In this manuscript, a new concept of 2D-semi-optimal-circular-3-arced-path manoeuvres with constant speed for multiple aircraft cooperative conflict resolution is presented. This type of manoeuvres is based on appropriate commands to heading, speed and manoeuvreing time. According to aircraft turning dynamics, each aircraft manoeuvre is composed of three tangent circular arcs. The optimality of manoeuvres is based on the minimisation of weighted sum of kinetic energy for aircraft two-legged manoeuvres. In comparison, aircraft with lower weight factors bear more responsibility to resolve the conflicts. The effectiveness of the proposed algorithm for real time conflict resolution is guaranteed, where the number of encountering aircraft is less than five. Otherwise, the current method could also be jointed to one of the fast resolution methods, like probabilistic resolution algorithm or genetic algorithm – as a tool to choose the convex domain – to become more computationally effective. Considerable number of case studies has been done to evaluate the effectiveness of the proposed methodology, while some are presented in the paper.

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In this paper, the problem of designing optimal conflict-free maneuvers for planar multiple aircraft encounters is studied. The maneuvers propose suitable heading changes for aircraft in a cooperative manner. The new mathematical approach provides optimal trajectories to resolve a wide variety of conflicts, especially in the presence of high-altitude Clear Air Turbulence (CAT). The proposed approach effectively uses Genetic Algorithms (GA), together with modified webs, to quickly find conflictresolving maneuvers. Different case studies show the method is fast enough to be used for real-time applications when resolving conflicts involving two aircraft. It is also efficient enough to resolve conflicts involving as many as 26 aircraft, which would be helpful in designing acrobatic maneuvers or in congested airspaces where emergency plans are needed. 1 2

In this paper, the problem of designing optimal conflict-free maneuvers for multiple aircraft encounters is studied. The proposed maneuvers are based on changes of heading, speed and maneuvering time. The optimality of maneuvers among the conflict-free constraint is based on minimization of a certain cost function based on kinetic energy of either aircraft involved. Some suitable priority weight factors are incorporated into the cost function so that optimal resolution maneuvers are such that aircraft with lower priorities assume more responsibility in resolving the conflicts. As for considering aircraft tuming dynamics, the circular 3-arced path with constant speed are proposed for each aircraft maneuver rather than the well known optimal two-legged solutions. Fairly thorough simulations have been done to evaluate the effectiveness of the methodology, while some are presented here to illustrate the effectiveness of the proposed algorithms for real time conflict resolution.