基于LPV 方法的Stewart 平台关节空间分散控制

为了提高Stewart 平台关节空间分散控制系统的性能,提出一种基于线性变参数(Linear Parameter Varying,LPV) 方法的控制策略．首先建立了平台关节空间动力学模型;通过分析平台惯性矩阵,指出单支路 子系统等效负载变化以及子系统间的耦合干扰是分散控制需要处理的主要问题．然后将平台惯性矩阵分解为 一个对角阵与一个耦合阵之和,子系统间耦合作用视为对单支路的干扰,从而得到每个子系统的动力学方程． 最后针对子系统等效负载随着上平台运动而在较大范围内变化的特点,引入LPV 控制方法,使控制器参数能 够适应子系统负载变化,减少了保守性．仿真结果表明了所提方法的有效性．     

二平动自由度高速轻型并联机械手控制技术研究

研究一种二平动自由度高速!轻型并联机械手的控制技术.针对这类机构的结构特点,利用虚位移原理和矩阵奇异值理论,估算出主动关节负载惯量随位形变化的规律.在此基础上,构建了单轴误差反馈控制系统,并通过计算机仿真预估出定增益PID调节器的参数.最后,通过实验验证了参数整定方法的正确性和有效性.􀁱     

The singularities and dynamics of a Stewart platform manipulator

The Stewart platform manipulator is a fully parallel kinematic linkage system that has major mechanical differences over typical serial link robots. Its closed kinematic chain and parallel linkage structure give it great rigidity and a high force-to-weight ratio. In this paper, based on the forward and inverse kinematic analysis, the Jacobian matrix and the dynamic equations of the six-degree-of-freedom Stewart platform are derived. The singularities of the Stewart platform are also studied. Four singular positions are proved and some other conditions under which the possible singular positions may occur are given. These results provide us with the necessary information to avoid passing through singular points. The dynamic equations in Cartesian space appear in a very simple form. Especially in some applications if there is no rotation about the fixed X-axis, then the inertia matrix reduces to a constant, diagonal matrix and the Coriolis and centrifugal matrix goes to zero, which makes the Stewart platform become a decoupled, linear system in Cartesian space.     

作业型飞行机器人动态滑翔抓取的鲁棒自适应控制

作业型飞行机器人是指将多自由度机械臂固连在飞行机器人上的一类新型机器人系统,它能够对周围环境施加主动影响,同时也存在较为复杂的动力学性能.本文针对作业型飞行机器人滑翔抓取物体时所受到的摩擦力和接触力问题以及在飞行过程中产生的转动惯量变化问题,设计了一种整体式鲁棒自适应控制策略.首先在作业型飞行机器人系统动力学建模中引入...     

参数不确定空间机械臂系统的鲁棒自适应混合控制

讨论了载体位置与姿态均不受控制的漂浮基空间机械臂系统的控制问题.对系统运动学、动力学的分析结果表明,结合系统动量守恒及动量矩守恒关系得到的系统广义Jacobi关系以及系统的动力学方程是系统惯性参数的非线性函数.证明了借助于增广变量法可以将系统的增广广义Jacobi矩阵及系统动力学方程表示为一组适当选择的(组合)惯性参数的线性函数.以此为基础,针对系统惯性参数不确定的情况,设计了空间机械臂末端抓手跟踪惯性空间期望轨迹的鲁棒自适应混合控制方案.仿真运算结果证实了方法的有效性.     

Singularity analysis and detection of 6-UCU parallel manipulator

6-UCU kind Gough–Stewart platform (GSP) has been used extensively in practice. The singularity of GSP has been studied by many scholars, but their works mainly focused on finding the methods to divide the cases of singularity or searching the solutions with Jacobian matrices. On the other hand, this paper studies the singularities of 6-UCU parallel manipulator caused by not only the active joints but also passive universal joints. Two types of singularity are derived based on a degree of freedom method by using screw theory. Singularity detection is essential to certify the absence of singularity within a prescribed workspace or a reachable workspace for a practical use of the 6-UCU parallel manipulator. Algorithms are proposed by using evolutionary strategy to detect the singularity in the desired or reachable workspace of the 6-UCU parallel manipulator. Case studies are presented to demonstrate the effectiveness of the proposed singularity detection methods.     

A New Approach for the Dynamic Analysis of Parallel Manipulators

A new approach for the dynamic analysis of parallel manipulators is presented in this paper. This approach is based on the principle of virtual work. The approach is firstly illustrated using a simple example, namely, a planar four-bar linkage. Then, the dynamic analysis of a spatial six-degree-of-freedom parallel manipulator with prismatic actuators (Gough–Stewart platform) is performed. Finally, a numerical example is given in order to illustrate the results. The approach proposed here can be applied to any type of planar and spatial parallel mechanism and leads to faster computational algorithms than the classical Newton–Euler approach when applied to these mechanisms.     

The Singularity Principle and Property of Stewart Parallel Manipulator

Based on the kinematic relationship of rigid body, this paper presents a new principle and method to analyze the singularity of a Stewart parallel manipulator. We study the sufficient and necessary condition that three velocities of three non‐collinear points in a body can determine a screw motion. All singularities of the Stewart parallel mechanism are classified into three different linear‐complex singularities. The various algebraic and geometrical properties as well as kinematics ones are analyzed in detail in different singular configurations. With the condition above, the singularity loci and distribution characteristics of a 3/6—Stewart parallel manipulator for some orientations of the mobile are studied in an oblique plane and in three‐dimensional space. © 2003 Wiley Periodicals, Inc.     

An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.     

A new index of serial-link manipulator performance combining dynamic manipulability and manipulating force ellipsoids

The inertia matching ellipsoid (IME) is proposed as a new index of dynamic performance for serial-link robotic manipulators. The IME integrates the existing dynamic manipulability and manipulating-force ellipsoids to achieve an accurate measure of the dynamic torque-force transmission efficiency between the joint torque and the force applied to a load held by an end-effector. The dynamic manipulability and manipulating-force ellipsoids can both be derived from the IME as limiting forms, with respect to the weight of the load. The effectiveness of the IME is demonstrated numerically through the selection of an optimal leg posture for jumping robots and optimal active stiffness control, and experimentally through application to a pick-up task using a commercial manipulator. The index is also extended theoretically to the case of a manipulator mounted on a free-flying satellite.     

并联型工业机器人的运动弹性动力学研究

从关联型机器人的通有模型出发，引入力域内的雅可比矩阵，将中央平台之后开链部分的质量和惯性计入模型，推导出完整形式的动力学模型，建立了基于弹性理论和有限元分析的运动弹性动力学方程，并以天府－Ｉ型点焊机械手为例进行了ＫＥＤ分析，编制了相应的软件，在建模时还采用了计算机符号－数据处理技术。     

Dynamic Modeling and Experimental Validation of a 3-PRR Parallel Manipulator with Flexible Intermediate Links

This paper presents the development of structural dynamic equations of motion for a 3-PRR parallel manipulator with three flexible intermediate links, based on the assumed mode method. Lagrange’s equation is used to derive the dynamic model of the manipulator system. Flexible intermediate links are modeled as Euler–Bernoulli beams with pinned–pinned boundary conditions. Dynamic equations of motion of a 3-PRR parallel manipulator with three flexible links are developed by adopting the assumed mode method. The effect of concentrated rotational inertia at both ends of intermediate links is included in this model. Numerical simulations of vibration responses, coupling forces and inertial forces are presented. The corresponding frequency spectra analysis is performed using the Fast Fourier Transform (FFT). Experimental modal tests are performed to validate the theoretical model through comparison and analysis of modal characteristics of the flexible manipulator system.     

Dynamic formulation and performance evaluation of the redundant parallel manipulator

The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.     

An efficient algorithm for generating manipulator inertia matrix using the minimum set of dynamics parameters

This article presents an efficient algorithm for computing the inertia matrix of rigid serial manipulators. The derivation of the algorithm is based on the closed-form formulation of the force and moment exerted on a link using a minimum set of dynamic parameters of the manipulator model. The minimum set of dynamic parameters can be derived completely from the original dynamic parameters using the recursive re-grouping method before starting the simulation and the control. The proposed computation method is suitable for the control and the simulation based on parameter estimates because the minimum set of dynamic parameters is an identifiable parameter set. The computational efficiency of the proposed methods is compared with other published methods. It is shown that the proposed algorithm is the most efficient approach for serial manipulators. As an example, the number of computations for the inertia matrix of a manipulator with n rotational joints is 11n²+9 n − 35 multiplications and 7n²+ 23 n − 57 additions by reformulating the dynamic model using the minimum set of dynamic parameters. © 1996 John Wiley &, Sons, Inc.     

Modeling and analysis of a multi-dimensional vibration isolator based on the parallel mechanism

A hybrid manipulator applied to vibration isolation of the manufacturing systems is proposed in this paper. The translations and rotations of the manipulator are decoupled, so the proposed isolator can isolate vibrations with wide range of frequency, at the same time it is fully capable of adjusting the orientations of the equipments. The scheme design, inverse kinematics, workspace and dexterity are carried out in this paper. A closed form dynamic model considering the external excitations on the base platform is performed based on the Newton–Euler approach. The optimum solutions of the forces in each actuating limb are obtained by using the Moor–Penrose inverse matrix. Furthermore, a novel dynamic performance index is proposed to evaluate the estimated maximum forces in the actuating limbs; this index can help to optimally design the parameters of motor, spring and damper. In order to evaluate the performance of isolation, the displacement transmissibility and acceleration transmissibility are also analyzed. The research work provides an analytical base for the development of the novel vibration isolator.     

基于AutoCAD平台的六自由度并联机器人

本文研究基于AutoCAD平台的六自由度并联机器人在姿态给定情况下工作空间(即位置工作空 间)的几何确定方法,该方法以机器人的运动学反解为基础,得出Stewart并联机器人和6-R TS并联机器人位置工作空间的边界方程,从而得出Stewart并联机器人的位置工作空 间是6个球体的交集,6-RTS并联机器人在姿态给定时其工作空间是6个相同的规则曲面体 的交集．基于AutoCAD平台,其交集以及交集的容积可以很容易的得出,该方法是确定六自 由度并联机器人工作空间的一种简单、有效方法．     

A New Approach to the Architecture Optimization of a General 3-PUU Translational Parallel Manipulator

This paper presents a new approach to the architecture optimization of a general 3-PUU translational parallel manipulator (TPM) based on the performance of a weighted sum of global dexterity index and a new performance index-space utility ratio (SUR). Both the inverse kinematics and forward kinematics solutions are derived in closed form, and the Jacobian matrix is derived analytically. The manipulator workspace is generated by a numerical searching method with the physical constraints taken into consideration. Simulation results illustrate clearly the necessity to introduce a mixed performance index using space utility ratio for architectural optimization of the manipulator, and the optimization procedure is carried out with the goal of reaching a compromise between the two indices. The analytical results are helpful in designing a general 3-PUU TPM, and the proposed design methodology can also be applied to architectural optimization for other types of parallel manipulators.     

On the dynamic model and kinematic analysis of a class of Stewart platforms

In this paper, a dynamic model for a class of Stewart platform (six degrees of freedom parallel link robotic manipulators) is derived by using tensor representation. A set of six Lagrange's equations are obtained. The kinematics analysis for a class of Stewart platform is conducted and a sixteenth order polynomial equation corresponding to the forward kinematic solution of the Stewart platform is obtained, which gives all possible global solutions of a manipulator configuration for a given set of six leg lengths.     

Indirect disturbance compensation control of a planar parallel (2-PRP and 1-PPR) robotic manipulator

This study addresses the dynamic modelling and indirect disturbance compensation control of planar parallel robotic motion platform with three degrees of freedom (3-DOF) in the presence of parameter uncertainties and external disturbances. The proposed planar parallel motion platform is a singularity free manipulator and has three manipulator legs located on the same plane linked with a moving platform. Of the three aforementioned manipulator legs, two legs have a prismatic–revolute–prismatic (PRP) joint configuration each with only one prismatic joint deliberated to be active, and the other leg consists of prismatic–revolute–prismatic (PPR) joint configuration with one active prismatic joint. The closed form kinematic solution (both forward and reverse kinematics) for the platform has been obtained in completion. In addition, the dynamic model for the platform has been communicated using the energy based Euler–Lagrangian formulation method. The proposed controller is based on a computer torque control with disturbance compensation integrated with it. Disturbance vectors comprising disturbances due to parameter variations, payload variations, frictional effects and other additional effects have been estimated using an extended Kalman filter (EKF). The EKF proposed for this specific platform uses only position and orientation measurements for estimation and noise mitigation. Simulations with a characteristic trajectory are presented and the results have been paralleled with traditional controllers such as the proportional integral derivative (PID) controller and computed torque controller (CTC). The results demonstrate satisfactory tracking performance for the proposed controller in the presence of parameter uncertainties and external disturbances.     

Optimal design of a 2-DOF parallel manipulator with actuation redundancy considering kinematics and natural frequency

In this paper, a planar 2-DOF parallel manipulator with actuation redundancy is proposed and the optimal design considering kinematics and natural frequency is presented. The stiffness matrix and mass matrix are derived, and the structural dynamics is modeled. The natural frequency is obtained on the basis of dynamic model. Based on the kinematic performance, the range for link length is given. Then, considering the natural frequency, the geometry is optimized. The natural frequency is simulated and compared with the corresponding non-redundant parallel manipulator. The designed redundant parallel manipulator has desired kinematic performance and natural frequency and is incorporated into a 4-DOF hybrid machine tool.