A problem of formation control on a line segment under protocols with communication delay

Abstract The problem of the equidistant deployment of a group of mobile agents on a line segment is studied. Both cases where agent dynamics is modeled by the first-order integrators and double integrators are considered. It is assumed that each agent receives information from its neighbors not directly, but via an auxiliary agent. The impact of communication delays on the agent deployment is investigated. Conditions are derived ensuring the convergence of agents to the equidistant distribution for any constant nonnegative delays. Efficiency of the obtained results is demonstrated by a numerical simulation.