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Trajectory tracking of underactuated surface vessels based on neural network and hierarchical sliding mode

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Abstract

Adaptive robust controllers are proposed for trajectory tracking and stabilization of underactuated surface vessels simultaneously in this paper. Hierarchical sliding mode is employed to deal with the underactuation of the model, and neural network is used as a tool for approximating unknown nonlinear function in the system; in this way, the robustness of the proposed controller is strengthened, and the chattering problem of sliding mode technique is relieved. The nonlinear damping terms of ship’s model are considered which are neglected in many studies, and the time-varying disturbances are taken into account to test the robustness of the designed controllers. Stability is guaranteed by Lyapunov theorem, and the proof is given. Numerical simulations are implemented to demonstrate the effectiveness and the robustness of the designed controllers.

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References

  1. Ashrafiuon H, Musk KR, McNinch LC (2010) Review of nonlinear tracking and setpoint control approaches for autonomous underactuated marine vehicles, 2010 American Control Conference, Baltimore, USA, pp 5203–5211

  2. Papoulias FA (1994) Cross track error and proportional turning rate guidance of marine vehicles. J Ship Res 38(2):123–132

    Google Scholar 

  3. Papoulias FA, Oral ZO (1995) Hopf bifurcations and nonlinear studies of gain margins in path control of marine vehicles. Appl Ocean Res 17(1):21–32

    Article  Google Scholar 

  4. Godhavn JM (1996) Nonlinear tracking of underactuated surface vessels. In: Proceedings of the 35th IEEE Conference on Decision and Control, pp 975–980

  5. Godhavn JM, Fossen TI, Berge SP (1998) Nonlinear and adaptive backstepping designs for tracking control of ships. Int J Adapt Control Signal Process 12(8):649–670

    Article  Google Scholar 

  6. Lefeber E, (2000) Tracking control of nonlinear mechanical systems, Ph. D. thesis, University of Twente

  7. Pettersen KY, Nijmeijer H (2001) Underactuated ship control: theory and experiments. Int J Control 74(14):1435–1446

    Article  MATH  MathSciNet  Google Scholar 

  8. Lefeber E, Pettersen KY, Nijmeijer H (2003) Tracking control of an underactuated ship. IEEE Trans Control Syst Technol 11(1):52–61

    Article  Google Scholar 

  9. Jiang ZP (2002) Global tracking control of underactuated ships by Lyapunov’s direct method. Automatica 38(1):301–309

    Article  MATH  Google Scholar 

  10. Do KD, Jiang ZP, Pan J (2002) Underactuated ship global tracking under relaxed conditions. IEEE Trans Autom Control 47(9):1529–1536

    Article  MathSciNet  Google Scholar 

  11. Do KD, Jiang ZP, Pan J (2002) Universal controllers for stabilization and tracking of underactuated ships. Syst Control Lett 47(4):299–317

    Article  MATH  MathSciNet  Google Scholar 

  12. Do KD, Pan J, Jiang ZP (2003) Robust adaptive control of underactuated ships on a linear course with comfort. Ocean Eng 30(17):2201–2225

    Article  Google Scholar 

  13. Cao KC, Tian YP (2007) A time-varying cascaded design for trajectory tracking control of non-holonomic systems. Int J Control 80(3):416–429

    Article  MATH  MathSciNet  Google Scholar 

  14. Peng Y, Han J Dand Song Q (2007) Tracking control of underactuated surface ships: using unscented Kalman filter to estimate the uncertain parameters. In: Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, Harbin, China, pp 1884–1889

  15. Ashrafiuon H, Muske KR, McNinch LC, Soltan RA (2008) Sliding-mode tracking control of surface vessels. IEEE Trans Ind Electron 55(11):4004–4012

    Article  Google Scholar 

  16. Soltan R A, Ashrafiuon H and Muske K R (2009) State-dependent trajectory planning and tracking control of unmanned surface vessels. In: Proceedings of the 2009 American Control Conference, St. Louis, USA, pp 3597–3602

  17. Li Z, Sun J, Oh SR (2009) Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels. Automatica 45(7):1649–1658

    Article  MATH  MathSciNet  Google Scholar 

  18. Oh SR, Sun J (2010) Path following of underactuated marine surface vessels using line-of-sight based model predictive control. Ocean Eng 37(2–3):289–295

    Article  Google Scholar 

  19. Chwa D (2011) Global tracking control of underactuated ships with input and velocity constraints using dynamic surface control method. IEEE Trans Control Syst Technol 19(6):1357–1370

    Article  Google Scholar 

  20. Movahhed M, Dadashi S and Danesh M (2011) Adaptive sliding mode control for autonomous surface vessel. In: Proceedings of the 2011 IEEE International Conference on Mechatronics, Istanbul, Turkey, pp 522–527

  21. Siramdasu Y, Fahimi F (2012) Incorporating input saturation for underactuated surface vessel trajectory tracking control. In: 2012 American Control Conference, Montréal, Canada, pp 6203–6208

  22. Wang W, Zhao D, Liu D (2004) Design of a stable sliding-mode controller for a class of second-order underactuated systems. IET Control Theory Appl 151(6):683–690

    Article  MathSciNet  Google Scholar 

  23. Ge SS, Hang CC, Lee TH, Zhang T (2001) Stable Adaptive Neural Network Control. Kluwer Academic, Norwell

    Google Scholar 

  24. Do KD, Jiang ZP, Pan J (2004) Robust adaptive path following of underactuated ships. Automatica 40(6):929–944

    Article  MATH  MathSciNet  Google Scholar 

  25. Pettersen K and Egeland O (1996) Exponential stabilization of an underactuated surface vessel. In: Proceedings of 35th Conference of Decision Control, Kobe, Japan, pp 967–971

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Acknowledgments

This work was supported by the Special Research Fund of Ministry of Education of China for the Doctoral Program (Grant No.: 20110073110009) and the National Natural Science Foundation of China (Grant No.: 51279106).

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Authors and Affiliations

  1. College of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Cheng Liu & Zaojian Zou

  2. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zaojian Zou

  3. College of Navigation, Dalian Maritime University, Dalian, 116600, China

    Jianchuan Yin

Authors
  1. Cheng Liu
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  2. Zaojian Zou
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  3. Jianchuan Yin
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Correspondence to Cheng Liu.

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Liu, C., Zou, Z. & Yin, J. Trajectory tracking of underactuated surface vessels based on neural network and hierarchical sliding mode. J Mar Sci Technol 20, 322–330 (2015). https://doi.org/10.1007/s00773-014-0285-y

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  • DOI: https://doi.org/10.1007/s00773-014-0285-y

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