There's a nice model of a gyro monorail shown in the video here: https://www.youtube.com/watch?v=jGYXJjRfgTM

I may be possible to do the same with Lego Mindstorms - certainly you can make self-balancing two-wheel robots: http://robotsquare.com/2014/07/01/tutorial-ev3-self-balancin...