应用坐标测量机的机器人运动学姿态的标定外文翻译@中英文翻译@外文文献翻译

南京理工大学泰州科技学院 毕业设计 (论文 )外文资料翻译 系 部： 机械工程系 专 业： 机械工程及自动化 姓 名： 钱 瑞 学 号： 0501510131 外文出处： The Internation Journal of Advanced Manufacturing Technology 附 件： 1.外文资料翻译译文； 2.外文原文。 指导教师评语： 签名： 年 月 日 注： 请将该封面与附件装订成册。 (用外文写 ) 附件 1：外文资料翻译译文 应用 坐标测量机的机器人运动 学姿态的标定 这篇文章报到的是用于机器人运动学标定中能获得全部姿态的操作装置 坐标测量机（ CMM）。运动学模型由于操作器得到发展 , 它们关系到基坐标和工件。 工件姿态是从实验测量中引出的讨论 , 同样地是识别方法学。允许定义观察策略的完全模拟实验已经实现。实验工作的目的是描写参数辨认和精确确认。用推论原则的那方法能得到在重复时近连续地校准机器人。 关键字：机器人标定 坐标测量 参数辨认 模拟学习 精确增进 1. 前言 机器手有合理的重复精度 (0.3毫米 )而知名 , 但仍有不好的精确性 (10.0 毫米 )。为了实现机器手精确性，机器人可能要校准也是好理解 。 在标定过程中， 几个连续的步骤能够精确地识别机器人运动学参数，提高精确性。这些步骤为如下描述： 1 操作器的运动学模型和标定过程本身是发展，和通常有标准运动学模型的工具实现的。作为结果的模型是定义基于厂商的运动学参数设置错误量 , 和识别未知的 ,实际的参数设置。 2 机器人姿态的实验测量法 (部分的或完成 ) 是拿走为了获得从联系到实际机器人的参数设置数据。 3 实际的运动学参数识别是系统地改变参数设置和减少在模型阶段错误量的定义。一个接近完成辨认由分析不同中 间姿态变量 P和运动学参数 K的微分关系决定： 于是等价转化得： 两者择一 , 问题可以看成为多维的优化问题，这是为了减少一些定义的错误功能到零点，运动学参数设置被改变。这是标准优化问题和可能解决用的众所周知的 方法。 4 最后一步是机械手控制中的机器人运动学识别和在学习之下的硬件系统的详细资料。 包含实验数据的这张纸用于标度过程。 可获得的几个方法是可用于完成这任务 , 虽然他们相当复杂，获得数据需要大量的成本和时间。这样的技术包括使用可视化的和自动化机械 ，伺服控制激光干涉计，有关声音的传感器和视觉传感 器 。理想测量系统将获得操作器的全部姿态 (位置和方向 )，因为这将合并机械臂各个位置的全部信息。上面提到的所有方法仅仅用于唯一部分的姿态 , 需要更多的数据是为了标度过程到进行。 2理论 文章中的理论描述，为了操作器空间放置的各自的位置，全部姿态是可测量的，虽然进行几个中间测量，是为了获得姿态。测量姿态使用装置是坐标测量机 (CMM),它是三轴的，棱镜测量系统达到 0.01毫米的精确。机器人操作器是能校准的， PUMA 560，放置接近于 CMM，特殊的操作装置能到达边缘。图 1显示了系统不同部分安排。在这部分运动学模 型将是发展 , 解释姿态估算法，和参数辨认方法。 2.1 运动学的参数 在这部分，操作器的基本运动学结构将被规定，它关系到完全坐标系统的讨论 , 和终点模型。从这些模型，用于可能的技术的运动学参数的识别将被规定，和描述决定这些参数的方法。 那些基础的模型工具用于描写不同的物体和工件操作器位置空间的关系的方法是 Denavit-Hartenberg方法，在 Hayati 有调整计划，停泊处 和当二连续的接缝轴是名义上地平行的用于说明不相称模型 。如图 2 这中方法存在于物体或相互联系的操作杆结构中，和运动学中需 要从一个坐标到另一个坐标这种同类变化是被定义的。这种变化是相同形式的 上面的关系可以解释通过四个基本变化操作实现坐标系 n-1到结构坐标系 n的变化。只有需要找到与前一个的关系的四个变化是必需的，在那个时候连续的轴是不平行的， n 定义为零点。 当应用于一个结构到下一个结构的等价变化坐标系与更改 Denavit-Hartenberg系相一致时，它们将被书写成矩阵元素实现运动学参数功能的矩阵形状。这些参数是变化的简单变量：关节角 n ，连杆偏置 nd , 连杆长度 na ，扭角 n ，矩阵通常表示如下： 对于多连接的 , 例如机械操作臂 ,各自连续的链环和两者瞬间的位置描写在前一个矩阵变化中。这种变化从底部链环开始到第 n链环因此关系如下： 图 3表示出 PUMA机器人在 Denavit-Hartenberg系中每一连杆，完全坐标系和工具结构。变化从世界坐标系到机器人底部结构需要仔细考 虑过，因为潜在的参数取决于被选择的改变类型。考虑到图 4,世界坐标www zyx ,，在 D-H系中定义的从世界坐标到机器人基坐标000 , zyx，坐标bbb zyx ,是 PUMA机器人定义的基坐标和机器人第二个 D-H结构中 坐标111 , zyx。 我们感兴趣的是从世界坐标到111 , zyx必需的最小的参数数量 。实现这种变化有两种路 径：路径 1，从www zyx ,到000 , zyxD-H变化包括四个参数，接着从000 , zyx到bbb zyx ,的变化将牵连二个参数 和 d 的变化 图 3 图 4 最后，另外从bbb zyx ,到 111 , zyx 的 D-H变化中有四个参数其中 1 和 两个参数是关于轴 Z0因此不能独立地识别， 1d 和 d 是沿着轴 Z0因此也不能是独立地识别。因此，用这路径它需要从世界坐标到 PUMA机器人的第一个坐标有八个独立的运动学参数。路径 2，同样地二中择一，从世界坐标到底部结构坐标bbb zyx ,的 变化可以是直接定义。因此坐标变换需要六个参数，如 Euler形式： 下面是从bbb zyx ,到 111 , zyx D H变化中的四个参数，但 1 与bbb ,相关联，1d 与 zbybxb ppp , 相关联 ，减少成两个参数。很显然这种 路径和路径 1一样需要八个参数，但是设置不同。 上面的方法可能使用于从世界坐标系到 PUMA机器人的第二 结构的移动中。在这工作中，选择路径 2。工具改变引起需要六个特殊参数的改变的 Euler形式： 用于运动学模型的参数总数变成 30，他们定义于表 1 2.2 辨认方法学 运动学的参数辨认将是进行多维的消去过程 , 因此避免了雅可比系统的标定，过程如下： 1. 首先假设运动学的参数 , 例如标准设置。 2. 为选择任意关节角的设置。 3. 计算 PUMA机器人末端操作器。 4. 测量 PUMA机器人末端操作器的位姿如关 节角，通常标准的和预言的位姿将是不同的。 5. 为了最好使预言位姿达到标准的位姿，在整齐的方式更改运动学的参数。 这个过程应用于不是单一的关节角设置而是一定数量的关节角，与物理测量数量等同的全部关节角设置是需要，必须满足 在这儿： Kp是识别的运动学参数的数量 N是测量位姿的数 Dr是测量过程中自由度的数量 文章中，给定了自由度的数量，赠值为 因此全部位姿是测量的。在实践中，更多的测量应该是在实验测量法去掉补偿结果。优化程序使用命名为 ZXSSO，和标准库功能的 IMSL。 2.3 位姿测量法 显然它是 从上面的方法确定 PUMA机器人全部位姿是必需的为了实现标定。这种方法现在将详细地描写。如图 5所示，末端操作器由五个确定的工具组成。 考虑到借助于工具坐标和世界坐标中间各个坐标的形式，如图 6 这些坐标的关系如下： ,ip 是关于世界 坐标 结构的第 i个球的 4x1列向量坐标 , Pi是关于工具 坐标 结构第 i个球的 4x1坐标的列向量 , T是从世界坐标结构到工具坐标结构变化的 4x4矩阵。 设定 Pi，测量出 ,ip ， 然后 算出 T，使用于在标定过程的位姿的测量。它是不会很简单，但是不可能由等式 (11)反求出 T。上面的过程由四个球 A, B, C和 D来实现，如下： 或为 由于 P, T和 P全部相符合，反解求的位姿矩阵 在实践中当 PUMA机器人放置在确定的位置上，对于 CMM由四个球决定 Pi是困难的。准确的测量三个球，第四球根据十字相乘可以获得 考虑到决定的球中心坐标的是基于球表面点的测量 ,没有分析可获到的程序。 另外，数字优化的使用是为了求惩罚函数的最小解 这里 ),( wvu 是确定球中心， ),(iii zyx是第 i 个 球表面点 的坐标且 r 是 球 的半径。在测试过程中，发现只测量四个表面上的点来确定中心点是非常有效的。 附件 2：外文原文 （复印件） Full-Pose Calibration of a Robot Manipulator Using a Coordinate- Measuring Machine The work reported in this article addresses the kinematic calibration of a robot manipulator using a coordinate measuring machine (CMM) which is able to obtain the full pose of the end-effector. A kinematic model is developed for the manipulator, its relationship to the world coordinate frame and the tool. The derivation of the tool pose from experimental measurements is discussed, as is the identification methodology. A complete simulation of the experiment is performed, allowing the observation strategy to be defined. The experimental work is described together with the parameter identification and accuracy verification. The principal conclusion is that the method is able to calibrate the robot successfully, with a resulting accuracy approaching that of its repeatability. Keywords: Robot calibration； Coordinate measurement； Parameter identification； Simulation study； Accuracy enhancement 1. Introduction It is well known that robot manipulators typically have reasonable repeatability (0.3 ram), yet exhibit poor accuracy (10.0 mm). The process by which robots may be calibrated in order to achieve accuracies approaching that of the manipulator is also well understood . In the calibration process, several sequential steps enable the precise kinematic parameters of the manipulator to be identified, leading to improved accuracy. These steps may be described as follows: 1. A kinematic model of the manipulator and the calibration process itself is developed and is usually accomplished with standard kinematic modelling tools. The resulting model is used to define an error quantity based on a nominal (manufacturers) kinematic parameter set, and an unknown, actual parameter set which is to be identified. 2. Experimental measurements of the robot pose (partial or complete) are taken in order to obtain data relating to the actual parameter set for the robot. 3.The actual kinematic parameters are identified by systematically changing the nominal parameter set so as to reduce the error quantity defined in the modelling phase. One approach to achieving this identification is determining the analytical differential relationship between the pose variables P and the kinematic parameters K in the form of a Jacobian, and then inverting the equation to calculate the deviation of the kinematic parameters from their nominal values Alternatively, the problem can be viewed as a multidimensional optimisation task, in which the kinematic parameter set is changed in order to reduce some defined error function to zero. This is a standard optimisation problem and may be solved using well-known methods. 4. The final step involves the incorporation of the identified kinematic parameters in the controller of the robot arm, the details of which are rather specific to the hardware of the system under study. This paper addresses the issue of gathering the experimental data used in the calibration process. Several methods are available to perform this task, although they vary in complexity, cost and the time taken to acquire the data. Examples of such techniques include the use of visual and automatic theodolites, servocontrolled laser interferometers , acoustic sensors and vidual sensors . An ideal measuring system would acquire the full pose of the manipulator (position and orientation), because this would incorporate the maximum information for each position of the arm. All of the methods mentioned above use only the partial pose, requiring more data to be taken for the calibration process to proceed. 2. Theory In the method described in this paper, for each position in which the manipulator is placed, the full pose is measured, although several intermediate measurements have to be taken in order to arrive at the pose. The device used for the pose measurement is a coordinate-measuring machine (CMM), which is a three-axis, prismatic measuring system with a quoted accuracy of 0.01 ram. The robot manipulator to be calibrated, a PUMA 560, is placed close to the CMM, and a special end-effector is attached to the flange. Fig. 1 shows the arrangement of the various parts of the system. In this section the kinematic model will be developed, the pose estimation algorithms explained, and the parameter identification methodology outlined. 2.1 Kinematic Parameters In this section, the basic kinematic structure of the manipulator will be specified, its relation to a user-defined world coordinate system discussed, and the end-point toil modelled. From these models, the kinematic parameters which may be identified using the proposed technique will be specified, and a method f o r d e t e r m i n i n g t h o s e p a r a m e t e r s d e s c r i b e d . The fundamental modelling tool used to describe the spatial relationship between the various objects and locations in the manipulator workspace is the Denavit-Hartenberg method , with modifications proposed by Hayati, Mooring and Wu to account for disproportional models when two consecutive joint axes are nominally parallel. As shown in Fig. 2, this method places a coordinate frame on each object or manipulator link of interest, and the kinematics are defined by the homogeneous transformation required to change one coordinate frame into the next. This transformation takes the familiar form The above equation may be interpreted as a means to transform frame n-1 into frame n by means of four out of the five operations indicated. It is known that only four transformations are needed to locate a coordinate frame with respect to the previous one. When consecutive axes are not parallel, the value of/3. is defined to be zero, while for the case when consecutive axes are parallel, d. is the variable chosen to be zero. When coordinate frames are placed in conformance with the modified Denavit-Hartenberg method, the transformations given in the above equation will apply to all transforms of one frame into the next, and these may be written in a generic matrix form, where the elements of the matrix are functions of the kinematic parameters. These parameters are simply the variables of the transformations: the joint angle 0., the common normal offset d., the link length a., the angle of twist a., and the angle /3. The matrix form is usually expressed as follows: For a serial linkage, such as a robot manipulator, a coordinate frame is attached to each consecutive link so that both the instantaneous position together with the invariant geometry are described by the previous matrix transformation. The transformation from the base link to the nth link will therefore be given by Fig. 3 shows the PUMA manipulator w i t h t h e Denavit-Hartenberg frames attached to each link, together with world coordinate frame and a tool frame. The transformation from the world frame to the base frame of the manipulator needs to be considered carefully, since there are potential parameter dependencies if certain types of transforms are chosen. Consider Fig. 4, which shows the world frame xw, y, z, the frame Xo, Yo, z0 which is defined by a DH transform from the world frame to the first joint axis of the manipulator, frame Xb, Yb, Zb, which is the PUMA manufacturers defined base frame, and frame xl, Yl, zl which is the second DH frame of the manipulator. We are interested in determining the minimum number of parameters required to move from the world frame to the frame x, Yl, z. There are two transformation paths that will accomplish this goal: Path 1: A DH transform from x, y, z, to x0, Yo, zo involving four parameters, followed by another transform from xo, Yo, z0 to Xb, Yb, Zb which will involve only two parameters b and d in the transform Finally, another DH transform from xb, Yb, Zb to Xt, y, Z which involves four parameters except that A01 and 4 are both about the axis zo and cannot therefore be identified independently, and Adl and d are both along the axis zo and also cannot be identified independently. It requires, therefore, only eight independent kinematic parameters to go from the world frame to the first frame of the PUMA using this path. Path 2: As an alternative, a transform may be defined directly from the world frame to the base frame Xb, Yb, Zb. Since this is a frame-to-frame transform it requires six parameters, such as the Euler form: The following DH transform from xb, Yb, zb tO Xl, Yl, zl would involve four parameters, but A0 may be resolved into 4, 0b, , and Ad resolved into Pxb, Pyb, Pzb, reducing the parameter count to two. It is seen that this path also requires eight parameters as in path i, but a different set. Either of the above methods may be used to move from the world frame to the second frame of the PUMA. In this work, the second path is chosen. The tool transform is an Euler transform which requires the specification of six parameters: The total number of parameters used in the kinematic model becomes 30, and their nominal values are defined in Table 1. 2.2 Identification Methodology The kinematic parameter identification will be performed as a multidimensional minimisation process, since this avoids the calculation of the system Jacobian. The process is as follows: 1. Begin with a guess set of kinematic parameters, such as the nominal set. 2. Select an arbitrary set of joint angles for the PUMA. 3. Calculate the pose of the PUMA end-effector. 4. Measure the actual pose of the PUMA end-effector for the same set of joint angles. In general, the measured and predicted pose will be different. 5. Modify the kinematic parameters in an orderly manner in order to best fit (in a least-squares sense) the measured pose to the predicted pose. The process is applied not to a single set of joint angles but to a number of joint angles. The total number of joint angle sets required, which also equals the number of physical measurement made, must satisfy Kp is the number of kinematic parameters to be identified N is the number of measureme nt s ( p o s e s) t a k e n Dr represents the number of degrees of freedom present in each measurement. In the system described in this paper, the number of degrees of freedom is given by since full pose is measured. In practice, many more measurements should be taken to offset the effect of noise in the experimental measurements. The optimisation procedure used is known as ZXSSO, and is a standard library function in the IMSL package . 2.3 Pose Measurement It is apparent from the above that a means to determine the full pose of the PUMA is required in order to perform the calibration. This method will now be described in detail. The end-effector consists of an arrangement of five precisiontooling balls as shown in Fig. 5. Consider the coordinates of the centre of each ball expressed in terms of the tool frame (Fig. 5) and t