A geometric approach to deploying robot swarms

Abstract

We discuss the fundamental problems and practical issues underlying the deployment of a swarm of autonomous mobile robots that can potentially be used to build mobile robotic sensor networks. For the purpose, a geometric approach is proposed that allows robots to configure themselves into a two-dimensional plane with uniform spatial density. Particular emphasis is paid to the hole repair capability for dynamic network reconfiguration. Specifically, each robot interacts selectively with two neighboring robots so that three robots can converge onto each vertex of the equilateral triangle configuration. Based on the local interaction, the self-configuration algorithm is presented to enable a swarm of robots to form a communication network arranged in equilateral triangular lattices by shuffling the neighbors. Convergence of the algorithms is mathematically proved using Lyapunov theory. Moreover, it is verified that the self-reparation algorithm enables robot swarms to reconfigure themselves when holes exist in the network or new robots are added to the network. Through extensive simulations, we validate the feasibility of applying the proposed algorithms to self-configuring a network of mobile robotic sensors. We describe in detail the features of the algorithm, including self-organization, self-stabilization, and robustness, with the results of the simulation.