Distributed fixed-time sliding mode control of time-delayed quadrotors aircraft for cooperative aerial payload transportation: Theory and practice

Abstract

This paper investigates a cooperative fixed-time control for networked-delayed and disturbed quadrotors in payload transportation missions. First, the input time-delayed tracking error system is adequately transformed into a delay-free system via Artstein’s reducing transformation. Second, a novel Distributed Cooperative Fixed-Time Stable Control Protocol (DCFTSCP) is proposed for the multi-quadrotor system to stabilize the geometrical spatial formation while carrying the payload. Furthermore, a disturbance observer is incorporated into the control framework to counteract the lumped disturbances and achieve the transportation task with a minimal swing. Overall, the designed DCFTSCP is able to stabilize the delayed tracking states at the origin in fixed-time uniformly to the Initial Conditions (ICs). It is worth mentioning that the proposed controller belongs to the homogeneous sliding mode control class. The reported related works rely on the bi-limit approximation method to prove the fixed-time convergence of the states. Nevertheless, this method suffers from a crucial shortcoming where it is unable mathematically to provide an explicit expression on the settling (convergence) time. In contrast, in the present study, the stability analysis is thoroughly investigated based on the algebraic Lyapunov tools, namely, Algebraic Lyapunov Equation (ALE) and Lyapunov Quadratic Function (LQF). Consequently, the upper-bound on the convergence-time is explicitly derived for the first time for time-delayed quadrotors aircraft used in cooperative payload transportation. MATLAB® simulations and real flight experiments are conducted to corroborate the theoretical studies of the paper. Overall, the results show that the proposed control protocol yields performance improvement regarding fixed-time tracking stability featuring fast transient, strong robustness, and high steady-state precision. In addition, the undesirable chattering problem of regular linear sliding mode control is noticeably attenuated. Furthermore, unlike conventional terminal sliding mode control techniques, the control input is singularity-free. Finally, several challenging issues in cooperative fixed-time control for networked-delayed quadrotors are highlighted for future research.