Rotational Error Metrics for Quadrotor Control

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.