A geometric optimization approach to aircraft conflict resolution

This paper presents a geometric optimization approach to aircraft conflict resolution, utilizing information on current positions and velocity vectors. The resolutions are optimal in the sense that they minimize the velocity vector changes required for conflict resolution, resulting in minimum deviations from the nominal trajectory. This approach utilizes the geometric characteristics of aircraft trajectories, along with intuitive reasoning, to obtain closed-form analytical solutions for optimal combinations of heading and speed commands for conflict resolution in the horizontal plane. For two-aircraft conflicts, the optimality of these simple analytical solutions has been validated by comparison with numerical solutions from a compute-intens ive optimization process utilizing a Semi-Definite Programming approach. Solutions for efficient conflict resolution commands using heading change alone and speed change alone are also obtained. Application of the geometric optimization solution to a two-aircraft conflict results in a single discrete trajectory modification to avoid the conflict. Multiple-aircraft conflicts are resolved sequentially, with each aircraft resolving its most immediate conflict at each update cycle. Solution families for two-aircraft conflicts have been generated as functions of conflict angle and speed ratios. The general properties of efficient conflict resolution maneuvers have been determined, based on observations about the structure of these solution families.