  A distributed control of vehicle platooning is referred to as distributed
consensus (DC) since many autonomous vehicles (AVs) reach a consensus to move
as one body with the same velocity and inter-distance. For DC control to be
stable, other AVs' real-time position information should be inputted to each
AV's controller via vehicle-to-vehicle (V2V) communications. On the other hand,
too many V2V links should be simultaneously established and frequently
retrained, causing frequent packet loss and longer communication latency. We
propose a novel DC algorithm called over-the-air consensus (AirCons), a joint
communication-and-control design with two key features to overcome the above
limitations. First, exploiting a wireless signal's superposition and
broadcasting properties renders all AVs' signals to converge to a specific
value proportional to participating AVs' average position without individual
V2V channel information. Second, the estimated average position is used to
control each AV's dynamics instead of each AV's individual position. Through
analytic and numerical studies, the effectiveness of the proposed AirCons
designed on the state-of-the-art New Radio architecture is verified by showing
a $14.22\%$ control gain compared to the benchmark without the average
position.
