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Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities

Author

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  • T. Tarnopolskaya

    (CSIRO Mathematical & Information Sciences)

  • N. Fulton

    (CSIRO Mathematical & Information Sciences)

Abstract

This paper presents a synthesis of an optimal control solution for cooperative collision avoidance strategies for aircraft (ships) with unequal turn capabilities in a close proximity coplanar encounter. The analytic expressions for the extremals are presented and their properties are analyzed. Simple algorithms for the synthesis of optimal control are developed. The structure of the synthesis is analyzed and its behavior with a change in the nondimensional turn rate ratio is studied. It is shown that Merz’s solution for identical aircraft (see Merz in Proc. Joint Automatic Control Conf., Paper 15-3, pp. 449–454, 1973; Navigation 20(2):144–152, 1973; Tarnopolskaya and Fulton in J. Optim. Theory Appl. 140(2):355–375, 2009) is a degenerate case of this more general solution. The results of this paper are useful for benchmarking and validating automated proximity management and collision avoidance systems.

Suggested Citation

  • T. Tarnopolskaya & N. Fulton, 2010. "Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 367-390, February.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:2:d:10.1007_s10957-009-9597-1
    DOI: 10.1007/s10957-009-9597-1
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    References listed on IDEAS

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    1. A. Miele & T. Wang & C. S. Chao & J. B. Dabney, 1999. "Optimal Control of a Ship for Collision Avoidance Maneuvers," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 495-519, December.
    2. Clements, John C., 1999. "The optimal control of collision avoidance trajectories in air traffic management," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 265-280, May.
    3. A. Miele & T. Wang & C. S. Chao & J. B. Dabney, 1999. "Optimal Control of a Ship for Course Change and Sidestep Maneuvers," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 259-282, November.
    4. T. Tarnopolskaya & N. Fulton, 2009. "Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 355-375, February.
    5. 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.
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    Cited by:

    1. A. Miele & T. Wang & J. A. Mathwig & M. Ciarcià, 2010. "Collision Avoidance for an Aircraft in Abort Landing: Trajectory Optimization and Guidance," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 233-254, August.
    2. Maksim Buzikov & Andrey Galyaev, 2023. "The Game of Two Identical Cars: An Analytical Description of the Barrier," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 988-1018, September.
    3. Alireza Rangrazjeddi & Andrés D. González & Kash Barker, 2023. "Applied Game Theory to Enhance Air Traffic Control in 3D Airspace," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1125-1154, March.
    4. T. Tarnopolskaya & N. Fulton & H. Maurer, 2012. "Synthesis of Optimal Bang–Bang Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Linear Speeds," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 115-144, October.
    5. Erick J. Rodríguez-Seda & Dušan M. Stipanović & Mark W. Spong, 2016. "Guaranteed Collision Avoidance for Autonomous Systems with Acceleration Constraints and Sensing Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 1014-1038, March.

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