  This dissertation presents nonlinear tracking control systems for quadrotor
unmanned aerial vehicles (UAV) under the influence of uncertainties. Assuming
that there exist unstructured disturbances in the translational dynamics and
the attitude dynamics, a geometric nonlinear adaptive controller is developed
directly on the special Euclidean group. In particular, a new form of an
adaptive control term is proposed to guarantee stability while compensating the
effects of uncertainties in quadrotor dynamics. Next, 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 asymptotically stabilize
the position of the quadrotor while aligning the links to the vertical
direction below the quadrotor. Finally, we focused on the dynamics and control
of arbitrary number of quadrotor UAVs transporting a rigid body payload. The
rigid body payload is connected to quadrotors via flexible cables. It is shown
that a coordinate-free form of equations of motion can be derived for arbitrary
numbers of quadrotors and links according to Lagrangian mechanics on a
manifold. A geometric nonlinear controller is presented to transport the rigid
body to a fixed desired position while aligning all of the links along the
vertical direction. Numerical simulation and experimental results are presented
and rigorous mathematical stability analysis are provided. These results will
be particularly useful for aggressive load transportation that involves large
deformation of the cable.
