Physics of a Ballbot

[Zeromonkey]

Thanks for all the guidance!
I'll try my best to use the information in your document Michael!

Two general thoughts on stabilizing the inverted pendulum:

1) correcting torque required increases as the pendulum leans further from vertical

2) stabilizing is easier if the pendulum is taller and heavier; this is so because height increases the moment of inertia, so that the pendulum leans away from vertical more slowly

So, to determine the torque needed, you must first decide how tall and heavy robot will be, and how far from vertical it will be able to lean without falling.

So, it would be more beneficial to increase the weight of the top of the robot? I have been thinking about trying to make it as light as possible, so the motors didn't have to move too much mass.
In regards to the height, I am expecting to use a basketball as the base of the robot, so the height comes out to about 9.5 inches from the ground, or 4.75 inches from the center of the ball. I am expecting the weight of the robot on top of the ball to be 1-2lbs. It shouldn't be much more than that. As for the max angle, it should be between 15 and 30 degrees.

With this information, I was told many different ways to approach the problem. Some I asked said to consider Kinetic Energy and Potential Energy. Another said to consider angular momentum. Most told me not to really think about this problem in terms of torque. Do you have some suggestions for what my next step should be? Like how to approach it?

Thank you all sooooo much for the help!