Crude preliminary tests have begun! Using (5) 350 farad maxwell ultracapacitors (in series) charged to 12.6 volts; the robot was released to "bump around" in my workroom. From 12.6 volts to 7.3 volts, the robot ran continuously for over 26 minutes. It could still run longer--probably to about 6.5 volts before starving the processor.

Charging at 4.5 amps takes about 90 seconds to go from 7.3 volts to 12.6. The video above starts at about 8.8 volts and goes to 12.6 in roughly 75 seconds.

What have I learned here?

The steel caster wheel is too noisy!

Motor speed and "bumped into something current" need to be adjusted on the fly as the capacitor voltage declines.

The robot doesn't need to run around continuously like a frenetic little puppy.

So . . . twenty minutes of robot socializing followed by 90 seconds of robot rest seems very doable.