A Discrete-Time Trajectory Tracking Controller for an Underactuated Quadrotor UAV

In this technical note, the design of a Lyapunov-based trajectory tracking controller is introduced for an underactuated quadrotor unmanned aerial vehicle (QUAV). First, the mathematical dynamics of QUAV are introduced, and then an approximate model is derived using the Euler approximation. Afterward, positive semi-definite Lyapunov functions are introduced for both attitude and position subsystems consid-ering the underactuated structure of the QUAV system. Based on positive semi-definite functions, the discrete-time nonlinear controllers are devised. These designs offer an approach that addresses the complex dynamics of the QUAV by ensuring the asymptotic stability of each subsystem while aiming to achieve the desired performance for the closed-loop system. In conclusion, the numerical simulation works are carried out to demonstrate the viability of the proposed discrete-time controller.