Optimal pursuer and moving target assignment using dynamic Voronoi diagrams

We consider a Voronoi-like partitioning problem for a team of pursuers distributed in the plane. Each element of the partition is uniquely associated with a pursuer in the following sense: if a moving target at a given instant of time resides inside a particular member of the partition, then the pursuer associated with this set can intercept this moving target faster than any other pursuer. In our problem formulation, the moving target does not necessarily travel along prescribed trajectories, as it is typically assumed in the literature but, instead, it can apply an "evading" strategy in response to the actions of its pursuer. It is further assumed that the structure of the evading strategy of the target is only partially known to the pursuers. We characterize an approximate solution to this problem by associating it with a standard Voronoi partitioning problem. Simulation results are presented to highlight the theoretical developments.