Skip to main content
SpringerLink
Log in

On broaching-to prevention using optimal control theory with evolution strategy (CMA-ES)

  • Original article
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

Broaching-to, an uncontrollable maneuvering problem that may occur in following and quartering seas, can induce large roll motion and sometimes capsizing due to violent yaw motions, e.g., Nicholson (Some Parametric Model Experiment to Investigate Broaching-to, pp 160–166, 1974). Broaching-to arises when a ship cannot maintain its desired course even under maximum steering effort. Previous experiments and numerical simulations of the broaching-to phenomenon have applied proportional-derivative (PD) control, which cannot provide the maximum steering effort. To maximize the steering effort, the previous study replaced PD control by optimal control theory by Maki et al. (J Jpn Soc Nav Archit Ocean Eng 7:207–212, 2008) and Maki et al. (J Jpn Soc Nav Archit Ocean Eng 8:115–122, 2008). A case of the ship control, when the ship developed large yaw motions despite the optimal control, was observed. However, because optimization techniques such as the variational method were insufficiently powerful for solving this highly nonlinear problem, the optimization could be performed only around local optima. The aim is to globally seek a better local solution among the numerous local optima. To achieve this goal, the authors applied the Covariance Matrix Adaption Evolution Strategy (CMA-ES), a state-of-the-art algorithm in evolutionary computation for derivative-free continuous optimization. The optimal rudder control for preventing broaching-to is then obtained, and its characteristics are discussed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Nicholson K (1974) Some parametric model experiment to investigate broaching-to. Proc Int Symp dynamics of marine vehicle and structure, pp.160–166

  2. Oakley OH, Paulling JR, Wood PD (1974) Ship motions and capsizing in astern seas. In: Proceedings of the 10th Naval Hydrodynamics Symposium, MIT, 1V-1, pp 1–51

  3. Maki A, Umeda N (2009) Bifurcation and chaos in yaw motion of a ship at lower speed in waves and its prevention using optimal control. In: Proceedings of the 10th International Conference on stability of ships and ocean vehicles, pp 429–440

  4. Umeda N, Hamamoto M (2000) Capsize of ship models in following/quartering waves: physical experiments and nonlinear dynamics. Philos Trans Math Phys Eng Sci 358(1771):1883–1904

    Article  Google Scholar 

  5. Umeda N, Yamamura S, Matsuda A, Maki A, Hashimoto H (2008) Model experiments on extreme motions of a wave-piercing tumblehome vessel in following and quartering waves. J Jpn Soc Naval Archit Ocean Eng 8:123–129

    Google Scholar 

  6. Hashimoto H, Umeda N, Matsuda A (2011) Broaching prediction of a wave-piercing tumblehome vessel with twin screws and twin rudders. J Mar Sci Technol 16(4):448–461

    Article  Google Scholar 

  7. Renilson MR (1986) The seabrake—a device of assessing in the prevention of broaching-to. Proc Int Conf Stab Ships Ocean Veh Gdansk 2:75–80

    Google Scholar 

  8. Umeda N, Matsuda M, Takagi M (1999) Model experiment on anti-broaching steering system. J Soc Naval Archit Jpn 185:41–48

    Article  Google Scholar 

  9. Maki A, Umeda N, Ueno S (2008) Application of optimal control theory to course keeping problem in following seas. J Jpn Soc Naval Archit Ocean Eng (In Japanese) 7:207–212

    Google Scholar 

  10. Maki A, Umeda N, Ueno S (2008) Investigation on broaching-to using optimal control theory. J Jpn Soc Naval Archit Ocean Eng (In Japanese) 8:115–122

    Google Scholar 

  11. Wu AK, Miel A (1980) Sequential conjugate gradient−restoration algorithm for optimal control problems with nondifferential constraints and boundary conditions Part l, Optimal control applications and methods, Vol. 1–1

  12. Ohtsu K (2004) The numerical solution of minimum time maneuvering problems by a NLP method. J Jpn Soc Naval Archit Ocean Eng 196:99–104

    Article  Google Scholar 

  13. Hansen N, Auger A (2014) Principled design of continuous stochastic search: from theory to practice. In: Borenstein Y, Moraglio A (eds) Theory and principled methods for designing metaheustics. Springer, Berlin, pp 145–180

  14. Hansen N (2016) The CMA evolution strategy: a tutorial. ArXiv e-prints, arXiv:1604.00772

  15. Renilson MR (1982) An investigation into the factors affecting the likelihood of broaching-to in following seas. In: Proceeding of the second international conference on stability of ships and ocean vehicles, Tokyo

  16. Renilson MR (1996) Summary of discussion on session 1, (Surf-riding, Broaching and Capsizing in Following/Quartering Seas). Proceeding of the Second Workshop on stability and operational safety of ships, Osaka

  17. Umeda N, Hashimoto H (2002) Qualitative aspects of nonlinear ships motions in following and quartering seas with high forward velocity. J Mar Sci Technol 6(3):111–121

    Article  Google Scholar 

  18. Motora S, Fujino M, Koyanagi M, Ishida S, Shimada K, Maki T (1981) A consideration on the mechanism of occurrence of the broaching-to phenomenon. J Jpn Soc Naval Archit Ocean Eng (in Japanese) 150:211–222

    Article  Google Scholar 

  19. Umeda N, Renilson MR (1992) In: Wilson PA (ed) Broaching—a dynamic analysis of yaw behavior of a vessel in a following sea, maneuvering and control of marine craft. Computational Mechanics Publications, Southampton

    Google Scholar 

  20. Htet TZ, Umeda N, Maki A, Matsuda A, Terada D (2019) Estimation of broaching probability using wave-induced forces and moments measured in captive model tests. J Mar Sci Technol 24(1):317–327

    Article  Google Scholar 

  21. Akimoto Y, Nagata Y, Ono I, Kobayashi K (2012) Theoretical foundation for CMA-ES from information geometry perspective. Algorithmica 64(4):698–716

    Article  MathSciNet  Google Scholar 

  22. Hansen N, Auger A, Ros R, Finck S, Pošík P (2010) Comparing results of 31 algorithms from the black-box optimization benchmarking BBOB-2009. Proceedings of the 12th annual conference companion on genetic and evolutionary computation, pp.1689–1696

  23. Rios LM, Sahinidis NV (2013) Derivative-free optimization: a review of algorithms and comparison of software implementations. J Glob Optim 56(3):1247–1293

    Article  MathSciNet  Google Scholar 

  24. Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In Proc. of the 2005 IEEE Congress on evolutionary computation, pp 1769–1776

  25. Nishida K, Akimoto Y (2018) PSA-CMA-ES: CMA-ES with population size adaptation. In Proc. of the genetic and evolutionary computation conference, GECCO 2018

  26. Sakamoto N, Akimoto Y (2017) Modified box constraint handling for the covariance matrix adaptation evolution strategy. In GECCO ’17 Companion, Berlin, Germany, July 15–19, 2017, New York, New York, USA, 2017, pp 183–184

  27. Maki A, Sakamoto N, Akimoto Y, Nishikawa H, Umeda N (2019) Application of optimal control theory based on the evolution strategy (CMA‑ES) to automatic berthing. J Mar Sci Technol, First online. doi: 10.1007/s00773-019-00642-3

  28. Akimoto Y (2012) Analysis of a natural gradient algorithm on monotonic convex-quadratic-composite functions. In Proc. of GECCO '12: genetic and evolutionary computation conference, pp 1293–1300

Download references

Acknowledgements

This work was supported by a Grant-in-Aid for Scientific Research from the Japan Society for Promotion of Science (JSPS KAKENHI Grant number 19H02360). The authors would like to thank Enago (www.enago.jp) for the English language review.

Author information

Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka, 565-0971, Japan

    Atsuo Maki, Yuki Banno, Sreenath Maniyappan & Naoya Umeda

  2. Department of Computer Science, Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Naoki Sakamoto

  3. Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Youhei Akimoto

  4. RIKEN Center for Advanced Intelligence Project, Nihonbashi 1-chome Mitsui Building, 15th floor, 1-4-1 Nihonbashi, Chuo-ku, Tokyo, 103-0027, Japan

    Youhei Akimoto

Authors
  1. Atsuo Maki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naoki Sakamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Youhei Akimoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuki Banno
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sreenath Maniyappan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Naoya Umeda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Atsuo Maki.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maki, A., Sakamoto, N., Akimoto, Y. et al. On broaching-to prevention using optimal control theory with evolution strategy (CMA-ES). J Mar Sci Technol 26, 71–87 (2021). https://doi.org/10.1007/s00773-020-00722-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00773-020-00722-9

Keywords

Search

Navigation