Robust control of robot manipulator with actuators

A Robust controller is designed for cascaded nonlinear uncertain systems that can be decomposed into two subsystems; that is, a series connection of two nonlinear subsystems, such as a robot manipulator with actuators. For such systems, a recursive design is used to include the second subsystem in the robust control. The recursive design procedure contains two steps. First, a fictitious robust controller for the first subsystem is designed as if the subsystem had an independent control. As the fictitious control, a nonlinearH∞ control using energy dissipation is designed in the sense ofL ₂-gain attenuation from the disturbance caused by system uncertainties to performance vector. Second, the actual robust control is designed recursively by Lyapunov’s second method. The designed robust control is applied to a robotic system with actuators, in which the physical control inputs are not the joint torques, but electrical signals to the actuators.     

Tracking control of robot manipulators via output feedback linearization

This paper presents a robot manipulator tracking controller based on output feedback linearization. A sliding mode perturbation observer (SPO) is designed to estimate unmeasurable states and system perturbations that involve system nonlinearities, disturbances and unmodelled dynamics. The use of SPO allows to input/output linearize and decouple the strongly coupled nonlinear robot manipulator system merely by the feedback of joint angles. The controller design does not need an accurate model of the robot manipulator. Simulation studies are undertaken based on a two-link robot manipulator to evaluate the proposed approach. The simulation results show that the proposed controller has more superior tracking control performance, with payload changing in a wide range, in comparison with a sliding mode controller (SMC) designed based on state feedback linearization with full states available. Selected from Journal of Shenzhen University (Science & Engineering), 2005, 22(3)     

基于绝对坐标的柔性机器人逆动力学建模和轨迹跟踪

采用了 Timoshenko梁理论和有限元法 ,由 L agrange方程建立了基于绝对坐标的柔性机器人逆动力学模型。由提出的非线性方程数值解法 ,求解出柔性机器人的输入关节角或驱动力矩 ,以此作为输入参量 ,可使机器人能够非常准确地跟踪末端轨迹。文中就三柔性臂机器人进行了仿真 ,验证了本方法的有效性     

基于非线性微分方程的机械臂运动位置控制方法

针对当前机械臂运动位置控制方法存在机械臂关节节点位置的跟踪效果差和机械臂运动位置控制能力差的问题,提出基于非线性微分方程的机械臂运动位置控制方法。首先对机械臂动力学进行分析,获取内部三连杆结构作用原理和机械臂动力学目标函数,再利用坐标求权矩阵重构机械臂动力学目标函数,获取机械臂相关的非线性微分方程,将非线性微分方程的输出结果,即机械臂动力学参数代入 CPG 神经网络中,构建机械臂运动控制模型。实验结果表明,所提方法的械臂关节节点位置跟踪效果好、机械臂运动位置控制能力强。     

2R欠驱动平面柔性机械臂的位置控制策略与试验研究

针对同时具有被动关节和柔性杆的欠驱动平面机械臂,提出一种简单易行的分段位置控制策略。以2R欠驱动平面柔性机械臂为研究对象,建立机械臂的假设模态动力学模型,分析系统的动力学耦合特性与可控性。通过被动关节处制动器的开闭切换,研究平面柔性机械臂的分段位置控制策略,采用PID方法分别设计各阶段主动、被动关节的控制算法。最后,基于自行开发的欠驱动平面机械臂的试验平台及实时控制系统,完成了2R欠驱动平面柔性机械臂位置控制的试验研究。仿真和试验结果表明,主动关节和被动关节在各阶段都能很好地跟踪目标值,进而实现机械臂的操作任务,验证了所提控制方法的可行性和有效性,以及欠驱动柔性机械臂动力学模型的正确性。     

H∞ observer-based event-triggered sliding mode control for a class of discrete-time nonlinear networked systems with quantizations

This paper investigates the problem of H_∞ observer-based event-triggered sliding mode control (SMC) for a class of uncertain discrete-time Lipschitz nonlinear networked systems with quantizations occurring in both input and output channels. The event-triggered strategy is used to save the limited network bandwidth. Then, based on the zero-order-hold (ZOH) measurement, a state observer is designed to reconstruct the system state, which facilitates the design of the discrete-time sliding surface. Considering the effects of quantizations, networked-induced constraints and event-triggered scheme, the nonlinear state error dynamics and sliding mode dynamics are converted into a unified linear parameter varying (LPV) time-delay system with the aid of a reformulated Lipschitz property. By using the Lyapunov-Krasovskii functional and free weighting matrix, a new sufficient condition is derived to guarantee the robust asymptotic stability of the resulting closed-loop system with prescribed H_∞ performance. And then the observer gain, event-triggering parameter and sliding mode parameter are co-designed. Furthermore, a novel SMC law is synthesized to force the trajectories of the observer system onto a pre-specified sliding mode region in a finite time. Finally, a single-link flexible joint robot example is utilized to demonstrate the effectiveness of the proposed method.     

Robust control of a 3-DOF hybrid robot manipulator

This paper introduces a 3-DOF hybrid robotic manipulator which is constructed by combining a parallel mechanism and a pantograph to increase the high stiffness, as well the as workspace. We analyze its kinematics and dynamics by applying Lagrange’s method. Subsequently, we propose a robust tracking controller based on the Lyapunov approach for the manipulator in the presence of uncertainty. The scheme consists of two parts. The first part is the model-based computed torque controller, which is used to stabilize the nominal robot system. The second part is a robust compensating controller, which is designed to handle the uncertainty in the system. We propose a controller designed in Cartesian coordinates. The proposed controller guarantees practical stability.     

漂浮基柔性空间机械臂协调运动的非线性鲁棒自适应控制

针对具有外部扰动与参数不确定或未知的情况,讨论漂浮基柔性空间机械臂系统的协调控制与柔性振动抑制问题。基于假设模态法对柔性臂杆进行近似描述,并利用第二类拉格朗日方程与系统动量守恒关系,推导带外部扰动的漂浮基柔性空间机械臂系统的动力学方程。以此为基础,提出漂浮基柔性空间机械臂系统协调运动的非线性鲁棒控制与非线性鲁棒自适应控制方案。此两种控制方案均可克服外部扰动对系统的影响,控制漂浮基柔性空间机械臂系统载体姿态与机械臂各关节铰完成期望的协调运动,同时有效地抑制了臂杆的柔性振动。除此之外,非线性鲁棒自适应控制方案还可以解决系统惯性参数不确定或未知的问题。系统数值仿真结果证实了所提控制方案的有效性和可行性。     

Analytical development of a robust controller for smart structural systems

This paper aims at demonstrating the feasibility of active control of beams with a multiobjective state-feedback control technique. The multiobjective state-feedback controller is designed on a linear matrix inequality (LMI) approach for the multiobjective synthesis. The design objectives are to achieve a mix ofH _∞ performance andH ₂ performance satisfying constraints on the closed-loop pole locations in the face of model uncertainties. The controller is also designed to reject the effects of the noise and external of disturbances. For the theoretical analysis, the governing equation of motion is derived by Hamilton’s principle to describe the dynamics of a smart structural system. Numerical examples are presented to demonstrate the effectiveness of the integrated robust controller in damping out the multiple vibration modes of the piezo/beam system.     

柔性机器人动力学分析与控制策略综述

综述了柔性机器人动力学分析和控制等相关问题,对柔性机器人动力学分析中变形场的离散化、建模方法、近似分析等问题进行了系统分析。详细介绍了被动控制、PID控制、模糊控制、神经网络控制、自适应控制、鲁棒控制、变结构控制、奇异摄动控制和非线性控制等在柔性机器人控制中的应用情况。指出了在柔性机器人动力学建模和控制中应解决的问题,这对包括柔性机器人在内的多柔体系统动力学建模与控制问题的研究有一定的促进作用。     

Comparison of some modeling and control issues for a flexible two link manipulator

The nonlinear dynamics of a flexible two link manipulator presents a challenging modeling and control problem with its lumped actuator dynamics coupled with distributed link dynamics. Issues related to modeling uncertainty and control robustness as well as a good understanding of the experimental issues are essential for advanced modeling and control for such systems. This paper reports some of the advanced modeling, control, and experimental issues for a flexible two link manipulator, including some novel approaches developed by the authors.     

未知环境下柔性二连杆机械臂的自适应阻抗控制

针对机器人与环境接触作业的需求,基于假设模态法建立了刚柔耦合动力学模型,并考虑环境参数不精确干扰,设计了自适应阻抗控制器,分析了其稳定条件。在MATLAB/Simulink中搭建了可对柔性机械臂进行自适应阻抗控制的仿真平台,计算了平面内二连杆柔性机械臂在含有三角形凹陷环境表面的接触运动和柔性变形模态。对比分析了刚性和柔性机械臂位控和力控效果及自适应项对控制响应的影响。基于Staubli机器人展开了实验。结果表明：柔性变形会使得机械臂的位控和力控效果变差;自适应阻抗控制会改善控制响应,对环境不确定具有鲁棒性。设计的自适应阻抗控制可实现柔性机械臂在不规则表面的稳定接触和运动。     

Application of symbolic manipulation to inverse dynamics and kinematics of elastic robots

An inverse dynamics and kinematics of a flexible manipulator is derived in symbolic form based on the recursive Lagrangian assumed mode method. A PC-based program has implemented the algorithm to automatically generate the inverse dynamics and kinematics for an elastic robot in a symbolic form. A case study is given to illustrate how to use this program for inverse dynamic and kinematic generation. Simulation results for a case study by considering different mode shape are compared with the rigid case.Nomenclature A _i joint transformation relates systemi to systemi-1 - E _i link transformation relates the deflection of systemi to systemi - F _i joint torque acting on jointi - g gravity vector expressed at the base coordinates - J inertia = - K kinetic energy of the system - l _i length of linki - M _i a mass concentrated at the joint i - m _i number of modes used to describe the deflection of link i - n number of links - q _h joint variable of thehth joint - q _hk time-varying amplitude of mode k of link h - R vector of remaining dynamics and external forcing terms = - r _i vector locating the centre of mass of linki - R _j dynamics from the joint equation j, excluding second derivatives of the generalized coordinates - R _if dynamics from the deflection equation jf, excluding second derivatives of the generalized coordinates - V potential energy - W _i transformation from the base to theith link - transformation from the base to the systemî - z the vector of generalised coordinates = - link density     

Trajectory tracking of a spatial flexible link manipulator using an inverse dynamics method

Discussed in this paper is the problem of trajectory tracking of a spatial flexible link manipulator. To solve this problem, an inverse dynamics method is proposed, based on which computed joint torques can be determined and used to drive the endpoint of a spatial flexible link manipulator to follow its given trajectory.     

Complete dynamic modeling and approximate state space equations of the flexible link manipulator

This work treats the problem of dynamic modeling and state space approximation for robotic manipulators with flexibility. Case studies are planar manipulators with a single flexible link together with clamped-free ends and tip mass conditions. In this paper, complete dynamic modeling of the flexible beam without premature linearization in the formulation of the dynamics equations is developed, whereby this model is capable of reproducing nonlinear dynamic effects, such as the beam stiffening due to the centrifugal and the Coriolis forces induced by rotation of the joints, giving it the capability to predict reliable dynamic behavior. On the other hand, in order to show the joint flexibility effects on the model dynamic behaviors, manipulator with structural and joint flexibility is considered. Thus, a reliable model for flexible beam is then presented. The model is founded on two basic assumptions: inextensibility of the neutral fiber and moderate rotations of the cross sections in order to account for the foreshortening of the beam due to bending. To achieve flexible manipulator control, the standard form of state space equations for a flexible manipulator system (flexible link and actuator) is very important. In this study, finite difference method for discretization of the dynamic equations is used and the state space equations of the flexible link with tip mass considering complete dynamic of the system are obtained. Simulation results indicated substantial improvements on dynamic behavior and it is shown that the joint flexibility has a considerable effect on the dynamic behavior of rotating flexible arm that should not be simply neglected. The effects of tip mass is proved to be increasing the elastic deformations?? amplitudes and increasing stability.     

A robot fuzzy motion planning approach in unknown environments

A fuzzy robot motion planning approach is proposed in unknown environments for three-degree industrial robots. The proposed planning system is composed of several separate fuzzy units, which control individually each manipulator joint. Each unit combines a repelling influence, which is related to the nearby obstacle, with the attracting influence produced by the final manipulator configuration, to generate actuating command for each link. Effectiveness of the proposed approach is verified through simulation. __________ Translated from Journal of Harbin Institute of Technology, 2005, 37(10) (in Chinese)     

载体位置、姿态均不受控的飘浮基柔性空间机器人的Terminal滑模控制

讨论了载体位置、姿态均不受控的飘浮基柔性空间机器人的Terminal滑模控制问题。为讨论既有柔性关节又有柔性臂的欠驱动系统,以一个具有两个柔性关节和一个柔性臂的飘浮基空间机器人为例,首先利用拉格朗日方程并结合系统总质心定义,得到了系统的动力学方程,然后利用奇异摄动法,将柔性空间机器人系统分解为一个柔性空间机械臂子系统和一个柔性关节快变子系统。以此为基础,提出了一种包含柔性空间机械臂子控制项和柔性关节快变子控制项的组合控制器。其中,柔性空间机械臂Terminal滑模子控制项实现了机械臂关节铰期望轨迹的跟踪,柔性关节快变子控制项使得快变子系统稳定在由柔性空间机械臂子控制项产生的机械臂关节轨迹上。系统的数值仿真结果表明,该方法能在抑制柔性关节的柔性振动的同时跟踪上机械臂关节期望轨迹。该控制方案的显著优点为不需要测量、反馈载体的位置、移动速度、移动加速度,同时可保证机械臂关节铰跟踪误差在任意指定有限时间内收敛到零。     

具有外部扰动的参数未知漂浮基柔性空间机械臂的对角递归神经网络控制

讨论载体位置和姿态均不受控情况下,存在外部扰动的参数未知漂浮基柔性空间机械臂系统关节运动的动力学控制问题。由假设模态法,利用拉格朗日方法建立漂浮基柔性空间机械臂的系统动力学方程。以此为基础,针对存在外部扰动和系统参数未知的情况,利用对角递归神经网络逼近柔性空间机械臂系统的逆动力学模型,设计基于对角递归神经网络的控制方案,以控制柔性空间机械臂的关节铰跟踪在关节空间的期望运动轨迹,同时能抑制柔性杆的振动。该方案由于没有专门设计主动控制器抑制柔性振动,因此不需要测量、反馈柔性振动模态,大大简化控制器的结构;无需预知控制对象的精确模型和系统参数,且能克服外部扰动的影响。计算机数值仿真证实所提方案的有效性和可行性。     

An automated arc spray tooling system for rapid die-making of large-sized automobile body panels

A creative robot wrist consisting of link mechanisms and a novel robot motion control method based on the cross-sectional vector contours of an STL-formatted model was proposed. By using the wrist and the control method, an industrial robot with five degrees of freedom for rapid tooling using metal arc spraying and electric brush plating techniques was developed. The wrist of the robot including a specially designed link mechanism can maintain the position of the spraying point on the surface of the master pattern whatever the orientation of the gun. Therefore, the kinematic nonlinear coupling between the position mechanism and orientation mechanism in a traditional robot can be avoided. The only input of the control system is the STL-formatted 3D CAD model of the pattern. Without the need of any manual programming, the metal arc spraying and brush plating (if necessary) processes can be performed automatically and efficiently after receiving the 3D CAD data of the pattern. Using this robot system in new car development and trial production, the cost and lead-time can be reduced substantially as compared with the conventional tool making method. __________ Translated from Journal of Xi’an Jiaotong University, 2004, 38 (11) (in Chinese)     

棉花异性纤维分拣机器人抓棉手的结构设计

棉花中的异性纤维影响纯棉产品质量，采用智能机器人替代人工作业是新的发展方向。文章设计了一款具有5自由度棉花异性纤维分拣机器人。该机器人主要由四轮移动小车、液压升降平台、腰部、大臂、小臂、机械手等组成。针对棉花抓取与分拣，对机器人的抓棉手进行了结构设计，以滑环和连杆作为设计变量，优化了抓棉手的机械尺寸；同时，文章针对抓棉手指采用有限元方法进行了应变和模态分析，结果显示手指设计合理。