  This paper addresses the attitude tracking of a rigid body using a quaternion
description. Global finite-time attitude controllers are designed with three
types of measurements, namely, full states, attitude plus constant-biased
angular velocity, and attitude only. In all three scenarios hybrid control
techniques are utilized to overcome the well-known topological constraint on
the attitude manifold, while coupled nonsmooth feedback inputs are designed via
homogeneous theory to achieve finite-time stability. Specially, a finite-time
bias observer is derived in the second scenario and a quaternion filter is
constructed to provide damping in the absence of velocity feedback. The
proposed methods ensure bounded control torques a priori and, in particular,
include several existing attitude controllers as special cases.
