應(yīng)用坐標(biāo)測(cè)量機(jī)的機(jī)器人運(yùn)動(dòng)學(xué)姿態(tài)的標(biāo)定外文翻譯@中英文翻譯@外文文獻(xiàn)翻譯

南京理工大學(xué)泰州科技學(xué)院 畢業(yè)設(shè)計(jì) (論文 )外文資料翻譯 系 部： 機(jī)械工程系 專 業(yè)： 機(jī)械工程及自動(dòng)化 姓 名： 錢 瑞 學(xué) 號(hào)： 0501510131 外文出處： The Internation Journal of Advanced Manufacturing Technology 附 件： 1.外文資料翻譯譯文； 2.外文原文。 指導(dǎo)教師評(píng)語(yǔ)： 簽名： 年 月 日 注： 請(qǐng)將該封面與附件裝訂成冊(cè)。 (用外文寫 ) 附件 1：外文資料翻譯譯文 應(yīng)用 坐標(biāo)測(cè)量機(jī)的機(jī)器人運(yùn)動(dòng) 學(xué)姿態(tài)的標(biāo)定 這篇文章報(bào)到的是用于機(jī)器人運(yùn)動(dòng)學(xué)標(biāo)定中能獲得全部姿態(tài)的操作裝置 坐標(biāo)測(cè)量機(jī)（ CMM）。運(yùn)動(dòng)學(xué)模型由于操作器得到發(fā)展 , 它們關(guān)系到基坐標(biāo)和工件。 工件姿態(tài)是從實(shí)驗(yàn)測(cè)量中引出的討論 , 同樣地是識(shí)別方法學(xué)。允許定義觀察策略的完全模擬實(shí)驗(yàn)已經(jīng)實(shí)現(xiàn)。實(shí)驗(yàn)工作的目的是描寫參數(shù)辨認(rèn)和精確確認(rèn)。用推論原則的那方法能得到在重復(fù)時(shí)近連續(xù)地校準(zhǔn)機(jī)器人。 關(guān)鍵字：機(jī)器人標(biāo)定 坐標(biāo)測(cè)量 參數(shù)辨認(rèn) 模擬學(xué)習(xí) 精確增進(jìn) 1. 前言 機(jī)器手有合理的重復(fù)精度 (0.3毫米 )而知名 , 但仍有不好的精確性 (10.0 毫米 )。為了實(shí)現(xiàn)機(jī)器手精確性，機(jī)器人可能要校準(zhǔn)也是好理解 。 在標(biāo)定過(guò)程中， 幾個(gè)連續(xù)的步驟能夠精確地識(shí)別機(jī)器人運(yùn)動(dòng)學(xué)參數(shù)，提高精確性。這些步驟為如下描述： 1 操作器的運(yùn)動(dòng)學(xué)模型和標(biāo)定過(guò)程本身是發(fā)展，和通常有標(biāo)準(zhǔn)運(yùn)動(dòng)學(xué)模型的工具實(shí)現(xiàn)的。作為結(jié)果的模型是定義基于廠商的運(yùn)動(dòng)學(xué)參數(shù)設(shè)置錯(cuò)誤量 , 和識(shí)別未知的 ,實(shí)際的參數(shù)設(shè)置。 2 機(jī)器人姿態(tài)的實(shí)驗(yàn)測(cè)量法 (部分的或完成 ) 是拿走為了獲得從聯(lián)系到實(shí)際機(jī)器人的參數(shù)設(shè)置數(shù)據(jù)。 3 實(shí)際的運(yùn)動(dòng)學(xué)參數(shù)識(shí)別是系統(tǒng)地改變參數(shù)設(shè)置和減少在模型階段錯(cuò)誤量的定義。一個(gè)接近完成辨認(rèn)由分析不同中 間姿態(tài)變量 P和運(yùn)動(dòng)學(xué)參數(shù) K的微分關(guān)系決定： 于是等價(jià)轉(zhuǎn)化得： 兩者擇一 , 問(wèn)題可以看成為多維的優(yōu)化問(wèn)題，這是為了減少一些定義的錯(cuò)誤功能到零點(diǎn)，運(yùn)動(dòng)學(xué)參數(shù)設(shè)置被改變。這是標(biāo)準(zhǔn)優(yōu)化問(wèn)題和可能解決用的眾所周知的 方法。 4 最后一步是機(jī)械手控制中的機(jī)器人運(yùn)動(dòng)學(xué)識(shí)別和在學(xué)習(xí)之下的硬件系統(tǒng)的詳細(xì)資料。 包含實(shí)驗(yàn)數(shù)據(jù)的這張紙用于標(biāo)度過(guò)程。 可獲得的幾個(gè)方法是可用于完成這任務(wù) , 雖然他們相當(dāng)復(fù)雜，獲得數(shù)據(jù)需要大量的成本和時(shí)間。這樣的技術(shù)包括使用可視化的和自動(dòng)化機(jī)械 ，伺服控制激光干涉計(jì)，有關(guān)聲音的傳感器和視覺(jué)傳感 器 。理想測(cè)量系統(tǒng)將獲得操作器的全部姿態(tài) (位置和方向 )，因?yàn)檫@將合并機(jī)械臂各個(gè)位置的全部信息。上面提到的所有方法僅僅用于唯一部分的姿態(tài) , 需要更多的數(shù)據(jù)是為了標(biāo)度過(guò)程到進(jìn)行。 2理論 文章中的理論描述，為了操作器空間放置的各自的位置，全部姿態(tài)是可測(cè)量的，雖然進(jìn)行幾個(gè)中間測(cè)量，是為了獲得姿態(tài)。測(cè)量姿態(tài)使用裝置是坐標(biāo)測(cè)量機(jī) (CMM),它是三軸的，棱鏡測(cè)量系統(tǒng)達(dá)到 0.01毫米的精確。機(jī)器人操作器是能校準(zhǔn)的， PUMA 560，放置接近于 CMM，特殊的操作裝置能到達(dá)邊緣。圖 1顯示了系統(tǒng)不同部分安排。在這部分運(yùn)動(dòng)學(xué)模 型將是發(fā)展 , 解釋姿態(tài)估算法，和參數(shù)辨認(rèn)方法。 2.1 運(yùn)動(dòng)學(xué)的參數(shù) 在這部分，操作器的基本運(yùn)動(dòng)學(xué)結(jié)構(gòu)將被規(guī)定，它關(guān)系到完全坐標(biāo)系統(tǒng)的討論 , 和終點(diǎn)模型。從這些模型，用于可能的技術(shù)的運(yùn)動(dòng)學(xué)參數(shù)的識(shí)別將被規(guī)定，和描述決定這些參數(shù)的方法。 那些基礎(chǔ)的模型工具用于描寫不同的物體和工件操作器位置空間的關(guān)系的方法是 Denavit-Hartenberg方法，在 Hayati 有調(diào)整計(jì)劃，停泊處 和當(dāng)二連續(xù)的接縫軸是名義上地平行的用于說(shuō)明不相稱模型 。如圖 2 這中方法存在于物體或相互聯(lián)系的操作桿結(jié)構(gòu)中，和運(yùn)動(dòng)學(xué)中需 要從一個(gè)坐標(biāo)到另一個(gè)坐標(biāo)這種同類變化是被定義的。這種變化是相同形式的 上面的關(guān)系可以解釋通過(guò)四個(gè)基本變化操作實(shí)現(xiàn)坐標(biāo)系 n-1到結(jié)構(gòu)坐標(biāo)系 n的變化。只有需要找到與前一個(gè)的關(guān)系的四個(gè)變化是必需的，在那個(gè)時(shí)候連續(xù)的軸是不平行的， n 定義為零點(diǎn)。 當(dāng)應(yīng)用于一個(gè)結(jié)構(gòu)到下一個(gè)結(jié)構(gòu)的等價(jià)變化坐標(biāo)系與更改 Denavit-Hartenberg系相一致時(shí)，它們將被書(shū)寫成矩陣元素實(shí)現(xiàn)運(yùn)動(dòng)學(xué)參數(shù)功能的矩陣形狀。這些參數(shù)是變化的簡(jiǎn)單變量：關(guān)節(jié)角 n ，連桿偏置 nd , 連桿長(zhǎng)度 na ，扭角 n ，矩陣通常表示如下： 對(duì)于多連接的 , 例如機(jī)械操作臂 ,各自連續(xù)的鏈環(huán)和兩者瞬間的位置描寫在前一個(gè)矩陣變化中。這種變化從底部鏈環(huán)開(kāi)始到第 n鏈環(huán)因此關(guān)系如下： 圖 3表示出 PUMA機(jī)器人在 Denavit-Hartenberg系中每一連桿，完全坐標(biāo)系和工具結(jié)構(gòu)。變化從世界坐標(biāo)系到機(jī)器人底部結(jié)構(gòu)需要仔細(xì)考 慮過(guò)，因?yàn)闈撛诘膮?shù)取決于被選擇的改變類型?？紤]到圖 4,世界坐標(biāo)www zyx ,，在 D-H系中定義的從世界坐標(biāo)到機(jī)器人基坐標(biāo)000 , zyx，坐標(biāo)bbb zyx ,是 PUMA機(jī)器人定義的基坐標(biāo)和機(jī)器人第二個(gè) D-H結(jié)構(gòu)中 坐標(biāo)111 , zyx。 我們感興趣的是從世界坐標(biāo)到111 , zyx必需的最小的參數(shù)數(shù)量 。實(shí)現(xiàn)這種變化有兩種路 徑：路徑 1，從www zyx ,到000 , zyxD-H變化包括四個(gè)參數(shù)，接著從000 , zyx到bbb zyx ,的變化將牽連二個(gè)參數(shù) 和 d 的變化 圖 3 圖 4 最后，另外從bbb zyx ,到 111 , zyx 的 D-H變化中有四個(gè)參數(shù)其中 1 和 兩個(gè)參數(shù)是關(guān)于軸 Z0因此不能獨(dú)立地識(shí)別， 1d 和 d 是沿著軸 Z0因此也不能是獨(dú)立地識(shí)別。因此，用這路徑它需要從世界坐標(biāo)到 PUMA機(jī)器人的第一個(gè)坐標(biāo)有八個(gè)獨(dú)立的運(yùn)動(dòng)學(xué)參數(shù)。路徑 2，同樣地二中擇一，從世界坐標(biāo)到底部結(jié)構(gòu)坐標(biāo)bbb zyx ,的 變化可以是直接定義。因此坐標(biāo)變換需要六個(gè)參數(shù)，如 Euler形式： 下面是從bbb zyx ,到 111 , zyx D H變化中的四個(gè)參數(shù)，但 1 與bbb ,相關(guān)聯(lián)，1d 與 zbybxb ppp , 相關(guān)聯(lián) ，減少成兩個(gè)參數(shù)。很顯然這種 路徑和路徑 1一樣需要八個(gè)參數(shù)，但是設(shè)置不同。 上面的方法可能使用于從世界坐標(biāo)系到 PUMA機(jī)器人的第二 結(jié)構(gòu)的移動(dòng)中。在這工作中，選擇路徑 2。工具改變引起需要六個(gè)特殊參數(shù)的改變的 Euler形式： 用于運(yùn)動(dòng)學(xué)模型的參數(shù)總數(shù)變成 30，他們定義于表 1 2.2 辨認(rèn)方法學(xué) 運(yùn)動(dòng)學(xué)的參數(shù)辨認(rèn)將是進(jìn)行多維的消去過(guò)程 , 因此避免了雅可比系統(tǒng)的標(biāo)定，過(guò)程如下： 1. 首先假設(shè)運(yùn)動(dòng)學(xué)的參數(shù) , 例如標(biāo)準(zhǔn)設(shè)置。 2. 為選擇任意關(guān)節(jié)角的設(shè)置。 3. 計(jì)算 PUMA機(jī)器人末端操作器。 4. 測(cè)量 PUMA機(jī)器人末端操作器的位姿如關(guān) 節(jié)角，通常標(biāo)準(zhǔn)的和預(yù)言的位姿將是不同的。 5. 為了最好使預(yù)言位姿達(dá)到標(biāo)準(zhǔn)的位姿，在整齊的方式更改運(yùn)動(dòng)學(xué)的參數(shù)。 這個(gè)過(guò)程應(yīng)用于不是單一的關(guān)節(jié)角設(shè)置而是一定數(shù)量的關(guān)節(jié)角，與物理測(cè)量數(shù)量等同的全部關(guān)節(jié)角設(shè)置是需要，必須滿足 在這兒： Kp是識(shí)別的運(yùn)動(dòng)學(xué)參數(shù)的數(shù)量 N是測(cè)量位姿的數(shù) Dr是測(cè)量過(guò)程中自由度的數(shù)量 文章中，給定了自由度的數(shù)量，贈(zèng)值為 因此全部位姿是測(cè)量的。在實(shí)踐中，更多的測(cè)量應(yīng)該是在實(shí)驗(yàn)測(cè)量法去掉補(bǔ)償結(jié)果。優(yōu)化程序使用命名為 ZXSSO，和標(biāo)準(zhǔn)庫(kù)功能的 IMSL。 2.3 位姿測(cè)量法 顯然它是 從上面的方法確定 PUMA機(jī)器人全部位姿是必需的為了實(shí)現(xiàn)標(biāo)定。這種方法現(xiàn)在將詳細(xì)地描寫。如圖 5所示，末端操作器由五個(gè)確定的工具組成。 考慮到借助于工具坐標(biāo)和世界坐標(biāo)中間各個(gè)坐標(biāo)的形式，如圖 6 這些坐標(biāo)的關(guān)系如下： ,ip 是關(guān)于世界 坐標(biāo) 結(jié)構(gòu)的第 i個(gè)球的 4x1列向量坐標(biāo) , Pi是關(guān)于工具 坐標(biāo) 結(jié)構(gòu)第 i個(gè)球的 4x1坐標(biāo)的列向量 , T是從世界坐標(biāo)結(jié)構(gòu)到工具坐標(biāo)結(jié)構(gòu)變化的 4x4矩陣。 設(shè)定 Pi，測(cè)量出 ,ip ， 然后 算出 T，使用于在標(biāo)定過(guò)程的位姿的測(cè)量。它是不會(huì)很簡(jiǎn)單，但是不可能由等式 (11)反求出 T。上面的過(guò)程由四個(gè)球 A, B, C和 D來(lái)實(shí)現(xiàn)，如下： 或?yàn)?由于 P, T和 P全部相符合，反解求的位姿矩陣 在實(shí)踐中當(dāng) PUMA機(jī)器人放置在確定的位置上，對(duì)于 CMM由四個(gè)球決定 Pi是困難的。準(zhǔn)確的測(cè)量三個(gè)球，第四球根據(jù)十字相乘可以獲得 考慮到?jīng)Q定的球中心坐標(biāo)的是基于球表面點(diǎn)的測(cè)量 ,沒(méi)有分析可獲到的程序。 另外，數(shù)字優(yōu)化的使用是為了求懲罰函數(shù)的最小解 這里 ),( wvu 是確定球中心， ),(iii zyx是第 i 個(gè) 球表面點(diǎn) 的坐標(biāo)且 r 是 球 的半徑。在測(cè)試過(guò)程中，發(fā)現(xiàn)只測(cè)量四個(gè)表面上的點(diǎn)來(lái)確定中心點(diǎn)是非常有效的。 附件 2：外文原文 （復(fù)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