Collisionless Gathering of Robots with an Extent

A. Cord-Landwehr, B. Degener, M. Fischer, M. Hüllmann, B. Kempkes, A. Klaas, P. Kling, S. Kurras, M. Märtens, F. Meyer auf der Heide, C. Raupach, K. Swierkot, D. Warner, C. Weddemann, D. Wonisch, in: 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011), Springer, 2011, pp. 178–189.

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Abstract
Gathering n mobile robots in one single point in the Euclidean plane is a widely studied problem from the area of robot formation problems. Classically, the robots are assumed to have no physical extent, and they are able to share a position with other robots. We drop these assumptions and investigate a similar problem for robots with (a spherical) extent: the goal is to gather the robots as close together as possible. More exactly, we want the robots to form a sphere with minimum radius around a predefined point. We propose an algorithm for this problem which synchronously moves the robots towards the center of the sphere unless they block each other. In this case, if possible, the robots spin around the center of the sphere. We analyze this algorithm experimentally in the plane. If R is the distance of the farthest robot to the center of the sphere, the simulations indicate a runtime which is linear in n and R. Additionally, we prove a theoretic upper bound for the runtime of O(nR) for a discrete version of the problem. Simulations also suggest a runtime of O(n + R) for the discrete version.
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Proceedings Title
37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011)
Issue
6543
Page
178-189
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Cord-Landwehr A, Degener B, Fischer M, et al. Collisionless Gathering of Robots with an Extent. In: 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011). Springer; 2011:178-189. doi:10.1007/978-3-642-18381-2_15
Cord-Landwehr, A., Degener, B., Fischer, M., Hüllmann, M., Kempkes, B., Klaas, A., … Wonisch, D. (2011). Collisionless Gathering of Robots with an Extent. In 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011) (pp. 178–189). Springer. https://doi.org/10.1007/978-3-642-18381-2_15
@inproceedings{Cord-Landwehr_Degener_Fischer_Hüllmann_Kempkes_Klaas_Kling_Kurras_Märtens_Meyer auf der Heide_et al._2011, title={Collisionless Gathering of Robots with an Extent}, DOI={10.1007/978-3-642-18381-2_15}, number={6543}, booktitle={37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011)}, publisher={Springer}, author={Cord-Landwehr, Andreas and Degener, Bastian and Fischer, Matthias and Hüllmann, Martina and Kempkes, Barbara and Klaas, Alexander and Kling, Peter and Kurras, Sven and Märtens, Marcus and Meyer auf der Heide, Friedhelm and et al.}, year={2011}, pages={178–189} }
Cord-Landwehr, Andreas, Bastian Degener, Matthias Fischer, Martina Hüllmann, Barbara Kempkes, Alexander Klaas, Peter Kling, et al. “Collisionless Gathering of Robots with an Extent.” In 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011), 178–89. Springer, 2011. https://doi.org/10.1007/978-3-642-18381-2_15.
A. Cord-Landwehr et al., “Collisionless Gathering of Robots with an Extent,” in 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011), 2011, no. 6543, pp. 178–189.
Cord-Landwehr, Andreas, et al. “Collisionless Gathering of Robots with an Extent.” 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011), no. 6543, Springer, 2011, pp. 178–89, doi:10.1007/978-3-642-18381-2_15.

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