Distributed Computing by Mobile Robots: Solving the Uniform Circle Formation Problem

  • Paola Flocchini
  • Giuseppe Prencipe
  • Nicola Santoro
  • Giovanni Viglietta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8878)

Abstract

Consider a set of n ≠ 4 simple autonomous mobile robots (decentralized, asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, deterministic) initially in distinct locations, moving freely in the plane and able to sense the positions of the other robots. We study the primitive task of the robots arranging themselves equally spaced along a circle not fixed in advance (Uniform Circle Formation). In the literature, the existing algorithmic contributions are limited to restricted sets of initial configurations of the robots and to more powerful robots. The question of whether such simple robots could deterministically form a uniform circle has remained open. In this paper, we constructively prove that indeed the Uniform Circle Formation problem is solvable for any initial configuration of the robots without any additional assumption. In addition to closing a long-standing problem, the result of this paper also implies that, for pattern formation, asynchrony is not a computational handicap, and that additional powers such as chirality and rigidity are computationally irrelevant.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Paola Flocchini
    • 1
  • Giuseppe Prencipe
    • 2
  • Nicola Santoro
    • 3
  • Giovanni Viglietta
    • 3
  1. 1.University of OttawaCanada
  2. 2.University of PisaItaly
  3. 3.Carleton UniversityCanada

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