This paper investigates the problem of attitude stabilization for a quadrotor unmanned aerial vehicle (UAV) in the presence of parametric uncertainties, control input saturation and external disturbances. Two robust adaptive control strategies, i.e. bounded adaptive control (BAC) and asymptotical adaptive control (AAC) are developed, respectively, where the construction of saturation auxiliary system and the design of adaptive laws for parameters and disturbance's bound are considered. As a result, the compensation of input saturation, the estimation of physical parameters and the suppression of external disturbance are achieved. In BAC, the real attitude tracking error is guaranteed to converge to a neighborhood of zero, and its transient performance is constrained to an explicit bounded range. In AAC, the real attitude tracking error is proved to be asymptotically stable, and its transient bound in terms of $L_{2}$ norm is derived by constructing an auxiliary equation, which is a computable bound. The simulation is carried out to verify the robustness and effectiveness of the proposed two control techniques.

The Rotary Inverted Pendulum (RIP) is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge. Despite the implementation of various control strategies to maintain equilibrium, optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive. Existing methods frequently rely on extensive experimental data or the designer’s expertise, presenting a notable drawback. This paper proposes a novel tracking control approach for RIP, utilizing a Linear Quadratic Regulator (LQR) in combination with a reduced-order observer. Initially, the RIP system is mathematically modeled using the Newton-Euler-Lagrange method. Subsequently, a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states. This approach enhances the controller’s robustness by eliminating differential terms from the observer, thereby attenuating unknown disturbances. Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below 50 Hz and achieve precise tracking below 1.4 rad, validating the effectiveness of the proposed control scheme.

Considering the problems of unknown external disturbances and parametric uncertainties in attitude tracking of a quadrotor, a backstepping sliding mode control method based on the time-varying gain extended state observer is proposed in this article. First, the mathematical model of the attitude system of the quadrotor is introduced. Second, a time-varying gain extended state observer is proposed to observe the unmeasurable states, total disturbance, and reduce the “peaking value” phenomenon, which often occurs in traditional linear extended state observers. It is proved that the observation errors are bounded. Third, a novel controller synthesized by backstepping sliding mode control method and the time-varying gain extended state observer is proposed for the attitude system of the quadrotor. Moreover, the designed controller can ensure that all signals of the closed-loop system are bounded. Finally, the effectiveness and superiority of the proposed control method are verified by simulation.

In this brief, the estimates of the upper bound of disturbance and all physical parameters of attitude dynamics of quadrotor system are considered, respectively. By virtue of the estimation result of the upper bound, any prior information of disturbance are not required in the construction of quadrotor controller. To compensate for saturation effect, an adaptive second-order saturation auxiliary system based on the parameter estimation result is proposed. Furthermore, a robust attitude trajectory tracking controller based on sliding mode approach is presented to guarantee that the defined tracking error is stabilized asymptotically. The bound of real transient attitude tracking error in terms of L2 norm is derived by designing an auxiliary equation. Finally, simulations are carried out to illustrate the effectiveness of the proposed controller.