As we have no experience at all at building a balancing robot of any kind, it is prudent that we build a test base for this purpose. The design we have can be found here:

The structure will will consist of 8mm thick laser cut acrylic. Laser cutting is the fastest and most economical prototyping means available to us. The holomonic wheels engages the bowling ball at an angle of 45 degrees, midway between the pole and equator of the ball.

Plates which are about 260mm in diameter are being held together by 10mm diameter spacers made of acrylic rods. Driver and balancing electronics will be mounted on the plate just on top of the stepper motors to minimize cable length. The battery which constitutes a bulk of the weight will be mounted high up for stability (akin to the configuration of an inverted pendulum). We will be using inexpensive Pd acid battery in the beginning which will probably be switched to LiPo in the future.