Last time I saw this posted here, people implemented various auto-pilots for this [0].
Here is a short video of my attempt: https://youtu.be/jWQQH2_UGLw
Given that this simulator supposedly maps closely to the actual interface on the spacecraft, it's funny to imagine SpaceX hooking it up to the real thing and seeing how it fares. Succeed or fail, it would be a pretty wild ride.
This autopilot doesn't use the rotation and translation rates as input, just the momentary values. It also uses the same control function for all axes.
Video: https://youtu.be/jLTr6UwuSd4
definitely not PID control
[1] https://gist.github.com/ggerganov/092b86a59fa34926998953701a...
I saw at least two autopilots that used PID control in a couple of different ways. They all needed tuning though because any moderate control input would send them spiraling off into the void.