Exploring simple grid polygons

Abstract

We investigate the online exploration problem of a short-sighted mobile robot moving in an unknown cellular room without obstacles. The robot has a very limited sensor; it can determine only which of the four cells adjacent to its current position are free and which are blocked, i.e., unaccessible for the robot. Therefore, the robot must enter a cell in order to explore it. The robot has to visit each cell and to return to the start. Our interest is in a short exploration tour, i.e., in keeping the number of multiple cell visits small. For abitrary environments without holes we provide a strategy producing tours of length S ≤ C+1/2E-3, where C denotes the number of cells - the area -, and E denotes the number of boundary edges - the perimeter - of the given environment. Further, we show that our strategy is competitive with a factor of 4/3, and give a lower bound of 7/6 for our problem. This leaves a gap of only 1/6 between the lower and the upper bound. © Springer-Verlag Berlin Heidelberg 2005.