Fixed-time trajectory tracking for a quadrotor with external disturbances: A flatness-based sliding mode control approach

Abstract

This study proposes a flatness-based fixed-time sliding mode control strategy to address the trajectory tracking problem for a quadrotor with external disturbances. Based on the differential flatness theory, the underactuated dynamics of the quadrotor is converted to four fully-actuated subsystems. As the velocity information of the desired trajectory cannot be obtained directly in some practical applications, a fixed-time state observer is presented to estimate the velocity of the desired trajectory. In order to enhance the system's robustness, a fixed-time disturbance observer is also constructed to estimate and compensate the lumped disturbances. Based on the fixed-time state observer and disturbance observer, the backstepping technique is utilized to perform the sliding mode controller design process, where a fixed-time differentiator is presented to estimate the virtual control inputs to avoid the problem of “explosion of complexity” suffered by the typical backstepping. The stability analysis is conducted to demonstrate the uniformly ultimately bounded stabilization of the closed-loop system with fixed-time convergence regardless of the initial conditions. Finally, the simulation results validate the superior performance of the proposed control scheme.