Meir Pachter, Air Force Institute of Technology
Many-on-one pursuit We consider swarm pursuit-evasion dierential games in the Euclidean plane where an evader is engaged by multiple pursuers and point capture is required. All the players have simple motion à la Isaacs and the pursuers are faster than the evader. It is shown that in group/swarm pursuit, when the players are in general position, capture is eected by one, two, or by three critical pursuers, and this irrespective of the size
N (> 3) of the pursuit pack. Thus, group pursuit devolves into pure pursuit by one of the pursuers, into a pincer movement pursuit by two pursuers, or cornering by three pursuers, who isochronously capture the evader, a mènage à trois. The solution of the Game of Kind is obtained and critical pursuers are identified. Concerning the Game of Degree, the players' state feedback optimal strategies are synthesized and the Value of the game is derived.
