Three-dimensional neural network tracking control of a moving target by underactuated autonomous underwater vehicles

  • Khoshnam Shojaei
Original Article


This paper investigates three-dimensional target tracking control problem of underactuated autonomous underwater vehicles (AUVs) by using coordinates transformation and multi-layer neural networks. The passive-boundedness assumption of sway and heave velocities of underactuated AUVs is used to design a controller in the actuated directions. For this purpose, a new Euler–Lagrange formulation is proposed based on range and bearing tracking errors with respect to a moving target in the body-fixed frame. Then, a tracking controller is proposed to make range and bearing tracking errors converge to zero. Multi-layer neural networks (MLNNs) are utilized to approximate unknown nonlinear-in-parameter dynamics of the system, and adaptive robust control techniques are adopted to compensate for MLNN approximation errors and time-varying environmental disturbances which are induced by waves, wind and ocean currents. The stability of the proposed control system is analysed based on Lyapunov’s approach which shows that target tracking errors are semi-globally uniformly ultimately bounded and exponentially tend to a small neighbourhood around the zero. At the end, simulation examples are given to demonstrate the competency of the proposed target tracking controller.


Autonomous underwater vehicles Multi-layer neural networks NLIP uncertainty Target tracking Three-dimensional control Underactuated systems 



The author would like to thank anonymous reviewers and associated editor for their helpful suggestions and comments. This work is supported in part by research and technology programme funded by Najafabad branch, Islamic Azad University, under Grant Number 51504920613004 under the research work entitled “Designing tracking controllers for the navigation of autonomous ocean vessels with limited information”.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interest for this paper.


  1. 1.
    Yuh J (2000) Design and control of autonomous underwater robots: a survey. Auton Robots 8:7–24CrossRefGoogle Scholar
  2. 2.
    Nakamura Y, Savant S (1992) Nonlinear tracking control of autonomous underwater vehicle. In: Proceedings of 1992 IEEE international conference on robotics and automation, Nice, France, pp A4–A9Google Scholar
  3. 3.
    Egeland O, Dalsmo M, Sordalen OJ (1996) Feedback control of a nonholonomic underwater vehicle with constant desired configuration. Int J Robot Res 15(1):24–35CrossRefGoogle Scholar
  4. 4.
    Leonard NE (1995) Control synthesis and adaptation for an underactuated autonomous underwater vehicle. IEEE J Ocean Eng 20(3):211–220CrossRefGoogle Scholar
  5. 5.
    Pettersen KY, Egeland O (1999) Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle. IEEE Trans Autom Control 44(1):112–115MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Zain ZMd, Watanabe K, Izumi K, Nagai I (2013) A discontinuous exponential stabilization law for an underactuated X4-AUV. J Artif Life Robot 17:463–469CrossRefGoogle Scholar
  7. 7.
    Woolsey CA, Techy L (2009) Cross-track control of a slender, underactuated AUV using potential shaping. Ocean Eng 36:82–91CrossRefGoogle Scholar
  8. 8.
    Batista P, Silvestre C, Oliviera P (2009) A sensor-based controller for homing of underactuated AUVs. IEEE Trans Robot 25(3):701–716CrossRefGoogle Scholar
  9. 9.
    Lapierre L, Jouvencel B (2008) Robust nonlinear path-following control of an AUV. IEEE J Ocean Eng 33(2):89–102CrossRefGoogle Scholar
  10. 10.
    Do KD, Pan J, Jiang ZP (2006) Robust and adaptive path following for underactuated autonomous underwater vehicles. Ocean Eng 31(16):1967–1997CrossRefGoogle Scholar
  11. 11.
    Aguiar AP, Pascoal AM (2007) Dynamic positioning and way-point tracking of underactuated AUVs in the presence of ocean currents. Int J Control 80(7):1092–1108MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Repoulias F, Papadopoulos E (2007) Planar trajectory planning and tracking control design for underactuated AUVs. Ocean Eng 34:1650–1667CrossRefGoogle Scholar
  13. 13.
    Bi FY, Wei YJ, Zhang JZ, Cao W (2009) Position-tracking control of underactuated autonomous underwater vehicles in the presence of unknown ocean currents. IET Control Theory Appl 4(11):2369–2380MathSciNetCrossRefGoogle Scholar
  14. 14.
    Qi X (2014) Adaptive coordinated tracking control of multiple autonomous underwater vehicles. Ocean Eng 91:84–90CrossRefGoogle Scholar
  15. 15.
    Cui R, Ge SS, Voon Ee How B, Sang Choo Y (2010) Leader-follower formation control of underactuated autonomous underwater vehicles. Ocean Eng 37(17):1491–1502CrossRefGoogle Scholar
  16. 16.
    Refsnes JE, Sorensen AJ, Pettersen KY (2008) Model-based output feedback control of slender-body underactuated AUVs: theory and experiments. IEEE Trans Control Syst Technol 16(5):930–946CrossRefGoogle Scholar
  17. 17.
    Subudhi B, Mukherjee K, Ghosh S (2013) A static output feedback control design for path following of autonomous underwater vehicle in vertical plane. Ocean Eng 63:72–76CrossRefGoogle Scholar
  18. 18.
    Xiang X, Lapierre L, Jouvencel B (2015) Smooth transition of AUV motion control: from fully-actuated to under-actuated configuration. Robot Auton Syst 67:14–22CrossRefGoogle Scholar
  19. 19.
    Xu J, Wang M, Qiao L (2015) Dynamical sliding mode control for the trajectory tracking of underactuated unmanned underwater vehicles. Ocean Eng 105:54–63CrossRefGoogle Scholar
  20. 20.
    Glotzbach T, Schneider M, Otto P (2015) Cooperative line of sight target tracking for heterogeneous unmanned marine vehicle teams: from theory to practice. Robot Auton Syst 67:53–60CrossRefGoogle Scholar
  21. 21.
    Yan Z, Yu H, Zhang W, Li B, Zhou J (2015) Globally finite-time stable tracking control of underactuated UUVs. Ocean Eng 107:132–146CrossRefGoogle Scholar
  22. 22.
    Park BS (2015) Adaptive formation control of underactuated autonomous underwater vehicles. Ocean Eng 96:1–7CrossRefGoogle Scholar
  23. 23.
    Chen Y, Zhang R, Zhao X, Gao J (2016) Adaptive fuzzy inverse trajectory tracking control of underactuated underwater vehicle with uncertainties. Ocean Eng 121:123–133CrossRefGoogle Scholar
  24. 24.
    Ismail ZH, Mokhar MBM, Putranti VWE, Dunnigan MW (2016) A robust dynamic region-based control scheme for an autonomous underwater vehicle. Ocean Eng 111:155–165CrossRefGoogle Scholar
  25. 25.
    Wang Y, Zhang M, Wilson PA, Liu X (2015) Adaptive neural network-based backstepping fault tolerant control for underwater vehicles with thruster fault. Ocean Eng 110:15–24CrossRefGoogle Scholar
  26. 26.
    Mukherjee K, Kar IN, Bhatt RKP (2015) Region tracking based control of an autonomous underwater vehicle with input delay. Ocean Eng 99:107–114CrossRefGoogle Scholar
  27. 27.
    Gao J, Proctor A, Bradley C (2015) Adaptive neural network visual servo control for dynamic positioning of underwater vehicles. Neurocomputing 167:604–613CrossRefGoogle Scholar
  28. 28.
    Liu Y-C, Liu S-Y, Wang N (2016) Fully-tuned fuzzy neural network based robust adaptive tracking control of unmanned underwater vehicle with thruster dynamics. Neurocomputing 196:1–13CrossRefGoogle Scholar
  29. 29.
    Li Y, Wei C, Wu Q, Chen P, Jiang Y, Li Y (2015) Study of 3 dimension trajectory tracking of underactuated autonomous underwater vehicle. Ocean Eng 105:270–274CrossRefGoogle Scholar
  30. 30.
    Shojaei K, Arefi MM (2015) On the neuro-adaptive feedback linearising control of underactuated autonomous underwater vehicles in three-dimensional space. IET Control Theory Appl 9(8):1264–1273MathSciNetCrossRefGoogle Scholar
  31. 31.
    Do KD (2013) Coordination control of underactuated ODINs in three-dimensional space. Robot Auton Syst 61(8):853–867CrossRefMATHGoogle Scholar
  32. 32.
    Shojaei K (2016) Neural network formation control of underactuated autonomous underwater vehicles with saturating actuators. Neurocomputing 194:372–384CrossRefGoogle Scholar
  33. 33.
    Do KD, Pan J (2009) Control of ships and underwater vehicles: design for underactuated and nonlinear marine systems. Springer, LondonCrossRefGoogle Scholar
  34. 34.
    Fossen TI (2002) Marine control systems. Marine Cybernetics, TrondheimGoogle Scholar
  35. 35.
    Peng Z, Wang D, Chen Z, Hu X, Lan W (2013) Adaptive dynamic surface control for formations of autonomous surface vehicles with uncertain dynamics. IEEE Trans Control Syst Technol 21(2):513–520CrossRefGoogle Scholar
  36. 36.
    Li JH, Lee PM, Jun BH, Lim YK (2008) Point-to-point navigation of underactuated ships. Automatica 44(12):3201–3205MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Lewis FL, Dawson DM, Abdallah CT (2004) Robot manipulator control theory and practice, 2nd edn. Marcel Dekker Inc., New YorkGoogle Scholar
  38. 38.
    Polycarpou MM (1996) Stable adaptive neural control scheme for nonlinear systems. IEEE Trans Autom Control 41:447–451MathSciNetCrossRefMATHGoogle Scholar
  39. 39.
    Liu C, Zou Z-J, Li T-S (2015) Path following of underactuated surface vessels with fin roll reduction based on neural network and hierarchical sliding mode technique. Neural Comput Appl 26(7):1525–1535CrossRefGoogle Scholar
  40. 40.
    Cao Z, Cheng L, Zhou C, Gu N, Wang X, Tan M (2015) Spiking neural network-based target tracking control for autonomous mobile robots. Neural Comput Appl 26(8):1839–1847CrossRefGoogle Scholar
  41. 41.
    Pan C, Lai X, Yang SX, Wu M (2015) A bioinspired neural dynamics-based approach to tracking control of autonomous surface vehicles subject to unknown ocean currents. Neural Comput Appl 26(8):1929–1938CrossRefGoogle Scholar
  42. 42.
    Peng Z, Wang D, Wang H, Wang W (2014) Coordinated formation pattern control of multiple marine surface vehicles with model uncertainty and time-varying ocean currents. Neural Comput Appl 25(7):1771–1783CrossRefGoogle Scholar
  43. 43.
    Shojaei K (2015) Leader-follower formation control of underactuated autonomous marine surface vehicles with limited torque. Ocean Eng 105:196–205CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Najafabad BranchIslamic Azad UniversityNajafabadIran

Personalised recommendations