This guy made a sweet little DIY balancing robot that balances without the help of fancy gyroscopes. It’s kind of like a poor man’s version of the Segway-esque A.M.P.bot, the main difference being that this one falls down a lot.
The robot uses a “simple switch as a sensor and stands on only two wheels with inverted pendulum mechanism. When the robot is going to fall the motor starts and moves the robot to the direction it is going to fall, so the motor torque about the center of gravity that is higher than the motor makes the robot balanced.” Check out this video to see it in action.
The maker helpfully put up a tutorial in case you’re inspired to make one of your own! Although I’m not sure why you’d do that, other than to mess with your cat or something.