A simple formation-tracking controller of mobile robots based on a “spanning-tree” communication

We solve the formation-tracking control problem for mobile robots via linear control. As in the classical tracking control problem for two nonholonomic systems, the swarm is driven by a fictitious robot which moves about freely. Only one “leader” robot communicates with the reference vehicle and in turn, acts as a leader to a second robot hence forming a fixed spanning tree. We show that a simple condition on the reference angular velocity (persistency of excitation) suffices to achieve consensus tracking.