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.     

饱和输入下四旋翼无人机滑模轨迹跟踪控制

为解决四旋翼无人机在饱和输入下的轨迹跟踪控制问题,同时兼顾系统存在的参数不确定性和外部风力扰动影响,设计了一种改进的抗干扰自适应鲁棒滑模控制方法;基于六自由度架构,设计四旋翼无人机简化的系统模型,进而降低控制器设计的复杂程度;引入带有误差信号的滑模函数,设计带有误差信号的饱和补偿自适应控制律,同时增加鲁棒控制项,降低由于饱和输入问题带来的抖振影响,并减小参数不确定和外部风力扰动对系统稳定性的影响;系统模型与抗干扰自适应控制律相结合,形成了改进的抗干扰自适应鲁棒滑模控制策略,实现四旋翼无人机的位置轨迹和姿态轨迹的稳定跟踪;最后通过数值仿真与传统PD控制算法进行仿真比较,验证控制方法的有效性和优越性。     

Robust Backstepping Control Based on Integral Sliding Modes for Tracking of Quadrotors

Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few. Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances. In these systems, it is preferred a formal control approach whose closed-loop system can predict an acceptable performance since deviations may produce instability and may lead to catastrophic results. Backstepping provides an intuitive solution since it solves underactuation iteratively through slaving the actuated subsystem so as to provide a virtual controller in order to stabilize the underactuated subsystem. However it requires a full knowledge of the plant and derivatives of the state, which it is prone to instability for any uncertainty; and although robust sliding mode has been proposed, discontinuities may be harmful for air- or water-borne nonlinear plants. In this paper, a novel robust backstepping-based controller that induces integral sliding modes is proposed for the Newton–Euler underactuated dynamic model of a quadrotor subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics. The chattering-free sliding mode compensates for persistent or intermittent, and possible unmatched state dependant disturbances with reduced information of the dynamic model. Representative simulations are presented and discussed.     

基于IBC-PID控制的四旋翼轨迹跟踪控制

针对四旋翼飞行器在阵风扰动下的轨迹跟踪控制问题,提出一种结合积分反步法控制与PID控制的混合控制算法.首先,分析了四旋翼飞行器的受力情况,并采用牛顿 欧拉法建立其动力学方程;其次,根据时间尺度原理,将四旋翼飞行器的控制结构分成位置控制回路与姿态控制回路,前者采用积分反步法进行抗干扰控制,后者采用PID控制进行镇定;同时,引入粒子群算法,利用其寻优优势对所设计的控制器参数进行调整;最后,通过一个螺旋线跟踪仿真对本文所提控制算法的有效性进行了验证.仿真结果表明,本文所提算法具有一定的鲁棒性、稳定性与适用性,能够满足四旋翼轨迹跟踪控制的需求.     

输出误差约束下四旋翼无人机预定性能反步控制

针对外界干扰和输出误差约束条件下的四旋翼无人机的跟踪控制问题,提出预定性能反步跟踪控制策略.首先,将四旋翼无人机动力学模型转换为带有外界干扰的严反馈形式;然后,利用反步法设计控制器,通过引入障碍Lyapunov函数保证跟踪误差的预定性能,设计干扰观测器对外界干扰进行估计,并通过滤波器估计姿态子系统中部分虚拟控制输入的导...     

四旋翼无人飞行器的轨迹跟踪与滑模事件驱动控制

四旋翼飞行器作为一个典型的欠驱动的系统,具有强耦合、非线性等特性.针对飞行器外部干扰、和通信资源受限条件下的轨迹跟踪控制问题,进行滑模事件驱动控制方法的研究.首先,分析动力学特性,通过时间尺度分解方法将系统解耦成位置子系统和姿态子系统.其次,将位置子系统转化为严格反馈形式,设计反步滑模控制器,实现位置轨迹稳定跟踪;针对姿态子系统存在时变有界扰动及通信受限,设计滑模事件驱动控制律,在抑制干扰的同时实现对虚拟姿态跟踪指令的跟踪.根据Lyapunov分析方法证明了所设计控制器的稳定性,并通过理论分析证明闭环控制系统不会出现Zeno现象.最后,仿真结果验证了滑模事件驱动控制律在存在外部扰动和通信受限时四旋翼无人飞行器轨迹跟踪的鲁棒性.     

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。     

Tracking of a moving ground target by a quadrotor using a backstepping approach based on a full state cascaded dynamics

In this paper, a tracking controller is formulated for a quadrotor to track a moving ground target. The quadrotor exhibits distinct hierarchical dynamics that allows its position to be controlled by its attitude. This motivates the use of backstepping control on the underactuated quadrotor. Most backstepping architecture controls the quadrotor position and attitude independently, and couples them with inverse kinematics. Inverse kinematics computes the attitude angles required to achieve a desired acceleration. However unmodeled effects are shown to cause inexact inversion resulting in tracking error. The approach proposed in this paper uses a re-formulated full state cascaded dynamics to eliminate the need for inverse kinematics in a full state backstepping control architecture. It is shown that zero steady state error is achieved in the presence of unmodeled aerodynamics effect and wind disturbance despite no integral action. In addition, a backstepping formulation is derived using contraction theory that guarantees the boundedness of state response under bounded disturbances such as wind. This improves the system performance. Numerical simulations are performed using the proposed controller to track a target moving along predefined paths and the results are compared with a benchmark controller derived using inverse kinematics. The results show that the proposed controller is able to achieve better tracking performance under unmodeled aerodynamic effects and wind disturbance as compared with the benchmark controller.     

基于模糊不确定观测器的四旋翼飞行器自适应动态面轨迹跟踪控制

针对具有未知外界扰动和系统不确定性的四旋翼飞行器,提出了一种基于模糊不确定观测器（Fuzzy uncertainty observer,FUO）的自适应动态面轨迹跟踪控制方法.通过将四旋翼飞行器系统分解为位置、姿态角和角速率三个动态子系统,使得各子系统虚拟控制器能够充分考虑欠驱动约束;采用一阶低通滤波器重构虚拟控制信号及其一阶导数,实现四旋翼跟踪控制设计的迭代解耦;设计了一种模糊不确定观测器,用以估计和补偿未知外界扰动与系统不确定性,从而确保闭环系统的稳定性和跟踪误差与其他系统信号的一致有界性.仿真研究验证了所提出的控制方法的有效性和优越性.     

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.     

Dynamic modeling and control for aerial arm-operating of a multi-propeller multifunction aerial robot

We proposed a multi-propeller multifunction aerial robot that is constructed by a quadrotor with two multi-DOF arms to enable aerial robotic operations. This paper addresses the dynamics and control problems for aerial arm-operation. The dynamic modeling considering the coupling between the arms and main-body subsystems is investigated using the Lagrange approach. The dynamics of the system are partitioned into the main-body dynamics, the arm dynamics, and the interaction dynamics. A composite controller consisting of a main-body sub-controller and an arm sub-controller are presented. Each sub-controller is designed based on the partitioned dynamics. The main-body sub-controller is designed using trajectory linearization control technique. This composite controller is appropriate for real-time implementation due to its simplicity. An optimal planning strategy that minimizes the interaction between main-body subsystem and arm subsystem is proposed. Experimental results are presented, verifying the effectiveness of the composite controller.     

基于固定时间扰动观测器的四旋翼无人机轨迹跟踪控制

针对六自由度小型四旋翼无人机在轨迹跟踪控制过程中,单一控制器构成的控制系统存在外部未知干扰,系统的鲁棒性以及轨迹跟踪精度容易产生较大的波动问题,该文章提出了一种基于固定时间扰动观测器的全闭环控制方案,即针对位置与姿态的双闭环控制;首先利用固定时间理论设计了两个扰动观测器,在固定时间内对扰动做出估计并进行补偿;在此观测器对扰动值的精确估计基础之上,设计了两个具有扰动补偿能力的非线性跟踪控制器;李雅普诺夫稳定性理论证明了所述方法的有效性;仿真实验中,为对比所述控制方法的有效性,同时采用传统单一控制器构成的无人机控制系统进行对比分析;在无人机质量为m=1.44 kg、环境重力加速度为g=9.8 m/s2以及其他模型参数一致的前提下,进行大量的仿真实验验证了所提出的基于固定时间扰动观测器的扰动补偿控制系统,能够保证小型四旋翼无人机六自由度受到复杂外部干扰时准确估计出外部干扰值,并实现无人机进行高精度轨迹跟踪控制,且轨迹跟踪精度与抗扰性能皆优于传统单一控制器构成的无人机控制系统.     

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.     

基于微分平滑的四旋翼运输系统轨迹跟踪控制

四旋翼系绳运输系统是一种具有8个自由度和4个控制输入的欠驱动、强耦合、多变量的非线性系统.为建立系统模型,将系统解耦为双质点系绳连接子系统和四旋翼姿态控制子系统,基于广义拉格朗日方程推导出系统的动力学模型.然后利用微分平滑理论证明了系统是以载荷位置和四旋翼偏航角为平滑输出的微分平滑系统.进而在等式限制条件下对平滑输出轨迹进行规划,获得前馈开环控制律.为抑制系统扰动并使跟踪误差收敛于原点,利用微分平滑特性推导出动态内反馈控制器.仿真实验验证了所提方法的有效性.     

基于自适应积分反步的四旋翼飞行器控制*

四旋翼飞行器系统是强耦合,多输入多输出（MIMO）和非线性的。首先,进行动力学建模,考虑模型参数确定与阵风干扰两种情况。接着,提出了一种自适应积分反步控制方法应用于飞行器跟踪期望轨迹。整个控制系统采用双闭环回路结构,内回路用于控制姿态,外回路用于稳定位置。最后,在模型参数确定的情况下,与积分反步法（Integral Backstepping,IB）做实验对比。在模型参数不确定情况下,对飞行器的期望姿态和位移进行跟踪,结果表明,应用自适应积分反步（Adaptive Integral Backstepping,AIB）控制算法的飞行器对外界较强阵风干扰和模型参数不确定具有一定的鲁棒性,能够较为精确地完成轨迹跟踪任务。     

Tracking control of small-scale helicopters using explicit nonlinear MPC augmented with disturbance observers

Small-scale helicopters are very attractive for a wide range of civilian and military applications due to their unique features. However, the autonomous flight for small helicopters is quite challenging because they are naturally unstable, have strong nonlinearities and couplings, and are very susceptible to wind and small structural variations.A nonlinear optimal control scheme is proposed to address these issues. It consists of a nonlinear model predictive controller (MPC) and a nonlinear disturbance observer. First, an analytical solution of the MPC is developed based on the nominal model under the assumption that all disturbances are measurable. Then, a nonlinear disturbance observer is designed to estimate the influence of the external force/torque introduced by wind turbulences, unmodelled dynamics and variations of the helicopter dynamics. The global asymptotic stability of the composite controller has been established through stability analysis. Flight tests including hovering under wind gust and performing very challenging pirouette have been carried out to demonstrate the performance of the proposed control scheme.     

共轴式无人直升机建模与鲁棒跟踪控制

针对共轴式无人直升机非线性、强耦合的动力学特性,本文提出了一种基于动态反馈线性化方法的鲁棒跟踪控制策略.首先根据叶素理论、Pitt-Peters动态入流模型、上下旋翼气动干扰分析建立了共轴式无人直升机的数学模型.然后对于高度-姿态子系统,通过扩展状态变量对其进行了动态反馈线性化,分析了零动态特性.根据内环期望跟踪特性对解耦后的子系统进行极点配置.通过设计鲁棒补偿器实现了对高度与姿态指令的鲁棒跟踪.在此基础上,针对水平面内的位置子系统设计了外环比例微分(proportional-derivative,PD)控制器以实现位置跟踪.最后,通过内环跟踪仿真验证了反馈线性化方法良好的解耦特性,通过干扰条件下的轨迹跟踪仿真验证了所设计控制器具有较好的控制性能与鲁棒性.     

Multivariable sliding mode backstepping controller design for quadrotor UAV based on disturbance observer

This paper deals with the tracking control problem of quadrotor unmanned aerial vehicles (QUAVs) with external disturbances. First, because the QUAV model contains two non-integrity constraints, the dynamic model of the QUAV is decomposed into two subsystems which are independently controlled, so as to reduce controller design complexity. Secondly, the nonlinear disturbance observer (DOB) technique is integrated into a backstepping control method to design the controller for the first subsystem, in which a DOB is applied to estimate the lumped uncertainty. Based on the double power reaching law and the DOB, a multivariable sliding mode control (MSMC) scheme is developed for the second subsystem. Thirdly, based on Lyapunov theory, the closed-loop system is proved to be asymptotically stable. Finally, our comparative simulation results demonstrate that the presented control scheme behaves better in terms of tracking performance than the adaptive backstepping control (ABC) approach.     

具有时变扰动的四旋翼无人机有限时间预定性能控制

针对外界扰动、模型不确定性以及输出误差约束情况下的四旋翼无人机轨迹跟踪问题,提出有限时间预定性能控制策略.首先,将无人机动力学模型解耦为姿态子系统和位置子系统;其次,引入误差转换函数和性能约束函数,通过合理设计快速终端滑模面,实现转换误差有限时间收敛,从而实现原系统输出误差约束控制;进一步,通过稳定性分析可以得出所设计的控制器能够保证系统有限时间稳定,并且具有良好的暂稳态性能;最后,通过实例仿真验证所设计方法的有效性。     

基于HOD的无模型四旋翼RBF滑模控制

为了探索解决在无模型控制算法中如何对系统的未知模型和扰动进行准确估计,提出一种基于高阶微分器(HOD)的无模型RBF神经网络滑模控制器(HODRBFSMC).引入HOD估计系统模型的各阶状态变量,并将系统模型的未知项和外界干扰统一归为总扰动,通过RBF神经网络对总扰动进行估计,并根据Lyapunov定理证明所设计控制器的闭环稳定性.为验证控制器的有效性,所设计的控制器被应用于四旋翼飞行器的轨迹控制,解决其模型参数复杂且飞行过程中易受外界干扰的问题.仿真实验表明,所提出方法能够有效估计并补偿总扰动,其轨迹跟踪能力和抗干扰性能相比PID和高阶微分反馈控制(HODFC)具有一定的优越性,能够很好地满足四旋翼飞行器控制的需求.