Composite Hierarchical Anti-Disturbance Control of a Quadrotor UAV in the Presence of Matched and Mismatched Disturbances

Quadrotor helicopter is an unstable system subject to matched and mismatched disturbances. To stabilize the quadrotor dynamics in the presence of these disturbances, the application of a composite hierarchical anti-disturbance controller, combining a sliding mode controller and a disturbance observer, is presented in this paper. The disturbance observer is used to attenuate the effect of constant and slow time-varying disturbances. Whereas, the sliding mode controller is used to attenuate the effect of fast time-varying disturbances. In addition, sliding mode control attenuates the effect of the disturbance observer estimation errors of the constant and slow time-varying disturbances. In this approach, the upper bounds of the disturbance observer estimation errors are required instead of the disturbances’ upper bounds. The disturbance observer estimation errors are found to be bounded when the disturbance observer dynamics are asymptotically stable and the disturbance derivatives and initial disturbances are bounded. Moreover, due to the highly nonlinear nature of the quadrotor dynamics, the upper bounds of a part of the quadrotor states and disturbance estimates are required. The nonlinear terms in the rotational dynamics are considered as disturbances, part of which is mismatched. This assumption simplifies the control system design by dividing the quadrotor’s model into a position subsystem and a heading subsystem, and designing a controller for each separately. The stability analysis of the closed loop system is carried out using Lyapunov stability arguments. The effectiveness of the developed control scheme is demonstrated in simulations by applying different sources of disturbances such as wind gusts and partial actuator failure.     

The Trajectory Tracking Problem of Quadrotor UAV: Global Stability Analysis and Control Design Based on the Cascade Theory

This paper deals with the trajectory tracking problem of a six‐degree of freedom (6‐DOF) quadrotor unmanned aerial vehicle (UAV). The problem of simplified kinematics based on Euler angles is analyzed and the modified Rodrigues parameters (MRPs) technique is introduced to model the rotational dynamics of the rigid body. A nonlinear system error model is established based on the trajectory tracking problem, and, due to the coupling property between the translational and rotational dynamics, we divide the complete closed‐loop system into two reduced‐order subsystems and a coupling term. The Rodrigues theorem is applied to analyze the internal connections between the coupling term and MRPs. Therefore, the global stability conclusions, by which the trajectory tracking controller of the quadrotor UAV could be designed based on the subsystem directly in future works, are proved based on several assumptions of the subsystems. Thereafter, the controllers, using the backstepping approach and nonlinear disturbance observer/sliding mode control approach, which stabilize the quadrotor UAV globally ‐exponentially and globally uniformly bounded, are proposed based on the stability theorem proofs mentioned above. Numerical simulations are provided to show that the theoretical conclusions and the controller proposed are effective.     

On Trajectory Tracking Model Predictive Control of an Unmanned Quadrotor Helicopter Subject to Aerodynamic Disturbances

In this article a model predictive control (MPC) strategy for the trajectory tracking of an unmanned quadrotor is presented. The quadrotor's dynamics are modeled using a hybrid systems approach and, specifically, a set of piecewise affine (PWA) systems around different operating points of the translational and rotational motions. The proposed control scheme is dual and consists of an integral MPC for the translational motions, followed by an MPC scheme for the tracking of the quadrotor's attitude motions. By the utilization of PWA representations, the controller is computed for a larger part of the quadrotor's flight envelope, which provides more control authority for aggressive maneuvering. The proposed dual control scheme is able to calculate optimal control actions with robustness against atmospheric disturbances (e.g. wind gusts) and with respect to the physical constraints of the quadrotor (e.g. maximum lifting forces or fixed thrust limitations in order to extend flight endurance). Extended simulation studies indicate the efficiency of the MPC scheme, both in trajectory tracking and aerodynamic disturbance attenuation.     

Robust nonlinear control of a variable-pitch quadrotor with the flip maneuver

This paper presents robust nonlinear control of a variable-pitch quadrotor with the flip maneuver. Backstepping approach is chosen for nonlinear control design. A control allocation loop dynamically computes the blade pitch angle of each rotor. A systematic method to select controller gains is presented that ensures closed-loop stability. Detailed analysis of the flip maneuver in the presence of input saturation is presented for the first time. Performance of the proposed control law is first verified through simulation. This is then implemented on a PixHawk open source autopilot board and flight tests are performed on an off-the-shelf variable-pitch quadrotor frame.     

Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer

In this paper, we present an extended state observer–based robust dynamic surface trajectory tracking controller for a quadrotor unmanned aerial vehicle subject to parametric uncertainties and external disturbances. First, the original cascaded dynamics of a quadrotor unmanned aerial vehicle is formulated in a strict form with lumped disturbances to facilitate the backstepping design. Second, based on the separate outer‐ and inner‐loop control methodologies, the extended state observers are constructed to online estimate the unmeasurable velocity states and lumped disturbances existed in translational and rotational dynamics, respectively. Third, to overcome the problem of “explosion of complexity” inherent in backstepping control, the technique of dynamic surface control is utilized for trajectory tracking and attitude stabilization, and with the velocity and disturbance estimates incorporated into the dynamic surface control, a robust dynamic surface flight controller that guarantees asymptotic tracking in the presence of lumped disturbances is synthesized. In addition, the stability analysis is given, showing that the present robust controller can ensure the ultimate boundedness of all signals in the closed‐loop system and make the tracking errors arbitrarily small. Finally, comparisons and extensive simulations under different flight scenarios are performed to validate the effectiveness and superiority of the proposed scheme in accurate tracking performance and enhanced antidisturbance capability.     

Trajectory Tracking Control for Quadrotor Robot Subject to Payload Variation and Wind Gust Disturbance

This work proposes a hierarchical nonlinear control scheme for quadrotor to track 3D trajectory subject to payload variation and fast time-varying wind gust disturbance. In terms of dynamics model, the 6 DOF dynamics model with parametric and nonparametric uncertainties is built up. Wind gust and propeller momentum drag model are implemented to quantify the wind impact (force and moment disturbances) on quadrotor. In terms of control design, adaptive robust controller is developed for dynamic subsystem to deal with moment disturbance and estimate the system parameters. Global sliding mode controller is implemented for kinematic subsystem to generate adequate desired attitude angles for tracking the planned 3D trajectory. Simulations and experiments under various conditions are carried out for verification, and the results indicate the effectiveness, adaptiveness and robustness of the control strategy.     

Backstepping Approach for Controlling a Quadrotor Using Lagrange Form Dynamics

The dynamics of a quadrotor are a simplified form of helicopter dynamics that exhibit the same basic problems of underactuation, strong coupling, multi-input/multi-output design, and unknown nonlinearities. Control design for the quadrotor is more tractable yet reveals corresponding approaches for helicopter and UAV control design. In this paper, a backstepping approach is used for quadrotor controller design. In contrast to most other approaches, we apply backstepping on the Lagrangian form of the dynamics, not the state space form. This is complicated by the fact that the Lagrangian form for the position dynamics is bilinear in the controls. We confront this problem by using an inverse kinematics solution akin to that used in robotics. In addition, two neural nets are introduced to estimate the aerodynamic components, one for aerodynamic forces and one for aerodynamic moments. The result is a controller of intuitively appealing structure having an outer kinematics loop for position control and an inner dynamics loop for attitude control. The control approach described in this paper is robust since it explicitly deals with unmodeled state-dependent disturbances and forces without needing any prior knowledge of the same. A simulation study validates the results obtained in the paper.     

四旋翼无人机鲁棒自适应姿态控制

 四旋翼无人机的姿态控制是自主飞行控制的核心,针对四旋翼姿态易受外界环境干扰和内部参数摄动等不确定性影响的问题,设计了一种鲁棒自适应反步控制器,以提高四旋翼的鲁棒性。建立了四旋翼完整的姿态运动模型,并将其转化为含有广义不确定性的多输入多输出非线性系统。根据该系统满足严格反馈的结构特点,设计了反步控制器; 针对系统中存在的外部干扰和内部参数摄动等不确定性,引入了一类鲁棒自适应函数来抵消该不确定性对系统的影响; 采用非线性跟踪微分器估计虚拟控制量的微分信号,减小了反步控制器设计中普遍存在的“计算膨胀”问题; 通过构造Lyapunov 函数证明闭环系统是稳定且指数收敛的。仿真结果表明,所设计控制器具有良好的控制效果和鲁棒性。     

A Novel Robust Attitude Control for Quadrotor Aircraft Subject to Actuator Faults and Wind Gusts

A novel robust fault tolerant controller is developed for the problem of attitude control of a quadrotor aircraft in the presence of actuator faults and wind gusts in this paper. Firstly, a dynamical system of the quadrotor taking into account aerodynamical effects induced by lateral wind and actuator faults is considered using the Newton-Euler approach. Then, based on active disturbance rejection control (ADRC), the fault tolerant controller is proposed to recover faulty system and reject perturbations. The developed controller takes wind gusts, actuator faults and measurement noises as total perturbations which are estimated by improved extended state observer (ESO) and compensated by nonlinear feedback control law. So, the developed robust fault tolerant controller can successfully accomplish the tracking of the desired output values. Finally, some simulation studies are given to illustrate the effectiveness of fault recovery of the proposed scheme and also its ability to attenuate external disturbances that are introduced from environmental causes such as wind gusts and measurement noises.      

Nonlinear robust control of a quadrotor helicopter with finite time convergence

In this paper, the control problem for a quadrotor helicopter which is subjected to modeling uncertainties and unknown external disturbance is investigated. A new nonlinear robust control strategy is proposed. First, a nonlinear complementary filter is developed to fuse the raw data from the onboard barometer and the accelerometer to decrease the negative effects from the noise associated with the low-cost onboard sensors Then the adaptive super-twisting methodology is combined with a backstepping method to formulate the nonlinear robust controller for the quadrotor''s attitude angles and the altitude position. Lyapunov based stability analysis shows that finite time convergence is ensured for the closed-loop operation of the quadrotor''s roll angle, pitch angle, row angle and the altitude position. Real-time flight experimental results, which are performed on a quadrotor flight testbed, are included to demonstrate the good control performance of the proposed control methodology.     

Robust attitude controller design for miniature quadrotors

This paper addresses the robust attitude control problem of miniature quadrotors. A simplified linear dynamical model is obtained for each attitude angle, whereas nonlinear dynamics, interaxis coupling, parameter perturbations, and external disturbances are considered as uncertainties. For each channel, a linear time‐invariant and decoupled robust controller are proposed based on a linear reduced‐order observer and a robust compensator. The observer is applied to estimate the angular velocities, and the robust compensator is introduced for reducing the effects of uncertainties. It is proven that the estimation errors of angular velocities and angular tracking errors can converge to the given neighborhood of the origin in a finite time. Experimental results on the miniature quadrotor are presented to verify the effectiveness of the proposed control approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Nonlinear robust adaptive Cartesian impedance control of UAVs equipped with a robot manipulator

In this paper, a new nonlinear robust adaptive impedance controller is addressed for Unmanned Aerial Vehicles (UAVs) equipped with a robot manipulator that physically interacts with environment. A UAV equipped with a robot manipulator is a novel system that can perform different tasks instead of human being in dangerous and/or inaccessible environments. The objective of the proposed robust adaptive controller is control of the UAV and its robotic manipulator’s end-effector impedance in Cartesian space in order to have a stable physical interaction with environment. The proposed controller is robust against parametric uncertainties in the nonlinear dynamics model of the UAV and the robot manipulator. Moreover, the controller has robustness against the bounded force sensor inaccuracies and bounded unstructured modeling (nonparametric) uncertainties and/or disturbances in the system. Tracking performance and stability of the system are proved via Lyapunov stability theorem. Using simulations on a quadrotor UAV equipped with a three-DOF robot manipulator, the effectiveness of the proposed robust adaptive impedance controller is investigated in the presence of the force sensor error, and parametric and non-parametric uncertainties.     

基于PD-ADRC的四旋翼控制器设计

针对四旋翼无人机强耦合、非线性的控制难点,研究设计了一种基于自抗扰控制和比例微分控制的双闭环控制器。首先,分析了小型四旋翼飞行器动力学模型,确定四旋翼无人机的六自由度方程。然后,利用自抗扰控制技术对强耦合、非线性的姿态模型进行了解耦,设计扩张状态观测器对其总扰动进行观测与补偿。其次,设计比例微分控制器对解耦后的系统进行位置跟踪,从而与姿态控制器组成双闭环系统。最后,通过仿真及试飞实验测试系统性能。仿真和试飞结果表明该系统能够完成对控制指令的实时跟踪,并且对干扰具有极强的抑制力。     

Hard Real-Time Implementation of a Nonlinear Controller for the Quadrotor Helicopter

A hard real-time implementation on a single processor of a nonlinear controller for trajectory tracking of the quadrotor helicopter is presented. An inertial measurement unit and an Optitrack positioning system provide the necessary state measurements. The nonlinear controller has been previously published, so that, this paper focuses on the details of its onboard implementation. In particular, we propose a hard real-time algorithm, a method to identify the aerodynamic characteristics of the actuators and a procedure to tune the nonlinear control gains. Flying tests are presented to illustrate the performance of the quadrotor closed loop dynamics.     

Nonlinear and Adaptive Intelligent Control Techniques for Quadrotor UAV – A Survey

Parametric uncertainties and coupled nonlinear dynamics are inherent in quadrotor configuration and infer adaptive nonlinear approaches to be used for flight control system. Numerous adaptive nonlinear and intelligent control techniques, which have been reported in the literature for designing quadrotor flight controller by various researchers, are investigated in this paper. As a priori, each conventional nonlinear control technique is discussed broadly and then its adaptive/observer based augmentation is conferred along with all possible variants. Among conventional nonlinear control approaches, feedback linearization, backstepping, sliding mode, and model predictive control, are studied. Intelligent control approaches incorporating fuzzy logic and neural networks are also discussed. In addition to adaption based parametric uncertainty handling, various other aspects of each control technique regarding stability, disturbance rejection, response time, asymptotic, exponential and finite time convergence etc., are discussed in sufficient depth. The contribution of this paper is the provision of detailed and in depth discussion on quadrotor nonlinear control approaches to the flight control designers.     

A new smooth robust control design for uncertain nonlinear systems with non-vanishing disturbances

In this paper, we consider the control problem for a general class of nonlinear system subjected to uncertain dynamics and non-varnishing disturbances. A smooth nonlinear control algorithm is presented to tackle these uncertainties and disturbances. The proposed control design employs the integral of a nonlinear sigmoid function to compensate the uncertain dynamics, and achieve a uniformly semi-global practical asymptotic stable tracking control of the system outputs. A novel Lyapunov-based stability analysis is employed to prove the convergence of the tracking errors and the stability of the closed-loop system. Numerical simulation results on a two-link robot manipulator are presented to illustrate the performance of the proposed control algorithm comparing with the layer-boundary sliding mode controller and the robust of integration of sign of error control design. Furthermore, real-time experiment results for the attitude control of a quadrotor helicopter are also included to confirm the effectiveness of the proposed algorithm.     

Nonlinear robust state feedback control system design for nonlinear uncertain systems

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.     

基于AFSMC算法的四旋翼飞行器控制策略研究

针对四旋翼飞行器在飞行过程中,控制系统存在非线性、强耦合、不确定性和鲁棒性差的问题,建立了关于四旋翼飞行器的动力学数学模型,将自适应控制、模糊控制和滑模控制相结合,提出基于自适应模糊滑模控制(AFSMC)的快速平稳控制策略。采用模糊系统推理方法实现理想控制律的逼近。在满足李雅普诺夫稳定性条件的前提下进行控制器的设计和稳定性分析,并结合四旋翼的数学模型和给定参数进行了MATLAB仿真。仿真结果表明,AFSMC控制器相比常规PID控制器具有良好的动态性能和抗干扰能力。     

输入饱和与姿态受限的四旋翼无人机反步姿态控制

本文针对四旋翼无人机研究了鲁棒反步姿态控制策略.由于四旋翼无人机结构复杂,其非线性数学模型难以精确建立,因此在控制器设计过程中需要综合考虑模型不确定性、未知外部干扰、输入饱和以及姿态受限等因素.针对模型中的不确定项,使用神经网络进行逼近;对于外部未知干扰,使用非线性干扰观测器进行补偿;使用双曲正切函数逼近饱和函数,解决输入饱和问题;同时使用界限Lyapunov函数设计控制器,确保姿态满足限制条件.最后,设计四旋翼无人机反步姿态控制器,并根据Lyapunov稳定性定理证明了闭环控制系统的有界稳定.仿真结果表明了所研究控制方法的有效性.