Programming the robot in tasks of inspection and interception

A pursuer ship - interceptor equipped with sonar, searches adversary submarine and it detected a submarine's periscope at a sea surface. Submarine at the same time, falling under the water starts to move in an unknown direction with an unknown speed. The pursuer P tries to complete the search process in the shortest possible time. It is assumed that the ship interceptor does not know exactly the speed of the submarine; however, it is informed of a finite set of possible speeds. To reduce the found guaranteed search time it is proposed to use the dynamic programming approach, which allows to choose best velocities ordering.