  In this paper we address the control problem of aerial cable suspended load
transportation, using multiple Unmanned Aerial Vehicles (UAVs). First, the
dynamical model of the coupled system is obtained using the Newton-Euler
formalism, for "n" UAVs transporting a load, where the cables are supposed to
be rigid and mass-less. The control problem is stated as a trajectory tracking
directly on the load. To do so, a hierarchical control scheme is proposed based
on the attractive ellipsoid method, where a virtual controller is calculated
for tracking the position of the load, with this, the desired position for each
vehicle along with their desired cable tensions are estimated, and used to
compute the virtual controller for the position of each vehicle. This results
in an underdetermined system, where an infinite number of drones'
configurations comply with the desired load position, thus additional
constrains can be imposed to obtain an unique solution. Furthermore, this
information is used to compute the attitude reference for the vehicles, which
are feed to a quaternion based attitude control. The stability analysis, using
an energy-like function, demonstrated the practical stability of the system, it
is that all the error signals are attracted and contained in an invariant set.
Hence, the proposed scheme assures that, given well posed initial conditions,
the closed-loop system guarantees the trajectory tracking of the desired
position on the load with bounded errors. The proposed control strategy was
evaluated in numerical simulations for three agents following a smooth desired
trajectory on the load, showing good performance.
