Nonlinear homogeneous sliding mode approach for fixed-time robust formation tracking control of networked quadrotors

Abstract

A formation flight control algorithm for a multi-agent system composed of a group of perturbated quadrotors is thoroughly investigated in this paper. Both theoretical and practical aspects are addressed in detail to design and implement the control algorithm in a distributed fashion among the networked agents. By adopting the sliding mode framework: (i) A novel Nonlinear Homogeneous Nonsingular Terminal Sliding Surface (NHNTSS) is designed. To ensure Global Asymptotic Stability (GAS) as well as fixed-time convergence of the states, the sliding surface design skillfully employs the generalized weighted homogeneity theory. (ii) A novel Distributed Fixed-Time Continuous Nonsingular Control Protocol (DFCNCP) is proposed for the position-loop of each quadrotor agent by utilizing the designed NHNTSS. Moreover, the control scheme comprises a disturbance observer to compensate for the lumped disturbances affecting the position dynamics and estimate the unmeasurable linear velocities of the quadrotors. Overall, the synthesized controller can drive the formation tracking errors into close vicinity of the origin in fixed-time uniformly to the values of the Initial Conditions (ICs), i.e., initial positions of the quadrotors in the 3D state-space. The mathematical proofs based on the bi-limit approximation in the existing related works can only indicate that the system is guaranteed to be fixed-time stable without any estimation of the settling (convergence) time. In contrast, rigorous stability analyses are conducted in the present work by virtue of algebraic Lyapunov tools, i.e., Algebraic Lyapunov Equation (ALE) and Lyapunov Quadratic Function (LQF). Thus, an expression of the upper-bound on the settling-time is given explicitly. Numerical simulations and real experiments in the form of exhaustive comparative studies are carried out to validate the findings of this research work. Overall, the obtained results confirm the superiority of the proposed control strategy in terms of uniform fast fixed-time convergence, strong disturbance rejection, chattering alleviation, and control precision.