Pursuit Differential Game with Slow Pursuers on the 1-Skeleton Graph of the Icosahedron

Abstract

A differential game of m, 3≤m≤6, pursuers and one evader is studied on an icosahedron in R3. All the players move only along the 1-skeleton graph of the icosahedron when the maximal speeds of the pursuers are less than the speed of the evader. Pursuit is said to be completed if the state of a pursuer coincides with the state of evader at some time. We give a sufficient condition of the completion of pursuit in the game.