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International Journal of Dynamics and Control

, Volume 7, Issue 4, pp 1306–1320 | Cite as

Modelling Subsea ROV robotics using the moving frame method

  • Katrine Oen Austefjord
  • Linn-Kristin Skeide Larsen
  • Martin Oddøy Hestvik
  • Thomas J. ImpellusoEmail author
Article

Abstract

This paper introduces a new method (notation and theory) in engineering dynamics. The goal of this paper is to apply this new method to the analysis of multi-body systems, specifically for the analysis of the motion of a Remotely Operated Vehicle (ROV). Norway conducts operations on a variety of structures in the North Sea. Research that can improve the efficiency of these operations are of high interest. This paper researches the motion of an ROV induced by the motion of the robotic manipulators, motor torques, and buoyancy. This research also introduces a new method in engineering dynamics: the Moving Frame Method (MFM). The MFM draws upon Lie group theory and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. While others have applied pieces and aspects of these mathematical tools, the notation presented here brings them together; it is accessible, programmable and simple. The notation for multi-body dynamics and single rigid body dynamics is the same. Most important, this paper presents a restricted variation of the angular velocity to use in Hamilton’s Principle to extract the equations of motion. This research solves the equations using a relatively simple numerical integration scheme. The Cayley-Hamilton theorem and Rodriguez’s formula reconstructs the rotation matrix for the ROV. This work displays the rotating ship in 3D, viewable on mobile devices. This paper presents the results qualitatively as a 3D simulation. This research demonstrates that the MFM is suitable for the analysis of “smart ROVs” as the next step in this work.

Keywords

Moving Frame Method Dynamics ROV motion Subsea Engineering Robotics 

List of symbols

\( I_{3 } ,I_{d } \)

3 × 3 identity matrix

Jc( α)

3 × 3 mass moment of inertia matrix

K

Kinetic energy

L

Lagrangian

\( \left[ M \right] \)

Mass matrix

\( \left[ {{\text{M}}^{*} } \right] \)

Reduced mass matrix

\( \left[ {{\text{N}}^{*} } \right] \)

Reduced non-linear velocity matrix

q

Generalized coordinates

\( \dot{q} \)

Generalized velocity

\( \ddot{q} \)

Generalized acceleration

R

Rotation matrix

r

Absolute position vector

s

Relative position vector

U

Potential energy

\( \left\{ {\dot{X}} \right\} \)

List of velocities

\( \delta \)

Variation

\( \delta W \)

Virtual work

\( \delta \Pi \)

Variation of frame connection matrix

\( \delta \dot{\tilde{X}} \)

Variation of the generalized rates

\( \delta \tilde{X} \)

Virtual generalized displacement

\( \delta \dot{X} \)

Virtual generalized velocity

\( \delta q \)

Virtual essential generalized displacement

\( \tilde{\delta }\pi \)

Virtual rotational displacement

\( \Omega \)

Time rate of frame connection matrix

\( \omega \)

Angular velocity vector

\( \tilde{\omega } \)

Skew symmetric angular velocity matrix

References

  1. 1.
    Oceaneering (2016) ROV systems. http://www.oceaneering.com/rovs/rov-systems/. 03 April 2017
  2. 2.
    Suzuki H et al (2017) Numerical analysis of the motion of ROV applying ANC method to the motion of tether cable. In: International society of offshore and polar engineers, The 27th international ocean and polar engineering conference, 25–30 June, San Francisco, California, USAGoogle Scholar
  3. 3.
    Quan W, Zhang Z, Zhang A (2014) Dynamics analysis of planar armored cable motion in deep-sea ROV system. J Cent South Univ 21:4456CrossRefGoogle Scholar
  4. 4.
    Driscoll F, Lueck R, Nahon M (2000) The motion of a deep-sea remotely operated vehicle system Part 1: motion observations. Ocean Eng 27(1):29–56CrossRefGoogle Scholar
  5. 5.
    Evjenth A, Moe O, Schøn I, Impelluso T (2017) A dynamic model for the motion of an ROV due to onboard robotics. In: ASME 2017 international mechanical engineering congress & exposition, Tampa, FloridaGoogle Scholar
  6. 6.
    Cartan É (1986) On manifolds with an affine connection and the theory of general relativity, translated by A. Magnon and A. Ashtekar, Napoli, Italy, BibiliopolisGoogle Scholar
  7. 7.
    Frankel T (2012) The geometry of physics, an introduction, 3rd edn. Cambridge University Press, New York (First edition published in 1997) zbMATHGoogle Scholar
  8. 8.
    Murray RM, Li Z, Sastry SS (1994) A mathematical introduction to robotic manipulation. CRC Press, Boca Raton, FloridazbMATHGoogle Scholar
  9. 9.
    Impelluso T (2017) The moving frame method in dynamics: reforming a curriculum and assessment. Int J Mech Eng Educ 46(2):158–191CrossRefGoogle Scholar
  10. 10.
    Impelluso T (2016) Rigid body dynamics: a new philosophy, math and pedagogy. In: Proceedings of the ASME 2016 international mechanical engineering congress & exposition, Houston, TexasGoogle Scholar
  11. 11.
    Murakami H (2015) A moving frame method for multi-body dynamics using SE(3). In: ASME 2015 international mechanical engineering congress & exposition, Houston, Texas, USAGoogle Scholar
  12. 12.
    Denavit J, Hartenberg R (1955) A kinematic notation for lower-pair mechanisms based on matrices. J Appl Mech 22:215–221MathSciNetzbMATHGoogle Scholar
  13. 13.
    Rios O, Murakami H, Impelluso T (2017) A theoretical and numerical study of the Dzhanibekov and Tennis racket phenomena. J Appl Mech.  https://doi.org/10.1115/1.4034318 CrossRefGoogle Scholar
  14. 14.
    Holm D (2008) Geometric mechanics, part II: rotating, translating and rolling. World Scientific, HackensackCrossRefGoogle Scholar
  15. 15.
    Wittenburg J (1977) Dynamics of rigid bodies. B. G. Teubner, StuttgartCrossRefGoogle Scholar
  16. 16.
    Wittenburg J (2008) Dynamics of multibody systems, 2nd edn. Springer, StuttgartzbMATHGoogle Scholar
  17. 17.
    https://www.khronos.org/webgl/. Accessed 1 May 2018
  18. 18.
    Norbach A, Fjetland K, Hestetun G, Impelluso T (2018) Gyroscopic wave energy converter for fish farms. In: ASME 2018 international mechanical engineering congress & exposition, Pittsburgh, PennsylvaniaGoogle Scholar
  19. 19.
    Jardim P, Rein J, Haveland Ø, Vinje J, Impelluso T (2018) Modeling crane induced ship motion using the moving frame method. In: ASME 2018 international mechanical engineering congress & exposition, IMECE2018-86190, Pittsburgh, PennsylvaniaGoogle Scholar
  20. 20.
    Flatlandsmo J, Torbjørn S, Halvorsen Ø, Vinje J, Impelluso T (2018) Modeling stabilization of crane and ship by gyroscopic control using the moving frame method. In: ASME 2018 international mechanical engineering congress & exposition, IMECE2018-86188, Pittsburgh, PennsylvaniaGoogle Scholar
  21. 21.
    Murakami T (2016) Development of an active curved beam model using a moving frame method. In: Proceedings of the ASME 2016 international mechanical engineering congress & exposition IMECE2016 November 11–17, 2016, IMECE2016-65294, Phoenix, Arizona, USAGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Mechanical and Marine EngineeringWestern Norway University of Applied Sciences (HVL)BergenNorway
  2. 2.SandsliNorway
  3. 3.LoddefjordNorway
  4. 4.AverøyNorway
  5. 5.BergenNorway

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