A differential game in three dimensions: The aerial dogfight scenario

Abstract

In this article, an aerial dogfight in three dimensions between two aircraft was modeled, with each aircraft having combined qualitative objectives of capture with avoidance. A spherical polar-coordinate system was devised to describe the system. From a standard point-mass model of aircraft dynamics for three-dimensional flight, a kinematic model was derived, with its corresponding controls for each aircraft. This kinematic model was then used, assuming bang-bang control functions for each aircraft, in order to determine a map of the game. A technique of trajectory dissection was introduced, whereby the airplane loci were decomposed in terms of regions of zero-level and saturation-level control values, and controllable and winning regions were determined for each aircraft using a Liapunov-function approach, the winning regions being calculated using the Getz-Leitmann theorem. A map of the game was constructed, and the barrier was found to be nonvoid. The concept of the posthumous mutual-kill strategy was introduced.