Low Thrust Relative Motion Control of Satellite Formations in Deep Space

Conference paper
Part of the Astrophysics and Space Science Proceedings book series (ASSSP, volume 44)


The problem of placing and controlling a formation of satellites on a Halo orbit is studied. The Earth-Sun circular restricted three body problem is considered. A family of artificial Halo orbits with the same periods, around the L1 and L2 Lagrange points in the Earth-Sun system is found using the pseudo-arc-length continuation method. The orbits are used are reference trajectories for satellites to track. The problem of orbit stability, bounding and controlling the relative motion by means of nonlinear control is addressed.



Claudiu Prioroc’s research has been funded by the European Commission through the Astrodynamics Network AstroNet-II, under Marie Curie contract PITN-GA-2011-289240.


  1. Biggs, J.D., McInnes, C.R.: An optimal gains matrix for time-delay feedback cntrol. In: 2nd IFAC Conference on the Analysis and Control of Chaotic Systems (2009)Google Scholar
  2. Biggs, J.D., McInnes, C.R.: Solar sail formation flying for deep space remote sensing. J. Spacecr. Rocket. 46, 670–678 (2009)ADSCrossRefGoogle Scholar
  3. Biggs, J.D., McInnes, C.R., Waters, T.: Stabilizing periodic orbits above the Ecliptic plane in the solar sail 3-body problem. In: 59th International Astronautical Congress, vol. 8 (2008)Google Scholar
  4. Biggs, J.D., Waters, T.J., McInnes, C.R.: New periodic orbits in the solar sail three-body problem. In: Nonlinear Science and Complexity. Springer, Dordrecht (2009)zbMATHGoogle Scholar
  5. Blackman, P.F.: Extremum-Seeking Regulators. The Macmillan Company, New York (1962)Google Scholar
  6. Chen, G., Yu, X.: On time-delayed feedback control of chaotic systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 46 (6), 767–772 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Chepfer, H., et al.: Estimation of cirrus cloud effective ice crystal shapes using visible reflectances from dual-satellite measurements. J. Geophys. Res. 107 (D23), AAC 21-1–AAC 21-16 (2002)Google Scholar
  8. Dhooge, A., Govaerts, W., Kuznetsov, Yu.A.: MATCONT: a Matlab package for numerical bifurcation analysis of ODEs. ACM SIGSAM Bull. 38 (1), 21–22 (2004)CrossRefzbMATHGoogle Scholar
  9. Doedel, E.J., et al.: Elemental periodic orbits associated with the libration points in the circular restricted 3-body problem. Int. J. Bifurc. Chaos Appl. Sci. Eng. 17 (8), 2625 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. Doedel, E.J., Krauskopf, B., Osinga, H.M.: Global bifurcations of the Lorenz manifold. Nonlinearity 19 (12), 2947 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  11. Gómez, G., Llibre, J., Martínez, R., Simó, C.: Dynamics and Mission Design Near Libration Points Vol. 1. Fundamentals: The Case of Collinear Libration Points. World Scientific, Singapore (2001)zbMATHGoogle Scholar
  12. Huber, M.C.E., Malinovsky-Arduini, M.: The SOHO concept and its realisation. Space Sci. Rev. 61, 301–334 (1992)ADSCrossRefGoogle Scholar
  13. King, M., et al.: Remote sensing of tropospheric aerosols from space: past, present and future. Bull. Am. Meteorol. Soc. 80 (11), 2229–2259 (1999)ADSCrossRefGoogle Scholar
  14. Poincaré, H.: Les Methodes Nouvelles de la Mecanique Celeste. Gauthier-Villars, Paris (1892)zbMATHGoogle Scholar
  15. Prioroc, C.L., Biggs, J.D.: Low-thrust propulsion formation flying around libration points. Math. Eng. Sci. Aerosp. 6 (1), 87–100 (2015)Google Scholar
  16. Prioroc, C.L., Mikkola, S.: Simple algorithm for relative motion of satellites. N. Astron. Sci. Aerosp. 34 (1), 41–46 (2015)Google Scholar
  17. Pyragas, K.: Continuous control of chaos by self-controlling feed-back. Phys. Lett. A 170 (1), 421–428 (1992)ADSCrossRefGoogle Scholar
  18. Slotine, J.J., Sastry, S.S.: Tracking control of nonlinear systems using sliding surfaces with applications to robot manipulator. Int. J. Control 38 (2), 465–492 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  19. Szebehely, V.: Theory of Orbits. Academic, New York (1967)Google Scholar
  20. Watzin, J.: The Triana Mission - next generation systems architecture ready for flight. In: Proceedings of the Aerospace Conference, vol. 7, pp. 277–285 (2000)Google Scholar
  21. Young, K.D., Utkin, V.I., Ozguner, U.: A control engineer’s guide to sliding mode control. IEEE Trans. Control Syst. Technol. 7 (3), 328–342 (1999)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of TurkuPiikkiöFinland

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