  We derived a coordinate-free form of equations of motion for a complete model
of a quadrotor UAV with a payload which is connected via a flexible cable
according to Lagrangian mechanics on a manifold. The flexible cable is modeled
as a system of serially-connected links and has been considered in the full
dynamic model. A geometric nonlinear control system is presented to
exponentially stabilize the position of the quadrotor while aligning the links
to the vertical direction below the quadrotor. Numerical simulation and
experimental results are presented and a rigorous stability analysis is
provided to confirm the accuracy of our derivations. These results will be
particularly useful for aggressive load transportation that involves large
deformation of the cable.
