Distributed Algorithms for Mobile Agent Deployment on a Line Segment Under Switching Topology and Communication Delays

This letter addresses to the problem of mobile agent deployment on a line segment. It is assumed that each agent receives information from some of its right and some of its left neighbors. A linear control protocol is proposed ensuring the agent convergence to the equidistant distribution on the segment. In addition, the problem of nonlinearly-uniform (uniform with respect to a given nonlinear function) deployment of agents is studied, and new control laws are designed providing such a deployment. It is proved that the proposed protocols are robust with respect to communication delays and switching of network topology. The results of a numerical simulation are presented demonstrating the efficiency of the developed approaches.

I. Introduction

Formation control problems have been intensively studied during the last decades (see, for instance, [1]–[7] and the references cited therein). This is motivated by their broad applications such as cooperative control of autonomous vehicles and robots, behavior of animals and social groups, etc.