  Trajectory generation for quadrotors with limited field-of-view sensors has
numerous applications such as aerial exploration, coverage, inspection,
videography, and target tracking. Most previous works simplify the task of
optimizing yaw trajectories by either aligning the heading of the robot with
its velocity, or potentially restricting the feasible space of candidate
trajectories by using a limited yaw domain to circumvent angular singularities.
In this paper, we propose a novel \textit{global} yaw parameterization method
for trajectory optimization that allows a 360-degree yaw variation as demanded
by the underlying algorithm. This approach effectively bypasses inherent
singularities by including supplementary quadratic constraints and transforming
the final decision variables into the desired state representation. This method
significantly reduces the needed control effort, and improves optimization
feasibility. Furthermore, we apply the method to several examples of different
applications that require jointly optimizing over both the yaw and position
trajectories. Ultimately, we present a comprehensive numerical analysis and
evaluation of our proposed method in both simulation and real-world
experiments.
