Capturing an Evader in a Building - Randomized and Deterministic Algorithms for Mobile Robots

A three-dimensional (3D) grid Gntimesntimesn, n ges 2, is the set of points (vertices) with integer coordinates in [0,n-1]times[0,n-1] together with their connecting edges, which is viewed as a connected 3D set. Alternatively, Gntimesntimesn can be viewed as the union of 2n2 horizontal line segments, called corridors, and n2 vertical line segments, called shafts. We view Gntimesntimesn as representing a building and consider a vision-based pursuit-evasion problem in which a group of mobile robots (pursuers) are required to search for and capture an evader (intruder) hiding in it. The robots and the evader-all called players-are represented by points that move continuously along the edges of Gntimesntimesn. (Two players can be at the same point at one time.) Any continuous move in Gntimesntimesn is allowed within the speed limit constraint, which is for the evader without loss of generality, and a constant s for the robots The evader is considered captured if there exists a time during the pursuit when his position coincides with the position of one of the robots.