Indeed, the inverted pendulum is a textbook exercise. This is how cranes work: you don't want the heavy thing at the end of the cable to swing. This is how helicopter-cranes work too, but with added wind. They almost look as if they were nailed to the sky: the only trick is to have fast sensors, which are a given for literally decades now.

The only change is that sensors are manufactured in such large quantities, that they are so cheap that they are omnipresent (ie. almost every phone -- inconceivable decades ago). Quadcopters are also more stable by design than one would think (easier to stabilize than conventional ones).