Three‐Dimensional Constrained Tracking Control Via Exact Differentiation Estimator of a Quadrotor Helicopter

In this paper, a constructive method is presented to design a three dimensional trajectory tracking controller that forces a quadrotor helicopter to track a bounded and sufficiently smooth reference trajectory asymptotically in the presence of constant force disturbances. The quadrotor helicopter under consideration has fewer independent thrusters than degrees of freedom to be controlled. Motivated by the vehicle's steering practices, the roll and pitch angles are regarded as virtual controls along with four control forces to fulfill the task of position and yaw angle reference tracking. To prevent position constraint violation, the barrier Lyapunov function (BLF) is employed in the vectorial backstepping procedure to guarantee that the position and attitude constraints are not violated. The backstepping procedure employs an exact and robust sliding mode differentiator of order two to facilitate the implementation of the attitude command signal without calculating the virtual control signal derivative analytically.