Abstract
This paper deals with systems of multiple mobile robots each of which observes the positions of the other robots and moves to a new position so that eventually the robots form a circle. In the model we study, the robots are anonymous and oblivious, in the sense that they cannot be distinguished by their appearance and do not have a common x-y coordinate system, while they are unable to remember past actions.
We propose a new distributed algorithm for circle formation on the plane. We prove that our algorithm is correct and provide an upper bound for its performance. In addition, we conduct an extensive and detailed comparative simulation experimental study with the DK algorithm described in [7]. The results show that our algorithm is very simple and takes considerably less time to execute than algorithm DK.
This work has been partially supported by the IST Programme of the European Union under contract numbers IST-2001-33116 (FLAGS) and IST-2001-33135 (CRESCCO).
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References
Ando, H., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. on Robotics and Automation 15(5), 818–828 (1999)
Aurenhammer, F.: Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345–405 (1991)
Chatzigiannakis, I.: Design and analysis of distributed algorithms for basic communication in ad-hoc mobile networks, Ph.D. dissertation, Dept. of Computer Engineering and Informatics, University of Patras, Greece (May 2003)
Chatzigiannakis, I., Nikoletseas, S., Spirakis, P.: On the average and worst-case efficiency of some new distributed communication and control algorithms for adhoc mobile networks. In: 1st ACM International Annual Workshop on Principles of Mobile Computing (POMC 2001), pp. 1–19 (2001)
Chatzigiannakis, I., Nikoletseas, S., Spirakis, P.: Distributed communication algorithms for ad hoc mobile networks. ACM Journal of Parallel and Distributed Computing (JPDC) 63(1), 58–74 (2003); Special issue on Wireless and Mobile Ad-hoc Networking and Computing, edited by A. Boukerche
Chirikjian, G.: Kinematics of a metamorphic robotic system. In: IEEE International Conference on Robotics and Automation, pp. 449–455 (1994)
Défago, X., Konagaya, A.: Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: 2nd ACM International Annual Workshop on Principles of Mobile Computing, POMC 2002 (2002)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous oblivious robots with limited visibility. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 93–102. Springer, Heidelberg (1999)
Gervasi, V., Prencipe, G.: Flocking by a set of autonomous mobile robots, Tech. report, Dipartmento di Informatica, Università di Pisa, TR-01-24 (October 2001)
Kornhauser, D., Miller, G., Spirakis, P.: Coordinating pebble motion on graphs, the diameter of permutation groups, and applications. In: 25th IEEE Annual Symposium of Foundations of Computer Science (FOCS 1984), pp. 241–250 (1984)
Mehlhorn, K., Näher, S.: LEDA: A platform for combinatorial and geometric computing. Cambridge University Press, Cambridge (1999)
Pamacha, A., Ebert-Uphoff, I., Chirikjian, G.: Useful metrics for modular robot motion planning. Transactions on Robotics and Automation 13(4), 531–545 (1997)
Skyum, S.: A simple algorithm for computing the smallest enclosing circle. Information Processing Letters 37(3), 121–125 (1991)
Sugihara, K., Suzuki, I.: Distributed motion coordination of multiple mobile robots. In: IEEE International Symposium on Intelligence Control, pp. 138–143 (1990)
Suzuki, I., Yamashita, M.: Agreement on a common x-y coordinate system by a group of mobile robots. In: Dagstuhl Seminar on Modeling and Planning for Sensor- Based Intelligent Robots, Dagstuhl, Germany (September 1996)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal of Computer Science 28(4), 1347–1363 (1999)
Walter, J.E., Welch, J.L., Amato, N.M.: Distributed reconfiguration of metamorphic robot chains. In: 19th ACM Annual Symposium on Principles of Distributed Computing (PODC 2000), pp. 171–180 (2000)
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Chatzigiannakis, I., Markou, M., Nikoletseas, S. (2004). Distributed Circle Formation for Anonymous Oblivious Robots. In: Ribeiro, C.C., Martins, S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24838-5_12
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DOI: https://doi.org/10.1007/978-3-540-24838-5_12
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