  This paper shows that the dynamics of a general class of aerial manipulators,
consist of an underactuated multi-rotor base with an arbitrary k-linked
articulated manipulator, are differentially flat. Methods of Lagrangian
Reduction under broken symmetries produce reduced equations of motion whose key
variables: center-of-mass linear momentum, vehicle yaw angle, and manipulator
relative joint angles become the flat outputs. Utilizing flatness theory and a
second-order dynamic extension of the thrust input, we transform the mechanics
of aerial manipulators to their equivalent trivial form with a valid relative
degree. Using this flatness transformation, a quadratic programming-based
controller is proposed within a Control Lyapunov Function (CLF-QP) framework,
and its performance is verified in simulation.
