On-line exploration of rectangular cellular environments with a rectangular hole

Abstract

This paper considers the problem of exploring an unknown rectangular cellular environment with a rectangular hole using a mobile robot. The robot's task is to visit each cell at least once and return to the start. The robot has limited visibility that can only detect four cells adjacent to it. And it has large amount of memory that can store a map of discovered cells. The goal of this work is to find the shortest exploration tour, that is, minimizing the total number of multiple visited cells. We consider the environment in four possible scenarios: rectangular, L-shaped, C-shaped or O-shaped grid polygon. An on-line strategy has been proposed for these scenarios. We prove that it is optimal for rectangular, L-shaped, C-shaped grid polygon, and is 4/3-competitive for O-shaped grid polygon.