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In realistic terms, maybe try getting as big of a battery as possible? maybe a car battery or a really big lipo (very expensive)?
The thing is, batteries running out of juice isn't necessarily a bad thing. The motors get really hot (especially because they are hauling a 150lbs robot around), the compressor needs to catch up (it only has like a 20% ish duty cylce) and it can give you a way to take turns.
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Converted ATX supplies are very realistic. They're designed to provide very consistent power for very sensitive components. The motor will only get severely hot if there is a significant difference between the forward voltage and back EMF. At free speed, the back EMF should match the forward voltage, meaning the motor won't heat up significantly. In other words, OP, don't put any force on the motor, let it spin freely.