  This paper proposes a novel maneuvering technique for the
complex-Laplacian-based formation control. We show how to modify the original
weights that build the Laplacian such that a designed steady-state motion of
the desired shape emerges from the local interactions among the agents. These
collective motions can be exploited to solve problems such as the shaped
consensus (the rendezvous with a particular shape), the enclosing of a target,
or translations with controlled speed and heading to assist mobile robots in
area coverage, escorting, and traveling missions, respectively. The designed
steady-state collective motions correspond to rotations around the centroid,
translations, and scalings of a reference shape. The proposed modification of
the weights relocates one of the Laplacian's zero eigenvalues while preserving
its associated eigenvector that constructs the desired shape. For example, such
relocation on the imaginary or real axis induces rotational and scaling
motions, respectively. We will show how to satisfy a sufficient condition to
guarantee the global convergence to the desired shape and motions. Finally, we
provide simulations and comparisons with other maneuvering techniques.
