Game-Theoretic Analysis of a Visibility Based Pursuit-Evasion Game in the Presence of a Circular Obstacle

In this work, we analyze a visibility-based pursuit-evasion game between an observer and a target in the presence of a circular obstacle. The objective of the observer is to maximize the time for which it can maintain visibility of the target. This is modeled as a pursuit-evasion game by assuming that the target is adversarial in nature, and wants to break the line-of-sight in minimum amount of time. We present the regular analysis of the problem, and depict the optimal trajectories near the terminal manifold by numerical computation.