On the construction of barrier in a visibility based pursuit evasion game

This work addresses a vision-based tracking problem between a mobile observer and a target in the presence of a circular obstacle. The task of keeping the target in the observer's field-of-view is modeled as a pursuit-evasion game by assuming that the target is adversarial in nature. The objective of the observer is to maintain a line-of-sight with the target at all times. The objective of the target is to break the line-of-sight in finite amount of time. Initially, the control of the players on the barrier is computed from a slight modification of the definition of the escape set and the capture set [10]. The barrier is constructed from the boundary of the usable part of the terminal manifold using the retrogressive equation for the normals to it. For a fixed initial position of the observer, a partition of the plane into escape and capture regions for the target is obtained from the construction of the barrier. This technique is extended to provide an approximation for the escape and capture set for a polygonal obstacle. Finally, numerical construction of iso-value surfaces is presented from the optimal strategies for the players in the escape set based on our earlier work in [5].