Trajectory Tracking Control for Underactuated Surface Vessels Based on Nonlinear Model Predictive Control

  • Chenguang LiuEmail author
  • Huarong Zheng
  • Rudy R. Negenborn
  • Xiumin Chu
  • Le Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9335)


An autonomous vessel can improve the intelligence, efficiency and economy of shipping logistics. To realize autonomous navigation control of underactuated vessels (USVs), this paper presents a controller that can make USV track a reference trajectory with only 2 inputs, i.e., surge and yaw. A nonlinear state-space model with 2 inputs considering environmental disturbances induced by wind, current and waves for a 3 degree of freedom (DOF) surface vessel is considered. Based on this model, a trajectory tracking controller using Nonlinear Model Predictive Control (NMPC) is designed. System constraints on inputs, input increment and output are incorporated in the NMPC framework. Simulation results show that the controller can track an ellipse trajectory well and that the tracking errors are within acceptable ranges, while system constraints are satisfied.


Underactuated surface vessels Nonlinear model predictive control Trajectory tracking Environmental disturbances 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Duan, A.Y., Zhao, Y.: Brief Discussion on the Problems of Safety Management of Carrying Cargo on Deck (in Chinese). Ship and Ocean Engineering 35, 124–126 (2006)Google Scholar
  2. 2.
    Serrano, M.E., Scaglia, G.J.E., Godoy, S.A., et al.: Trajectory Tracking of Underactuated Surface Vessels: A Linear Algebra Approach. IEEE Transactions on Control Systems Technology 22, 1103–1111 (2014)CrossRefGoogle Scholar
  3. 3.
    Lefeber, E., Pettersen, K.Y., Nijmeijer, H.: Tracking control of an underactuated ship. IEEE transactions on control systems technology 11, 52–61 (2003)CrossRefGoogle Scholar
  4. 4.
    Yan, Z., Wang, J.: Model predictive control for tracking of underactuated vessels based on recurrent neural networks. Oceanic Engineering 37, 717–726 (2012)CrossRefGoogle Scholar
  5. 5.
    Wang, X: Study on path following control for underactuated ships by using analytic model predictive control (in Chinese). School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai (2009)Google Scholar
  6. 6.
    Moreira, L., Soares, C.G.: Autonomous ship model to perform manoeuvring tests. Journal of Maritime Research 8, 29–46 (2011)Google Scholar
  7. 7.
    Ashrafiuon, H., Muske, K.R., McNinch, L.C., et al.: Sliding-mode Tracking Control of Surface Vessels. IEEE Transactions on Industrial Electronics 55, 4004–4012 (2008)CrossRefGoogle Scholar
  8. 8.
    Chen, H.: Model Predictive Control (in Chinese). Science Press, Beijing (2013)Google Scholar
  9. 9.
    Zheng, H., Negenborn, R.R., Lodewijks, G.: Survey of approaches for improving the intelligence of marine surface vehicles. In: Proceedings of the 16th International IEEE Conference on Intelligent Transportation, The Hague, The Netherlands, pp. 1217–1223 (2013)Google Scholar
  10. 10.
    Li, Z., Sun, J., Oh, S.: Path following for marine surface vessels with rudder and roll constraints: an MPC approach. In: American Control Conference, ACC 2009, pp. 3611–3616. IEEE (2009)Google Scholar
  11. 11.
    Liu, L., Liu, Z., Zhang, J.: LMI-based model predictive control for underactuated surface vessels with input constraints. In: Abstract and Applied Analysis. Hindawi Publishing Corporation (2014)Google Scholar
  12. 12.
    Perez, T., Fossen, T.I.: Kinematic Models for Manoeuvring and Seakeeping of Marine Vessels. Modeling, Identification and Control 28, 19–30 (2007)CrossRefGoogle Scholar
  13. 13.
    Fossen, T.I.: Handbook of Marine Craft Hydrodynamics and Motion Control. John Wiley & Sons, New Jersey (2011)CrossRefGoogle Scholar
  14. 14.
    Zheng, H., Negenborn, R.R., Lodewijks, G.: Trajectory tracking of autonomous vessels using model predictive control. In: Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, pp. 8812–8818 (2014)Google Scholar
  15. 15.
    Do, K.D., Jiang, Z.P., Pan, J.: Universal controllers for stabilization and tracking of underactuated ships. Systems and Control Letters. 47, 299–317 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Gong, J.W., Jiang, Y., Xu, W.: Model Predictive Control of Unmanned Vehicle (in Chinese). Beijing Institute of Technology Press, Beijing (2014)Google Scholar
  17. 17.
    Skjetne, R., Smogeli, Ø.N., Fossen, T.I.: A Nonlinear Ship Manoeuvering Model: Identification and adaptive control with experiments for a model ship. Modeling, Identification and Control 25, 3–27 (2004)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Chenguang Liu
    • 1
    • 2
    Email author
  • Huarong Zheng
    • 3
  • Rudy R. Negenborn
    • 3
  • Xiumin Chu
    • 1
  • Le Wang
    • 1
    • 4
  1. 1.Engineering Research Center for Transportation Safety, Ministry of EducationWuhan University of TechnologyWuhanPeople’s Republic of China
  2. 2.School of Energy and Power EngineeringWuhan University of TechnologyWuhanPeople’s Republic of China
  3. 3.Maritime and Transport TechnologyDelft University of TechnologyDelftThe Netherlands
  4. 4.School of Logistics EngineeringWuhan University of TechnologyWuhanPeople’s Republic of China

Personalised recommendations