Skip to main content
SpringerLink
Log in

Robust adaptive asymptotic trajectory tracking control for underactuated surface vessels subject to unknown dynamics and input saturation

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

In this paper, a robust adaptive control scheme is proposed for the trajectory tracking control of underactuated surface vessels (USVs) subject to unknown dynamics, external disturbances and input saturation. First, a coordinate transformation is introduced to deal with the underactuation problem of the USV. A Gaussian error function and an adaptive neural network (NN) are adopted to approximate the saturation function and the unknown dynamics, respectively. Then, an adaptive robust integral of the sign of the error (RISE) feedback term is introduced in feedback control design to compensate the NN and saturation approximation residual errors and unknown external disturbances. On the basis of the above, a robust adaptive trajectory tracking control law is proposed incorporating a coordinate transformation, Gaussian error function and NN into RISE method. In addition, the adjustable-online adaptive feedback gain reduces the conservativeness of the control design. The theoretical analysis indicates that the designed robust adaptive control law can force USVs to track the desired trajectory while guaranteeing the asymptotic tracking performance. Simulation results verify the effectiveness of the novel robust adaptive trajectory tracking control scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Pettersen KY, Nijmeijer H (1999) Global practical stabilization and tracking for an underactuated ship—a combined averaging and backstepping approach. Model Identif Control 20(4):189–200

    Article  Google Scholar 

  2. Ashrafiuon H, Muske KR, Mcninch LC (2010) Review of nonlinear tracking and setpoint control approaches for autonomous underactuated marine vehicles. In: Proceedings of the 2010 American control conference, Baltimore, MD, USA, Jul, pp 5203–5211

  3. Skjetne R, Smogeli Ø, Fossen TI (2004) Modeling, identification and adaptive maneuvering of Cybership II: A complete design with experiments. In: Proceedings of IFAC conference control applications in marine systems, Ancona, Italy, Jul, pp 203–208

  4. Du J, Yang Y, Wang D, Guo C (2013) A robust adaptive neural networks controller for maritime dynamic positioning system. Neurocomputing 110(1):128–136

    Article  Google Scholar 

  5. Shojaei K (2015) Neural adaptive robust control of underactuated marine surface vehicles with input saturation. Appl Ocean Res 53:267–278

    Article  Google Scholar 

  6. Ashrafiuon H, Nersesov S, Clayton G (2017) Trajectory tracking control of planar underactuated vehicles. IEEE Trans Autom Control 62(4):1959–1965

    Article  MathSciNet  MATH  Google Scholar 

  7. Fischer N, Hughes D, Walters P, Schwartz EM, Dixon WE (2014) Nonlinear RISE-based control of an autonomous underwater vehicle. IEEE Trans Robot 30(4):845–852

    Article  Google Scholar 

  8. He S, Dai SL, Luo F (2019) Asymptotic trajectory tracking control with guaranteed transient behavior for MSV with uncertain dynamics and external disturbances. IEEE Trans Ind Electron 66(5):3712–3720

    Article  Google Scholar 

  9. Ghommam J, Mnif F, Benali A, Derbel N (2006) Asymptotic backstepping stabilization of an underactuated surface vessel. IEEE Trans Control Syst Technol 14(6):1150–1157

    Article  Google Scholar 

  10. Yu R, Zhu Q, Xia G, Liu Z (2012) Sliding mode tracking control of an underactuated surface vessel. IET Control Theory Appl 6(3):461–466

    Article  MathSciNet  Google Scholar 

  11. 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 

  12. Qin J, Du J (2019) Adaptive fast nonsingular terminal sliding mode control for underactuated surface vessel trajectory tracking. In: International proceedings of the 19th conference on control, automation and systems, Jeju, Korea, Oct, pp 1365–1370

  13. Shojaei K, Arefi MM (2014) On the neuro-adaptive feedback linearising control of underactuated autonomous underwater vehicles in three-dimensional space. IET Control Theory Appl 9(8):1264–1273

    Article  MathSciNet  Google Scholar 

  14. Fossen TI, Breivik M, Skjetne R (2003) Line-of-sight path following of underactuated marine craft. In: Proceedings of 6th IFAC conference on manoeuvring and control of marine craft, Girona, Spain, Sep, pp 211–216

  15. Li J, Du J, Chang WJ (2019) Robust time-varying formation control for underactuated autonomous underwater vehicles with disturbances under input saturation. Ocean Eng 179:180–188

    Article  Google Scholar 

  16. Park BS, Kwon JW, Kim H (2017) Automatica-neural network-based output feedback control for reference tracking of underactuated surface vessels. Automatica 77:353–359

    Article  MathSciNet  MATH  Google Scholar 

  17. Xie W, Ma B (2015) Robust global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters. Int J Robust Nonlinear Control 25:1037–1050

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang L, Huang B, Liao Y, Wang B (2019) Finite-time trajectory tracking control for uncertain underactuated marine surface vessels. IEEE Access 7:102321–102330

    Article  Google Scholar 

  19. Peng Z, Wang J, Han QL (2019) Path-following control of autonomous underwater vehicles subject to velocity and input constraints via neurodynamic optimization. IEEE Trans Ind Electron 66(11):8724–8732

    Article  Google Scholar 

  20. Zhu G, Du J (2020) Global robust adaptive trajectory tracking control for surface ships under input saturation. IEEE J Ocean Eng 45(2):442–450

    Article  Google Scholar 

  21. Jia Z, Hu Z, Zhang W (2019) Adaptive output-feedback control with prescribed performance for trajectory tracking of underactuated surface vessels. ISA Trans 95:18–26

    Article  Google Scholar 

  22. Gao T, Huang J, Zhou Y, Song YD (2017) Robust adaptive tracking control of an underactuated ship with guaranteed transient performance. Int J Syst Sci 48(2):272–279

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Zheng Z, Huang Y, Xie L, Zhu B (2018) Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output. IEEE Trans Control Syst Technol 26(5):1851–1859

    Article  Google Scholar 

  25. Do KD (2010) Practical control of underactuated ships. Ocean Eng 37(13):1111–1119

    Article  Google Scholar 

  26. Du J, Hu X, Krstić M, Sun Y (2016) Robust dynamic positioning of ships with disturbances under input saturation. Automatica 73:207–214

    Article  MathSciNet  MATH  Google Scholar 

  27. Chen M, Ge SS, How BVE, Choo YS (2013) Robust adaptive position mooring control for marine vessels. IEEE Trans Control Syst Technol 21(2):395–409

    Article  Google Scholar 

  28. Dai S, He S, Wang M, Yuan C (2019) Adaptive neural control of underactuated surface vessels with prescribed performance guarantees. IEEE Trans Neural Netw Learn Syst 30(12):3686–3698

    Article  MathSciNet  Google Scholar 

  29. Chen L, Cui R, Yang C, Yan W (2020) Adaptive neural network control of underactuated surface vessels with guaranteed transient performance: theory and experimental results. IEEE Trans Ind Electron 67(5):4024–4035

    Article  Google Scholar 

  30. Liang K, Lin X, Chen Y, Li J, Ding F (2020) Adaptive sliding mode output feedback control for dynamic positioning ships with input saturation. Ocean Eng 206:107245

    Article  Google Scholar 

  31. Wang Y, Jiang X, She W, Ding F (2019) Tracking control with input saturation and full-state constraints for surface vessels. IEEE Access 7:144741–144755

    Article  Google Scholar 

  32. Zhu G, Du J, Kao Y (2020) Robust adaptive neural trajectory tracking control of surface vessels under input and output constraints. J Franklin Inst 357(13):8591–8610

    Article  MathSciNet  MATH  Google Scholar 

  33. Hu Y, Park GK, Wu H, Zhang Q (2017) Robust adaptive fuzzy design for ship linear-tracking control with input saturation. Int J eNavig Marit Econ 6:9–16

    Google Scholar 

  34. Zhang G, Zhang C, Yang T, Zhang W (2020) Disturbance observer-based composite neural learning path following control of underactuated ships subject to input saturation. Ocean Eng 216:108033

    Article  Google Scholar 

  35. Shen Z, Bi Y, Wang Y, Guo C (2020) MLP neural network-based recursive sliding mode dynamic surface control for trajectory tracking of fully actuated surface vessel subject to unknown dynamics and input saturation. Neurocomputing 377:103–112

    Article  Google Scholar 

  36. Qin H, Li C, Sun Y (2020) Adaptive neural network-based fault-tolerant trajectory-tracking control of unmanned surface vessels with input saturation and error constraints. IET Intell Transp Syst 14(5):356–363

    Article  Google Scholar 

  37. Yao Q (2020) Adaptive finite-time sliding mode control design for finite-time fault-tolerant trajectory tracking of marine vehicles with input saturation. J Franklin Inst 357(18):13593–13619

    Article  MathSciNet  MATH  Google Scholar 

  38. Elhaki O, Shojaei K (2020) A robust neural network approximation-based prescribed performance output-feedback controller for autonomous underwater vehicles with actuators saturation. Eng Appl Artif Intel 88:103382

    Article  Google Scholar 

  39. Shojaei K (2017) Output-feedback formation control of wheeled mobile robots with actuators saturation compensation. Nonlinear Dyn 89:2867–2878

    Article  MathSciNet  MATH  Google Scholar 

  40. Hu X, Wei X, Han J, Zhang Q (2020) Adaptive disturbance rejection for course tracking of marine vessels under actuator constraint. ISA Trans 100:82–91

    Article  Google Scholar 

  41. Qin H, Li C, Sun Y, Wang N (2020) Adaptive trajectory tracking algorithm of unmanned surface vessel based on anti-windup compensator with full-state constraints. Ocean Eng 200:106906

    Article  Google Scholar 

  42. Donaire A, Perez T (2012) Dynamic positioning of marine craft using a port-Hamiltonian framework. Automatica 48:851–856

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhang J, Xiang X, Zhang Q, Li W (2020) Neural network-based adaptive trajectory tracking control of underactuated AUVs with unknown asymmetrical actuator saturation and unknown dynamics. Ocean Eng 218:108193

    Article  Google Scholar 

  44. Xian B, Dawson DM, Queiroz MS, Chen J (2004) A continuous asymptotic tracking control strategy for uncertain nonlinear systems. IEEE Trans Autom Control 49(7):1206–1211

    Article  MathSciNet  MATH  Google Scholar 

  45. Reyhanoglu M (1997) Exponential stabilization of an underactuated autonomous surface vessel. Automatica 33(12):2249–2254

    Article  MathSciNet  MATH  Google Scholar 

  46. Ma J, Zheng Z, Li P (2015) Adaptive dynamic surface control of a class of nonlinear systems with unknown direction control gains and input saturation. IEEE Trans Cybern 45(4):728–741

    Article  Google Scholar 

  47. Cho GR, Li JH, Park D, Jung JH (2020) Robust trajectory tracking of autonomous underwater vehicles using back-stepping control and time delay estimation. Ocean Eng 201:107131

    Article  Google Scholar 

  48. Queiroz MS, Hu J, Dawson DM, Burg T, Donepudi SR (1997) Adaptive position/force control of robot manipulators without velocity measurements: theory and experimentation. IEEE Trans Syst Man Cybern Part B Cybern 27(5):796–809

    Article  Google Scholar 

  49. Horn R, Johnson CR (2012) Matrix analysis. Cambridge University Press, Cambridge

    Book  Google Scholar 

  50. Khalil HK, Grizzle JW (2002) Nonlinear systems, Theor 8.4, 3rd edn. Prentice Hall, Upper Saddle River

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Editor-in-Chief, the Associate Editor, and anonymous reviewers for their invaluable suggestions and comments. This work is supported by the National Natural Science Foundation of P. R. China (Grant number 51079013); the Dalian Science and Technology Innovation Fund Program (grant number 2020JJ26GX020).

Author information

Authors and Affiliations

  1. The School of Marine Electrical Engineering, Dalian Maritime University, Dalian, 116026, Liaoning, People’s Republic of China

    Junfeng Qin & Jialu Du

Authors
  1. Junfeng Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jialu Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jialu Du.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, J., Du, J. Robust adaptive asymptotic trajectory tracking control for underactuated surface vessels subject to unknown dynamics and input saturation. J Mar Sci Technol 27, 307–319 (2022). https://doi.org/10.1007/s00773-021-00835-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-021-00835-9

Keywords

Search

Navigation