Area Convergence of Monoculus Robots With Additional Capabilities

Debasish Pattanayak, Kaushik Mondal, Partha Sarathi Mandal, Stefan Schmid

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper considers the area convergence problem, which requires a group of robots to gather in a small area not defined a priori. While it is known that robots can gather at a point if they can precisely measure distances, we, in this paper, show that without any agreement on the coordinate system, it is impossible for robots to converge to an area if they cannot measure distances or angles. We denote these robots without the ability to measure distances or angles as monoculus robots. We present a counterexample showing that monoculus robots fail in area convergence even with the capability of measuring angles. However, monoculus robots with a weak notion of distance or minimal agreement on the coordinate system are sufficient to achieve area convergence. In particular, we present area convergence algorithms in asynchronous model for such monoculus robots with one of the two following simple additional capabilities: (1) locality detection (LD), a notion of distance or (2) orthogonal line agreement (OLA), a notion of direction. We discuss extensions corresponding to multiple dimensions and the termination. Additionally, we validate our findings using simulation and show the robustness of our algorithms in the presence of errors in observation or movement.

Original languageEnglish
Pages (from-to)1306-1319
Number of pages14
JournalComputer Journal
Issue number5
StatePublished - 1 May 2022
Externally publishedYes


  • area convergence
  • asynchronous
  • distributed algorithm
  • monoculus robots
  • oblivious mobile robots

ASJC Scopus subject areas

  • Computer Science (all)


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