Optimal Cooperative Collision Avoidance Strategy for Coplanar Encounter: Merz’s Solution Revisited

T. Tarnopolskaya () and N. Fulton ()
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T. Tarnopolskaya: CSIRO Mathematical & Information Sciences
N. Fulton: CSIRO Mathematical & Information Sciences

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 2, No 11, 355-375

Abstract: Abstract Analytic solutions for optimal collision avoidance strategies are of great importance when setting and validating air traffic rules and as a benchmark when validating automated proximity management and collision avoidance systems. Such a solution for optimal air collision avoidance strategies for a coplanar cooperative encounter between two identical aircraft (or ships) was first presented by Merz (Proc. Joint Automatic Control Conf., Pap. 15-3:449–454, 1973; Navigation 20(2):144–152, 1973). Unfortunately, Merz provided only a very brief indicative justification for his solution. This paper presents a rigorous analysis of the problem. New results include a characterization of a complete set of extremals, justification for optimal strategies and an analysis of the properties of the regions of different optimal strategies. A simple, practical and sufficiently accurate closed form approximation for dispersal curves that partition the plane of initial positions into the regions of different optimal strategies is also presented.

Keywords: Collision avoidance; Cooperative maneuvers; Optimal control; Mayer problem (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-008-9452-9

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