Model predictive and adaptive neural sliding mode control for three-dimensional path following of autonomous underwater vehicle with input saturation

  • Xuliang Yao
  • Xiaowei WangEmail author
  • Le Zhang
  • Xiaogang Jiang
Smart Data Aggregation Inspired Paradigm & Approaches in IoT Applns


With model uncertainties and input saturation, a novel control method is developed to steer an underactuated autonomous underwater vehicle that realizes the following of the planned path in three-dimensional (3D) space. Firstly, Serret–Frenet frame is applied as virtual target, and the path following errors model in 3D is built. Secondly, the control method which includes kinematic controller and dynamic controller was presented based on cascade control strategy. The kinematic controller, which is responsible for generating a series of constrained velocity signals, is designed based on model predictive control. The adaptive radial basis function neural network is used to estimate the model uncertainty caused by hydrodynamic parameters. Moreover, sliding mode control technology is applied in the design of dynamic controller to improve its robustness. Then, the control effect is compared with that of LOS guidance law and PID controller by simulation experiment. The comparison results show that the proposed algorithm can improve path following effect and reduce input saturation.


Autonomous underwater vehicle Path following MPC SMC RBFNN 



This work has been supported by the National Natural Science Foundation of China (51279039).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Behal A, Dawson DM, Dixon WE, Fang Y (2002) Tracking and regulation control of an underactuated surface vessel with nonintegrable dynamics. IEEE Trans Autom Control 47(3):495–500MathSciNetzbMATHGoogle Scholar
  2. 2.
    Moe S, Caharija W, Pettersen KY, Schjolberg I (2014) Path following of underactuated marine surface vessels in the presence of unknown ocean currents. In; American control conference. IEEE, pp 3856–3861Google Scholar
  3. 3.
    Park BS (2015) Neural network-based tracking control of underactuated autonomous underwater vehicles with model uncertainties. J Dyn Syst Meas Control 137(2):1–7Google Scholar
  4. 4.
    Fossen TI, Breivik M, Skjetne R (2003) Line-of-sight path following of underactuated marine craft. In: Proceedings of the 6th IFAC MCMC, Girona, Spain, pp 244–249Google Scholar
  5. 5.
    Lekkas AM, Fossen TI (2012) A time-varying lookahead distance guidance law for path following. IFAC Proc Vol 45(27):398–403Google Scholar
  6. 6.
    Caharija W, Pettersen KY, Bibuli M, Calado P, Zereik E, JoséBraga Gravdahl JT, Sørensen AJ, Milovanović M, Bruzzone G (2016) Integral line-of-sight guidance and control of underactuated marine vehicles: theory, simulations, and experiments. IEEE Trans Control Syst Technol 24(5):1623–1642Google Scholar
  7. 7.
    Borhaug E, Pavlov A, Pettersen KY (2008) Integral LOS control for path following of underactuated marine surface vessels in the presence of constant ocean currents. IEEE Conf Decis Control 30(2):4984–4991Google Scholar
  8. 8.
    Serrano ME, Scaglia GJE, Godoy SA, Mut V, Ortiz OA (2014) Trajectory tracking of underactuated surface vessel: a linear algebra approach. IEEE Trans Control Syst Technol 22(3):1103–1111Google Scholar
  9. 9.
    Lefeber E, Pettersen KY, Nijmeijer H (2003) Tracking control of an underactuated ship. IEEE Trans Control Syst Technol 11(1):52–61Google Scholar
  10. 10.
    Do KD, Jiang ZP, Pan J, Nijmeijer H (2004) A global output feedback controller for stabilization and tracking of underactuated ODIN: a spherical underwater vehicle. Automatica 40(1):117–124MathSciNetzbMATHGoogle Scholar
  11. 11.
    Bidyadhar S, Koena M, Sandip G (2013) A static output feedback control design for path following of autonomous underwater vehicle in vertical plane. Ocean Eng 63(1):72–76Google Scholar
  12. 12.
    Repoulias F, Papadopoulos E (2007) Planar trajectory planning and tracking control design for underactuated AUVs. Ocean Eng 34(11):1650–1667Google Scholar
  13. 13.
    Pettersen KY, Nijmeijer H (2001) Underactuated ship tracking control: theory and experiments. Int J Control 74(14):1435–1446MathSciNetzbMATHGoogle Scholar
  14. 14.
    Jiang ZP (2002) Global tracking control of underactuated ships by Lyapunov’s direct method. Automatica 38(1):301–309zbMATHGoogle Scholar
  15. 15.
    Lekkas AM, Fossen TI (2014) Minimization of cross-track and along-track errors for path tracking of marine underactuated vehicles. In: European control conference (ECC). IEEE, pp 3004–3010Google Scholar
  16. 16.
    Lapierre L, Soetanto D (2007) Nonlinear path-following control of an AUV. Ocean Eng 34(2):1734–1744Google Scholar
  17. 17.
    Silvestre C, Pascoal A, Kaminer I (2002) On the design of gain-scheduled trajectory tracking controllers. Int J Robust Nonlinear Control 12(9):797–839MathSciNetzbMATHGoogle Scholar
  18. 18.
    Antonelli G, Caccavale F, Chiaverini S, Fusco G (2003) A novel adaptive control law for underwater vehicles. IEEE Trans Control Syst Technol 11(2):221–232Google Scholar
  19. 19.
    Li JH, Lee PM (2005) Design of an adaptive nonlinear controller for depth control of an autonomous underwater vehicle. Ocean Eng 32(17–18):2165–2181Google Scholar
  20. 20.
    Zhang LJ, Qi X, Pang YJ (2009) Adaptive output feedback control based on DRFNN for AUV. Ocean Eng 36(9):716–722Google Scholar
  21. 21.
    Breivik M, Fossen TI (2004) Path following for marine surface vessels. OCEANS’04. MTTS/IEEE TECHNO-OCEAN’04. IEEE 4:2282–2289Google Scholar
  22. 22.
    Fossen TI, Lekkas AM (2017) Direct and indirect adaptive integral line-of-sight path-following controllers for marine craft exposed to ocean currents. Int J Adapt Control Signal Process 31(4):445–463MathSciNetzbMATHGoogle Scholar
  23. 23.
    Do KD, Pan J (2004) State-and output-feedback robust path- following controllers for underactuated ships using Serret-Frenetframe. Ocean Eng 31(5–6):587–613Google Scholar
  24. 24.
    Do KD, Pan J (2006) Global robust adaptive path following of underactuated ships. Automatica 42(10):1713–1722zbMATHGoogle Scholar
  25. 25.
    Lapierre L, Jouvencel B (2008) Robust nonlinear path-following control of an AUV. IEEE J Ocean Eng 33(2):89–102Google Scholar
  26. 26.
    Liao YL, Zhang MJ, Wan L (2015) Serret–Frenet frame based on path following control for underactuated unmanned surface vehicles with dynamic uncertainties. J Cent South Univ 22(1):214–223Google Scholar
  27. 27.
    Ji DX, Liu J, Zhao HY, Wang YQ (2014) Path following of autonomous vehicle in 2D space using multivariable sliding mode control. J Robot 2014:1–6Google Scholar
  28. 28.
    Xu J, Wang M, Qiao L (2015) Dynamical sliding mode control for the trajectory tracking of underactuated unmanned underwater vehicles. Ocean Eng 105:54–63Google Scholar
  29. 29.
    Liu C, Zou ZJ, Li TS (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):1525–1535Google Scholar
  30. 30.
    Pan CZ, Lai XZ, 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):1929–1938Google Scholar
  31. 31.
    Caharija W, Pettersen KY, Gravdahl JT, Borhaug E (2012) Path following of underactuated autonomous underwater vehicles in the presence of ocean currents. In: IEEE 51st IEEE conference on decision and control (CDC), pp 528–535Google Scholar
  32. 32.
    Borhaug E, Pettersen KY (2005) Cross-track control for underactuated autonomous vehicles. In: Proceedings of the 44th IEEE conference on decision and control, pp 602–608Google Scholar
  33. 33.
    Encarnacao P, Pascoal A (2002) 3D path-following for autonomous underwater vehicles. IEEE Conf Decis Control 3(11):2977–2982Google Scholar
  34. 34.
    Li Y, Wei C, Wu Q, Chen PY, Jiang YQ, Li YM (2015) Study of 3 dimension trajectory tracking of underactuated autonomous underwater vehicle. Ocean Eng 105:270–274Google Scholar
  35. 35.
    Do KD, Pan J, Jiang ZP (2004) Robust and adaptive path following for underactuated autonomous underwater vehicles. Ocean Eng 31(16):1967–1997Google Scholar
  36. 36.
    Aguiar AP, Hespanha JP (2007) Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty. IEEE Trans Autom Control 52(8):1362–1379MathSciNetzbMATHGoogle Scholar
  37. 37.
    Zheng ZW, Feroskhan M (2017) Path following of a surface vessel with prescribed performance in the presence of input saturation and external disturbances. Trans Mechatron 22(6):2564–2575Google Scholar
  38. 38.
    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):289–295Google Scholar
  39. 39.
    Yao XL, Yang GY, Peng Y (2017) Nonlinear reduced-order observer-based predictive control for diving of an autonomous underwater vehicle. Discrete Dyn Nat Soc 2017:1–15MathSciNetzbMATHGoogle Scholar
  40. 40.
    Fossen TI (2011) Handbook of marine craft hydrodynamics and motion control. Wiley, AmsterdamGoogle Scholar
  41. 41.
    Lin YC, Chen DD, Chen MS, Chen XM, Li J (2018) A precise BP neural network-based online model predictive control strategy for die forging hydraulic press machine. Neural Comput Appl 29(9):585–596Google Scholar
  42. 42.
    Saraswati S, Chand S (2010) Online linearization-based neural predictive control of air-fuel ratio in SI engines with PID feedback correction scheme. Neural Comput Appl 19(6):919–933Google Scholar
  43. 43.
    Jazayeri-Rad H (2004) The nonlinear model-predictive control of a chemical plant using multiple neural networks. Neural Comput Appl 13(1):2–15Google Scholar
  44. 44.
    Li JH, Lee PM, Jun BH, Lim YK (2008) Point-to-point navigation of underactuated ships. Automatica 44(12):3201–3205MathSciNetzbMATHGoogle Scholar
  45. 45.
    Prestero T (2001) Development of a six-degree of freedom simulation model for the REMUS autonomous underwater vehicle. In: Oceans//MTS/IEEE conference and exhibition. IEEE, pp 450–455Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of AutomationHarbin Engineering UniversityHarbinChina
  2. 2.College of Mechanical EngineeringJiujiang Vocational and Technical CollegeJiujiangChina

Personalised recommendations