Abstract
A fundamental problem in robotics is to compute a path for a robot from its current location to a given goal. In this paper we consider the problem of a robot equipped with an on-board vision system searching for a goal g in an unknown environment.
We assume that the robot is located at a point s in a polygon that belongs to the well investigated class of polygons called streets. A street is a simple polygon where s and g are located on the polygon boundary and the part of the polygon boundary from s to g is weakly visible to the part from g to s and vice versa.
Our aim is to minimize the ratio of the length of the path traveled by the robot to the length of the shortest path from s to g. In analogy to on-line algorithms this value is called the competitive ratio. We present two strategies. Our first strategy, continuous lad, extends the strategy lad which minimizes the Local Absolute Detour. We show that this extension results in a 2.03-competitive strategy, which significantly improves the best known bound of 4.44 for this class of strategies. Secondly, and most importantly, we present a hybrid strategy consisting of continuous lad and the strategy Move-in-Quadrant. We show that this combination of strategies achieves a competitive ratio of 1.73 which about halves the gap between the known √2 lower bound for this problem and the previously best known competitive ratio of 2.05.
This research is supported by the DFG-Project “Diskrete Probleme”, No. Ot 64/8-1.
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References
R. Baeza-Yates, J. Culberson and G. Rawlins. “Searching in the plane”, Information and Computation, Vol. 106, (1993), pp. 234–252.
A. Blum, P. Raghavan and B. Schieber. “Navigating in unfamiliar geometric terrain”, Proc. of 23rd ACM Symp. on Theory of Computing, (1991), pp. 494–504.
K-F. Chan and T. W. Lam. “An on-line algorithm for navigating in an unknown environment”, International Journal of Computational Geometry & Applications, Vol. 3, (1993), pp. 227–244.
X. Deng, T. Kameda and C. Papadimitriou. “How to learn an unknown environment I: The rectilinear case”, Technical Report CS-93-04, Dept. of Comp. Sci., York University, 1993. Also as Proc. 32nd IEEE Symp. on Foundations of Comp. Sci., (1991), pp. 298–303.
Ch. Icking. Ph. D. Thesis, Fernuniversität Hagen, 1994.
R. Klein. “Walking an unknown street with bounded detour”, Computational Geometry: Theory and Applications 1, (1992), pp. 325–351.
J. Kleinberg. “On-line search in a simple polygon”, Proc. of 5th ACM-SIAM Symp. on Discrete Algorithms, (1994), pp. 8–15.
A. Lopez-Ortiz and S. Schuierer. “Going home through an unknown street”, Proc. of 4th Workshop on Data Structures and Algorithms, 1995, LNCS 955, pp. 135–146.
A. Lopez-Ortiz and S. Schuierer. “Simple, Efficient and Robust Strategies to Traverse Streets”, Proc. 7th Canad. Conf. on Computational Geometry, 1995, pp. 217–222.
A. Mei and Y. Igarashi. “Efficient strategies for robot navigation in unknown environment” Proc. of 21st Intl. Colloquium on Automata, Languages and Programming, (1994).
E. Moise. “Elementary Geometry from an Advanced Standpoint”, 2nd ed., Addison-Wesley, 1973.
C. H. Papadimitriou and M. Yannakakis. “Shortest paths without a map”, Theoretical Computer Science 84, (1991), pp. 127–150.
D. D. Sleator and R. E. Tarjan. “Amortized efficiency of list update and paging rules”, Communications of the ACM 28, (1985), pp. 202–208.
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© 1996 Springer-Verlag Berlin Heidelberg
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López-Ortiz, A., Schuierer, S. (1996). Walking streets faster. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_144
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DOI: https://doi.org/10.1007/3-540-61422-2_144
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