# Is it possible to achieve control of 4 DOF in quadcopter?

I have been looking into non-linear control algorithms for controlling a quadcopter. I know that we have total 6 DOF for a quad (3 translation and 3 rotation) and our input belongs to $\mathbb{R}^4$, i.e. the 4 motor inputs. So if I look at a quad following a specified trajectory $x(t)$, where $x\in \mathbb{R}^3$. Then I am actually controlling only the desired position coordinates. Angles and angular velocity vary such that position is attained, but we don't actually command the angles.

So, my doubt is we have 4-degree input but only 3-degree controlled output. Is it possible to have position tracking along with a particular angle, such as yaw tracking? Controlling 4 states using 4 commands? Am I fundamentally wrong in my reasoning?

Alternatively, in terms of movements being directly actuated, we do have 3-moment torques and a thrust as an input. Would we consider this as 4 DOF command instead?

Any reference or paper would be welcome too.