Escape-avoid games with multiple defenders along a fixed circular orbit

In this paper, we address a particular multiplayer pursuit-evasion game, called as escape-avoid games, in which a number of defenders moving along a fixed circular orbit (FCO) in an evenly distributed formation are attempting to capture a single evader who strives to escape from the encirclement of the defenders. The analysis of this game plays an important role in aircraft control, motion planning and other applications involving cooperative and adversarial agents. Firstly, for the game of degree, the conditions under which the evader or defenders can win the game are discussed, and thus a barrier is constructed analytically such that the relative space is separated into two parts associated with each player's wining region. Secondly, the number of defenders which can guarantee the existence of successful capture is given. Finally, we fuse the game of kind and degree by taking the minimum terminal included angle as a payoff function, and the optimal control strategies for the players are also presented.