Evasion from a group of pursuers with double integrator kinematics

We consider the problem of characterizing an evading strategy for an agent traversing a convex polygon populated by a group of pursuers. We address the problem by associating it with a generalized Voronoi partitioning problem, which encodes information about the proximity relations between the evader and the pursuers based on the value function of a pursuit-evasion game involving the evader and each pursuer from the group individually. The generalized Voronoi partition furnishes a collection of continuous paths which have the following property: When the evader travels along any of these paths, none of the pursuers will have a unilateral incentive to initiate the pursuit against it. With the proposed approach, the problem of evasion from the group of pursuers admits an elegant geometric solution, which can be computed by means of known computational techniques. Numerical simulations that illustrate the theoretical developments are presented.