You will need a really nice servo for that-- something with good torque, capable of good speed and acceleration , and a precise encoder with a very good motor driver...
The video is of a similar project called "DJ I Robot" by Chris Csikszentmihályi and his research group, aka the MIT Media Lab's Computing Culture group. Check out the pictures, and the videos of it in action, as his group has done essentially the same thing. There's another video of it posted on the
site, and there is also a link below to the artist's site.
They use a custom-designed PID (proportional-integral-derivative) motor controller. This is sort of the rolls royce of motor controller designs and performance, especially considering who has designed it.
They have photos, block diagrams, etc online at this address
. Considering the design costs, time and complexity, you might be better off financially to modify a commercially available unit. There must be something around that already does this. Failing that, just plop down a stack of cash (500 each?) for some nice commercially designed and matched motors/drivers/encoders. Then you only task is writing some code to link the drivers to your software. Contrary to popular belief, good motor driver design is really complex, especially in a case like this.. which makes 500 for something that works perfectly kind of a bargain.