Wilmer Ariza Ramirez, Juš Kocijan, Zhi Quan Leong, Hung Duc Nguyen, Shantha Gamini Jayasinghe. Dynamic System Identification of Underwater Vehicles Using Multi-output Gaussian Processes. International Journal of Automation and Computing, vol. 18, no. 5, pp.681-693, 2021. https://doi.org/10.1007/s11633-021-1308-x
Citation: Wilmer Ariza Ramirez, Juš Kocijan, Zhi Quan Leong, Hung Duc Nguyen, Shantha Gamini Jayasinghe. Dynamic System Identification of Underwater Vehicles Using Multi-output Gaussian Processes. International Journal of Automation and Computing, vol. 18, no. 5, pp.681-693, 2021. https://doi.org/10.1007/s11633-021-1308-x

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

doi: 10.1007/s11633-021-1308-x
More Information
  • Author Bio:

    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.E-mail: wilmer.arizaramirez@utas.edu.auORCID iD: 0000-0002-2755-2281 (Corresponding author)

    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. E-mail: jus.kocijan@ijs.si

    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.E-mail: Zhi.Leong@utas.edu.au

    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.E-mail: h.d.nguyen@utas.edu.au

    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.E-mail: shantha.jayasinghe@utas.edu.au

  • Received Date: 2021-02-28
  • Accepted Date: 2021-06-08
  • Publish Online: 2021-07-13
  • Publish Date: 2021-10-01
  • 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.


  • 1https://github.com/ArizaWilmerUTAS/System-indetification-of-underwater-vehicles-with-Multi-Output-Gaussian-Processes
  • loading
  • [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: 10.1016/j.robot.2019.103408.
    J. Kocijan. Modelling and Control of Dynamic Systems Using Gaussian Process Models, Cham, Germany: Springer, 2016. DOI: 10.1007/978-3-319-21021-6.
    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. 317−326, 2017. DOI: 10.1007/978-3-319-48375-7_34.
    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: 10.1098/rsta.1970.0002.
    F. J. Velasco, E. R. Herrero, F. J. L. Santos, J. M. R. Rodríguez, 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: 10.1016/j.ifacol.2015.06.027.
    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: 10.1016/j.oceaneng.2017.10.032.
    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: 10.1016/j.apor.2020.102340.
    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: 10.3182/20130918-4-JP-3022.00026.
    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: 10.1016/j.oceaneng.2005.06.004.
    S. A. T. Randeni P, Z. Q. Leong, D. Ranmuthugala, A. L. Forrest, J. Duffy. Numerical investigation of the hydrodynamic interaction between two underwater bodies in relative motion. Applied Ocean Research, vol. 51, pp. 14–24, 2015. DOI: 10.1016/j.apor.2015.02.006.
    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: 10.1007/s11633-016-1004-4.
    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: 10.1016/j.apor.2017.07.001.
    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: 10.1007/s11633-006-0336-x.
    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: 10.5957/jsr.2000.44.3.186.
    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.
    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: 10.1016/S1474-6670(17)31759-7.
    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: 10.3182/20100906-3-IT-2019.00003.
    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: 10.1016/j.oceaneng.2014.09.013.
    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: 10.1016/j.apor.2018.10.015.
    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: 10.1016/j.oceaneng.2010.11.004.
    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: 10.1016/j.conengprac.2005.11.004.
    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: 10.1016/S1001-6058(11)60299-0.
    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: 10.1109/OCEANS-TAIPEI.2014.6964495.
    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: 10.1109/OCEANS.2004.1405750.
    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: 10.1016/j.oceaneng.2013.02.006.
    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: 10.1016/0954-1810(95)00029-1.
    J. Brownlee. Master Machine Learning Algorithms: Discover How They Work and Implement Them from Scratch. Machine Learning Mastery, 2016.
    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.
    S. Kashmiri, S. Payandeh. Robot navigation controller: A non-parametric regression approach. IFAC Proceedings Volumes, vol. 43, no. 22, pp. 22–27, 2010. DOI: 10.3182/20100929-3-RO-4017.00005.
    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.
    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: 10.1109/ICRA.2017.7989565.
    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.
    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: 10.1007/s10514-020-09922-z.
    M. A. Álvarez, N. D. Lawrence. Computationally efficient convolved multiple output Gaussian processes. Journal of Machine Learning Research, vol. 12, pp. 1459–1500, 2011.
    J. Zhao, S. L. Sun. Variational dependent multi-output Gaussian process dynamical systems. Journal of Machine Learning Research, vol. 17, pp. 1–36, 2016.
    M. A. Álvarez, 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.
    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: 10.1016/j.oceaneng.2018.07.056.
    T. I. Fossen. Guidance and Control of Ocean Vehicles, New York, USA: Wiley, 1994.
    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.
    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.
    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: 10.1016/j.oceaneng.2005.07.008.
    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.
    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: 10.1007/978-1-4471-0657-9_2.
    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.
    M. Alvarez, N. Lawrence. Multiple output Gaussian processes in Matlab. 2014.
    C. A. Micchelli, Y. S. Xu, H. Z. Zhang. Universal kernels. The Journal of Machine Learning Research, vol. 7, pp. 2651–2667, 2006.
    C. E. Rasmussen, C. K. I. Williams. Gaussian Processes for Machine Learning, Massachusetts, USA: The MIT Press, 2006.
    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.
  • 加载中


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(10)  / Tables(5)



    Article Metrics

    Article views (675) PDF downloads(146) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint