Visibility-based pursuit-evasion problems in polygons

Abstract

An autonomous mobile robot equipped with cameras or sensors can perform vision tasks such as model building, target tracking, or target finding. In this thesis we investigate a target finding problem that is known as the visibility-based pursuit-evasion problem. The goal of this problem is to plan the motion for a robot guard in a 2D workspace so as to guarantee that an evasive target will eventually be detected. The target is assumed to have an unknown initial position and to move unpredictably at an arbitrary speed. A robot guard moving with bounded speed should explore the workspace so that the target is driven into a corner. What makes this problem challenging is the issue of recontamination. It occurs when the target sneaks back to places already explored, which may allow the target to evade detection forever. We discuss motion strategies of robots to ensure the detection of the target regardless of how the target moves. The visibility-based pursuit-evasion problem is an interesting variant of the well-known art-gallery problem and watchman route problem: the former deals with stationary guards, and the latter with stationary targets. Our setting is dynamic, as both guard and target are moving. It models many practical applications such as military operations, toxic cleanup, surveillance systems, and architectural design of secure buildings. For example, suppose a security system of a building that involves autonomous mobile robots with vision. Any motion strategy for the robots to detect an unpredictable target provides a patrolling route that guarantees any intruder to be detected. Motion strategies can also be used for locating another mobile robot that is malfunctioning or locating people in a search-rescue effort. With these diverse applications, the visibility-based pursuit-evasion problem has attracted much attention and produced many variations for the last decade. To detect a target, a robot is equipped with omnidirectional vision or carries a num...