China Ocean Engineering

, Volume 31, Issue 2, pp 248–255 | Cite as

Attitude coordination of multi-HUG formation based on multibody system theory

  • Dong-yang Xue
  • Zhi-liang Wu
  • Er-mai Qi
  • Yan-hui Wang
  • Shu-xin Wang
Technical Notes


Application of multiple hybrid underwater gliders (HUGs) is a promising method for large scale, long-term ocean survey. Attitude coordination has become a requisite for task execution of multi-HUG formation. In this paper, a multibody model is presented for attitude coordination among agents in the HUG formation. The HUG formation is regarded as a multi-rigid body system. The interaction between agents in the formation is described by artificial potential field (APF) approach. Attitude control torque is composed of a conservative torque generated by orientation potential field and a dissipative term related with angular velocity. Dynamic modeling of the multibody system is presented to analyze the dynamic process of the HUG formation. Numerical calculation is carried out to simulate attitude synchronization with two kinds of formation topologies. Results show that attitude synchronization can be fulfilled based on the multibody method described in this paper. It is also indicated that different topologies affect attitude control quality with respect to energy consumption and adjusting time. Low level topology should be adopted during formation control scheme design to achieve a better control effect.

Key words

hybrid underwater gliders (HUGs) formation attitude coordination multibody system Kane’s equation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors appreciate all the team members for their contribution to this research.


  1. Alvarez, A., Caffaz, A., Caiti, A., Casalino, G., Gualdesi, L., Turetta, A. and Viviani, R., 2009. Fòlaga: A low-cost autonomous underwater vehicle combining glider and AUV capabilities, Ocean Engineering, 36(1), 24–38.CrossRefGoogle Scholar
  2. Alvarez, A., Chiggiato, J. and Schroeder, K., 2013. Mapping sub-surface geostrophic currents from altimetry and a fleet of gliders, Deep-Sea Research Part I: Oceanographic Research Papers, 74, 115–129.CrossRefGoogle Scholar
  3. Angeles, J., Ma, O. and Rojas, A., 1989. An algorithm for the inverse dynamics of n-axis general manipulators using Kane’s equations, Computers & Mathematics with Applications, 17(2), 1545–1561.CrossRefMATHGoogle Scholar
  4. Chen, Z.E., Yu, J.C., Zhang, A.Q. and Zhang, F.M., 2016. Design and analysis of folding propulsion mechanism for hybrid-driven underwater gliders, Ocean Engineering, 119, 125–134.CrossRefGoogle Scholar
  5. Chen, Z.E., Yu, J.C., Zhang, A.Q., Yi, R.W. and Zhang, Q.F., 2013. Folding propeller design and analysis for a hybrid driven underwater glider, 2013 OCEANS-San Diego, IEEE, San Diego, CA.Google Scholar
  6. Claus, B., Bachmayer, R. and Williams, C.D., 2010. Development of an auxiliary propulsion module for an autonomous underwater glider, Proceedings of the Institution of Mechanical Engineers Part M Journal of Engineering for the Maritime Environment, 224(4), 255–266.CrossRefGoogle Scholar
  7. Eriksen, C.C., Osse, T.J., Light, R.D., Wen, T., Lehman, T.W., Sabin, P.L., Ballard, J.W. and Chiodi, A.M, 2001. Seaglider: A long-range autonomous underwater vehicle for oceanographic research, IEEE Journal of Oceanic Engineering, 26(4), 424–436.CrossRefGoogle Scholar
  8. Fiorelli, E., Leonard, N.E., Bhatta, P., Paley, D.A., Bachmayer, R. and Fratantoni, D.M., 2006. Multi-AUV control and adaptive sampling in Monterey Bay, IEEE Journal of Oceanic Engineering, 31(4), 935–948.CrossRefGoogle Scholar
  9. Hanβmann, H., Leonard, N.E. and Smith, T.R., 2006. Symmetry and reduction for coordinated rigid bodies, European Journal of Control, 12(2), 176–194.MathSciNetCrossRefMATHGoogle Scholar
  10. Huston, R.L. and Kamman, J.W., 1982. Validation of finite segment cable models, Computers & Structures, 15(6), 653–660.CrossRefMATHGoogle Scholar
  11. Huston, R.L. and Liu, Y.W., 1991. Dynamics of Multibody System, Tianjin University Press, Tianjin. (in Chinese)Google Scholar
  12. Huston, R.L., 1989. Methods of analysis of constrained multibody systems, Mechanics of Structures and Machines, 17(2), 135–144.MathSciNetCrossRefGoogle Scholar
  13. Huston, R.L., 1990. Multibody Dynamics, Butterworth-Heinemann, Boston.MATHGoogle Scholar
  14. Kane, T.R. and Levinson, D.A., 1985. Dynamics: Theory and Applications, McGraw-Hill, New York.Google Scholar
  15. Leonard, N.E. and Graver, J.G., 2001. Model-based feedback control of autonomous underwater gliders, IEEE Journal of Oceanic Engineering, 26(4), 633–645.CrossRefGoogle Scholar
  16. Leonard, N.E., Paley, D.A., Davis, R.E., Fratantoni, D.M., Lekien, F. and Zhang, F.M., 2010. Coordinated control of an underwater glider fleet in an adaptive ocean sampling field experiment in Monterey Bay, Journal of Field Robotics, 27(6), 718–740.CrossRefGoogle Scholar
  17. Leonard, N.E., Paley, D.A., Lekien, F., Sepulchre, R., Fratantoni, D.M. and Davis, R.E., 2007. Collective motion, sensor networks, and ocean sampling, Proceedings of the IEEE, 95(1), 48–74.CrossRefGoogle Scholar
  18. Liang, X.L., Wu, W.C., Chang, D. and Zhang, F.M., 2012. Real-time modelling of tidal current for navigating underwater glider sensing networks, ANT 2012 and MobiWIS 2012, Niagara Falls, Canada, pp. 1121–1126.Google Scholar
  19. Liu, F., Wang, Y.H. and Wang, S.X., 2014. Development of the hybrid underwater glider PetreI-II, Sea Technology, 55(4), 51–54.Google Scholar
  20. Merckelbach, L.M., Briggs, R.D., Smeed, D.A. and Griffiths, G., 2008. Current measurements from autonomous underwater gliders, Proceedings of the IEEE/OES 9th Working Conference on Current Measurement Technology, IEEE, Charleston, SC, pp. 61–67.Google Scholar
  21. Nair, S. and Leonard, N.E., 2007. Stable synchronization of rigid body networks, Networks and Heterogeneous Media, 2(4), 597–626.MathSciNetCrossRefMATHGoogle Scholar
  22. Nair, S. and Leonard, N.E., 2008. Stable synchronization of mechanical system networks, SIAM Journal of Control and Optimization, 47(2), 661–683.MathSciNetCrossRefMATHGoogle Scholar
  23. Paley, D.A., Zhang, F.M. and Leonard, N.E., 2008. Cooperative control for ocean sampling: the glider coordinated control system, IEEE Transactions on Control Systems Technology, 16(4), 735–744.CrossRefGoogle Scholar
  24. Perry, R.L., DiMarco, S.F., Walpert, J., Guinasso, N.L., Jr. and Knap, A., 2013. Glider operations in the northwestern Gulf of Mexico, 2013 OCEANS-San Diego, IEEE, San Diego, CA.Google Scholar
  25. Ren, W., 2007. Distributed attitude alignment in spacecraft formation flying. International Journal of Adaptive Control and Signal Processing, 21(2–3), 95–113.MathSciNetCrossRefMATHGoogle Scholar
  26. Šalinić, S., Bošković, G. and Nikolić, M., 2014. Dynamic modelling of hydraulic excavator motion using Kane’s equations, Automation Construction, 44, 56–62.CrossRefGoogle Scholar
  27. Sarlette, A., Sepulchre, R. and Leonard, N.E., 2009. Autonomous rigid body attitude synchronization, Automatica, 45(2), 572–577.MathSciNetCrossRefMATHGoogle Scholar
  28. Sherman, J., Davis, R.E., Owens, W.B. and Valdes, J., 2001. The autonomous underwater glider “Spray”, IEEE Journal of Oceanic Engineering, 26(4), 437–446.CrossRefGoogle Scholar
  29. Smith, T.R., Hanβmann, H. and Leonard, N.E., 2001. Orientation control of multiple underwater vehicles with symmetry-breaking potentials, Proceedings of the 40th IEEE Conference on Decision and Control, IEEE, Orlando, FL, pp. 4598–4603.Google Scholar
  30. Wang, H.L. and Xie, Y.C., 2013. Cyclic constraint analysis for attitude synchronization of networked spacecraft agents, Journal of Dynamic Systems, Measurement, and Control, 135(6), 061019.CrossRefGoogle Scholar
  31. Wang, S.X., Sun, X.J., Wang, Y.H., Wu, J.G. and Wang, X.M., 2011. Dynamic modeling and motion simulation for a winged hybrid-driven underwater glider, China Ocean Engineering, 25(1), 97–112.CrossRefGoogle Scholar
  32. Wang, Y.H. and Wang, S.X., 2009. Dynamic modeling and three-dimensional motion analysis of underwater gliders, China Ocean Engineering, 23(3), 489–504.Google Scholar
  33. Wang, Y.H., Zhang, H.W. and Wang, S.X., 2009. Trajectory control strategies for the underwater glider, Proceedings of the 2009 International Conference on Measuring Technology and Mechatronics Automation, Zhangjiajie, Hunan, China, pp. 918–921.Google Scholar
  34. Webb, D.C., Simonetti, P.J. and Jones C.P., 2001. SLOCUM: An underwater glider propelled byenvironmental energy, IEEE Journal of Oceanic Engineering, 26(4), 447–452.CrossRefGoogle Scholar
  35. Xue, D.Y., Wu, Z.L. and Wang, S.X., 2015. Dynamical analysis of autonomous underwater glider formation with environmental uncertainties, IUTAM Symposium on Dynamical Analysis of Multibody Systems with Design Uncertainties, Germany, pp. 108–117.Google Scholar
  36. Yang, Y., Wang, S.X., Wu, Z.L. and Wang, Y.H., 2011. Motion planning for multi-HUG formation in an environment with obstacles, Ocean Engineering, 38(17–18), 2262–2269.CrossRefGoogle Scholar
  37. Zhao, J., Hu, C.M., Lenes, J.M., Weisberg, R.H., Lembke, C., English, D., Wolny, J., Zheng, L.Y., Walsh, J.J. and Kirkpatrick, G., 2013. Three-dimensional structure of a Karenia brevis bloom: Observations from gliders, satellites, and field measurements, Harmful Algae, 29, 22–30.CrossRefGoogle Scholar

Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Dong-yang Xue
    • 1
    • 2
  • Zhi-liang Wu
    • 1
    • 2
  • Er-mai Qi
    • 3
  • Yan-hui Wang
    • 1
    • 2
  • Shu-xin Wang
    • 1
    • 2
  1. 1.Key Laboratory of Mechanism Theory and Equipment Design of Ministry of EducationTianjin UniversityTianjinChina
  2. 2.School of Mechanical EngineeringTianjin UniversityTianjinChina
  3. 3.National Ocean Technology CenterTianjinChina

Personalised recommendations