[Nemo]

Let's say you already plan to take the above advice to avoid the various electrical and mechanical problems that can turn your battery power into waste heat. What remains?

You can use bigger gear reductions. That causes your elevator/arm/drive to have slower output speeds, while the motor itself has a faster speed. When the motor is turning faster, it is drawing less current. Drawing less current means not dropping your battery voltage and not hitting the brownout limits.

There are some cases when a bigger gear reduction will actually cause your mechanical output speed to be faster. This is the case when a smaller (faster) gear ratio would put the motor so close to its stall torque that its speed approaches zero.

Fast speeds sound great (and look great on the field when they actually work), but gearing things to go insanely fast isn't always the smartest thing for several reasons:
1) Your mechanical system often won't even start moving until you give it a significant percentage of full power, at which it jerks into fast motion instead of starting up smoothly.
2) You lose the ability to make small, controlled movements because of #1; you're either at nearly full power or nothing
3) You drain your battery a lot faster because it uses more current
4) Any sort of mechanical binding or electrical losses or battery issues can quickly bring your system from "running ok" to "not working at all" since you're pushing the limits pretty hard
5) With the combination of #3 and #4, you often get diminished performance in the tail end of matches as your battery runs down. That's especially painful if endgame is really important.
6) Your motors are producing more heat since they are taking so much more current. This can diminish performance of motors and make them burn out after a while.

You can also make sure your drive train is able to turn well generally. If you have lots of lateral traction in a skid steer drive, and the wheel base is long compared to the track width, you're going to pull a ton of current while turning. And that is compounded if the drive is geared to go really fast already. There are a variety of interesting things to look at in the drive to make it turn well. Drive design is a good topic to research on CD. Since the drive is going to have the most power going to it, making sure it's designed properly is probably the single biggest thing to look at if you don't want to brown out your robot.