The quadcopter model here is a higher dimensional, more realistic implementation of actual flight using multi-rotorcraft than the Planar Bi-Rotor Helicopter model. Though it is still considered to be an underactuated model relative to the full $SE(3)$ state dynamics model, if the output states are restricted to be the 3D position and the yaw, then the model becomes fully actuated. The pitch and roll dynamics become passive variables implicitly determined by the trajectory taken or being followed. Many physically motivated mobile robot systems have this property, which is known as differential flatness. Control designers and roboticists have taken advantage of the differential flatness property to design nonlinear controllers for quadcopters that have better stabilization properties than their linear counterparts.

NEED TO ADD EQUATIONS HERE.

For sure you need to be careful with these references. In addition to different reference frame conventions between Aerospace engineers and others, plus different ways of representing the $SE(3)$ Lie group state, there are actually slightly different dynamical equations for the quadcopter. The references below just give some idea for how static controllers are synthesized for these systems. The model chosen depends on what the authors wish to demonstrate or what kinds of constraints their control method has.

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