  This paper presents a novel control design for vehicular formations, which is
an alternative to the conventional second-order consensus protocol. 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 stability of the closed-loop system
under the minimum requirement of the underlying communication graphs each
containing a connected spanning tree -- something that is not true in general
for the conventional consensus protocols. Here, we show that the serial
consensus design also gives guarantees on the worst-case transient behavior of
the formation, which are independent of the number of vehicles and the
underlying graph structure. In particular this shows that the serial consensus
design can be used to guarantee string stability of the formation, and is
therefore suitable for directed formations. We show that it can be implemented
through message passing or measurements to neighbors at most two hops away. The
results are illustrated through numerical examples.
