Distributed Computing by Mobile Robots: Gathering

Abstract

Abstract. Consider a set of n > 2 identical mobile computational entities in the plane, called robots, operating in Look-Compute-Move cycles, without any means of direct communication. The Gathering Problem is the primitive task of all entities gathering in finite time at a point not fixed in advance, without any external control. The problem has been extensively studied in the literature under a variety of strong assumptions (e.g., synchronicity of the cycles, instantaneous movements, complete memory of the past, common coordinate system, etc.). In this paper we consider the setting without those assumptions, that is, when the entities are oblivious (i.e., they do not remember results and observations from previous cycles), disoriented (i.e., have no common coordinate system), and fully asynchronous (i.e., no assumptions exist on timing of cycles and activities within a cycle). The existing algorithmic contributions for such robots are limited to solutions for n ≤ 4 or for restricted sets of initial configurations of the robots; the question of whether such weak robots could deterministically gather has remained open. In this paper, we prove that indeed the Gathering Problem is solvable, for any n > 2 and any initial configuration, even under such restrictive conditions.

A Stochastic Approach to Shortcut Bridging in Programmable Matter

“…These systems can perform a variety of tasks including gathering [10], shape formation [15,24], and imitating the collective behavior of natural systems [6]; however, the individual robots typically have more powerful communication and processing capabilities than those we consider. Modular self-reconfigurable robotic systems focus on the motion planning and control of kinematic robots to achieve dynamic morphology [30], and metamorphic robots form a subclass of self-reconfiguring robots [9] that share some characteristics with our geometric amoebot model.…”

Zombie Swarms: An Investigation on the Behaviour of Your Undead Relatives

“…The model used in this paper is based on a more general model widely used in literature to describe the behavior of a set of autonomous and asynchronous entities that operate on a two dimensional plane: ASYNC (also known as CORDA) [9][10][11].…”

“…continue with the paper -and, above all, not to try to replicate our experiments without experienced supervision and emergency rescue personnel at hand! In order to be able to test the effectiveness of the survival solutions proposed in this paper, we model the Humans as entities that are able to asynchronously and independently move on the plane, following the ASYNC model [9][10][11]. Their aim is that of driving the Zs by emitting noise, trying to not become too close to the Zs.…”

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

“…For this type of robots, depending on the activation schedule and timing assumptions, three main models have been studied in the literature: the asynchronous one (ASYNC), where no assumptions are made on synchronization among the robots' cycles nor their duration, and the semi-synchronous fully synchronous models, denoted by SSYNC and F SYNC, respectively, where the robots, oblivious and disoriented, however operate in synchronous rounds, and each round is "atomic": all robots active in that round terminate their cycle by the next round; the only difference is whether all robots are activated in every round (F SYNC), or, subject to some fairness condition, a possibly different subset is activated in each round (SSYNC). All three models have been intensively studied (e.g., see [1,2,3,5,6,7,8,9,10,15,16,17,23,24]; for a detailed overview refer to the recent monograph [13]). …”

“…The class Point is the set consisting of a single point; point formation corresponds to the important Gathering problem requiring all robots to gather at a same location, not determined in advance (e.g., see [2,3,4,18,21]). The other important class of patterns is Uniform Circle: the points of the pattern form the vertices of a regular n-gon, where n is the number of robots (e.g., [1,6,7,8,10,11,12,20]).…”