Nonlinear Dynamics

, Volume 95, Issue 2, pp 1323–1346 | Cite as

Propellant-efficient station-keeping using a hybrid sail in the Earth–Moon system

  • Chen Gao
  • Jianping YuanEmail author
  • Junhua Zhang
  • Linli Guo
Original Paper


The problem of propellant-efficient station-keeping using a hybrid sail in the Earth–Moon system is investigated in this paper. To achieve high-precision station-keeping and minimize propellant consumption, the problem is addressed from perspectives of reference orbits design and control strategy design. A high-fidelity model of a hybrid sail, which consists of a solar electric propulsion (SEP) system and a solar sail covered by reflectivity control devices (RCDs), is exploited for reference orbits design in the Earth–Moon system using numerical methods. These hybrid-sail perturbed halo and Lyapunov orbits are parameterized by the sail’s reflectivity and are inherent unstable. An orbit-attitude control strategy is proposed for station-keeping which is composed of three parts: a nonlinear disturbance observer (NDO)-based optimal periodic orbital controller, SEP acceleration optimization, and a NDO-based robust backstepping attitude controller. In particular, RCDs are used in both orbital control and attitude control. Numerical results show that the proposed control strategy can guarantee high-precision station-keeping and effective reduction in propellant consumption.


Station-keeping Hybrid sail Reflectivity control devices The Earth–Moon system Halo orbits Lyapunov orbits 



This work is supported by the Major Program of National Natural Science Foundation of China under Grant Numbers 61690210 and 61690211, and National Natural Science Foundation of China under Grant Number 11572248.

Compliance with ethical standards

Conflict of interest

We have no conflict of interest to declare.


  1. 1.
    Macdonald, M., Hughes, G.W., McInnes, C.R., Lyngvi, A., Falkner, P., Atzei, A.: GeoSail: an elegant solar sail demonstration mission. J. Spacecr. Rockets 44(4), 784–796 (2007). CrossRefGoogle Scholar
  2. 2.
    West, J.L.: The GeoStorm warning mission: enhanced opportunities based on new technology. In: 14th AAS/AIAA Spaceflight Mechanics Conference, Maui, Hawaii (2004)Google Scholar
  3. 3.
    Gong, S., Li, J.: Solar sail heliocentric elliptic displaced orbits. J. Guid. Control Dyn. 37(6), 2021–2026 (2014). CrossRefGoogle Scholar
  4. 4.
    Fu, B., Sperber, E., Eke, F.: Solar sail technology-A state of the art review. Prog. Aerosp. Sci. 86, 1–19 (2016). CrossRefGoogle Scholar
  5. 5.
    Gong, S., Li, J., Simo, J.: Orbital motions of a solar sail around the \(L_2\) earth–moon libration point. J. Guid. Control Dyn. 37(4), 1349–1356 (2014). CrossRefGoogle Scholar
  6. 6.
    Ozimek, M.T., Grebow, D.J., Howell, K.C.: Design of solar sail trajectories with applications to lunar south pole coverage. J. Guid. Control Dyn. 32(6), 1884–1897 (2009). CrossRefGoogle Scholar
  7. 7.
    Heiligers, J., Hiddink, S., Noomen, R., McInnes, C.R.: Solar sail Lyapunv and halo orbits in the earth–moon three-body problem. Acta Astronaut. 116, 25–35 (2015). CrossRefGoogle Scholar
  8. 8.
    Heiligers, J., Macdonald, M., Parker, J.S.: Extension of earth–moon libration point orbits with solar sail propulsion. Astrophys. Space Sci. 361(7), 241 (2016). MathSciNetCrossRefGoogle Scholar
  9. 9.
    Heiligers, J., Parker, J.S., Macdonald, M.: Novel solar-sail mission concepts for high-latitude Earth and lunar observation. J. Guid. Control Dyn. 41(1), 212–230 (2018). CrossRefGoogle Scholar
  10. 10.
    Yuan, J., Gao, C., Zhang, J.: Periodic orbits of solar sail equipped with reflectance control device in earth–moon system. Astrophys. Space Sci. 363(2), 23 (2018). MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gong, S., Li, J.: Solar sail halo orbit control using reflectivity control devices. Trans. Jpn. Soc. Aeronaut. Space Sci. 57(5), 279–288 (2014). CrossRefGoogle Scholar
  12. 12.
    Heiligers, J., Ceriotti, M., McInnes, C.R., Biggs, J.D.: Displaced geostationary orbit design using hybrid sail propulsion. J. Guid. Control Dyn. 34(6), 1852–1866 (2011). CrossRefGoogle Scholar
  13. 13.
    Ceriotti, M., McInnes, C.R.: Generation of optimal trajectories for Earth hybrid pole sitters. J. Guid. Control Dyn. 34(3), 847–859 (2011). CrossRefGoogle Scholar
  14. 14.
    Baig, S., McInnes, C.R.: Artificial three-body equilibria for hybrid low-thrust propulsion. J. Guid. Control Dyn. 31(6), 1644–1655 (2008). CrossRefGoogle Scholar
  15. 15.
    Tamakoshi, D., Kojima, H.: Solar sail orbital control using reflectivity variations near the earth–moon \(L_2\) point. J. Guid. Control Dyn. 41(2), 417–430 (2018). CrossRefGoogle Scholar
  16. 16.
    Shirobokov, M., Trofimov, S., Ovchinnikov, M.: Survey of station-keeping techniques for libration point orbits. J. Guid. Control Dyn. 40(5), 1085–1105 (2017). CrossRefGoogle Scholar
  17. 17.
    Biggs, J.D., Henninger, H.C., Narula, A.: Enhancing station-keeping control with the use of extended state observers. Front. Appl. Math. Stat. 4, 1–9 (2018). CrossRefGoogle Scholar
  18. 18.
    Leipold, M., Götz, M.: Hybrid photonic/electric propulsion. In: Kayser-Threde, GmBH Rept. SOL4-TR-KTH-001,Munich, Germany (2002)Google Scholar
  19. 19.
    Biggs, J.D., McInnes, C.R.: Solar sail formation flying for deep-space remote sensing. J. Spacecr. Rockets 46(3), 670–678 (2009)CrossRefGoogle Scholar
  20. 20.
    Biggs, J.D., McInnes, C.R., Waters, T.: Control of solar sail periodic orbits in the elliptic three-body problem. J. Guid. Control Dyn. 32(1), 318–320 (2009). CrossRefzbMATHGoogle Scholar
  21. 21.
    Peng, H., Zhao, J., Wu, Z., Zhong, W.: Optimal periodic controller for formation flying on libration point orbits. Acta Astronaut. 69, 537–550 (2011). CrossRefGoogle Scholar
  22. 22.
    Narula, A., Biggs, J.D.: Fault-tolerant station-keeping on libration point orbits. J. Guid. Control Dyn. 41(4), 879–887 (2018). CrossRefGoogle Scholar
  23. 23.
    Bryson, A.E.: Time-varying linear-quadratic control. J. Optim. Theory Appl. 100, 515–525 (1999). MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Wang, Z., Wu, Z.: Nonlinear attitude control scheme with disturbance observer for flexible spacecrafts. Nonlinear Dyn. 81, 257–264 (2015). MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Lee, D.: Nonlinear disturbance observer-based robust control of attitude tracking of rigid spacecraft. Nonlinear Dyn. 88, 1317–1328 (2017). CrossRefzbMATHGoogle Scholar
  26. 26.
    Lou, Z., Zhang, K., Wang, Y., Gao, Q.: Active disturbance rejection station-keeping control for solar-sail libration-point orbits. J. Guid. Control Dyn. 39(8), 1917–1921 (2016). CrossRefGoogle Scholar
  27. 27.
    Funase, R., Shirasawa, Y., Mimasu, Y., Mori, O., Tsuda, Y., Saiki, T., Kawaguchi, J.: On-orbit verification of fuel-free attitude control system for spinning solar sail utilizing solar radiation pressure. Adv. Space Res. 48(11), 1740–1746 (2011). CrossRefGoogle Scholar
  28. 28.
    Mu, J., Gong, S., Li, J.: Coupled control of reflectivity modulated solar sail for GeoSail formation flying. J. Guid. Control Dyn. 38(4), 740–751 (2014). CrossRefGoogle Scholar
  29. 29.
    Liu, J., Chen, L., Cui, N.: Solar sail chaotic pitch dynamics and its control in Earth orbits. Nonlinear Dyn. 90, 1755–1770 (2017). MathSciNetCrossRefGoogle Scholar
  30. 30.
    Richardson, D.L.: Halo orbit formulation for the ISEE-3 mission. J. Guid. Control Dyn. 3(6), 543–548 (1980). CrossRefGoogle Scholar
  31. 31.
    Kulkarni, J.E., Campbell, M.E., Dullerud, G.E.: Stabilization of spacecraft flight in halo orbits: an H\(_{\infty } \) approach. IEEE Trans. Control Syst. Technol. 14(3), 572–578 (2006). CrossRefGoogle Scholar
  32. 32.
    Gao, C., Yuan, J., Zhao, Y.: ADRC for spacecraft attitude and position synchronization in libration point orbits. Acta Astronaut. 145, 238–249 (2018). CrossRefGoogle Scholar
  33. 33.
    Liu, J., Rong, S., Shen, F., Cui, N.: Dynamics and control of a flexible solar sail. Math. Probl. Eng. 2014(3), 1–25 (2014)Google Scholar
  34. 34.
    Wong, B., Patil, R., Misra, A.: Attitude dynamics of rigid bodies in the vicinity of the Lagrangian points. J. Guid. Control Dyn. 31(1), 252–256 (2008). CrossRefGoogle Scholar
  35. 35.
    Chen, W., Ballance, D.J., Gawthrop, P.J., O’Reilly, J.: A nonlinear disturbance observer for robotic manipulators. IEEE Trans. Ind. Electron. 47(4), 932–938 (2000). CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Chen Gao
    • 1
  • Jianping Yuan
    • 1
    Email author
  • Junhua Zhang
    • 1
  • Linli Guo
    • 2
  1. 1.School of AstronauticsNorthwestern Polytechnical UniversityXi’anChina
  2. 2.China Spacesat CO., LTDChina Academy of Space TechnologyBeijingChina

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