# Levy Flights in the Stochastic Dynamics of Robot Swarm Gathering

### Yechiel J. Crispin

#### 2006

#### Abstract

We consider the problem of gathering a swarm of robots which is initially randomly dispersed over a domain in the plane. A stochastic method for the cooperative control of a swarm of mobile robots is presented. The network of mobile robots is modeled by a swarm performing a directed random walk. The swarm dynamics are governed by a system of stochastic difference equations. The motion is controlled by a robot leader, which transmits the coordinates of the gathering point to the swarm as the network cooperative control signal. We study the case where the control signal is corrupted by noise and find that the gathering process is robust to noise and efficient. The swarm dynamics display anomalous diffusion and Levy flights, where the robots move along straight lines over many time steps, followed by short random walks in the vicinity of the gathering point.

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#### Paper Citation

#### in Harvard Style

J. Crispin Y. (2006). **Levy Flights in the Stochastic Dynamics of Robot Swarm Gathering** . In *Proceedings of the 2nd International Workshop on Multi-Agent Robotic Systems - Volume 1: MARS, (ICINCO 2006)* ISBN 978-972-8865-66-5, pages 3-12. DOI: 10.5220/0001225200030012

#### in Bibtex Style

@conference{mars06,

author={Yechiel J. Crispin},

title={Levy Flights in the Stochastic Dynamics of Robot Swarm Gathering},

booktitle={Proceedings of the 2nd International Workshop on Multi-Agent Robotic Systems - Volume 1: MARS, (ICINCO 2006)},

year={2006},

pages={3-12},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001225200030012},

isbn={978-972-8865-66-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Workshop on Multi-Agent Robotic Systems - Volume 1: MARS, (ICINCO 2006)

TI - Levy Flights in the Stochastic Dynamics of Robot Swarm Gathering

SN - 978-972-8865-66-5

AU - J. Crispin Y.

PY - 2006

SP - 3

EP - 12

DO - 10.5220/0001225200030012