Physics of a Ballbot

[GeeTwo]

I thought about a BB-8 for a good bit after the movie. I never actually did anything with it outside of mental modeling, but I seem to recall that my last design involved three mutually perpendicular omni wheels, all "above the equator" of the ball. If you get a regular die (chance cube), and imagine one wheel centered on the 1 face, oriented towards the 2 face, another centered on the 2 face oriented towards the 3 face, and the third centered on the 3 face, oriented towards the 1 face, then all rotated so that the corner common to the 1, 2, and 3 faces points up, you should get the idea.

Accelerometers in three mutually perpendicular dimensions are obviously essential. My thinking was that I would orient them with the same axes as the wheels, but I did not think it through very far before moving on to something else.