The optimal control of collision avoidance trajectories in air traffic management

A collision avoidance/conflict resolution model for aircraft traversing planar intersecting trajectories is developed based on the actual flight dynamics of each aircraft and the criteria that a flight regime correction is optimal if it represents a minimum-time safe deviation from a preassigned flight program. The formulation of the model leads to a singular optimal control problem where the control variable constraint is the maximum acceptable aircraft turn rate for passenger comfort and safety and the state variable constraint is defined in terms of the radius of the protected zone about a potentially conflicting aircraft. A robust, accurate real-time solution procedure is derived for computing the steering program for the execution of the optimal safe avoidance manoeuver. Several representative examples of pairwise trajectory conflicts are analysed in detail. A brief discussion of how the model might be generalized to incorporate changes in airspeed and altitude as well as more comprehensive dynamics is included.