Most robots are passively balanced by having multiple wheels on the ground. Walking robots balance actively without active gyros by moving their limbs.

Spacecraft (which most roboticists would call robots) typically orient themselves using a combination of reaction wheels, magnetic torquers and thrusters. The reaction wheels spin rotate the aircraft by “taking” angular momentum into their own rotation. They don’t require a local magnetic field or the expenditure of fuel, so are a nice choice.

> or are there implementations that don't require spinning wheels

Tons of different implementations out there for balancing. Maybe the most common one is the one we humans use, which requires zero wheels :)

Speaking of which, any good videos on how we balance ourselves when standing?

And beyond the muscle mechanics, do we understand what the brain is doing? For example, I find it fascinating that I cannot balance myself on one foot if I close my eyes. So obviously we use some visual cues to balance.

> I cannot balance myself on one foot if I close my eyes.

Skill issue. I'm good at balance sports and can say that balancing on one foot with closed eyes is hard but doable. Just train it :)

"the vestibular system"

How does ours work?

Legs

Some people can balance without legs.

I hope most healthy people are able to sit up without falling forward or backwards.

Input, processing, output.

Sensors, brain, muscle movement.

If you've got 2 wheels side by side like a Segway, all you need is the IMU and those 2 wheels.

True, but for something like this, would it work with a magnet?

This is what you'd need:

https://eu.mouser.com/ProductDetail/TDK-InvenSense/ICM-20948...