  This paper presents the design of a geometric trajectory tracking controller
for the cooperative task of two quadrotor UAVs (unmanned aerial vehicles)
carrying and transporting a rigid bar, 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 rod exponentially tracks a given desired trajectory
for its position and attitude, under some assumptions on initial error. We then
show that exponential tracking in the reduced model corresponds to exponential
tracking of the original elastic model. We also show that the previously
defined control scheme provides uniform ultimate boundedness in the presence of
unstructured bounded disturbances.
