## “Optimal Evasive Maneuver for a Ship in an Environment of Fixed Installations and Other Ships”Authors: Rolf Skjong and Kåre M. Mjelde,
Affiliation: Det Norske Veritas (DNV)
Reference: 1982, Vol 3, No 4, pp. 211-222. |

**Keywords:**Optimal control, differential game, offshore, ship, collision, manoeuvre

**Abstract:**Collision avoidance for encounters between several ships and installations in the open sea, is treated as a problem of optimal control, using the theory of differential games. Each ship is, in this idealized model, assumed to have two controls corresponding to rudder angle and engine setting. The objective function, which the shipmasters try to minimize in an optimal evasive manoeuvre, is defined as the collision risk. Numerical solutions for the M-ships and I-installations optimal evasive manoeuvre problem, can be found by the ping-pong algorithm. Numerical examples are given for up to five ships and two installations.

PDF (2412 Kb) DOI: 10.4173/mic.1982.4.2

**DOI forward links to this article:**

[1] Y. Yavin, T. Miloh and G. Zilman (1995), doi:10.1007/BF02192299 | |

[2] Y. Yavin, G. Zilman and T. Miloh (1994), doi:10.1016/0898-1221(94)00170-7 | |

[3] Y. Yavin, C. Frangos, G. Zilman and T. Miloh (1995), doi:10.1016/0898-1221(95)00034-V | |

[4] Y. Yavin, C. Frangos, G. Zilman and T. Miloh (1995), doi:10.1016/0898-1221(95)00157-T | |

[5] Y. Yavin, C. Frangos and T. Miloh (1995), doi:10.1016/0895-7177(94)00218-D | |

[6] Y. Yavin, G. Zilman and T. Miloh (1995), doi:10.1016/0898-1221(95)00158-U | |

[7] Thomas Statheros, Gareth Howells and Klaus McDonald Maier (2008), doi:10.1017/S037346330700447X | |

[8] Y. Yavin, C. Frangos, T. Miloh and G. Zilman (1997), doi:10.1023/A:1022693600078 | |

[9] Alexander I. Kozynchenko and Sergey A. Kozynchenko (2018), doi:10.1016/j.oceaneng.2018.07.012 | |

[10] Silvia Donnarumma, Massimo Figari, Michele Martelli and Raphael Zaccone (2020), doi:10.1007/978-3-030-43890-6_9 |

**References:**

[1] BREAKWELL, J.V. MERZ, A.W. (1969). Toward a complete solution of the Homicidal Chauffeur Game, Proceedings of the 1st International Conference on the Theory and Application of Differential Games, A. Herst, Mass., pp. III-1 to III-5.

[2] HOLT, D. MUKUNDAN, R. (1972). A Nash algorithm for a class of non-zero sum differential games, Int. J. Systems Sci., 1972, 2, 4, 379-387 doi:10.1080/00207727208920203

[3] ISAACS, R. (1965). Differential Games, New York, Krieger Publishing Company.

[4] JENSEN, A. (1970). Safety at Sea problems, Accident Analysis and Prevention, 1, 1.

[5] MERZ, A.W. (1973). Optimal Evasive Manoeuvres in Maritime Collision Avoidance, Navigation, 20, 144-152.

[6] MILOH, T. (1974). Determination of Critical Manoeuvres for Collision Avoidance Using the Theory of Differential Games, Institut für Shiffbau, Hamburg, Bericht Nr. 319.

[7] MILOH, T. SHARMA, S.D. (1975). Maritime Collision Avoidance as a Differential Game, Institut für Shiffbau, Hamburg, Bericht Nr. 329.

[8] MJELDE, K. (1977). An Analytical Minefield Evaluation Model without Space Averages, Naval res. log. quarterly, 24, 4, 640-650.

[9] SCHROETER, G. (1976). Probability of Kill and Expected Destroyed Value if the Underlying Distributions are Rotationally Symmetric, Opts. Res., 24, 586-591 doi:10.1287/opre.24.3.586

[10] STRATTON, A. (1971). Navigation, Traffic and the Community, Presidential Address. The institute of Navigation. The Journal, 24, 1.

[11] VINCENT, T.L., CLIFF, E.M., GRANTHAM, W.J., PENG, W.Y. (1972). A problem of Collision Avoidance, University of Arizona, Tucson, EES Series Rep. No. 39.

**BibTeX:**

@article{MIC-1982-4-2,

title={{Optimal Evasive Maneuver for a Ship in an Environment of Fixed Installations and Other Ships}},

author={Skjong, Rolf and Mjelde, Kåre M.},

journal={Modeling, Identification and Control},

volume={3},

number={4},

pages={211--222},

year={1982},

doi={10.4173/mic.1982.4.2},

publisher={Norwegian Society of Automatic Control}

};