Determining maximum current through 18 gauge wire in robot arm
Three things of note:


  The Maximum Amps for Chassis Wiring is also a conservative rating,


The AWG guidelines are very CYA. It says 16A, but that's probably anywhere from 60% to 90% of what it can actually handle.


  but is meant for wiring in air, and not in a bundle.


Multiple 18 gauge wires tied together will have a lower (derated) capacity than a single 18 gauge wire. And in a pipe less than in free air.


  For short lengths of wire, such as is used in battery packs you should trade off the resistance and load with size, weight, and flexibility.


But the biggest thing is really your application! Length is minimal, probably 1 meter (plus return path, so 2 meters), so the wire resistance is minimal, which means very little voltage droop.

But how many power wires are there? Is each motor individually cabled?

Is the full amperage running the full length of the cables? Is the 5 Amps for the computer actually going over the arm, or is it at the base? Can it be individually powered?

What duty cycle is to be expected? How often are the motors going to be on? How long will the entire setup be on?

For the most part, you need a wiring schematic. A plan on how everything is connected. Without that, you cannot really know what you need in terms of wire size. A schematic for the robot arm would be the best place to start.