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In this paper, we address pursuit-evasion problems involving multiplepursuers and multiple evaders. The pursuer and the evader teams are assumed tobe heterogeneous, in the sense that each team has agents with different speedcapabilities. The pursuers are all assumed to be following a constant bearingstrategy. A dynamic divide and conquer approach, where at every time instanteach evader is assigned to a set of pursuers based on the instantaneouspositions of all the players, is introduced to solve the multi-agent pursuitproblem. In this regard, the corresponding multi-pursuer single-evader problemis analyzed first. Assuming that the evader can follow any strategy, a dynamictask allocation algorithm is proposed for the pursuers. The algorithm is basedon the well-known Apollonius circle and allows the pursuers to allocate theirresources in an intelligent manner while guaranteeing the capture of the evaderin minimum time. The proposed algorithm is then extended to assign pursuers inmulti-evader settings that is proven to capture all the evaders in finite time.

Apollonius Allocation Algorithm for Heterogeneous Pursuers to Capture Multiple Evaders