OK Go Makes Lib Dubs Back
youtube.com
youtube.com
I would imagine they could run some wire out to a bunch of little LEDs (one at each position), and have the LED's light from a simple Raspberry Pi + Arduino setup (then it's just a matter of the umbrella people running to their mark, then opening and closing with the LED).
Any other ideas? Pretty good video.
It looks like the seat bot they used may have been the Asimo U3-X Personal Mobility[1] robot.
[1] http://asimo.honda.com/innovations/u3-x-personal-mobility/