Nonlinear Dynamics

, Volume 92, Issue 3, pp 1359–1367 | Cite as

A time-specified nonsingular terminal sliding mode control approach for trajectory tracking of robotic airships

  • Yueneng Yang
Original Paper


The robotic airships provide potential aerial platforms for various applications and require robust trajectory tracking to support these tasks. A time-specified nonsingular terminal sliding mode control (TS-NTSMC) scheme is proposed to address the problem of trajectory tracking for robotic airships, which can avoid the singularity problem and specify the convergence time of terminal sliding mode control. First, the problem of trajectory tracking of robotic airships is formulated. Second, a nonsingular terminal sliding manifold consisting of pre-specified nonlinear functions is proposed, and the TS-NTSMC law is designed for trajectory tracking. Time-specified convergence and stability of the closed-loop system can be guaranteed by Lyapunov theory. Finally, compared experimental simulations are given to illustrate the advantages of TS-NTSMC against NTSMC.


Trajectory control Terminal sliding mode control Time-specified convergence Robotic airship 



This work is supported by National Natural Science Foundation of China (No. 11502288) and Natural Science Foundation of Hunan Province (No. 2016JJ3019), and the authors also deeply indebted to the editors and reviewers.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


  1. 1.
    Chaugule, V.S., Rajkumar, P.Y.: Remotely controlled airship for aerial surveillance: from concept to reality in under a month. In: The 11th AIAA Aviation Technology, Integration, and Operations Conference. Virginia Beach, USA (2011)Google Scholar
  2. 2.
    Chu, A., Blackmore, M.: A novel concept for stratospheric communications and surveillance. In: AIAA Balloon System Conference. Williamsburge, USA (2007)Google Scholar
  3. 3.
    Douglas, G., Bruce, S., Sunil, S.: Feasibility study of a stratospheric airship observatory. In: Proceedings of SPIN-The International Society for Optical Engineering. Waikoloa, USA (2002)Google Scholar
  4. 4.
    Schafer, I., Reimund, K.: Airships as unmanned platforms challenge and chance. In: AIAA Technical Conference and Workshop on Unmanned Aerospace Vehicles. Virginia, USA (2008)Google Scholar
  5. 5.
    Zheng, Z.W., Xie, L.H.: Finite time path following control for a stratospheric airship with input saturation and error constraint. Int. J. Control (2017).
  6. 6.
    Moutinho, A., Azinheira, J.R.: Stability and robustness analysis of the AURORA airship control system using dynamic inversion. In: IEEE International Conference on robotics and Automation. Barcelona, Spain (2005)Google Scholar
  7. 7.
    Azinheira, J.R., Moutinho, A.: Airship hover stabilization using a backstepping control approach. J. Guid. Control Dyn. 29(4), 903–914 (2015)CrossRefGoogle Scholar
  8. 8.
    Beji, L., Abichou, A.: Tracking control of trim trajectories of a blimp for ascent and descent flight manoeuvres. Int. J. Control 78(10), 706–719 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Repoulias, F., Papadopoulos, E. Robotic airship trajectory tracking control using a backstepping methodology. In: IEEE International Conference on Robotics and Automation Pasadena, USA (2008)Google Scholar
  10. 10.
    Hygounenc, E., Soueres, P.: Automatic airship control involving backstepping techniques. In: IEEE International Conference on System, Man, and Cybernetics. USA (2002)Google Scholar
  11. 11.
    Yang, Y.N., Wu, J., Zheng, W.: Station-keeping control for a stratospheric airship platform via fuzzy adaptive backstepping approach. Adv. Space Res. 15, 1157–167 (2013)CrossRefGoogle Scholar
  12. 12.
    Lee, S.J., Kim, D.M.: Feedback linearization controller for semi station keeping of the unmanned airship. In: The 5th AIAA Aviation, Technology, Integration, and Operations Conference. Virginia, USA (2005)Google Scholar
  13. 13.
    Rao, J.J., Gong, Z.B., Luo, J.: Robotic airship mission path-following control based on ANN and human operator’s skill. Trans. Inst. Meas. Control 29(1), 5–15 (2007)CrossRefGoogle Scholar
  14. 14.
    Yang, Y.N., Yan, Y.: Trajectory tracking for robotic airships using sliding mode control based on neural network approximation and fuzzy gain scheduling. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 230(2), 184–196 (2016)CrossRefGoogle Scholar
  15. 15.
    Benjovengo, F.P.: Sliding mode control approaches for an autonomous unmanned airship. In: The 18th AIAA Lighter-Than-Air Systems Technology Conference. Washington, USA (2009)Google Scholar
  16. 16.
    Yang, Y.N., Wu, J., Zheng, W.: Trajectory tracking for an autonomous airship using fuzzy adaptive sliding mode control. J. Zhejiang Univ. Sci. C 13(7), 534–543 (2012)CrossRefGoogle Scholar
  17. 17.
    Incremona, G.P., Rubagotti, M., Ferrara, A.: Sliding mode control of constrained nonlinear systems. IEEE Trans. Autom. Control 62(6), 2965–2972 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    He, S.M., Lin, D.F., Wang, J.: Continuous second-order sliding mode based impact angle guidance law. Aerosp. Sci. Technol. 41, 199–208 (2015)CrossRefGoogle Scholar
  19. 19.
    Tiwari, P.M., Janardhanan, S., Nabi, M.: Rigid spacecraft attitude control using adaptive integral second order sliding mode. Aerosp. Sci. Technol. 42, 50–57 (2015)CrossRefGoogle Scholar
  20. 20.
    Ullah, N., Wang, S.P., Khattak, M.I.: Fractional order adaptive fuzzy sliding mode controller for a position servo system subjected to aerodynamic loading and nonlinearities. Aerosp. Sci. Technol. 43, 381–387 (2015)CrossRefGoogle Scholar
  21. 21.
    Jia, T.Z., Kang, G.W.: An RBF neural network-based nonsingular terminal sliding mode controller for robot manipulators. In: The third International Conference on Intelligent Control and Information Processing, pp.72–76. Dalian, China (2012)Google Scholar
  22. 22.
    Lin, F.J., Lee, S.Y., Chou, P.H.: Intelligent nonsingular terminal sliding-mode control using MIMO elman neural network for piezo-flexural nanopositioning stage. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59(12), 2716–2730 (2012)CrossRefGoogle Scholar
  23. 23.
    Solis, C.U., Clempner, J.B., Poznyak, A.S.: Fast terminal sliding-mode control with an integral filter applied to a Van Der Pol oscillator. IEEE Trans. Ind. Electron. 64(7), 5622–5628 (2017)CrossRefGoogle Scholar
  24. 24.
    Rath, J.J., Defoort, M., Karimi, H.R.: Output feedback active suspension control with higher order terminal sliding mode. IEEE Trans. Ind. Electron. 64(2), 1392–1403 (2017)CrossRefGoogle Scholar
  25. 25.
    Song, J., Niu, Y.G., Zou, Y.Y.: Finite-time stabilization via sliding mode control. IEEE Trans. Autom. Control 62(3), 1478–1483 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Feng, Y., Yu, X.H., Man, Z.H.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 38(12), 2159–2167 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Yu, S., Yu, X.H., Shirinzadehc, B.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Man, Z., Yu, X.: Terminal sliding mode control of MIMO linear systems. IEEE Trans. Circ. Syst. I Fund. Theory Appl. 44(11), 1065–1070 (1997)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Wu, Y., Yu, X., Man, Z.: Terminal sliding mode control design for uncertain dynamic systems. Syst. Control Lett. 34, 281–288 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Mueller, J.B., Paluzaek, M.A.: Development of an aerodynamic model and control law design for a high altitude airship. In: AIAA Unmanned Unlimited Technical Conference, Workshop and Exhibit, pp.6479–6495. Chicago, USA (2004)Google Scholar
  31. 31.
    Yang, Y.N., Wu, J., Zheng, W.: Positioning control for an autonomous airship. J. Aircr. 53(6), 1638–1646 (2016)CrossRefGoogle Scholar
  32. 32.
    Yang, Y.N., Yan, Y., Zhu, Z.L., Zheng, W.: Positioning control for an unmanned airship using sliding mode control based on fuzzy approximation. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 228(14), 2627–2640 (2014)CrossRefGoogle Scholar
  33. 33.
    Yang, Y.N., Wu, J., Zheng, W.: Attitude control for a station-keeping airship using feedback linearization and fuzzy sliding mode control. Int. J. Innov. Comput. Inf. Control 8(12), 8299–8310 (2012)Google Scholar
  34. 34.
    Yang, Y.N., Yan, Y.: Neural network gain-scheduling sliding mode control for three-dimensional trajectory tracking of robotic airships. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 229(6), 529–540 (2015)CrossRefGoogle Scholar
  35. 35.
    Yang, Y.N., Yan, Y.: Neural network approximation-based nonsingular terminal sliding mode control for trajectory tracking of robotic airships. Aerosp. Sci. Technol. 42, 50–57 (2016)Google Scholar
  36. 36.
    Zheng, Z.W., Zou, Y.: Adaptive integral LOS path following for an unmanned airship with uncertainties based on robust RBFNN backstepping. ISA Trans. 65, 210–219 (2016)CrossRefGoogle Scholar
  37. 37.
    Liu, H.T., Tian, X.H., Wang, G.: Finite-time H-infinity control for high-precision tracking in robotic manipulators using backstepping control. IEEE Trans. Ind. Electron. 63(9), 5501–5513 (2016)CrossRefGoogle Scholar
  38. 38.
    Wang, H., Man, Z.H., Kong, H.F.: Design and implementation of adaptive terminal sliding-mode control on a steer-by-wire equipped road vehicle. IEEE Trans. Ind. Electron. 63(9), 5774–5785 (2016)CrossRefGoogle Scholar
  39. 39.
    Yang, Y.N., Yan, Y.: Attitude regulation for unmanned quadrotors using adaptive fuzzy gain-scheduling sliding mode control. Aerosp. Sci. Technol. 54, 208–217 (2016)CrossRefGoogle Scholar
  40. 40.
    Hu, J.B., Zhuang, K.Y.: Theory and Application of Advanced Variable Structure Control. Northwestern Polytechnical University Press, Xi’an (2008)Google Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Space Technology, College of Aerospace Science and EngineeringNational University of Defense TechnologyChangshaChina

Personalised recommendations