Abstract
In this paper we study the Near-Gathering problem for a set of asynchronous, anonymous, oblivious and autonomous mobile robots with limited visibility moving in Look-Compute-Move (LCM) cycles: In this problem, the robots have to get close enough to each other, so that every robot can see all the others, without touching (i.e., colliding) with any other robot. The importance of this problem might not be clear at a first sight: Solving the Near-Gathering problem, it is possible to overcome the limitations of having robots with limited visibility, and it is therefore possible to exploit all the studies (the majority, actually) done on this topic, in the unlimited visibility setting. In fact, after the robots get close enough, they are able to see all the robots in the system, a scenario similar to the one where the robots have unlimited visibility. Here, we present a collision-free algorithm for the Near-Gathering problem, the first to our knowledge, that allows a set of autonomous mobile robots to nearly gather within finite time. The collision-free feature of our solution is crucial in order to combine it with an unlimited visibility protocol. In fact, the majority of the algorithms that can be found on the topic assume that all robots occupy distinct positions at the beginning. Hence, only providing a collision-free Near-Gathering algorithm, as the one presented here, is it possible to successfully combine it with an unlimited visibility protocol, hence overcoming the natural limitations of the limited visibility scenario. In our model, distances are induced by the infinity norm. A discussion on how to extend our algorithm to models with different distance functions, including the usual Euclidean distance, is also presented.
This work has been partially supported by MIUR of Italy under projects MadWeb and AlgoDEEP prot. 2008TFBWL4.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: A distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transaction on Robotics and Automation 15(5), 818–828 (1999)
Cieliebak, M.: Gathering Non-oblivious Mobile Robots. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 577–588. Springer, Heidelberg (2004)
Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: The power of lights: Synchronizing asynchronoys robots using visibile bits. In: The 32nd International Conference on Distributed Computing Systems, ICDCS (to appear, 2012)
Défago, X., Souissi, S.: Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity. Theoretical Computer Science 396(1-3), 97–112 (2008)
Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. ACM Transactions on Autonomous and Adaptive Systems 3(4) (2008)
Dieudonné, Y., Petit, F., Villain, V.: Leader Election Problem versus Pattern Formation Problem. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 267–281. Springer, Heidelberg (2010)
Efrima, A., Peleg, D.: Distributed Models and Algorithms for Mobile Robot Systems. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 70–87. Springer, Heidelberg (2007)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of robots with limited visibility. Theoretical Computer Science 337(1-3), 147–168 (2005)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous oblivious robots. Theoretical Computer Science 407, 412–447 (2008)
Katreniak, B.: Convergence with Limited Visibility by Asynchronous Mobile Robots. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 125–137. Springer, Heidelberg (2011)
Pagli, L., Prencipe, G., Viglietta, G.: Getting close without touching. Technical Report TR-12-05, Dipartimento di Informatica, Università di Pisa (2012)
Peleg, D.: Distributed Coordination Algorithms for Mobile Robot Swarms: New Directions and Challenges. In: Pal, A., Kshemkalyani, A.D., Kumar, R., Gupta, A. (eds.) IWDC 2005. LNCS, vol. 3741, pp. 1–12. Springer, Heidelberg (2005)
Prencipe, G.: The effect of synchronicity on the behavior of autonomous mobile robots. Theory of Computing Systems (TOCS) 38(5), 539–558 (2005)
Souissi, S., Défago, X., Yamashita, M.: Using eventually consistent compasses to gather memory-less mobile robots with limited visibility. ACM Transactions on Autonomous and Adaptive Systems 4(1), 1–27 (2009)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. Siam Journal on Computing 28(4), 1347–1363 (1999)
Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theoretical Computer Science 411(26-28) (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pagli, L., Prencipe, G., Viglietta, G. (2012). Getting Close without Touching. In: Even, G., Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2012. Lecture Notes in Computer Science, vol 7355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31104-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-31104-8_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31103-1
Online ISBN: 978-3-642-31104-8
eBook Packages: Computer ScienceComputer Science (R0)