[sjspry]

Yes, you would be able to put a computer directly on the robot. The batteries in the laptop are allowed so long as they only power the laptop, and seeing as it does not control the motors, etc, directly, it is somewhat analogous to a "custom circuit".

Others were talking about using a development board like a BeagleBoard or PandaBoard running linux, in which case you'd have to substitute the libfreenect libraries for the official microsoft ones (which do not have the skeletal tracking system -- but if it is on a robot, we'll assume you didn't need that).