A quad-rotor unmanned aerial vehicle is an under-actuated, strong coupled nonlinear system with parameters uncertainty and unknown external aerodynamic disturbance. The trajectory tracking control system with a nested double-loops structure is designed in this paper according to the coupling characteristic between the attitude angles and translational position. A PD control algorithm is proposed in the translational outer-loop to export the desired attitude signals to the attitude inner-loop. An adaptive backstepping control algorithm is designed in the inner-loop with respect to the uncertain rotational inertia and un-modeled disturbance, while in order to reduce the computational complexity the command filtered approach is introduced into the designing procedure. And finally, the numerical simulation results are presented for the trajectory tracking stabilization of a Quad-rotor, which demonstrates the excellent performance of the proposed control system and illustrate its robustness in face of disturbance and uncertain parameters.
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