  This paper presents decentralized algorithms for formation control of
multiple robots in three dimensions. Specifically, we leverage the mathematical
properties of cyclic pursuit along with results from contraction and partial
contraction theory to design decentralized control algorithms that ensure
global convergence to symmetric formations. We first consider regular polygon
formations as a base case, and then extend the results to Johnson solid and
other polygonal mesh formations. The algorithms are further augmented to allow
control over formation size and avoid collisions with other robots in the
formation. The robustness properties of the algorithms are assessed in the
presence of bounded additive disturbances and their effect on the quality of
the formation is quantified. Finally, we present a general methodology for
embedding the control laws on complex dynamical systems, in this case,
quadcopters, and validate this approach via simulations and experiments on a
fleet of quadcopters.
