  This paper proposes a novel distributed technique to induce collective
motions in affine formation control. Instead of the traditional leader-follower
strategy, we propose modifying the original weights that build the Laplacian
matrix so that a designed steady-state motion of the desired shape emerges from
the agents' local interactions. The proposed technique allows a rich collection
of collective motions such as rotations around the centroid, translations,
scalings, and shearings of a reference shape. These motions can be applied in
useful collective behaviors such as \emph{shaped} consensus (the rendezvous
with a particular shape), escorting one of the team agents, or area coverage.
We prove the global stability and effectiveness of our proposed technique
rigorously, and we provide some illustrative numerical simulations.
