Abstract
We consider simple models of swarms of identical, anonymous robots: they are points in the plane and “see” only their neighbors (robots within distance one). We will deal with distributed local protocols of such swarms that result in formations like “gathering at one point”. The focus will be on protocols assuming a continuous time model. We present upper and lower bounds on their run time and energy consumption, and compare different protocols both theoretically and experimentally.
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
Similar content being viewed by others
Notes
- 1.
Without loss of generality, we say an angle is positive if it is measured counterclockwise and negative if it is measured clockwise.
- 2.
As in the proof of Theorem 6, we identify vertices with the robots positioned on them.
References
Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: Proceedings of 10th International Symposium on Intelligent Control (ISIC), pp. 453–460, August 1995. https://doi.org/10.1109/ISIC.1995.525098
Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the robots gathering problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1181–1196. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-45061-0_90
Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34(6), 1516–1528 (2005). https://doi.org/10.1137/S0097539704446475
Degener, B., Kempkes, B., Langner, T., Meyer auf der Heide, F., Pietrzyk, P., Wattenhofer, R.: A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In: Rajaraman R., Meyer auf der Heide, F., (eds.) SPAA 2011: Proceedings of the 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures, San Jose, CA, USA, 4–6 June 2011 (Co-located with FCRC 2011), pp. 139–148. ACM (2011). https://doi.org/10.1145/1989493.1989515
Degener, B., Kempkes, B., Kempkes, P., Meyer auf der Heide, F.: Linear and competitive strategies for continuous robot formation problems. TOPC 2(1), 2:1–2:18 (2015). https://doi.org/10.1145/2742341
Dieudonné, Y., Petit, F.: Self-stabilizing deterministic gathering. In: Dolev, S. (ed.) ALGOSENSORS 2009. LNCS, vol. 5804, pp. 230–241. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05434-1_23
Gabriel, K.R., Sokal, R.R.: A new statistical approach to geographic variation analysis. Syst. Biol. 18(3), 259–278 (1969). https://doi.org/10.2307/2412323
Gordon, N., Wagner, I.A., Bruckstein, A.M.: Gathering multiple robotic a(ge)nts with limited sensing capabilities. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) ANTS 2004. LNCS, vol. 3172, pp. 142–153. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28646-2_13
Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: Gathering autonomous mobile robots with dynamic compasses: an optimal result. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 298–312. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75142-7_24
Katayama, Y., Tomida, Y., Imazu, H., Inuzuka, N., Wada, K.: Dynamic compass models and gathering algorithms for autonomous mobile robots. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 274–288. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72951-8_22
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). https://doi.org/10.1007/978-3-642-22212-2_12
Li, S., Meyer auf der Heide, F., Podlipyan, P.: The impact of the gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots. In: Chrobak, M., Fernández Anta, A., Gąsieniec, L., Klasing, R. (eds.) ALGOSENSORS 2016. LNCS, vol. 10050, pp. 62–79. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-53058-1_5
Li, S., Markarian, C., Meyer auf der Heide, F., Podlipyan, P.: A continuous strategy for collisionless gathering. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 182–197. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72751-6_14
Nguyen, H.G., Pezeshkian, N., Raymond, S.M., Gupta, A., Spector, J.M.: Autonomous communication relays for tactical robots. In: Proceedings of the 11th International Conference on Advanced Robotics (ICAR), pp. 35–40 (2003)
Olver, F.W., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions, 1st edn. Cambridge University Press, New York (2010)
Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384(2–3), 222–231 (2007). https://doi.org/10.1016/j.tcs.2007.04.023
Souissi, S., Défago, X., Yamashita, M.: Gathering asynchronous mobile robots with inaccurate compasses. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 333–349. Springer, Heidelberg (2006). https://doi.org/10.1007/11945529_24
Watton, A., Kydon, D.W.: Analytical aspects of the \(n\)-bug problem. Am. J. Phys. 37(2), 220–221 (1969). https://doi.org/10.1119/1.1975458
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kling, P., Meyer auf der Heide, F. (2019). Continuous Protocols for Swarm Robotics. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-11072-7_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11071-0
Online ISBN: 978-3-030-11072-7
eBook Packages: Computer ScienceComputer Science (R0)