  We consider the hovering control problem for a class of multi-rotor aerial
platforms with generically oriented propellers. Given the intrinsically coupled
translational and rotational dynamics of such vehicles, we first discuss some
assumptions for the considered systems to reject torque disturbances and to
balance the gravity force, which are translated into a geometric
characterization of the platforms that is usually fulfilled by both standard
models and more general configurations. Hence, we propose a control strategy
based on the identification of a zero-moment direction for the applied force
and the dynamic state feedback linearization around this preferential
direction, which allows to asymptotically stabilize the platform to a static
hovering condition. Stability and convergence properties of the control law are
rigorously proved through Lyapunov-based methods and reduction theorems for the
stability of nested sets. Asymptotic zeroing of the error dynamics and
convergence to the static hovering condition are then confirmed by simulation
results on a star-shaped hexarotor model with tilted propellers.
