This paper presents the design, analysis, and implementation of an adaptive backstepping controller for underactuated quadrotors to track time-varying trajectories with parameter uncertainties. Quadrotor systems are subject to complicated non-linearity and coupling dynamics, so the ignorance of parameter uncertainties may cause performance degradation and even instability. With the concept of nominal input, the uncertain mass and inertia are decoupled from the lifting force and moment torque. By utilizing the backstepping technique, the design procedure with adaptive laws for dynamic parameters is proposed to ensure stability and convergence of tracking errors to the origin asymptotically. The proposed control scheme is extended to control a quadrotor with velocity motor input while the motor coefficients and geometric parameters are handled by the adaptive laws. A trajectory generation for the proposed adaptive tracking controller is addressed subsequently. The proposed controller requires only the position and orientation of the quadrotor with the twice-differentiable trajectories, while previous work demanded acceleration information. Simulation and experimental results are illustrated to show the efficacy of tracking performance for object transportation.
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