Consider a set of n ̸= 4 simple autonomous mobile robots (decentralized, asynchronous, no common coordinate system, no iden- tities, 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 litera- ture, 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 assump- tion. In addition to closing a long-standing problem, the result of this paper also implies that, for pattern formation, asynchrony is not a com- putational handicap, and that additional powers such as chirality and rigidity are computationally irrelevant.
|Titolo:||Distributed Computing by Mobile Robots: Solving the Uniform Circle Formation Problem|
|Anno del prodotto:||2014|
|Appare nelle tipologie:||4.1 Contributo in Atti di convegno|