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 \(S \leq C + \frac{1}{2} E -- 3\), 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 \(\frac43\), and give a lower bound of \(\frac76\) for our problem. This leaves a gap of only \(\frac16\) between the lower and the upper bound.
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Icking, C., Kamphans, T., Klein, R., Langetepe, E. (2005). Exploring Simple Grid Polygons. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_53
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DOI: https://doi.org/10.1007/11533719_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
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