风浪流干扰及参数不确定欠驱动船舶航迹跟踪的滑模鲁棒控制

针对欠驱动船舶的模型参数不确定和外界风浪流干扰问题,为实现水平面的航迹跟踪控制,提出了一种基于上下界的滑模控制方法.首先利用反步法将控制器的设计分解为运动学回路和动力学回路.其次,在运动学回路中为实现位置跟踪误差的收敛,根据期望航迹与当前位置信息,设计船舶的纵向与侧移参考速度,并视为镇定位置误差的虚拟控制律;在动力学回路中,将虚拟控制律作为新的跟踪目标,利用滑模方法设计实际控制律实现对参考速度的跟踪控制,最终实现了欠驱动船舶的跟踪控制.最后对有无干扰下的欠驱动船模分别进行了仿真实验,仿真结果证明了控制律的有效性.     

基于浸入和不变技术的非线性跟踪控制

为实现欠驱动四旋翼飞行器的位置及偏航渐近跟踪,本文基于浸入和不变技术(immersion and invariance,II)提出非线性跟踪控制方法.针对四旋翼飞行器的欠驱动特性,设计了内/外环分别为姿态和位置的双闭环结构,并采用浸入和不变技术构建内/外环的稳定跟踪控制器,利用李雅普诺夫定理保证闭环系统的渐近稳定性.最后,在MATLAB/Simulink环境下进行数值仿真,验证了II控制方案的有效性.     

欠驱动惯性轮摆系统全局滑模控制

针对欠驱动惯性轮摆的镇定控制问题,本文提出了一种新型的滑模鲁棒控制策略,可在系统受到不确定性与外界干扰影响的情况下,实现全局渐近镇定控制.区别于现有方法,本文方法无需切换,且能将无驱动的摆杆摇起至竖直向上位置的同时,确保惯性轮回到初始位置.具体而言,首先对惯性轮摆系统的非线性模型进行非奇异坐标变换,将其变为类积分器形式.随后,根据转换后系统的形式,构造了一种新型的滑模面;经严格分析知,当系统状态处于该滑模面上时,它们将渐近收敛于平衡点.在此基础之上,设计了滑模控制律以确保系统状态始终处于该滑模面上,以实现镇定控制.最后,通过仿真验证了所提控制方法的有效性与鲁棒性,并与现有方法进行了对比.     

基于广义逆的欠驱动航天器姿态机动控制

针对欠驱动刚体航天器机动控制问题,应用广义逆方法设计了姿态机动控制器. 首先将三轴稳定欠驱动航天器动力学和运动学系统分解为三个子系统, 应用微分几何理论将欠驱动航天器子系统转化为逐点线性形式, 并设计了欠驱动航天器子系统渐近稳定控制器,进一步引入了动态尺度广义逆和摄动零控制向量, 实现了对另外两轴的控制.设计的广义逆姿态控制器保证了整个系统的渐近稳定性, 达到了控制要求. 数值仿真实验结果表明了所设计控制律的有效性.     

Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control

A general dynamic model is proposed for describing a large class of nonholonomic systems including extended chained systems, extended power systems, underactuated surface vessel systems etc. By introducing an assistant state variable and a time-varying state transformation based on the concept of minimal dilation degree, this class of nonholonomic systems is transformed into linear time-varying control systems, and the asymptotic exponential stability is thus achieved by using a smooth time-varying feedback control law. The existence and uniqueness of the minimal dilation degree for the discussed systems are also proved under certain conditions.     

A time differences of arrival‐based homing strategy for autonomous underwater vehicles

A new sensor‐based homing integrated guidance and control law is presented to drive an underactuated autonomous underwater vehicle (AUV) toward a fixed target, in 3‐D, using the information provided by an ultra‐short baseline (USBL) positioning system. The guidance and control law is first derived at a kinematic level, expressed on the space of the time differences of arrival (TDOAs), as directly measured by the USBL sensor, and assuming the plane wave approximation. Afterwards, the control law is extended for the dynamics of an underactuated AUV resorting to backstepping techniques. The proposed Lyapunov‐based control law yields almost global asymptotic stability (AGAS) in the absence of external disturbances and is further extended, keeping the same properties, to the case where known ocean currents affect the motion of the vehicle. Simulations are presented and discussed that illustrate the performance and behavior of the overall closed‐loop system in the presence of realistic sensor measurements and actuator saturation. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust Position Stabilization of Underactuated Surface Vessels With Unknown Modeling Parameters Via Simple P/D‐Like Feedback: The Center Manifold Approach

In this work, two smooth time‐invariant control laws are proposed to achieve asymptotic position stabilization of underactuated surface vessels despite modeling parameter uncertainties. The proposed control laws take a strikingly simple linear proportional derivative (PD)‐like feedback form or just a simplest proportional (P)‐like one, where the former relies on measuring the relative position error and surge/yaw velocity and the latter relies on measuring only the relative position error, decreasing or minimizing the sensing cost. The stabilities of the closed‐loop systems for the both control laws are strictly proved via the center manifold approach despite the unknown model parameters. The effectiveness of the proposed control laws is verified by simulation examples.     

欠驱动刚体航天器姿态机动滑模控制研究

针对欠驱动刚体航天器的姿态机动控制问题,提出一种滑模变结构姿态控制器的设计方法.首先给出3轴稳定的欠驱动航天器姿态动力学和运动学模型,分析其模型特点;然后,设计了欠驱动刚体航天器的渐近稳定滑模控制律,并证明了其李雅普诺夫意义下的全局渐近稳定性.最后的仿真结果表明,该方法能够有效实现欠驱动航天器的姿态控制,且系统具有全局稳定性和鲁棒性.     

A Sensor-Based Controller for Homing of Underactuated AUVs

A new sensor-based homing integrated guidance and control law is presented to drive an underactuated autonomous underwater vehicle (AUV) toward a fixed target, in three dimensions, using the information provided by an ultrashort baseline (USBL) positioning system. The guidance and control law is first derived using quaternions to express the vehicle's attitude kinematics, which are directly obtained from the time differences of arrival (TDOA) measured by the USBL sensor. The dynamics are then included resorting to backstepping techniques. The proposed Lyapunov-based control law yields global asymptotic stability in the absence of external disturbances and is further extended, keeping the same properties, to the case where constant known ocean currents affect the dynamics of the vehicle. Finally, a globally exponentially stable nonlinear TDOA and range-based observer is introduced to estimate the ocean current and uniform asymptotic stability is obtained for the overall closed-loop system. Simulations are presented illustrating the performance of the proposed solutions.      

基于自适应滑模的欠驱动无人艇轨迹跟踪控制算法

针对欠驱动水面无人艇在航行过程中存在的海洋环境干扰、数学模型参数不确定、执行器故障等问题,提出了一种基于扰动观测器与神经网络技术的自适应滑模轨迹跟踪策略。在无人艇三自由度模型的基础上,结合视线制导率,提出了一种新的轨迹跟踪制导策略。采用自适应滑模控制技术设计了欠驱动无人艇轨迹跟踪控制器,有效地抑制了执行器衰减故障对无人艇控制系统的影响;同时运用了非线性扰动观测器和自适应径向基函数神经网络分别对无人艇受到的外界干扰和模型参数不确定性进行补偿和拟合,提高了控制系统的抗干扰能力。基于Lyapunov定理证明了所设计的控制系统的稳定性,并在MATLAB中进行了仿真测试。仿真结果表明,所提出的轨迹跟踪控制算法可以在较为复杂的环境下实现对欠驱动无人艇的精准控制;相较于对比算法,位置的平均跟踪误差减小了80%以上,具备较高的稳定性和鲁棒性。     

无人机吊挂空运系统的自适应控制设计

针对四旋翼无人机吊挂空运系统存在的模型不确定性及欠驱动性问题,本文提出了一种基于能量耦合的自适应控制设计.首先,基于能量整形控制方法构造了一种新型的能量存储函数以处理状态耦合.然后利用神经网络对系统未建模动态特性进行在线估计,同时设计参数自适应律在线估计模型中的未知参数,并采用基于符号函数的鲁棒控制算法补偿神经网络的估计误差.本文运用李雅普诺夫方法和拉塞尔不变性原理对闭环系统的稳定性进行了证明,并且证明了负载摆动和无人机位置误差的渐近收敛性.最后,在室内实验平台上进行了飞行实验.实验结果表明,本文提出的非线性控制方法能够在有效抑制吊挂负载摆动的同时,实现无人机位置的精确控制.     

A new formation control of multiple underactuated surface vessels

This work investigates a new formation control problem of multiple underactuated surface vessels. The controller design is based on input-output linearisation technique, graph theory, consensus idea and some nonlinear tools. The proposed smooth time-varying distributed control law guarantees that the multiple underactuated surface vessels globally exponentially converge to some desired geometric shape, which is especially centred at the initial average position of vessels. Furthermore, the stability analysis of zero dynamics proves that the orientations of vessels tend to some constants that are dependent on the initial values of vessels, and the velocities and control inputs of the vessels decay to zero. All the results are obtained under the communication scenarios of static directed balanced graph with a spanning tree. Effectiveness of the proposed distributed control scheme is demonstrated using a simulation example.     

欠驱动船舶的光滑时变指数镇定

船舶水平面运动的欠驱动特性使船舶运动控制的研究具有了新的内涵．本文在船舶水平面运动的运动学及动力学模型基础上,将其演化为二阶系统方程组．针对其欠驱动的特性,借助微分同胚变换及控制输入变换将其转化为两个子系统,分别设计状态反馈控制律,从而得到了原系统的具有指数收敛速率的时变光滑反馈镇定律,实现闭环系统所有状态全局指数收敛至平衡点．该方法可用于欠驱动船舶动力定位或自动泊位控制．最后的仿真试验验证表明本方法是有效的．     

Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method

We present an asymptotic tracking controller for an underactuated quadrotor unmanned aerial vehicle using the sliding mode control method and immersion and invariance based adaptive control strategy in this paper. The control system is divided into two loops: the inner‐loop for the attitude control and the outer‐loop for the position. The sliding mode control technology is applied in the inner‐loop to compensate the unmatched nonlinear disturbances, and the immersion and invariance approach is chosen for the outer‐loop to address the parametric uncertainties. The asymptotic tracking of the position and the yaw motion is proven with the Lyapunov based stability analysis and LaSalle's invariance theorem. Real‐time experiment results performed on a hardware‐in‐the‐loop‐simulation testbed are presented to validate the good control performance of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

Spin-axis stabilisation of underactuated rigid spacecraft under sinusoidal disturbance

Spin-axis stabilisation of spacecraft is a problem of partial stabilisation for non-linear dynamical systems. In this article the analysis of spin-axis stabilisation of underactuated rigid spacecraft in the presence of sinusoidal disturbances is presented. By using the Euler–Poisson form to describe the equations of motion and assuming the disturbances in three axes are decoupled with known frequencies, the paper first studies the problem of the underactuated rigid axisymmetric spacecraft by applying the internal modal principle to eliminate the sinusoidal disturbance. Then the paper turns to the more complicated asymmetric spacecraft, where the boundedness of the angular velocity for the underactuated axis is analysed in detail. The paper also proves the global asymptotic stability of the closed-loop systems for both axisymmetric spacecraft and asymmetric spacecraft by combining the Lyapunov direct method with the LaSalle's theorem. The simulation results show that the proposed control law is effective in the presence of sinusoidal disturbance.     

欠驱动水面机器人变周期全局渐近镇定控制

为了实现欠驱动水面机器人的全局渐近镇定,首先借助微分同胚变换,将欠驱动水面机器人的镇定问题转化成对由两个串级子系统构成的二阶欠驱动系统的镇定问题.针对转换后的系统,本文提出一种光滑的变周期控制方法,以实现对该系统的全局渐近镇定.与已有文献中控制律使用常数周期的方法相比,本文方法根据系统状态实时调整控制律周期,从而提高系统在原点附近的收敛速率.随后,基于上述方法,给出了水面机器人变周期控制算法,实现原系统的全局渐近镇定.最后,仿真对比结果验证所提变周期控制方法的有效性.     

Asymptotic perturbed feedback linearisation of underactuated Euler's dynamics

A unifying methodology is introduced for smooth asymptotic stabilisation of underactuated rigid body dynamics under one and two degrees of actuation. The methodology is based on the concept of generalised inversion, and it aims to realise a perturbation from the unrealisable feedback linearising transformation. A desired linear dynamics in a norm measure of the angular velocity components about the unactuated axes is evaluated along solution trajectories of Euler's underactuated dynamical equations resulting in a linear relation in the control variables. This relation is used to assess asymptotic stabilisability of underactuated rigid bodies with arbitrary values of inertia parameters, and generalised inversion of the relation produces a control law that consists of particular and auxiliary parts. The generalised inverse in the particular part is scaled by a dynamic factor such that it uniformly converges to the Moore–Penrose inverse, and the null-control vector in the auxiliary part is chosen for asymptotically stable perturbed feedback linearisation of the underactuated system.     

Nonlinear asymptotic attitude tracking control of an underactuated 3-degree-of-freedom helicopter using neural network feedforward term

This paper proposes a new asymptotic attitude tracking controller for an underactuated 3-degree-of-freedom (DOF) laboratory helicopter system by using a nonlinear robust feedback and a neural network (NN) feedforward term. The nonlinear robust control law is developed through a modified inner-outer loop approach. The application of the NN-based feedforward is to compensate for the system uncertainties. The proposed control design strategy requires very limited knowledge of the system dynamic model, and achieves good robustness with respect to system parametric uncertainties. A Lyapunov-based stability analysis shows that the proposed algorithms can ensure asymptotic tracking of the helicopter’s elevation and travel motion, while keeping the stability of the closed-loop system. Real-time experiment results demonstrate that the controller has achieved good tracking performance.     

Control of a Class of Underactuated Mechanical Systems Using Sliding Modes

In this paper, we present a sliding mode control algorithm to robustly stabilize a class of underactuated mechanical systems that are not linearly controllable and violate Brockett's necessary condition for smooth asymptotic stabilization of the equilibrium, with parametric uncertainties. In defining the class of systems, a few simplifying assumptions are made on the structure of the dynamics; in particular, the damping forces are assumed to be linear in velocities. We first propose a switching surface design for this class of systems, and subsequently, a switched algorithm to reach this surface in finite time using conventional and higher order sliding mode controllers. The stability of the closed-loop system is investigated with an undefined relative degree of the sliding functions. The controller gains are designed such that the controller stabilizes the actual system with parametric uncertainty. The proposed control algorithm is applied to two benchmark problems: a mobile robot and an underactuated underwater vehicle. Simulation results are presented to validate the proposed scheme.     

Udwadia-Kalaba Equation Based Adaptive Robust Control for Two-wheeled Inverted Pendulum System: Underactuation and Uncertainty

A new adaptive robust control method based on Udwadia-Kalaba(U-K) approach which can be applied to the underactuated system is designed and used to a two-wheeled inverted pendulum system in this paper. We separate this typical underactuated system into two subsystems(forward subsystem and yaw subsystem), which are fully underactuated and actuated. For these different subsystems, we use different control methods. We apply an adaptive robust control method which has been proved many times to the fully actuated subsystem. Based on this adaptive robust method, a new control strategy can be redesigned and applied to the underactuated subsystem by modifying the adaptive law and other things. This adaptive robust control with a leakage-type adaptive law could guarantee the uniform boundedness and uniform ultimate boundedness of the system. Finally, the simulation is executed to demonstrate the advantage and simplicity of the proposed method.