Abstract
We consider swarms of luminous myopic robots that run in synchronous Look-Compute-Move cycles. These robots evolve in a finite grid and are disoriented, i.e., they have neither global compass nor a common chirality. In this context, we propose optimal solutions for the perpetual exploration of a finite grid. Precisely, we investigate optimality in terms of the visibility range, number of robots, number of colors. In more detail, under the optimal visibility range one, we give an algorithm which is optimal w.r.t. the number of robots: it uses three robots and three colors. Under visibility two, we design an algorithm that uses five robots and only one color, i.e., robots are oblivious.
This study was partially supported by the French anr projects ANR-16-CE40-0023 (descartes) and ANR-16 CE25-0009-03 (estate).
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
Notes
- 1.
Oblivious robots have no state and cannot remember past actions.
- 2.
The requirement on the numbers of lines and columns is only made for the sake of simplicity.
References
Baldoni, R., Bonnet, F., Milani, A., Raynal, M.: Anonymous graph exploration without collision by mobile robots. Inf. Process. Lett. 109(2), 98–103 (2008)
Blin, L., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Exclusive perpetual ring exploration without chirality. In: Lynch, N.A., Shvartsman, A.A. (eds.) Distributed Computing, DISC 2010. LNCS, vol. 6343, pp. 312–327. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15763-9_29
Bonnet, F., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Asynchronous exclusive perpetual grid exploration without sense of direction. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) Principles of Distributed Systems, OPODIS 2011. LNCS, vol. 7109, pp. 251–265. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25873-2_18
Bramas, Q., Devismes, S., Lafourcade, P.: Finding water on poleless using melomaniac myopic chameleon robots. In: FUN 2020, 10th International Conference on Fun with Algorithms. LiPICs, Favignana, Sicily, Italy, 28–30 September 2020).
Bramas, Q., Devismes, S., Lafourcade, P.: Infinite grid exploration by disoriented robots. In: Georgiou, C., Majumdar, R. (eds.) Networked Systems, NETYS 2020. LNCS, vol. 12129, pp. 129–145. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-67087-0_9
Bramas, Q., Devismes, S., Lafourcade, P.: Optimal exclusive perpetual grid exploration by luminous myopic opaque robots with common chirality. In: ICDCN 2021: International Conference on Distributed Computing and Networking, Virtual Event, pp. 76–85. ACM, Nara, Japan, 5–8 January 2021
Datta, A.K., Lamani, A., Larmore, L.L., Petit, F.: Enabling ring exploration with myopic oblivious robots. In: 2015 IEEE International Parallel and Distributed Processing Symposium Workshop, IPDPS 2015, pp. 490–499. IEEE Computer Society, Hyderabad, India, 25–29 May 2015
Devismes, S., Lamani, A., Petit, F., Raymond, P., Tixeuil, S.: Terminating exploration of a grid by an optimal number of asynchronous oblivious robots. Comput. J. 64(1), 132–154 (2020)
Devismes, S., Lamani, A., Petit, F., Tixeuil, S.: Optimal torus exploration by oblivious robots. Computing 101(9), 1241–1264 (2019)
Devismes, S., Petit, F., Tixeuil, S.: Optimal probabilistic ring exploration by semi-synchronous oblivious robots. Theor. Comput. Sci. (TCS) 498, 10–27 (2013)
Dieudonné, Y., Petit, F., Villain, V.: Leader election problem versus pattern formation problem. In: Lynch, N.A., Shvartsman, A.A. (eds.) Distributed Computing, DISC 2010. LNCS, vol. 6343, pp. 267–281. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15763-9_26
Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Remembering without memory: tree exploration by asynchronous oblivious robots. Theor. Comput. Sci. 411(14–15), 1583–1598 (2010)
Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: How many oblivious robots can explore a line. Inf. Process. Lett. 111(20), 1027–1031 (2011)
Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Computing without communicating: ring exploration by asynchronous oblivious robots. Algorithmica 65(3), 562–583 (2013)
Ooshita, F., Tixeuil, S.: Ring exploration with myopic luminous robots. In: Izumi, T., Kuznetsov, P. (eds.) Stabilization, Safety, and Security of Distributed Systems, SSS 2018. LNCS, vol. 11201, pp. 301–316. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03232-6_20
Peleg, D.: Distributed coordination algorithms for mobile robot swarms: new directions and challenges. In: Pal, A., Kshemkalyani, A.D., Kumar, R., Gupta, A. (eds.) Distributed Computing – IWDC 2005, IWDC 2005. LNCS, vol. 3741, pp. 1–12. Springer, Heidelberg (2005). https://doi.org/10.1007/11603771_1
Rauch, A., Bramas, Q., Devismes, S., Lafourcade, P., Lamani, A.: Optimal exclusive perpetual grid exploration by luminous myopic robots without chirality: the animations (2021). https://doi.org/10.5281/zenodo.4640462
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Rauch, A., Bramas, Q., Devismes, S., Lafourcade, P., Lamani, A. (2021). Optimal Exclusive Perpetual Grid Exploration by Luminous Myopic Robots Without Common Chirality. In: Echihabi, K., Meyer, R. (eds) Networked Systems. NETYS 2021. Lecture Notes in Computer Science(), vol 12754. Springer, Cham. https://doi.org/10.1007/978-3-030-91014-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-91014-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-91013-6
Online ISBN: 978-3-030-91014-3
eBook Packages: Computer ScienceComputer Science (R0)