Generalized Huber Loss Function and Gradient Flow Designed Fixed-Time Convergence Trajectory Tracking Controller for Quadcopter

In this paper, a trajectory tracking controller for unmanned aerial vehicles (UAVs) is proposed. The gradient flow method is utilized to design the controller which can make position and velocity errors converge to zero in fixed-time with concise form of equation. In the controller, desired velocity error formula from position error is designed to be a first layer of fixed-time convergence; an error exists between real and desired, which thus needs a second layer of fixed-time convergence to control the error to zero. A generalized Huber loss function combines the advantages of quadratic loss and absolute loss function to increases the stability of the proposed controller in this paper. Several numerical simulations are performed and prove the feasibility and effectiveness of the design.