A problem of the equidistant deployment for discrete-time multiagent systems

This article explores a discrete-time multiagent system on a line. This requires the design of a control protocol providing equidistant agent deployment on a given segment of the line under the constraint that each agent receives information about distances to its neighbors via an auxiliary agent. An approach to the solution of the stated problem is developed. This proves that, under the proposed control protocol, neither communication delay nor switching of communication graph destroy convergence of agents to the equidistant distribution. The results of a numerical simulation confirming the obtained theoretical conclusions are presented.