On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots

Roberto Baldoni (1) , François Bonnet (2) , Alessia Milani (1) , Michel Raynal (2)

1 MIDLAB - Middleware Laboratory
2 ASAP - As Scalable As Possible: foundations of large scale dynamic distributed systems

Given an arbitrary partial anonymous grid (a finite grid with possibly missing vertices or edges), this paper focuses on the exploration of such a grid by a set of mobile anonymous agents (called robots). Assuming that the robots can move synchronously, but cannot communicate with each other, the aim is to design an algorithm executed by each robot that allows, as many robots as possible (let k be this maximal number), to visit infinitely often all the vertices of the grid, in such a way that no vertex hosts more than one robot at a time, and each edge is traversed by at most one robot at a time. The paper addresses this problem by considering a central parameter, denoted p, that captures the view of each robot. More precisely, it is assumed that each robot sees the part of the grid (and its current occupation by other robots, if any) centered at the vertex it currently occupies and delimited by the radius p. Based on such a radius notion, the paper investigates the following cases and presents associated results. It first shows that there is no solution (i.e., k = 0) when = 0. It then shows that k p

Mots clés: Anonymity; Grid exploration; Partial grid; Mobile agent; Mutual exclusion; Robot; Synchronous system

Domaines: Robotique [cs.RO]

Roberto Baldoni, François Bonnet, Alessia Milani, Michel Raynal. On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots. [Research Report] PI 1892, 2008, pp.21. ⟨inria-00277344⟩