  We consider the problem of controlling an aerial robot connected to the
ground by a passive cable or a passive rigid link. We provide a thorough
characterization of this nonlinear dynamical robotic system in terms of
fundamental properties such as differential flatness, controllability, and
observability. We prove that the robotic system is differentially flat with
respect to two output pairs: elevation of the link and attitude of the vehicle;
elevation of the link and longitudinal link force (e.g., cable tension, or bar
compression). We show the design of an almost globally convergent nonlinear
observer of the full state that resorts only to an onboard accelerometer and a
gyroscope. We also design two almost globally convergent nonlinear controllers
to track any sufficiently smooth time-varying trajectory of the two output
pairs. Finally we numerically test the robustness of the proposed method in
several far-from-nominal conditions: nonlinear cross-coupling effects,
parameter deviations, measurements noise and non ideal actuators.
