Abstract
We study the rendezvous problem for two robots moving in the plane (or on a line). Robots are autonomous, anonymous, oblivious, and carry colored lights that are visible to both. We consider deterministic distributed algorithms in which robots do not use distance information, but try to reduce (or increase) their distance by a constant factor, depending on their lights’ colors.
We give a complete characterization of the number of colors that are necessary to solve the rendezvous problem in every possible model, ranging from fully synchronous to semi-synchronous to asynchronous, rigid and non-rigid, with preset or arbitrary initial configuration.
In particular, we show that three colors are sufficient in the non-rigid asynchronous model with arbitrary initial configuration. In contrast, two colors are insufficient in the rigid asynchronous model with arbitrary initial configuration and in the non-rigid asynchronous model with preset initial configuration.
Additionally, if the robots are able to distinguish between zero and non-zero distances, we show how they can solve rendezvous and detect termination using only three colors, even in the non-rigid asynchronous model with arbitrary initial configuration.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing for mobile robots: gathering. SIAM J. Comput. 41, 829–879 (2012)
Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: The power of lights: synchronizing asynchronous robots using visible bits. In: 32nd International Conference on Distributed Computing Systems, pp. 506–515 (2012)
Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool, San Rafael (2012)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of robots with limited visibility. Theor. Comput. Sci. 337, 147–168 (2005)
Izumi, T., Souissi, S., Katayama, Y., Inuzuka, N., Défago, X., Wada, K., Yamashita, M.: The gathering problem for two oblivious mobile robots with unreliable compasses. SIAM J. Comput. 411, 26–46 (2012)
Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384, 222–231 (2007)
Prencipe, G., Santoro, N.: Distributed algorithms for mobile robots. In: Navarro, G., Bertossi, L., Kohayakawa, Y. (eds.) TCS 2006. IFIP, vol. 209, pp. 47–62. Springer, Boston (2006)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28, 1347–1363 (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Viglietta, G. (2014). Rendezvous of Two Robots with Visible Bits. In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2013. Lecture Notes in Computer Science(), vol 8243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45346-5_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-45346-5_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45345-8
Online ISBN: 978-3-642-45346-5
eBook Packages: Computer ScienceComputer Science (R0)