lightweight, inexpensive speed controllers

[nuttle]

Bottom line is there's a ton of stuff already done for this particular application and you probably want to at least start with what is readily available and in widespread use. The underlying technology is similar, but you most likely do not want to try to build your own controller -- lots of optimization has already been done, just as for motors for this application. The terminology is different and seems to come from the RC plane/heli world. You want an "ESC" where you ask about motor controller and yes, these use PWM -- same RC background, which is really where PWM came into FRC I suspect. This is how most traditional RC systems send control signals over the air. And the motors need to run directly from the batteries, with the "battery eliminator" to supply power to other electronics that needs different voltage(s).

BTW, the reason for this is the same reason you don't try to regulate the voltage except by turning it on and off very quickly: trying to control voltage other than just on/off means turning power into heat / lower efficiency. You don't want low efficiency in anything that is battery powered, not that you ever really want this in anything besides a heater.