Skip to main content
Top

2016 | OriginalPaper | Chapter

Continuous Time Gathering of Agents with Limited Visibility and Bearing-only Sensing

Authors : Levi Itzhak Bellaiche, Alfred Bruckstein

Published in: Swarm Intelligence

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A group of mobile agents, identical, anonymous, and oblivious (memoryless), having the capacity to sense only the relative direction (bearing) to neighboring agents within a finite visibility range, are shown to gather to a meeting point in finite time by applying a very simple rule of motion. The agents’ rule of motion is: set your velocity vector to be the sum of the two unit vectors in \(\mathbb {R}^2\) pointing to your “extremal” neighbours determining the smallest visibility disc sector in which all your visible neighbors reside, provided it spans an angle smaller than \(\pi \), otherwise, since you are “surrounded” by visible neighbors, simply stay put. Of course, the initial constellation of agents must have a visibility graph that is connected, and provided this we prove that the agents gather to a common meeting point in finite time, while the distances between agents that initially see each other monotonically decreases.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Bellaiche, L.-I., Bruckstein, A.: Continuous time gathering of agents with limited visibility and bearing-only sensing (2015). arXiv:1510.09115 Bellaiche, L.-I., Bruckstein, A.: Continuous time gathering of agents with limited visibility and bearing-only sensing (2015). arXiv:​1510.​09115
2.
go back to reference Ji, M., Egerstedt, M.: Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans. Robot. 23(4), 693–703 (2007)CrossRef Ji, M., Egerstedt, M.: Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans. Robot. 23(4), 693–703 (2007)CrossRef
3.
go back to reference 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)CrossRef 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)CrossRef
4.
go back to reference Gordon, N., Wagner, I.A., Bruckstein, A.M.: A randomized gathering algorithm for multipe robots with limited sensing capabilities. In: MARS 2005 Workshop Proceedings (ICINCO 2005), Barcelona, Spain (2005) Gordon, N., Wagner, I.A., Bruckstein, A.M.: A randomized gathering algorithm for multipe robots with limited sensing capabilities. In: MARS 2005 Workshop Proceedings (ICINCO 2005), Barcelona, Spain (2005)
5.
go back to reference Gordon, N., Elor, Y., Bruckstein, A.M.: Gathering multiple robotic agents with crude distance sensing capabilities. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) ANTS 2008. LNCS, vol. 5217, pp. 72–83. Springer, Heidelberg (2008)CrossRef Gordon, N., Elor, Y., Bruckstein, A.M.: Gathering multiple robotic agents with crude distance sensing capabilities. In: Dorigo, M., Birattari, M., Blum, C., Clerc, M., Stützle, T., Winfield, A.F.T. (eds.) ANTS 2008. LNCS, vol. 5217, pp. 72–83. Springer, Heidelberg (2008)CrossRef
6.
go back to reference Olfati-Saber, R., Fax, V., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)CrossRef Olfati-Saber, R., Fax, V., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)CrossRef
8.
go back to reference Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. Robot. Autom. 15(5), 818–828 (1999)CrossRef Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. Robot. Autom. 15(5), 818–828 (1999)CrossRef
Metadata
Title
Continuous Time Gathering of Agents with Limited Visibility and Bearing-only Sensing
Authors
Levi Itzhak Bellaiche
Alfred Bruckstein
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-44427-7_8

Premium Partner