The forces involved in double pendulums are very well studied. As other posters have pointed out the robot has sensors on the two pivot points which makes it straight forward to counter the movement (once you have a precise robot, the right force equations and a PHD in physics) once the pendulum enters the required state.

ps I voted you up from you negative state, I don't see a reason for a downvote in your comment.

I know a little physics, and understand that the physics of double-pendulums is well studied (the case where it hangs with a stationary base is a standard grad school dynamics problem), but what little intuition I have tells me it can't work and would just collapse. Would love to see an illustrative/graphical/animated example of how it works.

I love the way the 150 second trial behaves... It makes the task seem effortless. Swinging the arm slowly and deliberately until the double pendulum is above the plane of motion, then quick small motions keep the system straight while longer slower motions swing the now straight system up to equilibrium...

I think it might be possible to do by hand now that I have seen it done like that.