Synthesis of Optimal Control for Cooperative Collision Avoidance in a Close Proximity Encounter: Special Cases

Abstract

AbstractThe paper studies the optimal cooperative collision avoidance strategies in a planar close proximity encounter, with turning rates of the participants as the control functions. The maximization of the terminal miss distance is adopted as a performance criterion. This paper extends earlier analyses to the important special case when participants have unequal linear speeds but equal turn capabilities. The analysis is based on the Pontryagin maximum principle and the study of the properties of the extremals. The analysis is outlined in a unified manner that covers all special cases of the problem, including the cases of identical participants and the participants with unequal turn capabilities but equal linear speeds. The distinctive features of the mathematical structure of the problem and the optimal control solutions for different special cases of the problem are identified. The results of this paper are useful for setting and validating air traffic rules and for benchmarking and validating automated proximity management and collision avoidance systems.