外文资料翻译--应用坐标测量机的机器人运动学姿态的标定翻译-精品

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

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外文出处：The Internation Journal of Advanced

(用外文写)

Manufacturing Technology

附件： 1.外文资料翻译译文；2.外文原文。

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年月日注：请将该封面与附件装订成册。

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 β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 θ，连杆偏置n d , 连杆长度n a ，扭角n β，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w w w z y x ,,，在D-H 系中定义的从世界坐标到机器人基坐标000,,z y x ，坐标b b b z y x ,,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,,z y x 。我们感兴趣的是从世界坐标到111,,z y x 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w w w z y x ,,到000,,z y x D-H 变化包括四

个参数，接着从000,,z y x 到b b b z y x ,,的变化将牵连二个参数` 和`d 的变化

图3

图4

最后，另外从b b b z y x ,,到111,,z y x 的D-H 变化中有四个参数其中1θ?和`φ两个参数是关于轴Z 0因此不能独立地识别， 1d ?和`d 是沿着轴Z 0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b b b z y x ,,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b b b z y x ,,到111,,z y x D －H 变化中的四个参数，但1θ?与b b b ?θφ,,相关联，1d ?与zb yb xb p p p ,,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：

p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,

i

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,

p，然后算出T，使用于在标定过程的位姿的测量。它是不会

i

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),,(w v u 是确定球中心，),,(i i i z y x 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 m a c h i n e(C M M)w h i c h i s a b l e t o o b t a i n t h e f u l l p o s e o f t h e e n d-e f f e c t o r.A k i n e m a t i c m o d e l i s d e v e l o p e d f o r t h e 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 m et ho d is a b le t o c al ib r a te t h e ro bot s ucc es sfu l l y, with a resulting accuracy approaching that of its repeatability.

Keywords: Robot calibration; Coordinate measurement; Parameter identification; Simulation study; Accuracy enhancement 1. Introduction

It is wel l known tha t robo t manip ula tors t ypical ly ha ve reasonable repeatability (0.3 ram), yet exhibit poor accuracy

(10.0m m).T h e p r o c e s s b y w h i c h r o b o t s m a y b e c a l i b r a t e d

i n o r d e r t o a c h i e v e a c c u r a c i e s a p p r o a c h i n g t h a t o f t h e m a n i p u l a t o r i s a l s o w e l l u n d e r s t o o d .I n t h e c a l i b r a t i o n process, several sequential steps enable the precise kinematic p ar am et er s o f th e m an ip u l ato r to be identifi ed, 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 s t a n d a r d k i n e m a t i c m o d e l l i n g t o o l s.T h e r e s u l t i n g m o d e l i s u s e d t o d e f i n e a n e r r o r q u a n t i t y b a s e d o n a n o m i n a l (m a n u f a c t u r e r's)k i n e m a t i c p a r a m e t e r s e t,a n d a n u n k n o w n, actual parameter set which is to be identified.

2. Ex pe ri me n ta l m ea su re m e nts o f th e rob ot po se (p art ial o r 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

c h a n g i n g t h e n o m i n a l p a r a m e t e r s e t s o a s t o r e

d u c

e t h e e r r o r q u a n t i t y d e

f i n e d i n t h e m o d e l l i n

g p

h a s e.O n e a p p r o a c h t o a c h

i e v i n g t h i s i d e n t i f i c a t i o n i s d e t e r m i n i n g

t h e a n a l y t i c a l d i f f e r e n t i a l r e l a t i o n s h i p b e t w e e n t h e p o s e v a r i a b l e s P a n d t h e k i n e m a t i c p a r a m e t e r s K i n t h e f o r m of a Jacobian,

and then inverting the equation to calculate the deviation of t h e k i n e m a t i c p a r a m e t e r s f r o m t h e i r n o m i n a l v a l u e s

Alternatively, the problem can be viewed as a multidimensional o p t i m i s a t i o n t a s k,i n w h i c h t h e k i n e m a t i c p a r a m e t e r set is changed in order to reduce some defined error function t o z e r o.T h i s i s a s t a n d a r d o p t i m i s a t i o n p r o b l e m a n d m a y be solved using well-known methods.

4. The final step involves the incorporation of the identified k i n e m a t i c p a r a m e t e r s i n t h e c o n t r o l l e r o f t h e r o b o t a r m, the details of which are rather specific to the hardware of the system under study.

This paper addresses the issue of gathering the experimental d a t a u s e d i n t h e c a l i b r a t i o n p r o c e s s.S e v e r a l m e t h o d s a r e available to perform this task, although they vary in complexity, c o s t a n d t h e t i m e t a k e n t o a c q u i r e t h e d a t a.E x a m p l e s o f s u c h t e c h n i q u e s i n c l u d e t h e u s e o f v i s u a l a n d a u t o m a t i c t h e o d o l i t e s,s e r v o c o n t r o l l e d l a s e r i n t e r f e r o m e t e r s, a c o u s t i c s e n s o r s a n d v i d u a l s e n s o r s .A n i d e a l m e a s u r i n g 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 m e n t i o n e d a b o v e u s e o n l y t h e p a r t i a l p o s e,r e q u i r i n g m o r e

d a t a t o b

e t a k e n

f o r t h e c a l i b r a t i o n p r o c e s s t o p r o c e e d.

2. Theory

In the method described in this paper, for eac h 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 m e a s u r e m e n t i s a c o o r d i n a t e-m e a s u r i n g m a c h i n e(C M M), w h i c h i s a t h r e e-a x i s,p r i s m a t i c m e a s u r i n g s y s t e m w i t h a q u o t e d a c c u r a c y o f0.01r a m.T h e r o b o t m a n i p u l a t o r t o b e c a l i b r a t e d,a P U M A560,i s p l a c e d c l o s e t o t h e C M M,a n d a special end-effector is attached to the flange. Fig. 1 shows the arrangement of the various parts of the system. In this s e c t i o n t h e k i n e m a t i c m o d e l w i l l b e d e v e l o p e d,t h e p o s e 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 m o d e l s,t h e k i n e m a t i c p a r a m e t e r s w h i c h m a y b e i d e n t i f i e d 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 m a n i p u l a t o r w o r k s p a c e i s t h e D e n a v i t-H a r t e n b e r g m e t h o d ,w i t h m o d i f i c a t i o n s p r o p o s e d b y H a y a t i,M o o r i n g a n d W u t o a c c o u n t f o r d i s p r o p o r t i o n a l m o d e l s w he n tw o co n se cu t iv e jo i n t a x e s ar e nom ina ll y p a r all el. A s s h o w n i n F i g.2,t h i s m e t h o d p l a c e s a c o o r d i n a t e f r a m e o n

each object or manipulator link of interest, and the kinematics a r e d e f i n e d b y t h e h o m o g e n e o u s t r a n s f o r m a t i o n r e q u i r e d t o change one coordinate frame into the next. This transformation takes the familiar form

T h e a b o v e e q u a t i o n m a y b e i n t e r p r e t e d a s a m e a n s t o t r a n s f o r m f r a m e n-1i n t o f r a m e n b y m e a n s o f f o u r o u t o f t h e f i v e o p e r a t i o n s i n d i c a t e d.I t i s k n o w n t h a t o n l y f o u r transformations are needed to locate a coordinate frame with r es pe ct t o t he p r ev io us o ne.W he n conse cut iv e a x e s a re no t 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.

W h e n c o o r d i n a t e f r a m e s a r e p l a c e d i n c o n f o r m a n c e w i t h the modified Denavit-Hartenberg method, the transformations given in the above equation will apply to all transforms of o n e f r a m e i n t o t h e n e x t,a n d t h e s e m a y b e w r i t t e n i n a g e n e r i c m a t r i x f o r m,w h e r e t h e e l e m e n t s o f t h e m a t r i x a r e 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 o f tw is t a., a nd th e an g l e /3.. Th e mat rix f orm i s u suall y 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 a r e d e s c r i b e d b y t h e p r e v i o u s m a t r i x t r a n s f o r m a t i o n.'T h e

transformation from the base link to the nth link will therefore be given by

F i g.3s h o w s t h e P U M A m a n i p u l a t o r w i t h t h e D e n a v i t-H a r t e n b e r g f r a m e s a t t a c h e d t o e a c h l i n k,t o g e t h e r with world coordinate frame and a tool frame. The transformation f r o m t h e w o r l d f r a m e t o t h e b a s e f r a m e o f t h e manipulator needs to be considered carefully, since there are potential parameter dependencies if certain types of transforms a r e c h o s e n.C o n s i d e r F i g.4,w h i c h s h o w s t h e w o r l d f r a m e x w,y,,z,,t h e f r a m e X o,Y o,z0w h i c h i s d e f i n e d b y a D H t r a n s f o r m f r o m t h e w o r l d f r a m e t o t h e f i r s t j o i n t a x i s o f t h e m a n i p u l a t o r,f r a m e X b,Y b,Z b,w h i c h i s t h e P U M A

manufacturer's defined base frame, and frame xl, Yl, zl which is the second DH frame of the manipulator. We are interested i n d e t e r m i n i n g t h e m i n i m u m n u m b e r o f p a r a m e t e r s r e q u i r e d to move from the world frame to the frame x~, Yl, z~. There are two transformation paths that will accomplish this goal: P a t h1:A D H t r a n s f o r m f r o m x,,y,,z,,t o x0,Y o,z o i n v o l v i n g f o u r p a r a m e t e r s,f o l l o w e d b y a n o t h e r t r a n s f o r m f r o m x o,Y o,z0t o X b,Y b,Z b w h i c h w i l l i n v o l v e o n l y t w o parameters ~b' and d' in the transform

Finally, another DH transform from xb, Yb, Zb to Xt, y~, Z~ w hi ch i nv ol v es f o ur p ar a m ete r s e xc ept t hat A01 a n d 4~' ar e b o t h a b o u t t h e a x i s z o a n d c a n n o t t h e r e f o r e b e i d e n t i f i e d independently, and Adl and d' are both along the axis zo and also cannot be identified independently. It requires, therefore, o nl y ei gh t i nd ep e nd en t k i nem a t ic p arame ter s to g o fr om th e 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:

T h e f o l l o w i n g D H t r a n s f o r m f r o m x b,Y b,z b t O X l,Y l,z l 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 e i g h t p a r a m e t e r s a s i n p a t h i,b u t a d i f f e r e n t s e t.

E i t h e r o f t h e a b o v e m e t h o d s m a y b e u s e d t o m o v e f r o m t h e w o r l d f r a m e t o t h e s e c o n d f r a m e o f t h e P U M A.I n t h i s w o r k,t h e s e c o n d p a t h i s c h o s e n.T h e t o o l t r a n s f o r m i s a n E u l e r t r a n s f o r m w h i c h r e q u i r e s t h e s p e c i f i c a t i o n o f s i x parameters:

T he t ot al n u mb er of p ar a m ete r s u se d in the k ine m a tic mode l 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. Be gi n wi t h a g ue ss s e t of k in em atic par am ete r s, 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.M e a s u r e t h e a c t u a l p o s e o f t h e P U M A e n d-e f f e c t o r f o r t he s am e se t o f j oi nt a n g les.In g enera l, th e m e a sur ed an d predicted pose will be different.

5. Mo di fy t h e ki n em at ic p ara m e te rs in a n o rd erl y man ner i n o r d e r t o b e s t f i t(i n a l e a s t-s q u a r e s s e n s e)t h e m e a s u r e d 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

s e t s r e q u i r e d,w h i c h a l s o e q u a l s t h e n u m b e r o f p h y s i c a l measurement made, must satisfy

K p i s t h e n u m b e r o f k i n e m a t i c p a r a m e t e r s t o b e i d e n t i f i e d N i s t h e n u m b e r o f m e a s u r e m e n t s(p o s e s)t a k e n D r r e p r e s e n t s t h e n u m b e r o f d e g r e e s o f f r e e d o m p r e s e n t i n 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 s h o u l d b e t a k e n t o o f f s e t t h e e f f e c t o f n o i s e i n t h e e xp er im en ta l m ea s ur em en t s. T h e o pt imisa tio n pro c e dur e use d 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 f u l l p o s e o f t h e P U M A i s r e q u i r e d i n o r d e r t o p e r f o r m t h e calibration. This method will now be described in detail. The end-effector consists of an arrangement of five precisiontooling b a l l s a s s h o w n i n F i g. 5.C o n s i d e r t h e c o o r d i n a t e s o f the centre of each ball expressed in terms of the tool frame (Fig. 5) and the world coordinate frame, as shown in Fig. 6. T h e r e l a t i o n s h i p b e t w e e n t h e s e c o o r d i n a t e s m a y b e w r i t t e n as:

w he re P i' i s t he 4 x 1 c o lum n ve ct or of th e coo r d ina tes o f the ith ball expressed with respect to the world frame, P~ is t he 4 x 1 c o lu mn ve ct or o f t h e c oo rdina tes o f t h e it h bal l expressed with respect to the tool frame, and T is the 4 ? 4 h o m o g e n i o u s t r a n s f o r m f r o m t h e w o r l d f r a m e t o t h e t o o l frame.

The n may be foun d, a n d use d as th e m easure d pose in t he calibration process. It is not quite that simple, however, since it is not possible to invert equation (11) to obtain T. The a bo ve p ro ce s s is pe rf or m e d f o r t he four ba ll s, A, B, C an d D, and the positions ordered as:

or in the form:

S i n c e P',T a n d P a r e a l l n o w s q u a r e,t h e p o s e m a t r i x m a y be obtained by inversion:

I n pr ac ti ce it m a y be d i f fic u l t fo r the CM M to a c ces s fou r b a i l s t o d e t e r m i n e P~w h e n t h e P U M A i s p l a c e d i n c e r t a i n configurations. Three balls are actually measured and a fourth ball is fictitiously located according to the vector cross product:

R e g a r d i n g t h e d e t e r m i n a t i o n o f t h e c o o r d i n a t e s o f t h e

c e n t r e o f a b a l l b a s e

d o n m

e a s u r e d p o i n t s o n i t s s u r

f a c e, n o a n a l y t i c a l p r o c e d u r e s a r e a v a i l a b l e.A n o t h e r n u m e r i c a l optimisation scheme was used for this purpose such that the penalty function:

w a s m i n i m i s e d,w h e r e(u,v,w)a r e t h e c o o r d i n a t e s o f t h e c e n t r e o f t h e b a l l t o h e d e t e r m i n e d,(x/,y~,z~)a r e t h e coordinates of the ith point on the surface of the ball and r i s th e ba ll di am e te r. I n the tes ts performed, it was found sufficient to measure only four points (i = 4) on the surface to determine the ball centre.