Linear quadratic optimal controller for cable-driven parallel robots

In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large workspace, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional-integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.     

Dynamic modeling of flexible-links planar parallel robots

This paper presents a finite element-based method for dynamic modeling of parallel robots with flexible links and rigid moving platform. The elastic displacements of flexible links are investigated while considering the coupling effects between links due to the structural flexibility. The kinematic constraint conditions and dynamic constraint conditions for elastic displacements are presented. Considering the effects of distributed mass, lumped mass, shearing deformation, bending deformation, tensile deformation and lateral displacements, the Kineto-Elasto dynamics (KED) theory and Lagrange formula are used to derive the dynamic equations of planar flexible-links parallel robots. The dynamic behavior of the flexible-links planar parallel robot is well illustrated through numerical simulation of a planar 3-RRR parallel robot. Compared with the results of finite element software SAMCEF, the numerical simulation results show good coherence of the proposed method. The flexibility of links is demonstrated to have a significant impact on the position error and orientation error of the flexible-links planar parallel robot.     

The robust design of parallel spherical robots

In this paper a robust methodology, reported in a previous work, is applied to the design of the unactuated joints of a spherical three-degree-of-freedom parallel robot, the Agile Wrist (AW). Robustness is needed because of the extremely difficult task of manufacturing a spherical mechanism with all its joint axes concurrent at a single point. In order to account for the unavoidable manufacturing errors, it is proposed here to replace the unactuated revolute (R) joints of an existing design by cylindrical (C) joints. The latter function even in the presence of nonconcurrent axes. A procedure, based on dual numbers, is used to solve the inverse kinematics of the entire mechanism in order to determine the rotations and translations of each C joint. Based on statistical results of the kinematic analysis, the C joints are suitably dimensioned.     

Vision/force control of parallel robots

In this paper, force and position control of parallel kinematic machines are discussed. Cartesian space computed torque control is applied to achieve force and position servoing directly in the task space within a sensor-based control architecture. The originality of the approach resides in the use of a vision system as an exteroceptive pose measurement of a parallel machine tool for force control purposes. Three different mechanical structures with different degrees of freedom are considered to validate the approach.     

Analysis of the dynamic stress of planar flexible-links parallel robots

This paper presents a method for the dynamic stress analysis of planar parallel robots with flexible links and a rigid moving platform. The finite element-based dynamic model of flexible parallel robots is proposed. The relation between elastic deformations and elastic displacements of the flexible links is investigated, considering the coupling effects of elastic motion and rigid motion. The elastic deformations of links are calculated. Considering the effects of bending-shearing strain and tensile-compression strain, the dynamic stress of the links and its position are derived by using the Kineto-Elastodynamics theory and the Timoshenko beam theory. Due to the flexibility of the links, the dynamic stresses are well illustrated through numerical simulation. Compared with the results of the finite element software SAMCEF, the numerical simulation results show the good coherence and advantages of the analysis method. The dynamic stress analysis is demonstrated to have a significant impact on the analysis, design and control of flexible parallel robots.     

四自由度并联机器人模型建立及运动学仿真

基于螺旋理论,运用四自由度对称并联机器人结构综合的方法,选择设计出一种2-RPS-2-UPS并联机器人.运用ADAMS软件建立了2-RPS-2-UPS四自由度并联机器人的模型,并进行了给定轨迹的运动仿真,得到了运动过程中执行构件的运动轨迹坐标值曲线.表明该四自由度并联机器人的运动是预定、可靠的.     

A robust forward-displacement analysis of spherical parallel robots

The forward-displacement analysis of spherical parallel robots (SPRs) is revisited. A robust approach, based on the input–output (I/O) equation of spherical four-bar linkages, is proposed. In this approach, the closed-loop kinematic chain of a SPR is partitioned into two four-bar spherical chains, whose I/O equations are at the core of the analysis reported here. These equations lead to a trigonometric equation in the joint angles, which is solved semigraphically to obtain the joint variables for the determination of the moving plate orientation. Examples are included to demonstrate the application of the method.     

多约束条件下的机器人时间最优轨迹规划

提出了一种工业机器人时间最优轨迹规划及控制的新方法。对于笛卡尔空间中给定路径上的离散路径点,通过运动学逆解求得与之对应的关节节点序列,采用三次样条插值方法构造各关节位移、速度、加速度均连续的轨迹。在考虑关节空间中速度、加速度、加加速度约束条件的同时,确保机器人在笛卡尔空间各离散路径点处满足由给定路径所决定的速度约束条件,减小机器人运动路径与给定路径之间的误差。采用序列二次规划法求解上述非线性约束优化问题,进而规划出沿特定曲线方程运动的机器人时间最优轨迹。最后将上述算法应用于剪带机器人,证明了该算法的有效性和可行性。     

支链偏置的并联机构工作空间分析及尺度综合

以设计结构紧凑、工作空间大的力/触觉反馈器为目标,研究了Delta并联机构的运动学和工作空间特性。在改进Delta机构的基础上,引入支链机构的偏置安装角度α,利用矢量法求解了机构的位置逆解和正解,并通过算例验证了方程求解正、逆解的正确性;根据逆解公式推导出单开链子空间包络体边界方程,绘制分析了驱动杆与摆动杆长短不同时3种情况下的子空间几何形状。然后,详细讨论了α对整体工作空间和机构总体外围尺寸的影响,采用数值法得出了偏置安装角度α与工作空间最大内切球体体积的关系图、偏置角度与整体外围尺寸的关系图,并利用matlab绘制出整体空间截面图。最后,以上述最大内切球体为设计空间,结合雅克比矩阵条件数给出设计实例。验证结果表明,采用该设计方法能够满足对Delta机构的优化设计要求。     

6-3-3并联机构尺度的优化综合

提出了以满足6-3-3并联机构使用功能为准则的尺度综合优化建模方法,即以功能要求的任务轨迹为动平台运动规划路径,以尺度参数和任务轨迹在工作空间的定位参数为设计变量,以机构空间结构尽可能紧凑,而工作空间尽可能大为目标函数、工作空间涵盖任务轨迹、主动件移动范围和关节转角不超过设定极限值为约束,建立优化模型并通过软件编程实现该模型的求解。最后,给出了一个算例。     

6-SPS并联机器人的奇异位形分析

以并联机构在奇异位形下产生的微小位移与关节约束和结构约束的关系为基础，研究了具有重合球铰中心的6-3式和6-4式并联机构的奇异位形，分别得到这两种机构奇异位形的三阶和四阶判别行列式及奇异位形的特殊情形。最后给出瞬时运动的位移螺旋。     

State-of-the-art on theories and applications of cable-driven parallel robots

Cable-driven parallel robot (CDPR) is a type of high-performance robot that integrates cable-driven kinematic chains and parallel mechanism theory. It inherits the high dynamics and heavy load capacities of the parallel mechanism and significantly improves the workspace, cost and energy efficiency simultaneously. As a result, CDPRs have had irreplaceable roles in industrial and technological fields, such as astronomy, aerospace, logistics, simulators, and rehabilitation. CDPRs follow the cutting-edge trend of rigid–flexible fusion, reflect advanced lightweight design concepts, and have become a frontier topic in robotics research. This paper summarizes the kernel theories and developments of CDPRs, covering configuration design, cable-force distribution, workspace and stiffness, performance evaluation, optimization, and motion control. Kinematic modeling, workspace analysis, and cable-force solution are illustrated. Stiffness and dynamic modeling methods are discussed. To further promote the development, researchers should strengthen the investigation in configuration innovation, rapid calculation of workspace, performance evaluation, stiffness control, and rigid–flexible coupling dynamics. In addition, engineering problems such as cable materials, reliability design, and a unified control framework require attention.     

Module-based method for design and analysis of reconfigurable parallel robots

This paper presents a method for the design and analysis of reconfigurable parallel robots. The inherent modularity in a parallel robot lends itself as a natural candidate for reconfiguration. By taking the branches as building blocks, many modular parallel robots can be constructed, from which a reconfigurable parallel robot can be realized. Among three types of reconfigurations, namely, geometry morphing, topology morphing, and group morphing, the method presented here is for the last two reconfigurations, thereby advancing the current research that is mainly limited to geometry morphing. It is shown that the module-based method not only provides a systematic way of designing a reconfigurable parallel robot, but also offers a unified modeling for robot analysis. Two examples are provided, one showing the topology morphing and the other showing the group morphing.     

3-RTT并联机器人奇异位形空间分析

采用基于机构瞬时运动分析的方法,建立了3—RTT并联机器人的奇异位形判别阵。分析了3—RTT机器人处于奇异位形时机构所满足的几何条件。编制了基于三维搜索算法的奇异位形空间分析程序,时实例进行搜索计算和分析,给出了3-RTT机器人的奇异位形空间的图形,并对其分布规律进行了分析。     

3-RRRT并联机器人工作空间与灵巧度的分析

旨在研究和分析3-RRRT并联机器人的工作空间和灵巧度。运用了齐次坐标系法对3-RRRT并联机器人机构进行了分析，给出属于工作空间点的判别条件，并进行了数值仿真；给出了3-RRRT并联机器人灵巧度的计算公式，并进行了数值仿真。     

并联机器人动态滑模轨迹跟踪控制研究

并联机器人是机器人研究与应用的重要部分,它具有刚度大、承载能力强、位置误差不积累等一系列优点,但它本身高度的非线性和强耦合}生,使对其精确控制极为困难.针对以交流伺服电机驱动的六自由度并联机器人机构,分析了其运动学逆解,进行了轨迹规划,设计了动态滑模变结构控制算法,建立了机器人支路的仿真模型,完成了对支路的期望运动轨迹的跟踪.仿真结果表明该算法系统抗干扰能力强,具有快速有效跟踪期望轨迹的优良性能.     

并联机构的六维鼠标研制开发

详细阐述了一种以并联机构为力敏元件的微型六维鼠标的设计与开发工作，分析了其设计思想和工作原理，阐述了在鼠标的力敏元件微型化方面所采取的措施，介绍了整个鼠标的系统构成，并将其用于虚拟6—SPS并联机器人控制系统中，控制结果表明该六维鼠标设计制造是成功的。     

Fuel optimal control of parallel hybrid electric vehicles

A mathematical model for fuel optimal control and its corresponding dynamic programming (DP) recursive equation were established for an existing parallel hybrid electric vehicle (HEV). Two augmented cost functions for gear shifting and engine stop-starting were designed to limit their frequency. To overcome the problem of numerical DP dimensionality, an algorithm to restrict the exploring region was proposed. The algorithm significantly reduced the computational complexity. The system model was converted into real-time simulation code by using MATLAB/RTW to improve computation efficiency. Comparison between the results of a chassis dynamometer test, simulation, and DP proves that the proposed method can compute the performance limitation of the HEV within an acceptable time period and can be used to evaluate and optimize the control strategy.     

Fuel optimal control of parallel hybrid electric vehicles

A mathematical model for fuel optimal control and its corresponding dynamic programming (DP) recursive equation were established for an existing parallel hybrid electric vehicle (HEV). Two augmented cost functions for gear shifting and engine stop-starting were designed to limit their frequency. To overcome the problem of numerical DP dimensionality, an algorithm to restrict the exploring region was proposed. The algorithm significantly reduced the computational complexity. The system model was converted into real-time simulation code by using MATLAB/RTW to improve computation efficiency. Comparison between the results of a chassis dynamometer test, simulation, and DP proves that the proposed method can compute the performance limitation of the HEV within an acceptable time period and can be used to evaluate and optimize the control strategy. __________ Translated from Journal of Shanghai Jiaotong University, 2006, 40(6): 947–951, 957 [译自: 上海交通大学学报]