Defending a Target Area With a Slower Defender

The target defense game is an abstraction of the counter-UAV mission, where a defender intends to intercept an invading drone before it enters a target area. While most studies on target defense games assume the defender travels faster, defending a target area with a slower defender is a less studied yet challenging problem, because capture cannot be guaranteed. This letter identifies two special cases where the defender has a chance to win, where the game region is bounded and where the target area is small. In the former case, the defender traps the invader at the corner. In the latter case, the defender delays the entering permanently by rotating around the target area at a sufficiently large angular speed. In both games, the optimal trajectory has a two-stage structure. Exploiting this feature, a novel method is proposed to solve for the barrier, which gives guidelines on how to deploy the defenders to ensure the target area been protected.