應用坐標測量機的機器人運動學姿態(tài)的標定外文翻譯@中英文翻譯@外文文獻翻譯

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： 年 月 日 注： 請將該封面與附件裝訂成冊。 (用外文寫 ) 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。實驗工作的目的是描寫參數辨認和精確確認。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，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的。作為結果的模型是定義基于廠商的運動學參數設置錯誤量 , 和識別未知的 ,實際的參數設置。 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系到實際機器人的參數設置數據。 3 實際的運動學參數識別是系統地改變參數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 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的詳細資料。 包含實驗數據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，獲得數據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) , 需要更多的數據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，和參數辨認方法。 2.1 運動學的參數 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的識別將被規(guī)定，和描述決定這些參數的方法。 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， n 定義為零點。 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運動學參數功能的矩陣形狀。這些參數是變化的簡單變量：關節(jié)角 n ，連桿偏置 nd , 連桿長度 na ，扭角 n ，矩陣通常表示如下： 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，因為潛在的參數取決于被選擇的改變類型?？紤]到圖 4,世界坐標www zyx ,，在 D-H系中定義的從世界坐標到機器人基坐標000 , zyx，坐標bbb zyx ,是 PUMA機器人定義的基坐標和機器人第二個 D-H結構中 坐標111 , zyx。 我們感興趣的是從世界坐標到111 , zyx必需的最小的參數數量 。實現這種變化有兩種路 徑：路徑 1，從www zyx ,到000 , zyxD-H變化包括四個參數，接著從000 , zyx到bbb zyx ,的變化將牽連二個參數 和 d 的變化 圖 3 圖 4 最后，另外從bbb zyx ,到 111 , zyx 的 D-H變化中有四個參數其中 1 和 兩個參數是關于軸 Z0因此不能獨立地識別， 1d 和 d 是沿著軸 Z0因此也不能是獨立地識別。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。路徑 2，同樣地二中擇一，從世界坐標到底部結構坐標bbb zyx ,的 變化可以是直接定義。因此坐標變換需要六個參數，如 Euler形式： 下面是從bbb zyx ,到 111 , zyx D H變化中的四個參數，但 1 與bbb ,相關聯，1d 與 zbybxb ppp , 相關聯 ，減少成兩個參數。很顯然這種 路徑和路徑 1一樣需要八個參數，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的改變的 Euler形式： 用于運動學模型的參數總數變成 30，他們定義于表 1 2.2 辨認方法學 運動學的參數辨認將是進行多維的消去過程 , 因此避免了雅可比系統的標定，過程如下： 1. 首先假設運動學的參數 , 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。 這個過程應用于不是單一的關節(jié)角設置而是一定數量的關節(jié)角，與物理測量數量等同的全部關節(jié)角設置是需要，必須滿足 在這兒： Kp是識別的運動學參數的數量 N是測量位姿的數 Dr是測量過程中自由度的數量 文章中，給定了自由度的數量，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標定。這種方法現在將詳細地描寫。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： ,ip 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 ,ip ， 然后 算出 T，使用于在標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，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，數字優(yōu)化的使用是為了求懲罰函數的最小解 這里 ),( wvu 是確定球中心， ),(iii zyx是第 i 個 球表面點 的坐標且 r 是 球 的半徑。在測試過程中，發(fā)現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 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