Barrier Lyapunov function and adaptive backstepping-based control of a quadrotor UAV

Abstract

This paper presents backstepping control and backstepping constraint control approaches for a quadrotor unmanned aerial vehicle (UAV) control system. The proposed methods are applied to a Parrot Mambo drone model to control rotational motion along the $x$ , $y$ , and $z$ axes during hovering and trajectory tracking. In the backstepping control approach, each state of the system controls the previous state and is called “virtual control.” The last state is controlled by the real control input. The idea is to compute, in several steps, a control law that ensures the asymptotic stability of the system. The backstepping constraint control method, based on barrier Lyapunov functions (BLFs), is designed not only to track the desired trajectory but also to guarantee no violation of the position and angle constraints. Symmetric BLFs are introduced in the design of the controller. A nonlinear mathematical model is considered in this study. Based on Lyapunov stability theory, it can be concluded that the proposed controllers can guarantee the stability of the UAV system and the state converges asymptotically to the desired trajectory. To make the control robust, an adaptation law is applied to the backstepping control that estimates the unknown parameters and ensures their convergence to their respective values. Validation of the proposed controllers was performed by simulation on a flying UAV system.

Editorial to the special issue on “Modeling and control of innovative robots”

“…Departing from the concept of fractional order control, in "Fractional Order Inspired Weighted Sum PD-type Feedback in Fixed Point Iteration-based Adaptive Control" [5], a control scheme is proposed that has similar properties as fractional order controllers but a simpler structure. The control of a quadrotor UAV is addressed in "Barrier Lyapunov function and adaptive backstepping-based control of a quadrotor UAV" [6] using barrier Lyapunov functions to account for the constraint satisfaction. A bioinspired single-track mobile robot is reported in the paper "Porcospino, Spined Single-Track Mobile Robot for Inspection of Narrow Spaces" [7].…”

Distributed safe formation tracking control of multiquadcopter systems using barrier Lyapunov function

“… Ganguly (2022) used the BLF technique to design a controller for an N-degrees-of-freedom Euler–Lagrange system and numerically evaluated its effectiveness; this method was recently used for multirobot applications for interagent collision avoidance and tracking using second-order kinematics in two-dimensional cases ( Jin et al, 2021 ). It is worth mentioning that Khadhraoui et al (2023) and Mughees and Ahmad (2023) used BLFs for single quadcopter systems, in addition to Sadeghzadeh-Nokhodberiz and Meskin (2023) , who recently employed BLFs for formation tracking of multiquadcopter systems without considering the collision avoidance problem.…”

Anti-Swing Control for Quadrotor-Slung Load Transportation System with Underactuated State Constraints

“…However, this issue is still an ongoing research topic [21]. Various control strategies, such as the barrier Lyapunov method [22][23][24][25], model predictive control [26,27], adaptive fuzzy control [28,29], and the neuroadaptive learning algorithm [30] have been proposed for state constraint systems. Among these methods, the barrier Lyapunov method exhibits excellent performance on state constraint limitation while ensuring the robustness of the controller.…”

“…Among these methods, the barrier Lyapunov method exhibits excellent performance on state constraint limitation while ensuring the robustness of the controller. It has been applied in various systems, such as high-order nonlinear systems [22,23], variant unmanned aerial vehicles [24], and quadrotor UAVs [25]. However, the existing methods mainly focus on fully actuated systems with output constraints [31] and fullstate constraints [32].…”

“…Control accuracy: Some control strategies [11,24,33,34] for nonlinear systems can only achieve uniformly ultimately bounded results, rather than asymptotic stability. As a result, the control accuracy cannot be assured.…”