Coordinated Search for a Conditionally Deterministic Target Motion in the Plane

Abstract

Two unit speed searchers at (0,0) seek for a Conditionally Deterministic moving target in the plane in which any time information of the target position is not available to the searchers. The objective is to find the conditions under which the expected value of the first meeting time for the searchers to return to (0,0) after one of them has met the target is finite. And, to show the existence of
an optimal search plan which made the expected value is minimum. In addition, we find the necessary conditions that make the search strategy be optimal.