On a pursuit-evasion problem related to motion coordination of mobile robots

A pursuit-evasion problem is discussed in which a team of mobile robots (called searchers) is required to capture a mobile robot (called a fugitive) in an N×N grid graph G_N under various conditions. An algorithm for the problem is presented under the condition that the fugitive is not allowed to stop anywhere or change direction while on an edge. This algorithm is shown to be optimal with respect to both the number of searchers and the time required to capture the fugitive. A second algorithm is presented under the condition that the fugitive can stop on a vertex but cannot change direction while on the edge. A third algorithm, with no restrictions, is presented and shown to be optimal with respect to the number of searchers required and to be optimal within a constant factor with respect to the time required in the worst case