  Groups of unmanned aerial vehicles (UAVs) are increasingly utilized in
transportation task as the combined strength allows to increase the maximum
payload. However, the resulting mechanical coupling of the UAVs impose new
challenges in terms of the tracking control. Thus, we design a geometric
trajectory tracking controller for the cooperative task of four quadrotor UAVs
carrying and transporting a rigid body, which is attached to the quadrotors via
inflexible elastic cables. The elasticity of the cables together with
techniques of singular perturbation allows a reduction in the model to that of
a similar model with inelastic cables. In this reduced model, we design a
controller such that the position and attitude of the load exponentially
converges to a given desired trajectory. We then show that this result leads to
an uniformly converging tracking error for the original elastic model under
some assumptions. Furthermore, under the presence of unstructured disturbances
on the system, we show that the error is ultimately bounded with an arbitrarily
small bound. Finally, a simulation illustrates the theoretical results.
