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Abstract: Maintenance of high performance formation control is important for low Earth orbit (LEO) formation missions of small spacecraft. In this paper, a model of nonlinear relative motion dynamics is built, and then nonlinear and important perturbations affecting the formation configuration, such as J₂ and atmospheric drag, are analyzed as disturbances. Global navigation satellite system based relative positioning with nonlinear filtering is adopted to provide state information associated with the perturbations. By combining disturbance observer based control with H_∞; state feedback, a composite disturbance attenuation controller is proposed for maintenance of continuous and accurate formation. With consideration of precise control relying on micro thrusters, a composite disturbance attenuation based saturated controller is designed and its stability is proved. Finally, through numerical simulations, we demonstrate that control accuracy is improved after effectively avoiding perturbations and that stabilization can be satisfied using this method.

[1]Alfriend, K.T., Schaub, H., Gim, D.W., 2000. Gravitational Perturbations, Nonlinearity and Circular Orbit Assumption Effect on Formation Flying Control Strategies. American Astronautical Society Guidance & Control Conf., AAS 00-012, p.1-20.

[2]Buist, P.J., Teunissen, P.J.G., Verhagen, S., Giorgi, G., 2011. A vectorial bootstrapping approach for integrated GNSS-based relative positioning and attitude determination of spacecraft. Acta Astron., 68(7-8):1113-1125.

[3]Canuto, E., 2007. Embedded model control: outline of the theory. ISA Trans., 46(3):363-377.

[4]Canuto, E., Molano-Jimenez, A., Perez-Montenegro, C., Massotti, L., 2011. Long-distance, drag-free, low-thrust, LEO formation control for Earth gravity monitoring. Acta Astron., 69(7-8):571-582.

[5]Clohessy, W.H., Wiltshire, R.S., 1960. Terminal guidance system for satellite rendezvous. J. Aerosp. Sci., 27(9):653-658.

[6]de Souza, C.E., Xie, L., 1992. On the discrete-time bounded real lemma with application in the characterization of static state feedback H_∞ controllers. Syst. Control Lett., 18(1):61-71.

[7]Fang, J.C., Gong, X.L., 2010. Predictive iterated Kalman filter for INS/GPS integration and its application to SAR motion compensation. IEEE Trans. Instrum. Meas., 59(4):909-915.

[8]Guo, L., Chen, W.H., 2005. Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. Int. J. Rob. Nonl. Control, 15(3):109-125.

[9]Guo, L., Feng, C.B., Chen, W.H., 2006. A survey of disturbance-observer-based control for dynamic nonlinear system. Dynam. Cont. Discr. Impul. Syst., 13:79-84.

[10]Han, K., Hao, W., Jin, Z.H., 2010. Magnetometer-only linear attitude estimation for bias momentum pico-satellite. J. Zhejiang Univ.-Sci. A (Appl. Phys. & Eng.), 11(6):455-464.

[11]Massioni, P., Keviczky, T., Gill, E., Verhaegen, M., 2011. A decomposition-based approach to linear time-periodic distributed control of satellite formations. IEEE Trans. Control Syst. Technol., 19(3):481-492.

[12]Schaub, H., Vadali, S.R., Junkins, J.L., Alfriend, K.T., 2000. Spacecraft formation flying control using mean orbit elements. J. Astron. Sci., 48(1):69-87.

[13]Sun, D., Zhou, F.Q., Zhou, J., 2004. Robust control for multiple spacecraft flying. J. Proj. Rock. Miss. Guid., 24(2):279-281.

[14]Vaddi, S.S., Vadali, S.R., Alfriend, K.T., 2003. Formation flying: accommodating nonlinearity and eccentricity perturbations. J. Guid. Control Dyn., 26(2):214-223.

[15]Wang, Z.K., Zhang, Y.L., 2007. Design and verification of a robust formation keeping controller. Acta Astron., 61(7-8):565-574.

[16]Winternitz, L.M.B., Bamford, W.A., Heckler, G.W., 2009. A GPS receiver for high-altitude satellite navigation. IEEE J. Sel. Top. Signal Process., 3(4):541-556.

[17]Wnuk, E., Golebiewska, J., 2007. Relative satellite motion in a formation. Adv. Space Res., 40(1):35-42.

[18]Xu, G.Y., Wang, D.W., 2008. Nonlinear dynamic equations of satellite relative motion around an oblate Earth. J. Guid. Control Dyn., 31(5):1521-1524.

[19]Yoon, S., Lundberg, J.B., 2001. Euler angle dilution of precision in GPS attitude determination. IEEE Trans. Aerosp. Electron. Syst., 37(3):1077-1083.

[20]You, Z.H., Li, B., Dong, Z.H., 2005. Status and key technologies of spacecraft formation on Sun-Earth Lagrange point. Aerosp. China, 5(7):27-31 (in Chinese).

[21]Zhang, J.X., Cao, X.B., Wang, J.H., Lin, X.H., 2009. Configuration, orbit design of InSAR formation based on mean elements. IEEE Trans. Aerosp. Electron. Syst., 45(2):747-752.

[22]Zhang, Y.L., Zeng, G.Q., Wang, Z.K., 2008. Theories and Applications of Distributed Satellites System. Science Publishing Company, Beijing (in Chinese).