A new set of linearized differential equations governing relative motion between satellites in a formation is derived, taking into account the effects of as well as atmospheric drag. This set of equations is more convenient than the corresponding nonlinear equations for designing formation control system or for implementing guidance algorithms. It is assumed that the eccentricity of the chief's orbit is small. In addition, the corresponding constant linearized equations are also proposed without numerical integrated, which is more convenient for engineering applications. Simulations show that the results obtained from the linearized model are quite close to those obtained by integrating the nonlinear dynamics model.
NeeckSPMagnerTJPaulesGE. NASA's small satellite missions for earth observation. Acta Astronaut2005; 56: 187–192.
2.
Folta D, Bristow J, Hawkins A, et al. NASA's autonomous formation flying technology demonstration, earth observing-1. In: First international symposium on formation flying missions and technologies, Center National d'Etudes Spatiales, France, October 2002, pp.29–30.
3.
Cabeza I and Maetinez A. Smart-2: An ESA mission to demonstrate the key technologies for formation flying and drag-free control. In: Proceedings of the 1st international symposium on formation flying missions and technologies, Center National d'Etudes Spatiales, France, October 2002, pp.29–30.
4.
AlfriendKTVadaliSRGurfilP. Spacecraft formation flying dynamics. control and navigation, Oxford, UK: Elsevier, 2010.
5.
KristiansenRNicklassonPJ. Spacecraft formation flying: A review and new results on state feedback control. Acta Astronaut2009; 65: 1537–1552.
6.
BauerFBristowJCarpenterJ. Enabling spacecraft formation flying in any earth orbit through spaceborne GPS and enhanced autonomy technologies. Space Technol2001; 20: 175–185.
7.
WeiCZParkSYParkC. Linearized dynamics model for relative motion under a J2-perturbed elliptical reference orbit. Int J Nonlinear Mech2013; 55: 55–69.
8.
Lawson P. The terrestrial planet finder. In: IEEE Aerospace conference proceedings, vol. 4, IEEE Publications, Piscataway, NJ, USA, 10–17 March 2001, pp.2005–2011.
9.
How J, Twiggs R, Weidow D, et al. Orion: A low-cost demonstration of formation flying in space using GPS. In: AIAA/AAS Astrodynamics specialist conference, AIAA, August 1998, pp.98–4398.
10.
Persson S, Jacobsson B and Gill E. Prisma: Demonstration mission for advanced rendezvous and formation flying technologies and sensors. In: International Astronautical Federation: 56th international astronautical congress 2005, vol. 4, International Astronautical Congress Paper 05-B56B07, Paris, October 2005.
11.
Borde J, Schinmann T, Barillot P, et al. Ground validation of formation flying techniques and technologies. In: Proceedings of the 3rd international symposium on formation flying, missions, and technologies, ESA, Noordwijk, The Netherlands, April 2008, pp.23–25.
12.
Barret D, Belloni T, Bhattacharyya S, et al. Science with the XEUS high time resolution spectrometer. In: Proceedings of the SPIE, The international society for optical engineering, space telescopes, and instrumentation 2008: Ultraviolet to Gamma Ray, vol. 7011, SPIE, Bellingham, WA, 23 June 2008, pp.1–5.
13.
Folta D and Quinn D. Enhanced formation flying for the earth observing-1 (EO-1) new millennium mission. In: Proceedings of the flight mechanics symposium, NASA Goddard Space Flight Center, Greenbelt, MD, 1997, pp.405–406.
14.
TapleyBDBettadpurSRiesJC. GRACE measurements of mass variability in the earth system. Science2004; 305: 503–505.
15.
Burns RD, Naasz BJ, Gaylor D, et al. An environment for hardware-in-the-loop formation navigation and control. In: The AIAA/AAS astrodynamics specialist conference and exhibit, AIAA-2004-4735, 2004.
16.
SchweigartSASedwickRJ. High-fidelity linearized model for satellite formation flight. J Guid Control Dyn2002; 25: 1073–1080.
17.
ClohessyWHWiltshirePS. Terminal guidance system for satellite rendezvous. J Aerosp Sci1960; 27: 653–674.
18.
TschaunerJHempelP. Rendezvous with a target describing an elliptical trajectory. Acta Astronaut1965; 11: 104–109.
19.
CarterTHumiM. Rendezvous equations in a central-force field with linear drag. J Guid Control Dyn2002; 25: 74–79.
20.
CarterTHumiM. Clohessy-Wilthire equations modified to include quadratic drag. J Guid Control Dyn2002; 25: 1595–1607.
21.
GimDWAlfriendK. State transition matrix of relative motion for the perturbed noncircular reference orbit. J Guid Control Dyn2003; 26: 956–971.
Roberts JA and Roberts PCE. The development of high fidelity linearized models for satellite formation flying control. American Astronautical Society, AAS Paper 04-162, Cranfield University, UK, 2004.
24.
ReidTMisraAK. Formation flight of satellites in the presence of atmospheric drag. J Aerosp Eng Sci Appl2011; III: 64–91.
25.
SenguptaPVadaliSR. Relative motion and the geometry of formation in Keplerian elliptic orbits. J Guid Control Dyn2007; 30: 953–964.
26.
HamelJFde LafontaineJ. Linearized dynamics of formation flying spacecraft on -perturbed elliptical orbit. J Guid Control Dyn2007; 30: 1649–1658.
27.
ChoHCParkSY. Analytic solution for fuel-optimal reconfiguration in relative motion. J Optimiz Theory Appl2009; 141: 495–512.
28.
WeiCZParkSYParkC. Linearized dynamics model for relative motion under a -perturbed elliptical reference orbit. Int J Nonlinear Mech2013; 55: 55–69.
29.
Francis B. Satellite formation maintenance using differential atmospheric drag. McGill University, Montreal, November 2011.
30.
ValladoDA. Fundamentals of astrodynamics and applications, 3rd ed. Hawthorne, CA: Microcosm Press, 2005. .
31.
SchaubHJunkinsL. Analytical mechanics of space systems, Reston, VA: American Institute of Aeronautics and Astronautics, 2003.
32.
Vaddi SS and Vadali SR. Linear and nonlinear control laws for formation flying. AAS Paper 03-109, Advances in the Astronautical Sciences, vol. 114, 2003, pp.171–187.
33.
Sabatini M and Palmerini GB. Linearized formation-flying dynamics in a perturbed orbital environment. In: 2008 IEEE aerospace conference, 1 March 2008–8 March 2008, pp.1–13.
