  The control task of tracking a reference pointing direction (the attitude
about the pointing direction is irrelevant) while obtaining a desired angular
velocity (PDAV) around the pointing direction using geometric techniques is
addressed here. Existing geometric controllers developed on the two-sphere only
address the tracking of a reference pointing direction while driving the
angular velocity about the pointing direction to zero. In this paper a tracking
controller on the two-sphere, able to address the PDAV control task, is
developed globally in a geometric frame work, to avoid problems related to
other attitude representations such as unwinding (quaternions) or singularities
(Euler angles). An attitude error function is constructed resulting in a
control system with desired tracking performance for rotational maneuvers with
large initial attitude/angular velocity errors and the ability to negotiate
bounded modeling inaccuracies. The tracking ability of the developed control
system is evaluated by comparing its performance with an existing geometric
controller on the two-sphere and by numerical simulations, showing improved
performance for large initial attitude errors, smooth transitions between
desired angular velocities and the ability to negotiate bounded modeling
inaccuracies.
