  We analyze and experimentally compare various rotational error metrics for
use in quadrotor controllers. Traditional quadrotor attitude controllers have
used Euler angles or the full rotation to compute an attitude error and scale
that to compute a control response. Recently, several works have shown that
prioritizing quadrotor tilt, or thrust vector error, in the attitude controller
leads to improved position control, especially in situations with large yaw
error. We provide a catalog of proposed rotational metrics, place them into the
same framework, and show that we can independently reason about and design the
magnitude of the response and the direction of the response. Existing
approaches mainly fall into two categories: (1) metrics that induce a response
in the shortest direction to correct the full rotation error and (2) metrics
that combine a response in the shortest direction to correct tilt error with
the shortest direction to correct yaw error. We show experimental results to
highlight the salient differences between the rotational error metrics. See
https://alspitz.github.io/roterrormetrics.html for an interactive simulation
visualizing the experiments performed.
