[Gdeaver]

You might do some research on inverted pendulums. This would give you some of the math and algorithms you'll need. There's allot on the web since biped robots have become popular. The basic stamp is kind of limited. there are better choices for processors and programming when you need fast response. Have you looked at adding a gyroscope to stabilize the platform?
The problem with gyroscopic stabilization is not so much getting the mass up to the required speed as it is containing the fragments if and when it fails. Tilt sensors that are not influenced by acceleration are available but, they will hurt the bank account. May be if you used 2 IR distance senors on the front and rear you could subtract the outputs and have the error to plug into the control system. This would work on smooth floors. Maybe that Segway isn't too expensive.