[dtengineering]

There is, as far as I can tell, no reason you can't put some significant capacitance across the power input to the Pi, so long as the capacitors are charged by the robot battery. (Dropped to 5V, of course...) The rule doesn't say that you cannot store electrical energy, only that the electrical energy has to come from the battery.

The standard way to power a Pi from a 12V battery is to simply use a car "cigarette lighter" charger. Most of them should contain a 5V switching power supply capable of delivering at least one amp.

I'd say, find an old car charger that you've got kicking around, hook it up to a variable power supply and your Pi, and slowly turn down the voltage on the power supply until the Pi stops.

Jason

P.S. My hope for the year 2040...

"Mum, why did that old guy call the power port a cigarette lighter?"
"Because people used to use that to light cigarettes, dear."
"Yeah, but what's a cigarette?"

Although more likely it will be...

"Mum, did you really have to plug your chargers in to something and use wires?"

or...

"Mum, what is 'USB'?"