Single Pursuer and Two Cooperative Evaders in the Border Defense Differential Game

An interest in border defense, surveillance, and interdiction has recently increased for a variety of reasons related to issues of illegal immigration, terrorism, drug and human trafficking, and other potential threats. Unmanned aerial vehicles (UAVs) offer an attractive alternative to supporting and defending various threats at borders. This paper applies a differential game to define a border defense scenario where one UAV (pursuer) seeks to capture two intruders (evaders) before they reach a designated border. The evaders can be UAVs, marine or ground vehicles, or human agents, but they have a lower maximum speed than the pursuer throughout the game. Simple motion is assumed for the pursuer and evaders with complete state information shared across all agents. The game is played within a rectangular area with a parallel top and bottom border of length L and left and right borders with a length of W, for a game aspect ratio of L/W. The value of the game is the minimum distance to the bottom border achieved by the evaders at any time before capture of both evaders. Within the region where the pursuer wins, the game of degree is explored and the optimal policy for both the evaders and pursuer is derived using geometric properties.