Game-theoretic analysis of a visibility based pursuit-evasion game in the presence of obstacles

In this paper, we present a game theoretic analysis of a visibility based pursuit-evasion game in an environment containing obstacles. The pursuer and the evader are holonomic having bounded speeds. Both players have a complete map of the environment. Both players have omnidirectional vision and have knowledge about each other's current position as long as they are visible to each other. Under this information structure, the pursuer wants to maintain visibility of the evader for maximum possible time and the evader wants to escape the pursuer's sight as soon as possible. We present strategies for the players that are in Nash Equilibrium. The strategies are a function of the value of the game. Using these strategies, we construct a value function by integrating the retrogressive path equations backward in time from the termination situations provided by the corners in the environment. From these value functions we recompute the control strategies for them to obtain optimal trajectories for the players near the termination situation.