I do not understand how tightrope walkers return themselves to equilibrium.
I am not concerned with the direction along the rope or wire where their base can be large, and they are able to move their foot forwards or backwards.
I am thinking about the system through the wire. For simplicity, can we assume the wire is perfectly taut so the contact point is fixed? The walker is a mass (or connected articulated masses) balanced above a point (the wire) to which they are connected by a low friction pivot.
The walker is at equilibrium when their centre of mass is directly above the tightrope.
I've read the top few Google hits. They mention a rod or other device may be carried, to provide a larger moment of inertia that will damp the onset of rotations. They also mention that it lowers the centre of gravity, which will reduce the turning moment that begins rotation. This makes sense and I can see that would help. What they don't mention is how a walker returns themselves to equilibrium once they have moved away from it.
This is probably very confused, but whatever a walker does, they as a whole (system) must conserve centre of mass (and momentum), right? Because of this I don't understand how anything that they can do (moving a leg out, say) can actually make a difference! Any change they make just leaves them with their mass differently spread about but the centre of mass in the same place, and still not at equilibrium.
Standing on one leg
I think that a similar system is at play when I balance on one leg. I've noticed that if I stand on my right leg and force myself out of equilibrium by falling to the right, then I will lift up my left leg to somehow balance myself. Why doesn't conservation ensure that lifting my leg like this simply topples me further to the right?
Given that a tightrope walker can balance, it must surely be possible to build a (compound) inverted pendulum that can balance without moving its ground contact point in the way that these control systems typically do?