In this paper, we consider optimal resolution of air traffic (AT) conflicts. Aircraft are assumed to cruise within a given altitude layer and are modeled as a kinematic system with constant velocity and curvature bounds. Aircraft cannot get closer to each other than a predefined safety distance. For such system of multiple aircraft, we consider the problem of planning optimal paths among given waypoints. Necessary conditions for optimality of solutions are derived and used to devise a parameterization of pos- sible trajectories that turns into efficient numerical solutions to the problem. Simulation results for a realistic aircraft conflict scenario are provided. A decentralized implementation of the optimal con- flict resolution scheme is introduced that may allow free-flight coordination in a cooperative airspace management scheme. Impact of decentralization on performance and safety is finally discussed with the help of extensive simulations.
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