Skip to main content
SpringerLink
Log in

Dynamic System Identification of Underwater Vehicles Using Multi-Output Gaussian Processes

  • Research Article
  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

Non-parametric system identification with Gaussian processes for underwater vehicles is explored in this research with the purpose of modelling autonomous underwater vehicle (AUV) dynamics with a low amount of data. Multi-output Gaussian processes and their aptitude for modelling the dynamic system of an underactuated AUV without losing the relationships between tied outputs are used. The simulation of a first-principle model of a Remus 100 AUV is employed to capture data for the training and validation of the multi-output Gaussian processes. The metric and required procedure to carry out multi-output Gaussian processes for AUV with 6 degrees of freedom (DoF) is also shown in this paper. Multi-output Gaussian processes compared with the popular technique of recurrent neural network show that multi-output Gaussian processes manage to surpass RNN for non-parametric dynamic system identification in underwater vehicles with highly coupled DoF with the added benefit of providing the measurement of confidence.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Rodriguez, H. Castañeda, J. L. Gordillo. Lagrange modeling and navigation based on quaternion for controlling a micro AUV under perturbations. Robotics and Autonomous Systems, vol. 124, Article number 103408, 2020. DOI: https://doi.org/10.1016/j.robot.2019.103408.

  2. J. Kocijan. Modelling and Control of Dynamic Systems Using Gaussian Process Models, Cham, Germany: Springer, 2016. DOI: https://doi.org/10.1007/978-3-319-21021-6.

    Book  MATH  Google Scholar 

  3. B. Allotta, R. Costanzi, L. Pugi, A. Ridolfi, A. Rindi. Fast calibration procedure of the dynamic model of an autonomous underwater vehicle from a reduced set of experimental data. Advances in Italian Mechanism Science, G. Boschetti, A. Gasparetto, Eds., Cham, Germany: Springer, pp. 317–366, 2017. DOI: https://doi.org/10.1007/978-3-319-48375-7_34.

    Chapter  Google Scholar 

  4. R. E. D. Bishop, A. G. Parkinson. On the planar motion mechanism used in ship model testing. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 266, no. 1171, pp. 35–61, 1970. DOI: https://doi.org/10.1098/rsta.1970.0002.

    Google Scholar 

  5. F. J. Velasco, E. R. Herrero, F. J. L. Santos, J. M. R. Rodriguez, J. J. D. Hernández, L. M. V. Antolín. Measurements of hydrodynamic parameters and control of an underwater torpedo-shaped vehicle. IFAC-PapersOnLine, vol. 48, no. 2, pp. 167–172, 2015. DOI: https://doi.org/10.1016/j.ifacol.2015.06.027.

    Article  Google Scholar 

  6. B. Allotta, R. Costanzi, L. Pugi, A. Ridolfi. Identification of the main hydrodynamic parameters of typhoon AUV from a reduced experimental dataset. Ocean Engineering, vol. 147, pp. 77–88, 2018. DOI: https://doi.org/10.1016/j.oceaneng.2017.10.032.

    Article  Google Scholar 

  7. J. Park, S. H. Rhee, H. K. Yoon, S. Lee, J. Seo. Effects of a propulsor on the maneuverability of an autonomous underwater vehicle in vertical planar motion mechanism tests. Applied Ocean Research, vol. 103, Article number 102340, 2020. DOI: https://doi.org/10.1016/j.apor.2020.102340.

  8. H. Suzuki, J. Sakaguchi, T. Inoue, Y. Watanabe, H. Yoshida. Evaluation of methods to estimate hydrodynamic force coefficients of underwater vehicle based on CFD. IFAC Proceedings Volumes, vol. 46, no. 33, pp. 197–202, 2013. DOI: https://doi.org/10.3182/20130918-4-JP-3022.00026.

    Article  Google Scholar 

  9. A. Tyagi, D. Sen. Calculation of transverse hydrodynamic coefficients using computational fluid dynamic approach. Ocean Engineering, vol. 33, no. 5–6, pp. 798–809, 2006. DOI: https://doi.org/10.1016/j.oceaneng.2005.06.004.

    Article  Google Scholar 

  10. S. A. T. Randeni P. Z. Q. Leong, D. Ranmuthugala, A. L. Forrest, J. Duffy. Numerical investigation of the hydro-dynamic interaction between two underwater bodies in relative motion. Applied Ocean Research, vol. 51, pp. 14–24, 2015. DOI: https://doi.org/10.1016/j.apor.2015.02.006.

    Article  Google Scholar 

  11. B. Das, B. Subudhi, B. B. Pati. Cooperative formation control of autonomous underwater vehicles: An overview. International Journal of Automation and Computing, vol. 13, no. 3, pp. 199–225, 2016. DOI: https://doi.org/10.1007/s11633-016-1004-4.

    Article  Google Scholar 

  12. S. K. Shariati, S. H. Mousavizadegan. The effect of appendages on the hydrodynamic characteristics of an underwater vehicle near the free surface. Applied Ocean Research, vol. 67, pp. 31–43, 2017. DOI: https://doi.org/10.1016/j.apor.2017.07.001.

    Article  Google Scholar 

  13. J. D. Liu, H. S. Hu. Biologically inspired behaviour design for autonomous robotic fish. International Journal of Automation and Computing, vol. 3, no. 4, pp. 336–347, 2006. DOI: https://doi.org/10.1007/s11633-006-0336-x.

    Article  Google Scholar 

  14. D. Sen. A study on sensitivity of maneuverability performance on the hydrodynamic coefficients for submerged bodies. Journal of Ship Research, vol. 45, no. 3, pp. 186–196, 2000. DOI: https://doi.org/10.5957/jsr.2000.44.3.186.

    Article  Google Scholar 

  15. K. P. Rhee, S. Y. Lee, Y. J. Sung. Estimation of manoeuvring coefficients from PMM test by genetic algorithm. In Proceedings of International Symposium and Workshop on Force Acting on a Manoeuvring Vessel, Val de Reuil, France, pp. 77–87, 1998.

  16. A. Ross, T. I. Fossen, T. A. Johansen. Identification of underwater vehicle hydrodynamic coefficients using free decay tests. IFAC Proceedings Volumes, vol. 37, no. 10, pp. 363–368, 2004. DOI: https://doi.org/10.1016/S1474-6670(17)31759-7.

    Article  Google Scholar 

  17. E. Shahinfar, M. Bozorg, M. Bidoky. Parameter estimation of an AUV using the maximum likelihood method and a Kalman filter with fading memory. IFAC Proceedings Volumes, vol. 43, no. 16, pp. 1–6, 2010. DOI: https://doi.org/10.3182/20100906-3-IT-2019.00003.

    Article  Google Scholar 

  18. M. T. Sabet, P. Sarhadi, M. Zarini. Extended and unscented Kalman filters for parameter estimation of an autonomous underwater vehicle. Ocean Engineering, vol. 91, pp. 329–339, 2014. DOI: https://doi.org/10.1016/j.oceaneng.2014.09.013.

    Article  Google Scholar 

  19. H. Shariati, H. Moosavi, M. Danesh. Application of particle filter combined with extended Kalman filter in model identification of an autonomous underwater vehicle based on experimental data. Applied Ocean Research, vol. 82, pp. 32–40, 2019. DOI: https://doi.org/10.1016/j.apor.2018.10.015.

    Article  Google Scholar 

  20. T. Perez, T. I. Fossen. Practical aspects of frequency-domain identification of dynamic models of marine structures from hydrodynamic data. Ocean Engineering, vol. 38, no. 2–3, pp. 426–435, 2011. DOI: https://doi.org/10.1016/j.oceaneng.2010.11.004.

    Article  Google Scholar 

  21. P. W. J. van de Ven, T. A. Johansen, A. J. Sørensen, C Flanagan, D. Toal. Neural network augmented identification of underwater vehicle models. Control Engineering Practice, vol. 15, no. 6, pp. 715–725, 2007. DOI: https://doi.org/10.1016/j.conengprac.2005.11.004.

    Article  Google Scholar 

  22. F. Xu, Z. J. Zou, J. C. Yin, J. Cao. Parametric identification and sensitivity analysis for autonomous underwater vehicles in diving plane. Journal of Hydrodynamics, vol. 24, no. 5, pp. 744–751, 2012. DOI: https://doi.org/10.1016/S1001-6058(11)60299-0.

    Article  Google Scholar 

  23. M. Zhang, Y. X. Xu, B. Li, D. N. Wang, W. Xu. A modular autonomous underwater vehicle for environmental sampling: System design and preliminary experimental results. In Proceedings of OCEANS 2014 — TAIPEI, IEEE, Taipei, China, pp. 1–5, 2014. DOI: https://doi.org/10.1109/OCEANS-TAIPEI.2014.6964495.

    Google Scholar 

  24. P. van de Ven, C. Flanagan, D. Toal. Identification of underwater vehicle dynamics with neural networks. In Proceedings of OCEANS’04 MTTS/IEEE Techno-Ocean, IEEE, Kobe, Japan, pp. 1198–1204, 2004. DOI: https://doi.org/10.1109/OCEANS.2004.1405750.

    Google Scholar 

  25. F. Xu, Z. J. Zou, J. C. Yin, J. Cao. Identification modeling of underwater vehicles’ nonlinear dynamics based on support vector machines. Ocean Engineering, vol. 67, pp. 68–76, 2013. DOI: https://doi.org/10.1016/j.oceaneng.2013.02.006.

    Article  Google Scholar 

  26. V. S. Kodogiannis, P. J. G. Lisboa, J. Lucas. Neural network modelling and control for underwater vehicles. Artificial Intelligence in Engineering, vol. 10, no. 3, pp. 203–212, 1996. DOI: https://doi.org/10.1016/0954-1810(95)00029-1.

    Article  Google Scholar 

  27. J. Brownlee. Master Machine Learning Algorithms: Discover How They Work and Implement Them from Scratch. Machine Learning Mastery, 2016.

  28. M. P. Deisenroth, C. E. Rasmussen. PILCO: A model-based and data-efficient approach to policy search. In Proceedings of the 28th International Conference on Machine Learning, ACM, Bellevue, USA, pp. 465–472, 2011.

    Google Scholar 

  29. S. Kashmiri, S. Payandeh. Robot navigation controller: A non-parametric regression approach. IFAC Proceedings Volumes, vol. 43, no. 22, pp. 22–27, 2010. DOI: https://doi.org/10.3182/20100929-3-RO-4017.00005.

    Article  Google Scholar 

  30. D. G. Krige. A statistical approach to some basic mine valuation problems on the witwatersrand. Journal of the Southern African Institute of Mining and Metallurgy, vol. 52, no. 6, pp. 119–139, 1951.

    Google Scholar 

  31. B. Wehbe, M. Hildebrandt, F. Kirchner. Experimental evaluation of various machine learning regression methods for model identification of autonomous underwater vehicles. In Proceedings of IEEE International Conference on Robotics and Automation, IEEE, Singapore, pp. 4885–4890, 2017. DOI: https://doi.org/10.1109/ICRA.2017.7989565.

    Google Scholar 

  32. J. Kocijan, A. Grancharova. Gaussian process modelling case study with multiple outputs. Comptes Rendus de l’Académie Bulgare des Sciences, vol. 63, no. 4, pp. 601–607, 2010.

    Google Scholar 

  33. W. Ariza Ramirez, Z. Q. Leong, H. D. Nguyen, S. G. Jayasinghe. Exploration of the applicability of probabilistic inference for learning control in underactuated autonomous underwater vehicles. Autonomous Robots, vol. 44, no. 6, pp. 1121–1134, 2020. DOI: https://doi.org/10.1007/s10514-020-09922-z.

    Article  Google Scholar 

  34. M. A. Alvarez, N. D. Lawrence. Computationally efficient convolved multiple output Gaussian processes. Journal of Machine Learning Research, vol. 12, pp. 1459–1500, 2011.

    MathSciNet  MATH  Google Scholar 

  35. J. Zhao, S. L. Sun. Variational dependent multi-output Gaussian process dynamical systems. Journal of Machine Learning Research, vol. 17, pp. 1–36, 2016.

    MathSciNet  MATH  Google Scholar 

  36. M. A. Alvarez, N. D. Lawrence. Sparse convolved Gaussian processes for multi-output regression. In Proceedings of the 21st International Conference on Neural Information Processing Systems, Vancouver, Canada, pp. 57–64, 2009.

  37. W. Ariza Ramirez, Z. Q. Leong, H. Nguyen, S. G. Jayasinghe. Non-parametric dynamic system identification of ships using multi-output Gaussian processes. Ocean Engineering, vol. 166, pp. 26–36, 2018. DOI: https://doi.org/10.1016/j.oceaneng.2018.07.056.

    Article  Google Scholar 

  38. T. I. Fossen. Guidance and Control of Ocean Vehicles, New York, USA: Wiley, 1994.

    Google Scholar 

  39. M. Gertler, G. R. Hagen. Standard Equations of Motion for Submarine Simulation, Technical Report 2510, David W Taylor Naval Ship Research and Development Center, Bethesda, USA, 1967.

    Book  Google Scholar 

  40. T. Prestero. Verification of A Six-degree of Freedom Simulation Model for the Remus Autonomous Underwater Vehicle, Master dissertation, Massachusetts Institute of Technology, USA, 2001.

    Book  Google Scholar 

  41. J. Kim, W. K. Chung. Accurate and practical thruster modeling for underwater vehicles. Ocean Engineering, vol. 33, no. 5–6, pp. 566–586, 2006. DOI: https://doi.org/10.1016/j.oceaneng.2005.07.008.

    Article  Google Scholar 

  42. M. Ebden. Gaussian Processes for Regression: A Quick Introduction, The Website of Robotics Research Group in Department on Engineering Science, University of Oxford, UK, 2008.

    Google Scholar 

  43. D. Higdon. Space and space-time modeling using process convolutions. Quantitative Methods for Current Environmental Issues, C. W. Anderson, V. Barnett, P. C. Chatwin, A. H. El-Shaarawi, Eds., London, UK: Springer, pp. 37–56, 2002. DOI: https://doi.org/10.1007/978-1-4471-0657-9_2.

    Chapter  Google Scholar 

  44. P. Boyle, M. R. Frean. Dependent Gaussian processes. In Proceedings of the 17th International Conference on Neural Information Processing Systems, Vancouver, Canada, pp. 217–224, 2004.

  45. M. Alvarez, N. Lawrence. Multiple output Gaussian processes in Matlab. 2014.

  46. C. A. Micchelli, Y. S. Xu, H. Z. Zhang. Universal kernels. The Journal of Machine Learning Research, vol. 7, pp. 2651–2667, 2006.

    MathSciNet  MATH  Google Scholar 

  47. C. E. Rasmussen, C. K. I. Williams. Gaussian Processes for Machine Learning, Massachusetts, USA: The MIT Press, 2006.

    MATH  Google Scholar 

  48. R. Hall, S. Anstee. Trim Calculation Methods for A Dynamical Model of the Remus 100 Autonomous Underwater Vehicle, Technical Report DSTO-TR-2576, Defence Science and Technology Organisation, Edinburgh, Australia, 2011.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Australian Maritime College, University of Tasmania, Newnham, 7248, Australia

    Wilmer Ariza Ramirez, Zhi Quan Leong, Hung Duc Nguyen & Shantha Gamini Jayasinghe

  2. Jožef Steftan Institute, Ljubljana, SI-1000, Slovenia

    Juš Kocijan

  3. School of Engineering and Management, University of Nova Gorica, Vipara, SI-5271, Slovenia

    Juš Kocijan

Authors
  1. Wilmer Ariza Ramirez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juš Kocijan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi Quan Leong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hung Duc Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shantha Gamini Jayasinghe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wilmer Ariza Ramirez.

Additional information

Colored figures are available in the online version at https://link.springer.com/journal/11633

Wilmer Ariza Ramirez received the B. Sc. degree in mechatronic engineering from Universidad San Buenaventura, Colombia in 2009, and the M. Eng. degree in advances manufacturing technology from Swinburne University of Technology, Australia in 2013. He is currently a Ph.D. degree candidate in maritime engineering at Australian maritime College, University of Tasmania, Australia.

His research interests include simultaneous localization and mapping, navigation, path planning, intelligent systems, and nonlinear control with the use of machine learning algorithms for underwater vehicles.

Juš Kocijan received the Ph. D. degree in electrical engineering from Faculty of Electrical Engineering, University of Ljubljana, Slovenia in 1993. He is currently a senior researcher with the Jožef Stefan Institute, Slovenia, and a professor of electrical engineering with University of Nova Gorica, Slovenia. His other activities include serving as editor and on the editorial boards of research journals, serving as a member of the IFAC technical committee on computational intelligence in control. He is a senior member of the IEEE Control Systems Society, and a member of SLOSIM — Slovenian Society for Simulation and Modelling and Automatic Control Society of Slovenia.

His research interests include modeling and control of dynamic systems.

Zhi Quan Leong received the B. Eng. degree in ocean engineering and the Ph. D. degree in maritime engineering from Australian Maritime College, University of Tasmania, Australia in 2015. He is currently a research fellow (DSTG) at Australian Maritime College, and a lecture of hydrodynamics, computational fluid dynamics at University of Tasmania, Australia. He is currently involved in an international research team led by Australia’s Defence Science and Technology Group to refine the methods that will be used to test the hydrodynamic performance of underwater vehicles.

His research interests include ship and platform hydrodynamics, naval architecture, marine engineering, ocean engineering, special vehicles, maritime engineering, navigation and position fixing.

Hung Duc Nguyen received the B. Eng. degree in ship navigation engineering from Vietnam Maritime University, Vietnam in 1991, and the M. Eng. and Ph. D. degrees in marine systems engineering from Tokyo University of Marine Science and Technology, Japan in 2001. He is currently a lecturer of marine control engineering with National Centre for Maritime Engineering and Hydrodynamics, Australian Maritime College, University of Tasmania, Australia.

His research interests include guidance, navigation and control of marine vehicles and offshore structures, ship maneuvering dynamics and manoeuvrability, global positioning system (GPS), global navigation satellite system (GNSS) and inertial navigation systems, linear and non-linear control systems, modeling and recursive/stochastic estimation of marine and offshore control systems, fault detection and monitoring based on modeling and estimation, instrumentation and process control, sea-keeping and roll stabilization systems, and marine robots and control applications in marine vehicles including underwater vehicles.

Shantha Gamini Jayasinghe received the B. Sc. degree in electronics and telecommunication engineering from University of Moratuwa, Sri Lanka in 2003, and the Ph.D. degree in electrical engineering from Nanyang Technological University, Singapore in 2013. From 2011 to 2015, he worked as an electrical systems engineer at Rolls Royce Advanced Technology Centre in Singapore. He is currently a lecturer of maritime electrical engineering at Australian Maritime Collage, University of Tasmania, Australia. He has authored or co-authored over 70 international journal and conference papers and three book chapters. He holds seven US/UK patents.

His research interests include power electronic converters, renewable energy technologies, grid integration of energy systems, shipboard power systems, electric propulsion and control systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramirez, W.A., Kocijan, J., Leong, Z.Q. et al. Dynamic System Identification of Underwater Vehicles Using Multi-Output Gaussian Processes. Int. J. Autom. Comput. 18, 681–693 (2021). https://doi.org/10.1007/s11633-021-1308-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-021-1308-x

Keywords

Search

Navigation