Homography-Based Visual Servo Control With Imperfect Camera Calibration

In this technical note, a robust adaptive uncalibrated visual servo controller is proposed to asymptotically regulate a robot end-effector to a desired pose. A homography-based visual servo control approach is used to address the six degrees-of-freedom regulation problem. A high-gain robust controller is developed to asymptotically stabilize the rotation error, and an adaptive controller is developed to stabilize the translation error while compensating for the unknown depth information and intrinsic camera calibration parameters. A Lyapunov-based analysis is used to examine the stability of the developed controller.      

An observer‐based output feedback robust MPC approach for constrained LPV systems with bounded disturbance and noise

The present paper addresses an observer‐based output feedback robust model predictive control for the linear parameter varying system with bounded disturbance and noise subject to input and state constraints. The main contribution is that the on‐line convex optimization problem not only simultaneously optimizes the observer and controller gains to stabilize the augmented closed‐loop system but also incorporates the refreshment of bounds of the estimation error set. The optimization problem steers the nominal augmented closed‐loop system to converge to the origin, and the real augmented closed‐loop system bounded within robust positive invariant set converges to a neighborhood of the origin such that recursive feasibility of the optimization and robust stability of the controlled system are ensured. Two numerical examples are given to illustrate the effectiveness of the method.     

On input‐to‐state stability of rigid‐body attitude control with quaternion representation

The concept of input‐to‐state stability (ISS) is important in robust control, as the state of an ISS system subject to disturbances can be stably regulated to a small region around the origin. In this study, the ISS property of the rigid‐body attitude system with quaternion representation is thoroughly investigated. It has been known that the closed loop with continuous controllers is not ISS with respect to arbitrarily small external disturbances. To deal with this problem, hybrid proportional‐derivative controllers with hysteresis are proposed to render the attitude system ISS. The controller is far from new, but it is investigated in a new aspect. To illustrate the applications of the results about ISS, 2 new robust hybrid controllers are designed. In the case of large bounded time‐varying disturbances, the hybrid proportional‐derivative controller is designed to incorporate a saturated high‐gain feedback term, and arbitrarily small ultimate bounds of the state can be obtained; in the case of constant disturbances, a hybrid adaptive controller is proposed, which is robust against small estimate error of inertia matrix. Finally, simulations are conducted to illustrate the effectiveness of the proposed control strategies.     

基于干扰观测器的一类奇异系统H∞控制

提出了一种基于干扰观测器的奇异系统鲁棒H_∞控制方法.外部干扰广泛存在于奇异系统中,为了降低其对系统的影响,设计了一种奇异系统干扰观测器以估计系统干扰.然后给出闭环系统相容的条件,设计一种基于干扰观测器的鲁棒控制器,并基于李雅普诺夫稳定性理论证明了闭环系统的渐近稳定性,通过设计指标函数得到闭环系统具有鲁棒性能的条件.相对于传统鲁棒控制方法,基于干扰观测器的方法降低了系统设计的保守性.最后,通过仿真实验验证了所提出方法的正确性和有效性.     

直线伺服系统非线性自适应鲁棒控制器的优化设计

对永磁直线电动机伺服系统提出了非线性自适应鲁棒控制器的优化设计方法.在系统非线性数学模型的基础上,建立了误差系统的动态模型.将跟踪和干扰抑制归结为非线性自适应鲁棒控制器的设计问题,通过构造存储函数得到自适应鲁棒控制器的定理,以及电阻和电感的辨识算法.证明了定理给出的控制器能满足干扰抑制和系统渐近稳定,并用遗传算法对控制器的参数进行优化.仿真结果验证了该方法是有效的.     

基于对偶四元数的机器人方位与手眼关系同时标定方法

针对相机姿态估计及机器人运动学正解存在测算偏差时,手眼标定及机器人坐标系-世界坐标系标定结果不能准确收敛到全局最优解的问题,提出了一种基于对偶四元数理论的机器人方位与手眼关系同时标定方法.该方法首先将标定方程中坐标系刚体变换关系用螺旋轴、旋转角度和平移量参数化表示,再结合全局优化算法对平移量进行优化.搭建了PUMA560机器人数值仿真系统和工业机器人实测实验平台,将该方法与经典的四元数和对偶四元数标定方法进行了比较分析.仿真和实测结果表明,在相机姿态估计及机器人运动学正解存在测量误差的情况下,该方法无需初值估计和数据筛选依然可以保证求解结果的最优性.     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust sliding mode‐based extremum‐seeking controller for reaction systems via uncertainty estimation approach

This paper deals with the design of a robust sliding mode‐based extremum‐seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input–output linearizing method with variable‐structure feedback, such that the closed‐loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum‐seeking control algorithms, the control scheme includes a dynamic modelling‐error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient‐based optimization algorithm. Practical stabilizability for the closed‐loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

基于Youla参数化的动态随机系统最小误差熵控制

针对具有随机干扰的动态系统,提出一种最小误差熵控制方法。基本思想是应用Youla参数化公式构建具有闭环稳定性的反馈控制策略。其中Renyis熵被作为跟踪误差信息以测度闭环系统的不确定性,Youla参数被优化以使闭环系统误差熵最小,且一个仿真实例也表明了所提算法的有效性。     

A two‐degree‐of‐freedom ℋ︁∞ control design method for robust model matching

We propose an ??_∞ controller design method which achieves a closed‐loop transfer function equal or otherwise sensibly close to a desired transfer function, viz. a model reference design. The proposed controller design method inherits the model reference feature of the internal model control design method and incorporates the weighting scheme of the ??_∞ loop‐shaping. It utilizes Youla–Kucera parameterization in a two‐degree‐of‐freedom scheme to achieve robust model reference and high performance design while ensuring a sensible robust stability margin, and can be readily applied to the generic class of LTI systems (SISO, MIMO, stable, unstable). Copyright © 2006 John Wiley & Sons, Ltd.     

A robust adaptive control method for Wiener nonlinear systems

This paper proposes a new robust adaptive control method for Wiener nonlinear systems with uncertain parameters. The considered Wiener systems are different from the previous ones in the sense that we consider nonlinear block approximation error, process noise, and measurement noise. The parameterization model is obtained based on the inverse of the nonlinear function block. The adaptive control method is derived from a modified criterion function that can overcome non‐minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. Theoretical analysis indicates that the closed‐loop system stability can be guaranteed under mild conditions. Numerical examples including an industrial problem are studied to validate the results. Copyright © 2016 John Wiley & Sons, Ltd.     

Asymptotic moving object tracking with trajectory tracking extension: A homography‐based approach

In this paper, a homography‐based visual servo controller is developed for a rigid body to track a moving object in three‐dimensional space with a fixed relative pose. Specifically, a monocular camera is mounted on the rigid body, and the desired relative pose is expressed by a pre‐recorded reference image. Homography is exploited to obtain the orientation and scaled position for controller design. Considering the unknown moving object's velocities and distance information, a continuous nonlinear visual controller is developed using the robust integral of the signum of the error methodology. To facilitate the stability analysis, the system uncertainties regarding the moving object's velocities and distance information are divided into the error‐unrelated system uncertainties and the error‐related system uncertainties. After that, the upper bounds of the error‐related system uncertainties are derived with composited system errors. An asymptotic tracking of the leading object is proved based on the Lyapunov methods and the derived upper bounds. In addition, the proposed controller is extended to address the trajectory tracking problem. Simulation results validate the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.     

Controller design and analysis for singularly perturbed switched systems with actuator saturation

This paper investigates the problems of controller design and stability analysis for singularly perturbed switched systems subject to actuator saturation. A set of well‐defined sufficient conditions for the existence of state feedback controllers is proposed, under which the closed‐loop system is locally asymptotically stable for arbitrary switching law as long as the singular perturbation parameter is sufficiently small. With the obtained controller, the estimation problem of stability bound and basin of attraction of the closed‐loop system is reduced to solving a convex optimization problem. A numerical example and a hydraulic servo position system are used to illustrate the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

凸松弛全局优化机器人手眼标定

针对机器人运动学正解及相机的外参数标定存在偏差时,基于非线性最优化的手眼标定算法无法确保目标函数收敛到全局极小值的问题,提出基于四元数理论的凸松弛全局最优化手眼标定算法。考虑到机械手末端相对运动旋转轴之间的夹角对标定方程求解精度的影响,首先利用随机抽样一致性（RANSAC）算法对标定数据中旋转轴之间的夹角进行预筛选,再利用四元数参数化旋转矩阵,建立多项式几何误差目标函数和约束,采用基于线性矩阵不等式（LMI）凸松弛全局优化算法求解全局最优手眼变换矩阵。实测结果表明,该算法可以求得全局最优解,手眼变换矩阵几何误差平均值不大于1.4 mm,标准差小于0.16 mm,结果稍优于四元数非线性最优化算法。     

Exponential stability of output‐based event‐triggered control for switched singular systems

This paper presents the exponential stability of output‐based event‐triggered control for switched singular systems. An event‐triggered mechanism is introduced based on measure output, by employing the Lyapunov functional method and average dwell time approach, some sufficient conditions for exponential stability of the switched singular closed‐loop systems are derived. Furthermore, dynamic output feedback controller parameters are obtained. Lastly, a numerical example is given to illustrate the validity of the proposed solutions.     

Position‐dependent disturbance rejection using spatial‐based adaptive feedback linearization repetitive control

In this paper, we propose a new design of spatial‐based repetitive control for a class of rotary motion systems operating at variable speeds. The open‐loop system in spatial domain is obtained by reformulating a nonlinear time‐invariant system with respect to angular displacement. A two‐degree‐of‐freedom control structure (comprising two control modules) is then proposed to robustly stabilize the open‐loop system and improve the tracking performance. The first control module applies adaptive feedback linearization with projected parametric update and concentrates on robust stabilization of the closed‐loop system. The second control module introduces a spatial‐based repetitive controller cascaded with a loop‐shaping filter, which not only further reduces the tracking error, but also improves parametric adaptation. The overall control system is robust to model uncertainties of the system and capable of rejecting position‐dependent disturbances under varying process speeds. Stability proof for the overall system is given. A design example with simulation is provided to demonstrate the applicability of the proposed design. Copyright © 2008 John Wiley & Sons, Ltd.     

A Robust Adaptive Terminal Sliding Mode Control for Rigid Robotic Manipulators

In this paper, a robust adaptive terminal sliding mode controller is developed for n-link rigid robotic manipulators with uncertain dynamics. An MIMO terminal sliding mode is defined for the error dynamics of a closed loop robot control system, and an adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties in the Lyapunov sense. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated and a finite time error convergence in the terminal sliding mode can be guaranteed. Also, a useful bounded property of the derivative of the inertial matrix is explored, the convergence rate of the terminal sliding variable vector is investigated, and an experiment using a five bar robotic manipulator is carried out in support of the proposed control scheme.     

移动机器人自适应视觉伺服镇定控制

对有单目视觉的移动机器人系统,提出了一种自适应视觉伺服镇定控制算法;在缺乏深度信息传感器并且摄像机外参数未知的情况下,该算法利用视觉反馈实现了移动机器人位置和姿态的渐近稳定.由于机器人坐标系与摄像机坐标系之间的平移外参数(手眼参数)是未知的,本文利用静态特征点的位姿变化特性,建立移动机器人在摄像机坐标系下的运动学模型.然后,利用单应矩阵分解的方法得到了可测的角度误差信号,并结合2维图像误差信号,通过一组坐标变换,得到了系统的开环误差方程.在此基础之上,基于Lyapunov稳定性理论设计了一种自适应镇定控制算法.理论分析、仿真与实验结果均证明了本文所设计的单目视觉控制器在摄像机外参数未知的情况下,可以使移动机器人渐近稳定到期望的位姿.     

基于观测器的H∞鲁棒次优性能回复设计

提出了一种基于状态观测器的H∞鲁棒次优性能回复设计方案.对于具有不确定性的 被控对象,当存在满足给定的H∞鲁棒次优性能准则的状态反馈阵,且状态不可测量时,引入 适当的状态观测器可使闭环系统的H∞鲁棒次优性能任意接近状态反馈系统.     

LINEAR OPTIMAL FEEDBACK AND LOAD‐DECOUPLED CONTROL OF A BUCK DC‐DC CONVERTER

This paper describes a new controller design procedure and tuning method for a PWM buck dc‐dc converter. First, linear optimal feedback is designed using the LQR approach. Then the designed control law is implemented using a PID controller incorporated with a load‐decoupled PD compensator. The PID controller is tuned to achieve the optimal design based on the output error voltage directly, instead of using an estimator. When the proposed PD compensator is used, the converter is robust with respect to the input voltage and output current changes and the parameter perturbations. We also provide the conditions for the robust stability assurance of the closed‐loop system.