I designed this robot to autonomously balance a 1" steel ball on the 10" x 10" green plate. The plate is mounted on a custom-designed universal joint, and actuated along the pitch and roll axis through stepper motors connected by 4-bar linkages. I made it in CAD, and then 3D printed it.
There's a resistive touch pad that measures the ball position, and the plate angle is tracked through counting steps on the stepper motors. Its powered from a 20V supply, that's regulated down for the Arduino that controls it.
I have not yet implement the control system, but the plan is a PID architecture, informed by a physical model of the system based on the dynamics of a ball rolling on an angled plate.