One way to balance a table
We can use two mini-vehicles along the axes of a square table.
We simply run the two mini-vehicles linearly inside the table on tracks,
(one on top of the other, so they don't bump into each other).
One mini-vehicle compensates for shifting weight along one axis,
the other compensates for shifting weight along the orthogonal axis.
A nice thing about this strategy is that the control can be very simple; there is no need for computer software in the control loop. Each of the two tilt sensors can simply drive the voltage (through a suitable conditioning curve) of the motor that powers the corresponding mini-vehicle.
You can see the principle in the java applet to the left, which shows a schematic top view. Try dragging the blue "weight" around with your mouse, and watch the two red mini-vehicles slide so as to counterbalance the table.