2919 集裝箱波紋板焊接機器人機構運動學分析及車體結構,集裝箱,波紋,焊接,機器人,機構,運動學,分析,車體,結構 南京理工大學泰州科技學院畢業(yè)設計(論文)外文資料翻譯系　　部： 機械工程系 專 業(yè)： 機械工程及自動化 姓 名： 錢 瑞 學 號： 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。 指導教師評語：簽名： (用外文寫) 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用坐標測量機的機器人運動學姿態(tài)的標定這篇文章報到的是用于機器人運動學標定中能獲得全部姿態(tài)的操作裝置——坐標測量機（CMM）。運動學模型由于操作器得到發(fā)展, 它們關系到基坐標和工件。 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。允許定義觀察策略的完全模擬實驗已經實現(xiàn)。實驗工作的目的是描寫參數(shù)辨認和精確確認。用推論原則的那方法能得到在重復時近連續(xù)地校準機器人。關鍵字：機器人標定 坐標測量 參數(shù)辨認 模擬學習 精確增進1. 前言機器手有合理的重復精度 (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)機器手精確性，機器人可能要校準也是好理解 。 在標定過程中， 幾個連續(xù)的步驟能夠精確地識別機器人運動學參數(shù)，提高精確性。這些步驟為如下描述：1 操作器的運動學模型和標定過程本身是發(fā)展，和通常有標準運動學模型的工具實現(xiàn)的。作為結果的模型是定義基于廠商的運動學參數(shù)設置錯誤量, 和識別未知的,實際的參數(shù)設置。2 機器人姿態(tài)的實驗測量法(部分的或完成) 是拿走為了獲得從聯(lián)系到實際機器人的參數(shù)設置數(shù)據(jù)。3 實際的運動學參數(shù)識別是系統(tǒng)地改變參數(shù)設置和減少在模型階段錯誤量的定義。一個接近完成辨認由分析不同中間姿態(tài)變量P 和運動學參數(shù)K 的微分關系決定：于是等價轉化得：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，運動學參數(shù)設置被改變。這是標準優(yōu)化問題和可能解決用的眾所周知的 方法。4 最后一步是機械手控制中的機器人運動學識別和在學習之下的硬件系統(tǒng)的詳細資料。包含實驗數(shù)據(jù)的這張紙用于標度過程。 可獲得的幾個方法是可用于完成這任務, 雖然他們相當復雜，獲得數(shù)據(jù)需要大量的成本和時間。這樣的技術包括使用可視化的和自動化機械 ，伺服控制激光干涉計，有關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)是為了標度過程到進行。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)使用裝置是坐標測量機(CMM),它是三軸的，棱鏡測量系統(tǒng)達到0.01毫米的精確。機器人操作器是能校準的，PUMA 560 ，放置接近于 CMM，特殊的操作裝置能到達邊緣。圖 1顯示了系統(tǒng)不同部分安排。在這部分運動學模型將是發(fā)展, 解釋姿態(tài)估算法，和參數(shù)辨認方法。2.1 運動學的參數(shù)在這部分，操作器的基本運動學結構將被規(guī)定，它關系到完全坐標系統(tǒng)的討論, 和終點模型。從這些模型，用于可能的技術的運動學參數(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系的方法是Denavit-Hartenberg方法，在Hayati 有調整計劃，停泊處 和當二連續(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)系的操作桿結構中，和運動學中需要從一個坐標到另一個坐標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系可以解釋通過四個基本變化操作實現(xiàn)坐標系n-1到結構坐標系n的變化。只有需要找到與前一個的關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。n?當應用于一個結構到下一個結構的等價變化坐標系與更改Denavit-Hartenberg系相一致時，它們將被書寫成矩陣元素實現(xiàn)運動學參數(shù)功能的矩陣形狀。這些參數(shù)是變化的簡單變量：關節(jié)角 ，連桿偏置 , 連桿長度 ，扭角 ，矩陣通常n?ndnan?表示如下：對于多連接的, 例如機械操作臂,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)因此關系如下：圖3表示出PUMA機器人在Denavit-Hartenberg系中每一連桿，完全坐標系和工具結構。變化從世界坐標系到機器人底部結構需要仔細考慮過，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 ，在D-H系中定義的從世wzyx,界坐標到機器人基坐標 ，坐標 是 PUMA機器人定義的基坐標和機器0,zyxbz,人第二個D-H結構中坐標 。我們感興趣的是從世界坐標到 必需的最1 1,zyx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w,0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0,zyxbz, `?d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bzyx,1,z 1??`?數(shù)是關于軸Z 0因此不能獨立地識別， 和 是沿著軸Z 0因此也不能是獨立地識d?`別。因此，用這路徑它需要從世界坐標到PUMA機器人的第一個坐標有八個獨立的運動學參數(shù)。路徑2，同樣地二中擇一，從世界坐標到底部結構坐標 的變bzyx,化可以是直接定義。因此坐標變換需要六個參數(shù)，如Euler形式：下面是從 到 D－H變化中的四個參數(shù)，但 與 相關聯(lián)，bzyx,1,z 1??b??,與 相關聯(lián)，減少成兩個參數(shù)。很顯然這種路徑和路徑1一樣需要八1d?zbp,個參數(shù)，但是設置不同。上面的方法可能使用于從世界坐標系到PUMA機器人的第二結構的移動中。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：用于運動學模型的參數(shù)總數(shù)變成30，他們定義于表12.2 辨認方法學運動學的參數(shù)辨認將是進行多維的消去過程, 因此避免了雅可比系統(tǒng)的標定，過程如下：1. 首先假設運動學的參數(shù), 例如標準設置。2. 為選擇任意關節(jié)角的設置。3. 計算PUMA機器人末端操作器。4. 測量PUMA機器人末端操作器的位姿如關節(jié)角，通常標準的和預言的位姿將是不同的。5. 為了最好使預言位姿達到標準的位姿，在整齊的方式更改運動學的參數(shù)。這個過程應用于不是單一的關節(jié)角設置而是一定數(shù)量的關節(jié)角，與物理測量數(shù)量等同的全部關節(jié)角設置是需要，必須滿足在這兒：Kp是識別的運動學參數(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，更多的測量應該是在實驗測量法去掉補償結果。優(yōu)化程序使用命名為ZXSSO，和標準庫功能的IMSL。2.3 位姿測量法顯然它是從上面的方法確定PUMA機器人全部位姿是必需的為了實現(xiàn)標定。這種方法現(xiàn)在將詳細地描寫。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和世界坐標中間各個坐標的形式，如圖6這些坐標的關系如下：是關于世界坐標結構的第i個球的4x1列向量坐標, Pi是關于工具坐標結構,p第i個球的4x1坐標的列向量, T是從世界坐標結構到工具坐標結構變化的4x4矩陣。設定Pi，測量出 ，然后算出T，使用于在標定過程的位姿的測量。它是不,ip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PUMA機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。準確的測量三個球，第四球根據(jù)十字相乘可以獲得考慮到決定的球中心坐標的是基于球表面點的測量,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 個球表面點的坐標且 是球的半徑。),(wvu),(iizyx r在測試過程中，發(fā)現(xiàn)只測量四個表面上的點來確定中心點是非常有效的。附件 2：外文原文（復印件）Full-Pose Calibration of a Robot Manipulator Using a Coordinate-Measuring MachineThe work reported in this article addresses the kinematiccalibration of a robot manipulator using a coordinate measuringmachine (CMM) which is able to obtain the full pose ofthe end-effector. A kinematic model is developed for themanipulator, its relationship to the world coordinate frame andthe tool. The derivation of the tool pose from experimentalmeasurements is discussed, as is the identification methodology.A complete simulation of the experiment is performed, allowingthe observation strategy to be defined. The experimental workis described together with the parameter identification andaccuracy verification. The principal conclusion is that themethod is able to calibrate the robot successfully, with aresulting accuracy approaching that of its repeatability.Keywords: Robot calibration; Coordinate measurement; Parameteridentification; Simulation study; Accuracy enhancement1. IntroductionIt is well known that robot manipulators typically havereasonable repeatability (0.3 ram), yet exhibit poor accuracy(10.0 mm). The process by which robots may be calibratedin order to achieve accuracies approaching that of themanipulator is also well understood . In the calibrationprocess, several sequential steps enable the precise kinematicparameters of the manipulator to be identified, leading toimproved accuracy. These steps may be described as follows:1. A kinematic model of the manipulator and the calibrationprocess itself is developed and is usually accomplished withstandard kinematic modelling tools. The resulting modelis 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 orcomplete) are taken in order to obtain data relating to theactual parameter set for the robot.3.The actual kinematic parameters are identified by systematicallychanging the nominal parameter set so as to reducethe error quantity defined in the modelling phase. Oneapproach to achieving this identification is determiningthe analytical differential relationship between the posevariables P and the kinematic parameters K in the formof a Jacobian,and then inverting the equation to calculate the deviation ofthe kinematic parameters from their nominal valuesAlternatively, the problem can be viewed as a multidimensionaloptimisation task, in which the kinematic parameterset is changed in order to reduce some defined error functionto zero. This is a standard optimisation problem and maybe solved using well-known methods.4. The final step involves the incorporation of the identifiedkinematic parameters in the controller of the robot arm,the details of which are rather specific to the hardware ofthe system under study.This paper addresses the issue of gathering the experimentaldata used in the calibration process. Several methods areavailable to perform this task, although they vary in complexity,cost and the time taken to acquire the data. Examples ofsuch techniques include the use of visual and automatictheodolites, servocontrolled laser interferometers ,acoustic sensors and vidual sensors . An ideal measuringsystem would acquire the full pose of the manipulator (positionand orientation), because this would incorporate the maximuminformation for each position of the arm. All of the methodsmentioned above use only the partial pose, requiring moredata to be taken for the calibration process to proceed.2. TheoryIn the method described in this paper, for each position inwhich the manipulator is placed, the full pose is measured,although several intermediate measurements have to be takenin order to arrive at the pose. The device used for the posemeasurement is a coordinate-measuring machine (CMM),which is a three-axis, prismatic measuring system with aquoted accuracy of 0.01 ram. The robot manipulator to becalibrated, a PUMA 560, is placed close to the CMM, and aspecial end-effector is attached to the flange. Fig. 1 showsthe arrangement of the various parts of the system. In thissection the kinematic model will be developed, the poseestimation algorithms explained, and the parameter identificationmethodology outlined.2.1 Kinematic ParametersIn this section, the basic kinematic structure of the manipulatorwill be specified, its relation to a user-defined world coordinatesystem discussed, and the end-point toil modelled. From thesemodels, the kinematic parameters which may be identifiedusing the proposed technique will be specified, and a methodfor determining those parameters described.The fundamental modelling tool used to describe the spatialrelationship between the various objects and locations in themanipulator workspace is the Denavit-Hartenberg method, with modifications proposed by Hayati, Mooringand Wu to account for disproportional models when two consecutive joint axes are nominally parallel. Asshown in Fig. 2, this method places a coordinate frame oneach object or manipulator link of interest, and the kinematicsare defined by the homogeneous transformation required tochange one coordinate frame into the next. This transformationtakes the familiar formThe above equation may be interpreted as a means totransform frame n-1 into frame n by means of four out ofthe five operations indicated. It is known that only fourtransformations are needed to locate a coordinate frame withrespect to the previous one. When consecutive axes are notparallel, the value of/3. is defined to be zero, while for thecase when consecutive axes are parallel, d. is the variablechosen to be zero.When coordinate frames are placed in conformance withthe modified Denavit-Hartenberg method, the transformationsgiven in the above equation will apply to all transforms ofone frame into the next, and these may be written in ageneric matrix form, where the elements of the matrix arefunctions of the kinematic parameters. These parameters aresimply the variables of the transformations: the joint angle0., the common normal offset d., the link length a., the angleof twist a., and the angle /3.. The matrix form is usuallyexpressed as follows:For a serial linkage, such as a robot manipulator, a coordinateframe is attached to each consecutive link so that both theinstantaneous position together with the invariant geometryare described by the previous matrix transformation. 'Thetransformation from the base link to the nth link will thereforebe given byFig. 3 shows the PUMA manipulator with theDenavit-Hartenberg frames attached to each link, togetherwith world coordinate frame and a tool frame. The transformationfrom the world frame to the base frame of themanipulator needs to be considered carefully, since there arepotential parameter dependencies if certain types of transformsare chosen. Consider Fig. 4, which shows the world framexw, y,, z,, the frame Xo, Yo, z0 which is defined by a DHtransform from the world frame to the first joint axis ofthe manipulator, frame Xb, Yb, Zb, which is the PUMAmanufacturer's defined base frame, and frame xl, Yl, zl whichis the second DH frame of the manipulator. We are interestedin determining the minimum number of parameters requiredto move from the world frame to the frame x~, Yl, z~. Thereare two transformation paths that will accomplish this goal:Path 1: A DH transform from x,, y,, z,, to x0, Yo, zoinvolving four parameters, followed by another transformfrom xo, Yo, z0 to Xb, Yb, Zb which will involve only twoparameters ~b' and d' in the transformFinally, another DH transform from xb, Yb, Zb to Xt, y~, Z~which involves four parameters except that A01 and 4~' areboth about the axis zo and cannot therefore be identifiedindependently, and Adl and d' are both along the axis zo andalso cannot be identified independently. It requires, therefore,only eight independent kinematic parameters to go from theworld frame to the first frame of the PUMA using this path.Path 2: As an alternative, a transform may be defined directlyfrom the world frame to the base frame Xb, Yb, Zb. Since thisis a frame-to-frame transform it requires six parameters, suchas the Euler form:The following DH transform from xb, Yb, zb tO Xl, Yl, zlwould involve four parameters, but A0~ may be resolved into4~,, 0b, ~, and Ad~ resolved into Pxb, Pyb, Pzb, reducing theparameter count to two. It is seen that this path also requireseight parameters as in path i, but a different set.Either of the above methods may be used to move fromthe world frame to the second frame of the PUMA. In thiswork, the second path is chosen. The tool transform is anEuler transform which requires the specification of sixparameters:The total number of parameters used in the kinematic modelbecomes 30, and their nominal values are defined in Table 1.2.2 Identification MethodologyThe kinematic parameter identification will be performed asa multidimensional minimisation process, since this avoids thecalculation of the system Jacobian. The process is as follows:1. Begin with a guess set of kinematic parameters, such asthe 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 forthe same set of joint angles. In general, the measured andpredicted pose will be different.5. Modify the kinematic parameters in an orderly manner inorder to best fit (in a least-squares sense) the measuredpose to the predicted pose. The process is applied not to a single set of joint angles butto a number of joint angles. The total number of joint anglesets required, which also equals the number of physicalmeasurement made, must satisfyKp is the number of kinematic parameters to be identifiedN is the number of measurements (poses) takenDr represents the number of degrees of freedom present ineach measurement.In the system described in this paper, the number of degreesof freedom is given bysince full pose is measured. In practice, many more measurementsshould be taken to offset the effect of noise in theexperimental measurements. The optimisation procedure usedis known as ZXSSO, and is a standard library function in theIMSL package .2.3 Pose MeasurementIt is apparent from the above that a means to determine thefull pose of the PUMA is required in order to perform thecalibration. This method will now be described in detail. Theend-effector consists of an arrangement of five precisiontoolingballs as shown in Fig. 5. Consider the coordinates ofthe 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 writtenas:where Pi' is the 4 x 1 column vector of the coordinates ofthe ith ball expressed with respect to the world frame, P~ isthe 4 x 1 column vector of the coordinates of the ith ballexpressed with respect to the tool frame, and T is the 4 ? 4homogenious transform from the world frame to the toolframe.Then may be found, and used as the measured pose in thecalibration process. It is not quite that simple, however, sinceit is not possible to invert equation (11) to obtain T. Theabove process is performed for the four balls, A, B, C andD, and the positions ordered as:or in the form:Since P', T and P are all now square, the pose matrix maybe obtained by inversion:In practice it may be difficult for the CMM to access fourbails to determine P~ when the PUMA is placed in certainconfigurations. Three balls are actually measured and a fourthball is fictitiously located according to the vector cross product:Regarding the determination of the coordinates of thecentre of a ball based on measured points on its surface,no analytical procedures are available. Another numericaloptimisation scheme was used for this purpose such that thepenalty function:was minimised, where (u, v, w) are the coordinates of thecentre of the ball to he determined, (x/, y~, z~) are thecoordinates of the ith point on the surface of the ball and ris the ball diameter. In the tests performed, it was foundsufficient to measure only four points (i = 4) on the surfaceto determine the ball centre.