Robot

Algorithm

Constraint (computer-aided design)

Economics

Set (abstract data type)

Computer science

Integer (computer science)

Grid

Line segment

Psychology

Mathematics

Position (finance)

Psychotherapist

Generality

Mobile robot

Artificial intelligence

Geometry

Combinatorics

Point (geometry)

Programming language

Finance

Randomized algorithm

Line (geometry)

Constant (computer programming)

IEEE Robotics & Automation Magazine

A three-dimensional (3D) grid G ntimesntimesn , 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, G ntimesntimesn can be viewed as the union of 2n 2 horizontal line segments, called corridors, and n 2 vertical line segments, called shafts. We view G ntimesntimesn 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 G ntimesntimesn . (Two players can be at the same point at one time.) Any continuous move in G ntimesntimesn 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.

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