Unbelievable balancing robot - stabilizes an articulated inverted pendulum 
The guy whose thesis this was comments on it here: <a href="http://www.reddit.com/r/math/comments/ebql6/double_inverted_pendulum_crosspost_from_rphysics/" rel="nofollow">http://www.reddit.com/r/math/comments/ebql6/double_inverted_...</a><p>I had guessed they were using visual sensing because of how the two halves of the pendulum were painted in contrasting, bright colors, but I was wrong. There are angular sensors at the joints of the pendulum, and a position sensor in the wagon at the bottom. The control system also needs the velocities of the parts of the pendulum, which it gets through a state observer (<a href="http://en.wikipedia.org/wiki/State_observer" rel="nofollow">http://en.wikipedia.org/wiki/State_observer</a>).<p>The interesting part for me was how the control system stands the pendulum up: it figures out the potential energy the pendulum will have when upright, then jerks the wagon around to add that amount of energy into the system as kinetic energy, then guides the system around a constant-energy landscape until it's upright. Pretty clever!