  We present a trajectory tracking controller for a quadrotor unmanned aerial
vehicle (UAV) configured on $SU(2)\times R^3$, and relate this result to a
family of geometric tracking controllers on $SO(3)\times R^3$. The theoretical
results are complemented by simulation examples, and the controller is
subsequently implemented in practice and integrated with a simultaneous
localization and mapping (SLAM) system through an extended Kalman filter (EKF).
This facilitates the operation of the UAV without external motion capture
systems, and we demonstrate that the proposed control system can be used for
inventorying tasks in a supermarket environment without external positioning
systems.
