Three-dimensional air combat: Numerical solution using randomised trajectory

This paper investigates a complex pursuit-evasion game in three dimensions with complete information. Both players are using actual aerodynamic and performance constraints in calculating the dynamics. To find an optimal trajectory for the evader, populations of trajectories are randomly generated for a time length. The optimal evader¿s trajectory is a trajectory that gives the best payoff, i.e. a trajectory which gives the closest distance greater than the prescribed captured-distance, and, also within the same time length, gives the maximum separation distance. The pursuer uses proportional navigation guidance system to guide itself to the evader. As an illustrative example, the evasion of an aircraft which is very agile but slower ¿ from a pursuing missile ¿ which is faster but less agile is investigated. The flight of the aircraft is restricted by various control and state variable inequality constraints. Several factors are studied in the paper to see its relationship to capturability. The factors are capture radius, turning radius and speed. This study assumes both players to fly at a constant speed for ease of analysis. The technique is able to find optimal trajectory for the evader in order to avoid interception. The optimal trajectories exh ibit several well know tactical maneuvers such as horizontal-S and vertical-S, but the maneuvers are performed in a timely manner to get the optimal evasion. It is found that the factors that influence capturability are capture-radius, maximum turning radius for both evader and pursuer, and their respective velocities.