力学与控制.北京:北京航空航天大学出版社,2005
108 Brown,C.D.Elements of Spacecraft Design, AIAA Education Series.2002
109易照华.天体力学.南京:南京大学出版社.1993
110刘暾.空间飞行器动力学与控制.哈尔滨:哈尔滨工业大学出版社.2003
111郑学塘,倪彩霞.天体力学与天文动力学.北京师范大学出版社.1987
112 R. K. Yedavalli; A. G. Sparks,“Satellite formation flying control design based on hybrid control system stability analysis,”American Control Conference, pp. 2210-2214, Vol. 3, Chicago, IL, June 28-30, 2000
113 S. M. Veres, S. B ,Gabriel, E. Rogers, D. Q. Mayne,“Analysis of formation flying control of a pair of nano-satellites,”Decision and Control, pp. 1095-1100, Vol. 2, Orlando, FL, December 2001
114 P.A.Stadter,“Discrete event command and control for formation flying of distributed small spacecraft systems,”13th AIAA/USU Conference on Small Satellites, SSC-99-VI-4, Logan, Utah, August 23-26,1999
115 Kang, W.; Xi, N.; Sparks, A,“Theory and applications of formation control in a perceptive referenced frame,”IEEE Decision and Control Conference, pp. 352-357 Vol. 1,Sydney, Australia, December, 2000
116 Johathan Lawton, Randal W.Beard, and Fred Y. Hadaegh,“An adaptive control approach to satellite formation flying with relative distance constraints,”American Control Conference, pp. 1545-1549, Vol. 3, San Diego, California, June 2-4, 1999
117 Andrew Robertson, Gokhan Inalhan, and Jonathan P. How,“Formation control strategies for a separated spacecraft interferometer,”American Control Conference, pp. 4142-4147, Vol. 6, San Diego, California, June 2-4, 1999
118 Haizhou Pan; Kapila, V.,“Adaptive nonlinear control for spacecraft formation flying with coupled translational and attitude dynamics,”IEEE Decision and Control Conference, pp. 2057 -2062, Vol. 3, Orlando, FL, December, 2001
119段广仁.线性系统理论.哈尔滨:哈尔滨工业大学,1998
120 McInnes,C,“Autonomous rendezvous using artificial potential functions,”Journal of guidance, control and dynamics, Vol.18,No.2, 1995:237-241
121 Geoffrey T. Huntington and Anil V. Rao.“Optimal configuration ofspacecraft formations via a Gauss Pseudospectral Method,”Advances inthe Astronautical Sciences 120, 33-50, 2005 AAS 05-103
122 TG Gomez, M Marcote, JJ Masdemont, JM Mondelo.“TNatural ConfigurationsAnd Controlled Motions Suitable For Formation Flying,”Advances in theAstronautical Sciences 123, 1513-1530, 2006
123 TFY Hadaegh, DP Scharf, SR Ploen.“TInitialization of Distributed Spacecraftfor Precision Formation Flying,”TProceedings of aerospace Conference2003:1463-1468
124 TD Zimpfer, P Kachmar, S Tuohy.,“T TAutonomous Rendezvous, Capture and In-Space Assembly: Past, Present and FuturTe,”1st Space ExplorationConference: Continuing the Voyage of Discovery. 30 January -1 February2005, Orlando, Florida. AIAA 2005-2523
125 TDP Scharf, FY Hadaegh, SR Ploen.“TA Survey of Spacecraft FormationFlying Guidance and Control (Part I): Guidance. [C],”Proceedings of theAmerican Control Conference, Deriver, Colorado. June 4-6,2003
126 Scharf DP, Hadaegh FY, Ploen S R,“A survey of spacecraft formation flyingguidance and control (Part II):Control[C],”Proceedings of American ControlConference. Pasadena: Jet Propulsion Laboratory, NASA, 2004:2976-2985
127 V. M. Guibout and D. J. Scheeres,“Spacecraft formation dynamics anddesign,”Journal of Guidance, Control, and Dynamics, vol. 29, no. 1, pp.121–133, 2006
128 A. B. Hoskins and E. M. Atkins,“Spacecraft formation optimization with amulti-impulse design,”in Proceedings of the AIAA Guidance, Navigation,and Control Conference and Exhibit, San Francisco, California, Aug 2005,AIAA 2005-5835
129 TSG Kim, JL Crassidis, Y Cheng, AM Fosbury, JL.“T TKalman Filtering forRelative Spacecraft Attitude and Position Estimation,”TVol. 30, No. 1,January–February 2007:133-138
130 TL Breger, JP How.“T TGauss's variational equation-based dynamics and controlfor formation flying spacecraft,”TJournal of guidance, control, and dynamics30:22, 2007: 437-448
131 Veres, SM, Thanapalan, K, Gabriel, SB and Rogers, E.“Reconfigurablecontroller design for operational safety in satellite formation flying,”UKACC International Control Conference 2006, Glasgow, UK, 30 August - 1 September 2006
132 F. Bacconi, E. Mosca, A. Casavola.,“Hybrid constrained formation flying control of micro-satellites,”IET Control Theory & Applications 2007
133 Mohinder S. Grewal, Angus P.Andrews, Kalman filtering :theory and practice using Matlab, Second Edition, John Wiley & Sons, 2001: 358-405
134 Simon Haykim, Kalman filtering and neural networks, John Wiley & Sons,2001:200-351
135 Joseph J,La Viola Jr. "A comparsion of unscented and extended kalman filtering for estimation quaternion motion[J]," 2003,IEEE,2435-2440
136 Norgaard M,Poulsen N K,Ravn O."New developments in the state estimation for nonlinear system[J]," Automatica,2000,36(11):1627-1638
137 Lawrence. David, Carl A. Badeward, Bayesian multiple target tracking, Artach House, 1999:400-451
138刘曙光,费佩岩,侯志敏.遗传算法的进展和展望[J].现代电子技术,2000,(6):75-79
139席裕庚,柴天佑,恽为民.遗传算法综述[J].控制理论与应用,1996(12):102-106
140 Hisashi Tanizaki, Nonlinear filters:estimation and applications, Springer-Verlag, 1996
141 A.Bech and M.Teboulle,”Global optimality conditions for quadratic optimization problems with binary constraints,”SIAM Journal on Optimization,2000,11(1):179-188
142 S.Burer, R.D.C.Monteiro and Y.Zhang."Solving a class of semidefinite programs via nonlinear programming," Math,Program,2002,93(1):97-122
143 F.Alizadeh. "Interior point methods in semidefinite programming with applications to combinatorial optimization," SIAM J.Optim.,1995,5:13-51
144袁亚湘,非线性规划数值方法.上海:上海科学技术出版社,1993
145袁亚湘,孙文渝,最优化理论与方法.北京:科学出版社,1995
146唐焕文,秦学志,最优化方法.大连:大连理工大学出版社,1993
147 P.Rogata, E.Di Sotto, M.Graziano, F.Graziani“Guess Value for Interplanetary Transfer Design Through Genetic Algorithms,”13thAAS/AIAA Space Flight Mechanics Meeting, Puerto Rico, 9-13 February 2003, AAS03-140
148王仁宏.数值逼近.北京:高等教育出版社,1999
149 Joachins, Parallel Genetic Algorithms: Theory and Applications. ISO press, 1993
150周明,孙树栋,遗传算法原理及应用.北京:国防工业出版社,1999
151玄光男,程润传,遗传算法与工程设计.北京:科学出版社,2000
152 Holland J.H, Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan press ,1975
153徐晓静,张恒源,李智.空间作战中的轨道拦截建模与仿真.装备指挥技术学院学报,2005, 16(5):61-63
154汤一华,陈士橹,徐敏,万自明.轨道拦截问题的一种精确初制导方法研究.飞行力学,2006,24(4):53-56
155程龙,陈勇.一种拦截轨道的确定方法. 2005, 23(1): 65-68