Exploring Grid Polygons Online

We investigate the exploration problem of a short-sighted mobile robot moving in an unknown cellular room. To explore a cell, the robot must enter it. Once inside, the robot knows which of the 4 adjacent cells exist and which are boundary edges. The robot starts from a specified cell adjacent to the room’s outer wall; it visits each cell, and returns to the start. Our interest is in a short exploration tour; that is, in keeping the number of multiple cell visits small. For abitrary environments containing no obstacles we provide a strategy producing tours of length S ≤ C + 1 2 E − 3, and for environments containing obstacles we provide a strategy, that is bound by S ≤ C + 1 2 E + 3H +Wcw − 2, where C denotes the number of cells—the area—, E denotes the number of boundary edges—the perimeter—, and H is the number of obstacles, and Wcw is a measure for the sinuosity of the given environment. The strategies were implemented in a Java applet [13] that can be found in http://www.geometrylab.de/Gridrobot/