I suspect it's simpler than that. I'm rebuilding a 3-axis mill. It'll be a 5-axis mill with ATC when I'm done, so six axes. 30 years ago those were just AC servos. Now? Well, now you you need to start this video at 3:57. Back when I was a strapping young lad the cheaters put something called a "Sabine feedback destroyer" inline with their conference systems. What it did was analyze the signal for what mathematically looked like runaway feedback (the "ringing" you hear sound systems do whenever someone in Hollywood wants to create tension at a High School dance). It would then mathematically apply a filter to the center frequency of that resonance and the feedback goes away. That was over 26 years ago. The difference between electrical and mechanical oscillation is... nonexistent from a programming standpoint. You use the same math to model them. It's all Diff EQ, and if you sample the output and the feedback often enough you can balance a dozen angels on the head of a pin. I'm running Sigma 7s, which run at 3100 Hz. So... every 0.3 microseconds, the servos compare "where am I" to "where am I supposed to be" and adjust accordingly. Turns out, Boston Dynamics uses Yaskawa, too. After that it's all degrees of freedom. Atlas had 28, whatever they're doing now prolly has more. Makes for some yucky math - and I'll bet their "AI" is nothing more than "train the simulator to goal-seek for stability with a few dozen degrees of freedom" and then they just overlay macros on top of that. The happy dances, then, are macro overlays on an armature that fundamentally keeps itself in pose through feedback loops. Here's a guess - a dog's hip joint is pretty easy from a mechanical standpoint. It's got one degree of freedom. That's a planetary, or a harmonic drive. Doesn't matter, I own a half dozen of them. A human's hip joint, however, is a ball joint. Closest you can get to that is a hollow-shaft harmonic drive with a right-angle harmonic drive through the middle. You can get the motion you need that way but it's gonna look like this: https://www.fanuc.eu/~/media/corporate/products/robots/m20/m-20id-12l/m20id12l.png I've been looking at this stuff a lot lately and I gotta say - I dunno how I'd do "hip joint" using mechanicals.but it seems like they're going with "AI" for the low level reflex-type movements.
Personally I have to say the dog-type robots are farther along the uncanny valley - the humanoids have a "chair-shaped-ass" leg and hip posture that isn't threatening and it's hard to dance with such an underdeveloped booty.