基于符号计算研究一类6-SPS并联机器人运动学正解问题

并联机器人运动学正解问题是一个重要而且难以解决 的问题．本文利用符号计算工具,应用Dialytic消元法,对一类6-SPS并联机器人的运动学 正 解问题进行研究．得到一个变元多项式方程,给出了正解的解析解. 在此基础上确定其工作 空间,求出其解范围内全部实解．此种方法对于一般6-SPS同样适用．     

一种新型简单6－SPS并联机器人及其位置正解

本文提出一种新型简单６－ＳＰＳ并联机器人机构，给出了它的变形型式并讨论了其位置正解．该机构的位置正解通过依次求解三个一元二次代数方程即可得到．本文最后给出了数值实例．     

基于CoDeSys环境下的并联机器人非线性方程求解

机器人技术发展到现在,虽然已经得到了突飞猛进的进步,但是对于并联机器人运动学正解的封闭解问题依然是机器人技术的瓶颈,在实际应用中采用的广义几何法和方程组的数值解法等,不但推导过程非常复杂,而且在求解的过程中还存在解不唯一的问题。为了避免上述问题,根据多元函数的Taylor公式推导出了一种基于三元非线性方程组牛顿迭代法的并联机器人运动学正解算法;同时,基于其数学原理,也可以得到并联机器人的反解。Taylor法以其自身的优势,巧妙地解决繁琐的并联机器人运动学正解多解取舍问题,直接获得了工作空间内满足运动连续性的合理解。该算法的迭代次数少,收敛速度快,是一种非常有潜力的方法。最后将该算法应用到CoDeSys开发环境,通过配置方式,证明Codesys环境下并联机器人运动学可实时灵活应用。     

基于神经网络的并联3自由度机器人位置正解

并联机器人位置正解是机器人运动学中难点问题之一,常规求解方法比较复杂且难度较大,通常需要对大量的非线性方程组进行推导计算且得到的解不唯一。该文提出了一种将人工神经网络用于并联机器人位置正解求解的通用方法,并结合实际机构对并联3自由度机器人进行了具体求解。通过对神经网络拓扑结构的设计以及选取有效的学习算法并用大量的位置反解数据对神经网络进行训练,获得了用于求解位置正解的神经网络模型,该网络可以实现位置正解问题的求解计算,从而避免了复杂的推导和演算。计算机仿真与实验结果表明了该方法的有效性与可行性。     

6－6型Stewart机器人的可操作性分析及其定义

本文根据并联机器人的特点，运用可操作度的概念，进一步提出了位置可操作度和姿态可操作度的定义。通过对位置反解直接求导，建立了６－６型ｓｔｅｗａｒｔ机器人的位置、姿态和综合可操作度的公式，为并联机器人的运动学分析提供了依据。     

6—6型Stewart机器人的可操作性分析及其定义

本文根据并联机器人的特点，运用可操作度的概念，进一步提出了位置可操作度和姿态可操作度的定义。通过对位置反解直接求导，建立了６－６型ｓｔｅｗａｒｔ机器人的位置，恣态和综合可操作度的公式，为并联机器人的运动学分析提供了依据。     

平行导路6-PSS并联机构运动学研究

文中提出了一种新型平行导路6-PSS结构并联机器人,介绍了这种机构的特点并对其运动学相关算法进行了深入研究,其中包括运动学反解、雅可比矩阵以及正解的求解方法,同时还与6-SPS结构并联机器人运动学相关的算法进行了比较.由于文中采用构造法计算雅可比矩阵,避免了以往对反解方程直接求导的计算方式,从而使雅可比矩阵的计算大为简化,而且也减少了正解的计算量、精度得到提高.实验结果证明,这些算法正确、实用.     

3-TCT并联机器人运动学仿真

以Pro/E环境下建立的3-TCT并联机器人的模型为研究对象,在ADAMS/View模块下,对其添加约束和驱动后,进行运动学仿真.给定动甲台的位移,测量驱动杆杆长的变化曲线,利用ADAMS/Postprocessor模块对测量结果进行后处理,可得运动学逆解;以逆解得到的驱动杆杆长的变化曲线作为驱动,添加到驱动杆上可进行运动学正向求解.正逆解仿真结果对比表明,动平台正解时的运动轨迹和逆解时的运动轨迹完伞吻合.方法避免了大量的数学计算和计算机语言编程工作,通过CAE仿真软件实现了对并联机器人的运动学仿真,为并联机器人实际样机的调试和控制提供了一套有效的分析方法.     

一种运动旋量逆解子问题的求解及其应用

旋量理论在机器人运动学逆解过程中将运动方程分解为若干子问题,目前常见的子问题组合并不能完成所有机器人的逆解问题．本文提出了在机器人逆解过程中会遇到的另一种子问题的解法,并给出构造该子问题的限定条件．运用该解法,给出具有RTS运动链并联机器人的运动学逆解方法,并归纳出利用未知量组中对参考点起相同作用的旋量组合来简化计算的方法．该子问题的解决扩充、便利了旋量理论在机器人运动学逆解中的应用．     

基于运动学正解的三转动并联机构迭代补偿控制

首先建立三转动并联机构的运动学方程,研究该并联机构的运动学反解和运动学正解,然后建立该机 构的动力学方程并分析其动力学特性．基于该机构研制了能复现自行武器行进时的车体姿态变化过程的动态模拟器 试验台．该试验台利用运动学反解算法进行闭环控制,并采用基于运动学正解的开环迭代补偿控制算法修正姿态驱 动信号,使试验台的响应逐渐逼近期望的姿态指令．测试表明该系统时域波形复现精度优于95%,验证了迭代补偿 控制的有效性．     

Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator

This article introduces an exact method to solve the forward kinematics problem (FKP) specifically applied to spatial parallel manipulators. The majority can modeled by the 6-6 parallel manipulator. This manipulator is a hexapod made up of a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two ball or Cardan joints. In order to implement algebraic methods, the parallel manipulator kinematics will be formulated as polynomial equations systems where the equation number is equal to the unknown numbers. One position-based kinematics model will be identified to solve the difficult FKP. The selected proven algebraic method implements Gröbner bases and constructs an equivalent univariate polynomial system. The exact resolution of this last system determines the real solution which exactly corresponds to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. We provide several examples of various hexapod types yielding eight real solutions. This algebraic method is exact and computes certified results.     

空间机器人柔性臂的动力学轨迹跟踪控制

机器人柔性擘控制问题是目前机器人研究中的一个重点和难点，本文动用基于关节的求逆技术，得到了有关大质量负载的空间机器人柔性臂动力学轨迹跟踪非线性控制问题的有效方法，并以一平面二杆空间机器人柔性臂为例进行了控制的仿真研究，仿真研究的结果表明，该方法具有较高的可靠性和良好的控制效果。     

Analtical- form direct kinematicefor the second scheme of a 5–5 general-geometry fully parallel manipulator

This article presents the direct kinematics of a 6 degrees of freedom fully parallel manipulator that features five connection points on both base and platform. The considered leg arrangement is one of the two possible, the other having been referred to in a previous paper. The base and platform have a general geometry, i.e., the connection points are not bound to lie on planes. The direct kinematics is solved in analytical form, which allows determination of every possible solution. After a suitable set of five equations in five unknowns has been laid down, and an original elimination procedure applied, a final polynomial equation of the 24th order is found whose 24 solutions correspond to as many assembly configurations for the considered fully parallel manipulator. A case study is reported. © 1995 John Wiley & Sons, Inc.     

Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.     

Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling

This paper deals with the performance analysis of a 3-degree-of-freedom (3-DOF) planar parallel manipulator with actuation redundancy. Closed-form solutions are developed for both the inverse and direct kinematics about the redundant parallel manipulator. In performance analysis phase, the dexterity is analyzed, three kinds of singularities are investigated, and the stiffness is estimated. Compared with the corresponding non-redundant parallel manipulator with the redundant link removed, the redundantly actuated one has better dexterity, litter singular configurations and higher stiffness. The redundantly actuated parallel manipulator was applied to the design of a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.     

Dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy

In this paper, based on the conventional Newton–Euler approach, a simplification method is proposed to derive the dynamic formulation of a planar 3-DOF parallel manipulator with actuation redundancy. Closed-form solutions are developed for the inverse kinematics. Based on the kinematics, the Newton–Euler approach in simplification form is used to derive the inverse dynamic model of the redundant parallel manipulator. Then, the driving force optimization is performed by minimizing an objective function which is the square of the sum of four driving forces. The dynamic simulations are done for the parallel manipulator with both the redundant and non-redundant actuations. The result shows that the dynamic characteristics of the manipulator in the redundant case are better than that in the non-redundancy. The redundantly actuated parallel manipulator was incorporated into a 4-DOF hybrid machine tool which includes a feed worktable.     

Kinematics analysis of an offset 3-UPU translational parallel robotic manipulator

The parallel robotic manipulator has attracted many researchers’ attention and it also has growing applications to different areas. This paper proposes a 3-UPU (universal–prismatic–universal) translational parallel robotic manipulator with an equal offset in its six universal joints, based on the zero offset 3-UPU parallel manipulator. The kinematics of the new manipulator is analyzed and its inverse and forward kinematics solutions are provided. The conclusion is that its forward kinematics has 16 solutions instead of two in the zero offset manipulator.     

Synthesis on forward kinematics problem algebraic modeling for the planar parallel manipulator: displacement-based equation systems

Based on a proven exact method which solves the forward kinematics problem (FKP) this article investigates the FKP formulation specifically applied to planar parallel manipulators. It focuses on the displacement-based equation systems. The majority of planar tripods can modeled by the 3-RPR parallel manipulator, which is a tripod constituted by a fixed base and a triangular mobile platform attached to three kinematics chains with linear (prismatic) actuators located between two revolute joints. In order to implement the algebraic method, the parallel manipulator kinematics are formulated as polynomial equation systems where the number of equations is equal to or exceeds the number of unknowns. Three geometrical formulations are derived to model the difficult FKP. The selected proven algebraic method uses Gröbner bases from which it constructs an equivalent univariate system. Then, the real roots are isolated using this last system. Each real solution exactly corresponds to one manipulator assembly mode, which is also called a manipulator posture. The FKP resolution of the planar 3-RPR parallel manipulator outputs six complex solutions which become a proven real solution number upper bound. In several typical examples, the resolution performances (computation times and memory usage) are given. It is then possible to compare the models and to reject one. Moreover, a number of real solutions are obtained and the corresponding postures drawn. The algebraic method is exact and produces certified results.     

Synthesis of the forward kinematics problem algebraic modeling for the general parallel manipulator: displacement-based equations

This paper closes a triptic to address the issue of the forward kinematics problem (FKP) aimed at certified solving with an exact algebraic method. This solving method was described in the first article published in Advanced Robotics. The second one investigated the formulation specifically applied to the planar parallel manipulators. This third paper is the logical one in the footsteps of the formersones, since it continues the formulation analyses and brings them to the general spatial parallel manipulator. Hence, this paper focuses on the displacement-based equation systems. This paper is the first one to present a synthesis on forward kinematics modeling focusing on finding an optimal mathematical formulation based on the displacement-based equation systems. The majority of parallel manipulators in applications can be modeled by the 6-6 hexapod or so-called Gough platform which is constituted by a fixed base and a mobile platform attached to six kinematics chains with linear (prismatic) actuators located between two revolute or Cardan joints. Again, in order to implement algebraic methods, the parallel manipulator kinematics shall be formulated as polynomial equations systems where the equation number is at least equal to the unknown numbers. Six geometric formulations were derived. The selected algebraic proven method is implementing Gröbner bases from which it constructs an equivalent univariate polynomial system. The resolution of this last system exactly determines the real solutions which correspond to the manipulator postures. The FKP resolution of the general 6-6 parallel manipulator outputs 40 complex solutions. Several instantiations shall be computed in order to select the model which leads to the FKP resolution with the lowest response times and smaller file sizes. It was possible to reject three modelings leading to bad performances or resolution failure. It was possible to determine one formulation where the solving computations were definitely better than the others.     

Position,Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.