Encyclopedia of Robotics

Living Edition
| Editors: Marcelo H Ang, Oussama Khatib, Bruno Siciliano

Modeling of Underwater Vehicles

  • Thor I. FossenEmail author
  • Kristin Y. Pettersen
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-41610-1_12-1



A mathematical model of an underwater vehicle is used to simulate or control the motions of the vehicle in six degrees of freedom in a Cartesian coordinate system. The vehicle model is represented as ordinary differential equations, which are numerically integrated in order to obtain position, velocity, and attitude as a function of time.

Key Research Findings

Underwater vehicles are usually modeled using the Newtonian-Euler framework. The equations of motion are formulated in 6 degrees of freedom using Euler angles or quaternions for attitude, while the forces and moments are due to rigid-body dynamics, hydrodynamic damping and added mass, gravity and buoyancy. In addition, models of propellers, moving masses and control surfaces are included to describe the control forces. Underwater vehicles are exposed...

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  1. Allmendinger E (ed) (1990) Submersible vehicle systems design. SNAME, Jersey CityGoogle Scholar
  2. Antonelli G (2014) Underwater robots: motion and force control of vehicle-manipulator systems, 3rd edn. Springer, Berlin/New YorkGoogle Scholar
  3. Antonelli G, Fossen TI, Yoerger D (2016) Modeling and Control of Underwater Robotics. In the Springer Handbook on Robotics, Siciliano B, Khatib O, (eds), 2nd edition, Springer-Verlag, ISBN 978-3-319-32550-7, 51, pp. 1285–1304Google Scholar
  4. Boyer F, Porez M, Khalil W (2016) Macro-continuous computed torque algorithm for a three-dimensional. IEEE Trans Robot 22(4):763–775Google Scholar
  5. Faltinsen O (1990) Sea loads on ships and offshore structures. Cambridge University Press, Cambridge, UKGoogle Scholar
  6. Fan S, Woolsey CA (2013) Underwater vehicle control and estimation in nonuniform currents. In: Proceedings of American control conference (ACC), Washington, DC, pp 1400–1405Google Scholar
  7. Fossen TI (1994) Guidance and control of ocean vehicles. Wiley, Chichester/New YorkGoogle Scholar
  8. Fossen TI (2011) Handbook of marine craft hydrodynamics and motion control. Wiley, ChichesterGoogle Scholar
  9. Inzartsev AV (2009) Intelligent underwater vehicles. I-Tech Education and Publishing. http://www.intechweb.org
  10. Lewanddowski EM (2004) The dynamics of marine craft. World Scientific Publishing, SingaporeGoogle Scholar
  11. Newman JN (1977) Marine hydrodynamics. MIT, CambridgeGoogle Scholar
  12. Ridao P, Carreras M, Ribas D, Sanz PJ, Oliver G (2014) Intervention AUVs: the next challenge. In: Proceedings of 19th IFAC world congress (IFAC-WC), Cape Town, pp 12146–12159Google Scholar
  13. SNAME (1950) Nomenclature for treating the motion of a submerged body through a fluid. SNAME, Tech Res Bull Vol. 1–5:1–15Google Scholar
  14. Sutton R, Roberts G (2006) Advances in unmanned marine vehicles. IEE control series. The Institution of Engineering and Technology, StevenageGoogle Scholar
  15. Wadoo S, Kachroo P (2010) Autonomous underwater vehicles: modeling, control design and simulation. CRC Press, Taylor & Francis Group, Boca Raton, FL, USAGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Engineering CyberneticsNTNU Norwegian University of Science and TechnologyTrondheimNorway

Section editors and affiliations

  • Gianluca Antonelli
    • 1
  1. 1.University of Cassino and Southern LazioCassinoItaly