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

Distributed formation maneuver control by manipulating the complex Laplacian