A new 3-D pursuit-evasion differential game between two bank-to-turn airborne vehicles

The differential game of a 3-D encounter between a fast bank-to-turn pursuer (with bounded curvature) and a slower but highly manoeuvrable evader (with unlimited rate of turn) has been solved as a ‘Game of Kind’ and presented in a few earlier papers by the authors. In this paper, not only the pursuer, but also the evader is modelled as a bank-to-turn curvature-bound vehicle. Thus, the complexity of the game is increased, and it also turns out to be a more realistic case of spatial pursuit-evasion. The results of this paper may be considered as a first attempt towards the generalization of Isaacs' classical ‘Game of Two Cars’ for a genuine 3-D pursuit-evasion encounter.