機(jī)械手-集裝箱波紋板焊接機(jī)器人機(jī)構(gòu)運(yùn)動學(xué)分析及車體結(jié)構(gòu),機(jī)械手,集裝箱,波紋,焊接,機(jī)器人,機(jī)構(gòu),運(yùn)動學(xué),分析,車體,結(jié)構(gòu) 南京理工大學(xué)泰州科技學(xué)院 畢業(yè)設(shè)計(論文)外文資料翻譯 系　　部： 機(jī)械工程系 專 業(yè)： 機(jī)械工程及自動化 姓 名： 錢 瑞 學(xué) 號： 0501510131 (用外文寫) 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)教師評語： 簽名： 年 月 日 注：請將該封面與附件裝訂成冊。 附件1：外文資料翻譯譯文 應(yīng)用坐標(biāo)測量機(jī)的機(jī)器人運(yùn)動學(xué)姿態(tài)的標(biāo)定 這篇文章報到的是用于機(jī)器人運(yùn)動學(xué)標(biāo)定中能獲得全部姿態(tài)的操作裝置——坐標(biāo)測量機(jī)（CMM）。運(yùn)動學(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)是從實驗測量中引出的討論, 同樣地是識別方法學(xué)。允許定義觀察策略的完全模擬實驗已經(jīng)實現(xiàn)。實驗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)定過程中， 幾個連續(xù)的步驟能夠精確地識別機(jī)器人運(yùn)動學(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)動學(xué)模型和標(biāo)定過程本身是發(fā)展，和通常有標(biāo)準(zhǔn)運(yùn)動學(xué)模型的工具實現(xiàn)的。作為結(jié)果的模型是定義基于廠商的運(yùn)動學(xué)參數(shù)設(shè)置錯誤量, 和識別未知的,實際的參數(shù)設(shè)置。 2 機(jī)器人姿態(tài)的實驗測量法(部分的或完成) 是拿走為了獲得從聯(lián)系到實際機(jī)器人的參數(shù)設(shè)置數(shù)據(jù)。 3 實際的運(yùn)動學(xué)參數(shù)識別是系統(tǒng)地改變參數(shù)設(shè)置和減少在模型階段錯誤量的定義。一個接近完成辨認(rèn)由分析不同中間姿態(tài)變量P和運(yùn)動學(xué)參數(shù)K的微分關(guān)系決定： 于是等價轉(zhuǎn)化得： 兩者擇一, 問題可以看成為多維的優(yōu)化問題，這是為了減少一些定義的錯誤功能到零點(diǎn)，運(yùn)動學(xué)參數(shù)設(shè)置被改變。這是標(biāo)準(zhǔn)優(yōu)化問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)動學(xué)識別和在學(xué)習(xí)之下的硬件系統(tǒng)的詳細(xì)資料。 包含實驗數(shù)據(jù)的這張紙用于標(biāo)度過程。 可獲得的幾個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間。這樣的技術(shù)包括使用可視化的和自動化機(jī)械 ，伺服控制激光干涉計，有關(guān)聲音的傳感器和視覺傳感器 。理想測量系統(tǒng)將獲得操作器的全部姿態(tài)(位置和方向)，因為這將合并機(jī)械臂各個位置的全部信息。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)是可測量的，雖然進(jìn)行幾個中間測量，是為了獲得姿態(tài)。測量姿態(tài)使用裝置是坐標(biāo)測量機(jī)(CMM),它是三軸的，棱鏡測量系統(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)動學(xué)的參數(shù) 在這部分，操作器的基本運(yùn)動學(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)動學(xué)參數(shù)的識別將被規(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)動學(xué)中需要從一個坐標(biāo)到另一個坐標(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)系可以解釋通過四個基本變化操作實現(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的關(guān)系的四個變化是必需的，在那個時候連續(xù)的軸是不平行的，定義為零點(diǎn)。 當(dāng)應(yīng)用于一個結(jié)構(gòu)到下一個結(jié)構(gòu)的等價變化坐標(biāo)系與更改Denavit-Hartenberg系相一致時，它們將被書寫成矩陣元素實現(xiàn)運(yùn)動學(xué)參數(shù)功能的矩陣形狀。這些參數(shù)是變化的簡單變量：關(guān)節(jié)角，連桿偏置, 連桿長度，扭角，矩陣通常表示如下： 對于多連接的, 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矩陣變化中。這種變化從底部鏈環(huán)開始到第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，因為潛在的參數(shù)取決于被選擇的改變類型?？紤]到圖4,世界坐標(biāo)，在D-H系中定義的從世界坐標(biāo)到機(jī)器人基坐標(biāo)，坐標(biāo)是PUMA機(jī)器人定義的基坐標(biāo)和機(jī)器人第二個D-H結(jié)構(gòu)中坐標(biāo)。我們感興趣的是從世界坐標(biāo)到必需的最小的參數(shù)數(shù)量。實現(xiàn)這種變化有兩種路徑：路徑1，從到D-H變化包括四個參數(shù)，接著從到的變化將牽連二個參數(shù)和的變化 圖3 圖4 最后，另外從到的D-H變化中有四個參數(shù)其中和兩個參數(shù)是關(guān)于軸Z0因此不能獨(dú)立地識別， 和是沿著軸Z0因此也不能是獨(dú)立地識別。因此，用這路徑它需要從世界坐標(biāo)到PUMA機(jī)器人的第一個坐標(biāo)有八個獨(dú)立的運(yùn)動學(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)的變化可以是直接定義。因此坐標(biāo)變換需要六個參數(shù)，如Euler形式： 下面是從到D－H變化中的四個參數(shù)，但與相關(guān)聯(lián)，與相關(guān)聯(lián)，減少成兩個參數(shù)。很顯然這種路徑和路徑1一樣需要八個參數(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)的移動中。在這工作中，選擇路徑2。工具改變引起需要六個特殊參數(shù)的改變的Euler形式： 用于運(yùn)動學(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)動學(xué)的參數(shù)辨認(rèn)將是進(jìn)行多維的消去過程, 因此避免了雅可比系統(tǒng)的標(biāo)定，過程如下： 1. 首先假設(shè)運(yùn)動學(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. 計算PUMA機(jī)器人末端操作器。 4. 測量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)動學(xué)的參數(shù)。 這個過程應(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是識別的運(yùn)動學(xué)參數(shù)的數(shù)量 N是測量位姿的數(shù) Dr是測量過程中自由度的數(shù)量 文章中，給定了自由度的數(shù)量，贈值為 因此全部位姿是測量的。在實踐中，更多的測量應(yīng)該是在實驗測量法去掉補(bǔ)償結(jié)果。優(yōu)化程序使用命名為ZXSSO，和標(biāo)準(zhǔn)庫功能的IMSL。 2.3 位姿測量法 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)中間各個坐標(biāo)的形式，如圖6 這些坐標(biāo)的關(guān)系如下： 是關(guān)于世界坐標(biāo)結(jié)構(gòu)的第i個球的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，測量出，然后算出T，使用于在標(biāo)定過程的位姿的測量。它是不會很簡單，但是不可能由等式(11)反求出T。上面的過程由四個球A, B, C和D來實現(xiàn)，如下： 或為 由于P`, T和P全部相符合，反解求的位姿矩陣 在實踐中當(dāng)PUMA機(jī)器人放置在確定的位置上，對于CMM由四個球決定Pi是困難的。準(zhǔn)確的測量三個球，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)的測量,沒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 這里是確定球中心，是第個球表面點(diǎn)的坐標(biāo)且是球的半徑。在測試過程中，發(fā)現(xiàn)只測量四個表面上的點(diǎn)來確定中心點(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 (manufacturer's) 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 for determining those parameters described. 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 with the 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 manufacturer's 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 measurements (poses) taken 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 the world coordinate frame, as shown in Fig. 6. The relationship between these coordinates may be written as: where Pi' is the 4 x 1 column vector of the coordinates of the ith ball expressed with respect to the world frame, P~ is the 4 x 1 column vector of the coordinates of the ith ball expressed with respect to the tool frame, and T is the 4 ? 4 homogenious transform from the world frame to the tool frame. Then may be found, and used as the measured pose in the calibration process. It is not quite that simple, however, since it is not possible to invert equation (11) to obtain T. The above process is performed for the four balls, A, B, C and D, and the positions ordered as: or in the form: Since P', T and P are all now square, the pose matrix may be obtained by inversion: In practice it may be difficult for the CMM to access four bails to determine P~ when the PUMA is placed in certain configurations. Three balls are actually measured and a fourth ball is fictitiously located according to the vector cross product: Regarding the determination of the coordinates of the centre of a ball based on measured points on its surface, no analytical procedures are available. Another numerical optimisation scheme was used for this purpose such that the penalty function: was minimised, where (u, v, w) are the coordinates of the centre of the ball to he determined, (x/, y~, z~) are the coordinates of the ith point on the surface of the ball and r is the ball diameter. In the tests performed, it was found sufficient to measure only four points (i = 4) on the surface to determine the ball centre.