On the optimal conflict resolution for air traffic control

We consider optimal resolution of air traffic conflicts. Aircraft are assumed to cruise within a given altitude layer and are modeled as a kinematic system with velocity constraints and curvature bounds. Aircraft can not 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 way-points. Necessary conditions for optimality of solutions are derived and used to devise a parametrization of possible trajectories that turns into efficient numerical solutions to the problem. Simulation results for a simplified aircraft conflict scenario are provided.