Advertisement

Nonlinear Dynamics

, Volume 95, Issue 3, pp 2275–2291 | Cite as

Adaptive finite time distributed 6-DOF synchronization control for spacecraft formation without velocity measurement

  • Yi HuangEmail author
  • Yingmin Jia
Original Paper

Abstract

In this paper, the problem of distributed finite time six-degree-of-freedom (6-DOF) synchronization control for spacecraft formation flying (SFF) with the external disturbances and parameter uncertainties is investigated. Firstly, a continuous adaptive finite time distributed control protocol with full state feedback is proposed, which can overcome the chattering problem and reduce the convergence time in the reaching phase. Subsequently, an adaptive sliding mode observer with finite time convergence is designed to estimate the velocity information. Then a new observer-based continuous adaptive finite time distributed control protocol is designed. Rigorous proofs show that these two distributed controllers both can guarantee that the attitude and relative position tracking errors can converge to the origin within finite time rather than the bounded regions around the origins. Finally, the effectiveness of the designed distributed control protocols is demonstrated by simulation results.

Keywords

Spacecraft formation system 6-DOF synchronization control Finite time convergence Adaptive control Without velocity measurement 

Notes

Acknowledgements

This work was supported by the NSFC (61327807,61521091, 61520106010, 61134005) and the National Basic Research Program of China (973 Program: 2012

CB821200, 2012CB821201), and the Academic Excellence Foundation of BUAA for PhD Students.

Compliance with ethical standards

Conflict of interest

The authors declared that they have no conflict of interest.

References

  1. 1.
    Zou, A.M., de Ruiter, A.H.J., Kumar, K.D.: Distributed finite-time velocity-free attitude coordination control for spacecraft formations. Automatica 67, 46–53 (2016)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Huang, D., Wang, Q., Duan, Z.: Distributed attitude control for multiple flexible spacecraft under actuator failures and saturation. Nonlinear Dyn. 88, 529–546 (2017)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chen, T., Chen, G.: Distributed adaptive tracking control of multiple flexible spacecraft under various actuator and measurement limitations. Nonlinear Dyn. 91, 1571–1586 (2018)CrossRefzbMATHGoogle Scholar
  4. 4.
    Tang, Z., Park, J.H., Zheng, W.X.: Distributed impulsive synchronization of Lur’e dynamical networks via parameter variation methods. Int. J. Robust Nonlinear Control 28, 1001–1015 (2018)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Ren, W.: Distributed cooperative attitude synchronization and tracking for multiple rigid bodies. IEEE Trans. Control Syst. Technol. 18, 383–392 (2010)CrossRefGoogle Scholar
  6. 6.
    Hu, Q., Dong, H., Zhang, Y., Ma, G.: Tracking control of spacecraft formation flying with collision avoidance. Aerosp. Sci. Technol. 42, 353–364 (2015)CrossRefGoogle Scholar
  7. 7.
    He, X., Wang, Q., Yu, W.: Finite-time distributed cooperative attitude tracking control for multiple rigid spacecraft. Appl. Math. Comput. 256, 724–734 (2015)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Zhang, F., Duan, G.: Robust adaptive integrated translation and rotation control of a rigid spacecraft with control saturation and actuator misalignment. Acta Astronaut. 86, 167–187 (2013)CrossRefGoogle Scholar
  9. 9.
    Xia, K., Huo, W.: Robust adaptive backstepping neural networks control for spacecraft rendezvous and docking with uncertainties. Nonlinear Dyn. 84, 1683–1695 (2016)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Kristiansen, R., Nicklasson, P.J., Gravdahl, J.T.: Spacecraft coordination control in 6 DOF: integrator backstepping vs passivity-based control. Automatica 44, 2896–2901 (2008)CrossRefzbMATHGoogle Scholar
  11. 11.
    Wu, J., Liu, K., Han, D.: Adaptive sliding mode control for six-DOF relative motion of spacecraft with input constraint. Acta Astronaut. 87, 64–76 (2013)CrossRefGoogle Scholar
  12. 12.
    Du, H., Li, S., Qian, C.: Finite-time attitude tracking control of spacecraft with application to attitude synchronization. IEEE Trans. Autom. Control 56, 2711–2717 (2011)CrossRefMathSciNetzbMATHGoogle Scholar
  13. 13.
    Xiao, B., Hu, Q., Zhang, Y.: Finite-time attitude tracking of spacecraft with fault-tolerant capability. IEEE Trans. Control Syst. Technol. 23, 1338–1350 (2015)CrossRefGoogle Scholar
  14. 14.
    Cheng, Y., Du, H., He, Y., Jia, R.: Distributed finite-time attitude regulation for multiple rigid spacecraft via bounded control. Inf. Sci. 328, 144–157 (2016)CrossRefGoogle Scholar
  15. 15.
    Hu, Q., Zhang, J.: Relative position finite-time coordinated tracking control of spacecraft formation without velocity measurements. ISA Trans. 54, 60–74 (2015)CrossRefGoogle Scholar
  16. 16.
    Lee, D.: Nonlinear disturbance observer-based robust control of attitude tracking of rigid spacecraft. Nonlinear Dyn. 88, 1317–1328 (2017)CrossRefzbMATHGoogle Scholar
  17. 17.
    Huang, Y., Jia, Y.: Robust adaptive fixed-time tracking control of 6-DOF spacecraft fly-around mission for noncooperative target. Int. J. Robust Nonlinear Control 28, 2598–2618 (2018)CrossRefMathSciNetzbMATHGoogle Scholar
  18. 18.
    Zhao, L., Jia, Y.: Decentralized adaptive attitude synchronization control for spacecraft formation using nonsingular fast terminal sliding mode. Nonlinear Dyn. 78, 2779–2794 (2014)CrossRefzbMATHGoogle Scholar
  19. 19.
    Zhou, N., Xia, Y., Wang, M., Fu, M.: Finite-time attitude control of multiple rigid spacecraft using terminal sliding mode. Int. J. Robust Nonlinear Control 25, 1862–1876 (2015)CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    Mobayen, S.: Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method. Nonlinear Dyn. 80, 669–683 (2015)CrossRefMathSciNetzbMATHGoogle Scholar
  21. 21.
    Moreno, J.A., Osorio, M.: Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans. Autom. Control 57, 1035–1040 (2012)CrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    Pukdeboon, C.: Output feedback second order sliding mode control for spacecraft attitude and translation motion. Int. J. Control Autom. 14, 411–424 (2016)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Lu, K., Xia, Y.: Finite-time attitude control for rigid spacecraft-based on adaptive super-twisting algorithm. IET Control Theory Appl. 8, 1465–1477 (2014)CrossRefGoogle Scholar
  24. 24.
    Wang, J., Sun, Z.: 6-DOF robust adaptive terminal sliding mode control for spacecraft formation flying. Acta Astronaut. 73, 76–87 (2012)CrossRefGoogle Scholar
  25. 25.
    Huang, Y., Jia, Y.: Distributed finite-time output feedback synchronisation control for six DOF spacecraft formation subject to input saturation. IET Control Theory Appl. 12, 532–542 (2017)CrossRefMathSciNetGoogle Scholar
  26. 26.
    Abdessameud, A., Tayebi, A.: Attitude synchronization of a group of spacecraft without velocity measurements. IEEE Trans. Autom. Control 54, 2642–2648 (2009)CrossRefMathSciNetzbMATHGoogle Scholar
  27. 27.
    Zou, A.M., Kumar, K.D., Hou, Z.G.: Attitude coordination control for a group of spacecraft without velocity measurements. IEEE Trans. Control Syst. Technol. 20, 1160–1174 (2012)CrossRefGoogle Scholar
  28. 28.
    Ran, D., Chen, X., Misra, A.K.: Finite time coordinated formation control for spacecraft formation flying under directed communication topology. Acta Astronaut. 136, 125–136 (2017)CrossRefGoogle Scholar
  29. 29.
    Zhou, N., Xia, Y., Lu, K., Li, Y.: Decentralised finite-time attitude synchronisation and tracking control for rigid spacecraft. Int. J. Syst. Sci. 46, 2493–2509 (2015)CrossRefMathSciNetzbMATHGoogle Scholar
  30. 30.
    Meng, Z., Ren, W., You, Z.: Distributed finite-time attitude containment control for multiple rigid bodies. Automatica 46, 2092–2099 (2010)CrossRefMathSciNetzbMATHGoogle Scholar
  31. 31.
    Sun, L., Huo, W.: 6-DOF integrated adaptive backstepping control for spacecraft proximity operations. IEEE Trans. Aerosp. Electron. Syst. 51, 2433–2443 (2015)CrossRefGoogle Scholar
  32. 32.
    Schaub, H., Akella, M.R., Junkins, J.L.: Adaptive control of nonlinear attitude motions realizing linear closed loop dynamics. J. Guid. Control Dyn. 24, 95–100 (2001)CrossRefGoogle Scholar
  33. 33.
    Tiwari, P.M., Janardhanan, S., un Nabi, M.: Rigid spacecraft attitude control using adaptive integral second order sliding mode. Aerosp. Sci. Technol. 42, 50–57 (2015)CrossRefzbMATHGoogle Scholar
  34. 34.
    Sun, L., Huo, W., Jiao, Z.: Disturbance observer-based robust relative pose control for spacecraft rendezvous and proximity operations under input saturation. IEEE Trans. Aerosp. Electron. Syst. 54, 1605–1617 (2018)CrossRefGoogle Scholar
  35. 35.
    Zhao, L., Jia, Y.: Finite-time attitude tracking control for a rigid spacecraft using time-varying terminal sliding mode techniques. Int. J. Control 88, 1150–1162 (2015)CrossRefMathSciNetzbMATHGoogle Scholar
  36. 36.
    Du, H., Li, S.: Finite-time attitude stabilization for a spacecraft using homogeneous method. J. Guid. Control Dyn. 35, 740–748 (2012)CrossRefGoogle Scholar
  37. 37.
    Zhao, Y., Duan, Z., Wen, G.: Distributed finite-time tracking of multiple Euler–Lagrange systems without velocity measurements. Int. J. Robust Nonlinear Control 25, 1688–1703 (2015)CrossRefMathSciNetzbMATHGoogle Scholar
  38. 38.
    Yu, S., Yu, X., Shirinzadeh, B., Man, Z.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41, 1957–1964 (2005)CrossRefMathSciNetzbMATHGoogle Scholar
  39. 39.
    Sun, H., Li, S., Sun, C.: Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dyn. 73, 229–244 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  40. 40.
    Levant, A.: Principles of 2-sliding mode design. Automatica 43, 576–586 (2007)CrossRefMathSciNetzbMATHGoogle Scholar
  41. 41.
    Moreno, J.A., Osorio, M.A.: Lyapunov approach to second-order sliding mode controllers and observers. In: Proceedings of the 47th IEEE Conference on Decision and Control, pp. 2856–2861 (2008)Google Scholar
  42. 42.
    Liu, J., Laghrouche, S., Harmouche, M., Wack, M.: Adaptive-gain second-order sliding mode observer design for switching power converters. Control Eng. Pract. 30, 124–131 (2014)CrossRefGoogle Scholar
  43. 43.
    Tian, B., Yin, L., Wang, H.: Finite-time reentry attitude control based on adaptive multivariable disturbance compensation. IEEE Trans. Ind. Electron. 62, 5889–5898 (2015)CrossRefGoogle Scholar
  44. 44.
    Besancon G.: An overview on observer tools for nonlinear systems. In: Nonlinear Observers and Applications. Springer, Berlin, Heidelberg, pp. 1–33 (2007)Google Scholar
  45. 45.
    Zhang A., Li Y.: A modified unscented Kalman filter for autonomous navigation of distributed satellite systems. In: IEEE Proceedings of the Chinese Control Conference, pp. 5811–5816 (2017)Google Scholar
  46. 46.
    Nagesh, I., Edwards, C.: A multivariable super-twisting sliding mode approach. Automatica 50, 984–988 (2014)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.The Seventh Research Division and the Center for Information and Control, School of Automation Science and Electrical EngineeringBeihang University (BUAA)BeijingChina

Personalised recommendations