  The control of a quadrotor is typically split into two subsequent problems:
finding desired accelerations to control its position, and controlling its
attitude and the total thrust to track these accelerations and to track a yaw
angle reference. While the thrust vector, generating accelerations, and the
angle of rotation about the thrust vector, determining the yaw angle, can be
controlled independently, most attitude control strategies in the literature,
relying on representations in terms of quaternions, rotation matrices or Euler
angles, result in an unnecessary coupling between the control of the thrust
vector and of the angle about this vector. This leads, for instance, to
undesired position tracking errors due to yaw tracking errors. In this paper we
propose to tackle the attitude control problem using an attitude representation
in the Cartesian product of the 2-sphere and the 1-sphere, denoted by
$\mathcal{S}^2\times \mathcal{S}^1$. We propose a non-linear tracking control
law on $\mathcal{S}^2\times \mathcal{S}^1$ that decouples the control of the
thrust vector and of the angle of rotation about the thrust vector, and
guarantees almost global asymptotic stability. Simulation results highlight the
advantages of the proposed approach over previous approaches.
