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New Approach To The Collision Avoidance Problem For A Ship

Author

Listed:
  • A. MIELE

    (Research Professor, Aero-Astronautics Group, Rice University, Houston, Texas, USA)

  • T. WANG

    (Senior Research Scientist, Aero-Astronautics Group, Rice University, Houston, Texas, USA)

Abstract

A new algorithm is developed to solve the collision avoidance problem for a host ship subject to kinematic, dynamic, and moment equations and steeredviarudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. The objective of the collision avoidance maneuver is to maximize with respect to the state and control history the timewise minimum distance between a host ship and an intruder ship. Two limiting cases are considered: (i) the intruder ship is uncooperative and keeps its course unchanged during the encounter; (ii) the intruder ship is cooperative. In both cases, a differential game formulation is avoided and the collision avoidance problem is formulated as a maximin problem of optimal control.Four problems are investigated and their solutions compared: Problems P1 and P2 deal with uncooperative collision avoidance, while Problems P3 and P4 deal with cooperative collision avoidance.Numerical results show that the optimal control histories always involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values.

Suggested Citation

  • A. Miele & T. Wang, 2004. "New Approach To The Collision Avoidance Problem For A Ship," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 137-155.
    • Handle: RePEc:wsi:igtrxx:v:06:y:2004:i:01:n:s0219198904000113
    DOI: 10.1142/S0219198904000113
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    Citations

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    Cited by:

    1. A. Miele & T. Wang, 2006. "Optimal Trajectories and Guidance Schemes for Ship Collision Avoidance," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 1-21, April.
    2. A. Miele & T. Wang, 2005. "Maximin Approach to the Ship Collision Avoidance Problem via Multiple-Subarc Sequential Gradient-Restoration Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 29-53, January.

    More about this item

    Keywords

    Equations of motion; kinematics; dynamics; hydrodynamics; ship maneuvers; optimal ship maneuvers; collision avoidance maneuvers; control transformations; singularity avoiding transformations; sequential gradient-restoration algorithms; Chebyshev problems; maximin problems; minimax problems;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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