Conflict detection and planar resolution for air traffic control

Abstract

An algorithm for planar (i.e. no altitude change) conflict resolution in air traffic control (ATC) is presented. By using the point-line duality in 2D of the parallel coordinates methodology, and a field of particles incorporating the motion constraints associated with the aircraft, a "map" in time-and-space of the conflict as well as the conflict-free regions is obtained. Then the algorithm constructs maneuvers, satisfying the constraints, which move the aircraft in conflict to the nearest available conflict-free trajectories. In the process, it is ensured that the maneuvers do not generate new conflicts. The resolution problem, being in general NP-hard, may require very high complexity even in real situations. The need for real-time solutions is handled by cascading (or running in parallel) the algorithm in levels of increasing complexity O(qN/sup (p+1)/logN), where q and N are the number of allowable maneuvers and the number of aircraft respectively, and where the minimum p=1, 2, ..., R needed to resolve a complex conflict scenario is a measure of the scenarios' (i.e. input) complexity. As an illustration, a complex conflict scenario is resolved with complexity O(N/sup 2/logN). The resolution problem is in a sense "dual" to the interception problem. An example is given where the aforementioned time-space map provides specific solutions of the One-Shot problem, which is in general NP-complete. That is "shots", if they exist, are found which intercept all the aircraft.