Closed-loop design for scalable performance of vehicular formations

This paper presents a novel control design for vehicular formations as an alternative to alignment through conventional consensus protocols for second-order systems. The design is motivated by the closed-loop system, which we construct as first-order systems connected in series, and is therefore called serial consensus. The serial consensus design will guarantee the stability of the closed-loop system under the minimum requirement of the underlying communication graph containing a directed spanning tree—which is not generally true for conventional consensus. As our main result, we show that the serial consensus design gives bounds on the worst-case transient behavior of the formation, which is independent of the number of vehicles and the underlying graph structure. In particular, this shows that the serial consensus design guarantees string stability of the formation and is, therefore, suitable for directed formations and communication topologies. We show that serial consensus can be implemented through message passing or measurements to neighbors at most two hops away. We illustrate our results through numerical examples.