A cooperative pursuit-evasion game of a high speed evader

This paper studies a pursuit-evasion game of multiple pursuers and a high speed evader for holonomic systems. A group of pursuers uses the idea of perfectly encircled formation to capture an evader. The perfectly encircled formation is a formation in which an evader does not have an instantaneous escape path and it is defined using the concept of Apollonius circle. The paper initially presents the conditions required to create a perfectly encircled formation. It is then argued that if a perfectly encircled formation shrinks over time by maintaining the connectivity between the Apollonius circles, then capture is guaranteed. This paper shows that it is not possible to maintain the connectivity while shrinking with minimum number of pursuers. Hence in this case, the capture can not be guaranteed. An escape strategy is suggested that enables an evader to escape from the perfectly encircled formation. The proposed escape strategy is evaluated through numerical simulations and future directions are discussed.