[Isamu]

I was looking for an explanation of how you deal with the fact that quad rotors are under-actuated, and therefore you lack the complete control authority to do any arbitrary motion in space. So path planning has to take this into account, but how is this described?

[the__alchemist]

Pitch and roll are coupled to fwd/back and Left/right respectively. So, you can make it move however you want, but its attitude can't be set independently of its motion. That's a simplification. One consequence is, for example, if you have a fixed camera mounted fwd etc, the angle it looks will correlate with the speed you have it move.

If you are just concerned with moving the center of mass to different locations in space, or have it travel with a specific velocity, you're fine.

This sort of limitation is common vehicles of all sorts; having 4 independent DOF is above average!