Acta Astronautica 61 (2007) 553 – 564 www.elsevier.com/locate/actaastro Satellite formation flying using along-track thrust K.D. Kumar a , ∗ , H.C. Bang b , M.J. Tahk b a Department of Aerospace Engineering, Ryerson University, 350 Victoria Street, Toronto, Ont., Canada M5B 2K3 b Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejeon 305-701, Republic of Korea Received 14 June 2005; received in revised form 22 December 2006; accepted 22 January 2007 Available online 16 April 2007 Abstract The formation flying of satellites using thrust in along-track direction is explored in the present paper. The system comprising of a leader and a follower satellite is considered and a linear controller is developed to achieve a desired formation. The performance of the proposed controller is tested using numerical simulation of the governing nonlinear system equations of motion considering several factors including variations in initial conditions, formation size, presence of disturbance forces, and orbital eccentricity of the leader satellite. It is found that the controller using only along-track thrust can provide bounded relative position errors with the maximum control acceleration, in m/s 2 , of 0.0718 times the product of square of the orbital rate of the leader satellite and the along-track error. The proposed controller was successful in establishing circular as well as projected circular formations of leader and follower satellites within relative position errors of ± 10 m. © 2007 Elsevier Ltd. All rights reserved. 1. Introduction The formation flying of satellites has been identi- fied as an enabling technology for many future space missions [1–4]. Compared to a single spacecraft mis- sion, this approach has several advantages including the ability to enhance and/or enable missions through longer baseline observations, high failure tolerance, being real-time reconfigurable, adaptable to highly dynamic demands, and lower life cycle cost [4]. How- ever, its development involves tremendous challenges ranging from spacecraft formation initialization to re- configuration, coordination, and formation trajectory generation. Satellite mass, power, fuel, and communic- ∗ Corresponding author. Tel.: +1 416 979 5000x4908; fax: +1 416 979 5056. E-mail address: krishnadevkumar@yahoo.com (K.D. Kumar). 0094-5765/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2007.01.069 ations are significant constraints and the guidance, navigation, and control (GNC) tasks become highly complicated for larger formations. The satellite forma- tion flying may experience environmental disturbances from gravitational perturbation, atmospheric drag, solar radiation pressure and electromagnetic forces. With a view to tackle these challenges, innovative methods for achieving satellite formation flying with the minimum station keeping requirements are sought. The formation flying dynamics has been studied using orbital elements [5–8] as well as relative Carte- sian coordinates [9–22] (Fig. 1). Several investigations [9–12] considered linearized relative motion equations in a Cartesian coordinate frame, called the Hill’s Equa- tions [9] or the Clohessy–Wiltshire equations [10]. Satellite formation initialization is an important step in achieving a desired formation. Several researchers in- cluding Sabol et al. [12], Inalhan et al. [13], and Vaddi et al. [14] have discussed about this problem with