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

Levi Itzhak Bellaiche, Alfred Bruckstein

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 ℝ2 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 π, 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.

Original languageEnglish
Title of host publicationSWARM INTELLIGENCE
EditorsXiaodong Li, Manuel López-Ibáñez, Carlo Pinciroli, Marco Dorigo, Mauro Birattari, Thomas Stützle, Kazuhiro Ohkura
Number of pages12
StatePublished - 2016
Event10th International Conference on Swarm Intelligence, ANTS 2016 - Brussels, Belgium
Duration: 7 Sep 20169 Sep 2016

Publication series

NameLecture Notes in Computer Science


Conference10th International Conference on Swarm Intelligence, ANTS 2016


  • Bearing-only
  • Convex polygon
  • Gathering

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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