Bearing-only pursuit

We study a variant of a well-known pursuit evasion game, the lion and man game. In this game a lion (the pursuer) tries to capture a man (the evader). The players move in turns. At each time step, they can move a unit distance. We focus on a version which takes place in an unbounded arena: the positive quadrant of the plane. The novelty of our formulation is in the sensor model. In the original formulation, the lion can sense the precise location of the man at all times. In our version, which is inspired by mobile robots equipped with monocular vision systems, the lion can only obtain bearing information about the man´s location. We present a pursuit strategy which guarantees that the distance between the players is reduced to the step size in a bounded number of steps.