You’re assuming they’re using a linear controller, and they’re way ahead of you [1].

But I don’t think they’re overshooting per se. I think they’re landing the centers in the right place, but the outer pieces account for most of the moment of inertia, and they’re flexible, so the overall assembly is deforming. Deriving the optimal control law for that could be a bit messy. I would guess that it involves bringing the center piece nearly to a stop slightly short of 90 degrees and then gently bringing it the rest of the way.

[1] https://build-its-inprogress.blogspot.com/2017/12/controls-r...

I wonder if slightly overshooting on purpose, then running the motor in reverse for a moment would actually be faster.

They talked about how "mistakes" in the tuning often resulted in exploding cubes. I have a feeling they probably tried that or something like it but it just puts too much stress on the cube.

>> It looks like they have some overshoot on their servos.

Even in simple linear systems with a PID, a bit of overshoot may improve the response time. It's not always desirable but in this case there is no problem with it. I also liked the other commenters idea that perhaps the parts of the cube are moving further than the centers and then falling back in place.

With the right cube, like the one they’ve used, one with fairly large-radius corners on the centre piece and inside corners of the other pieces, you can / should be able to start turning the next face before the current face as come to rest.

Though I suspect the thing might fly apart if timed wrong. That’d be worth watching.

There is indeed a video on YouTube of the cube being turned into pieces. I think it was linked in the Ars Technica article.

Oh, indeed there is. I didn't scroll much past the first video.