Here is a challenge, something I just thought about.
A Segway is a vehicle on two wheels that uses a gyroscope to keep the rider upright, accelerating the motors when the user tilts forward and slows down when leaning back so the rider doesn't fall.
This would create a two wheel robot, but if the motors were mounted at right angles and drive a ball in the opposite way a ball mouse works. One motor drives forwards and back, the other turns the robot clockwise and counter clockwise. If the robot tilts to the left, the motor drives to the right to stabilise.