I'm developing a small scale cart-pole balancing robot consisting of two wheels driven by a single motor at the base (essentially like a unicycle, but with two wheels to constrain balance to a one dimensional problem).
I'm not sure what qualities to look for in that motor. I think the motor should be able to accelerate quickly in directions opposite of motion as dictated by the control system. However, i'm not sure if this rapid acceleration should correlate with higher torque motors or faster speed motors. I think higher torque motors would be too slow to react to control commands. In contrast, fast speed motors may not be able to overcome the momentum of the cart.
Are there any design equations or other calculations i can make based on my robot's dimensions and weight to determine the right specs needed for my robot's motor? How can i determine the right motor specs for this application without resorting to brute-force trial & error experiments?