Uniform multi-agent deployment on a ring

Abstract

a b s t r a c tWe consider two variants of the task of spreading a swarm of agents uniformly on a ring graph. Ant-like oblivious agents having limited capabilities are considered. The agents are assumed to have little memory, they all execute the same algorithm and no direct communication is allowed between them. Furthermore, the agents do not possess any global information. In particular, the size of the ring (n) and the number of agents in the swarm (k) are unknown to them. The agents are assumed to operate on an unweighted ring graph. Every agent can measure the distance to his two neighbors on the ring, up to a limited range of V edges.The first task considered, is dynamical (i.e. in motion) uniform deployment on the ring.We show that if either the ring is unoriented, or the visibility range is less than ⌊n/k⌋, this is an impossible mission for the agents. Then, for an oriented ring and V ≥ ⌈n/k⌉, we propose an algorithm which achieves the deployment task in optimal time. The second task discussed, called quiescent spread, requires the agents to spread uniformly over the ring and stop moving. We prove that under our model, in which every agent can measure the distance only to his two neighbors, this task is impossible. Subsequently, we propose an algorithm which achieves quiescent but only almost uniform spread. The algorithms we present are scalable and robust. In case the environment (the size of the ring) or the number of agents changes during the run, the swarm adapts and re-deploys without requiring any outside interference.

Positioning multiple mobile robots for geometric pattern formation: An empirical analysis

“…Recently the pattern formation problem by multiple mobile robots has been discussed from computational perspective. In the process of generalization of this problem several approaches [3,18,19,[22][23][24][25][26][27][28] have treated the robots as a point in Euclidean plane R2. Common assumptions which have been taken in all these works are, all robots are Anonymous-cannot be distinguished from each other i.e., there are no identification marks on them.…”

“…Rather it can be considered as first step towards coordination. In this paper we have reviewed several pattern formation algorithms by multiple mobile robots [3,18,19,[22][23][24][25][26][27][28]. In particular we have studied the circle formation problem.…”

On the self-stabilization of mobile oblivious robots in uniform rings

“…To the best of our knowledge, the work in [19] is the only one that considers the uniform distribution on a ring. The work proposes deterministic algorithms in a weaker model but they also assume that each node is occupied by at most one robot in the initial configuration.…”

Optimal deployment of heterogeneous mobile agents on a circle

“…Deployment of mobile agents in one-dimensional space has received increasing attention in recent years [15][16][17][18][19]. In [15], a Kuramoto-like model is proposed for balanced deployment of multiple robots on a circle, where the goal is to distribute the robots equally on a circle.…”

“…In [17], one-dimensional deployment problem is investigated for a network of robots with rate-constrained digital links. In [18], scalable and robust algorithms are developed to address uniform multi-agent deployment problem on a ring graph.…”