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XXX业设计(XX)外文资料翻译院 系专业学生姓名班级学号外文出处www.sciencedirect.com指导教师评语：指导教师签名： 年 月 日附件2：外文原文Applied iterative closest point algorithm to automated inspection of gear box toothSalim Boukebbab, Hichem Bouchenitfa, Hamlaoui Boughouas, Jean Marc LinaresAbstract The development of a complete system and quality control of manufactured parts requires the coordination of a set complex processes allowing data acquisition, their dimensional evaluation and their comparison with a reference model. By definition, the parts inspection is the comparison between measurements results and the theoretical surfaces definition in order to check the conformity after manufacturing phase. The automation of this function is currently based on alignment methods of measured points resulting from an acquisition process and these nominal surfaces, in a way that they “fit best”. The distance between nominal surface and measured points(i.e. form defects) calculated after alignment stages are necessary for the correction of the manufacturing parameters(Henke, Summerhays, Baldwin, Cassou, &Brown, 1999).In the work, a method for automated control based on association of complex surfaces to a cloud points using the Iterative Closest Point(I.C.P)algorithm for alignment stage is proposed. An industrial application concerning a tooth gear manufactured in our countrys tractor engines is presented.2007 Elsevier Ltd. All rights reserved. Keywords: CMMs; Complex surfaces; ICP; Gear; Manufacturing process 1. IntroductionThe design and manufacture of complex surfaces became a current practice in industry. These surfaces can be conceived by a direct method based on the use of Computer Aided Design(CAD)software , or an indirect method which consists in a treatment of a discrete representation of an object model to obtain its CAD model. This last can be obtained throughout an acquisition process, allowing then a much more rapid safeguard, modification, manufacture, automatic inspection, prototypes checking and a much easier analysis (Lai & Ueng, 2000). The last year, the development process has covered all automated production phases, from design to the parts inspection passing by manufacture. Since the design and the manufacture of complex surfaces became a current practice in industry, then the problem related to the parts conformity are being felt more and more. The automation and the flexibility of a three-dimensional measurement machine with or without contact have made a considerable reduction in the acquisition time and the measurements treatment. In the current state of the metrology software, the inspection of elementary surfaces (plane, cylinder, cone, etc.)became a very easy practice. On the other hand the inspection of complex surfaces remains a problem to overcome (Tucker & Kurfess, 2003). The ascending complexity of parts geometry and the need for reducing production costs impose the use of more powerful tools for the inspection of complex parts surfaces, for a better service functionality description during its assembly with the conjugate mechanism parts (Tholath & Radhakrishnan, 1999). Our work is placed accordingly and consists to establish a procedure for modeling and inspecting complex parts surfaces, enabling the correction of relative deviations within production means. The method used is based on the iterative-closest-point(ICP)algorithm, which is a well-known method for registering a 3D set of points to a 3D model that minimizes the sum of squared residual errors between the set and the model. This choice is motivated by the robustness of this method and it is important to underline here that; no attempt to implement it within Coordinate Measuring Machines (CMMs) software has been reported in the three-dimensional metrology literature. A numerical application treating the case of a tooth of the toothed wheel which equips the gear box tractor manufactured at the engines and tractors factory in our country is presented, the comparison between the real surface obtained by acquisition and the ideal model has led to the calculation of the form defects on the two flanks of the tooth gear.2. Problems and adopted algorithm The principle of the software of Coordinate Measuring Machines consists generally in individually associating an elementary mathematical model (plane, cylinder, etc) to each digitized surface. The function to be minimized is based on the distance di between the digitized point Mi and the theoretical surface (Fig.2). As already pointed out in the introduction, in current state of the metrology software, the inspection of elementary surfaces (plane, cylinder, cone, etc,) is not a problem, and most CMMs correct remaining alignment deviations numerically (alignment means to evaluate an optimum transformation T mapping the measured points to the corresponding nominal points in a way that they “fit best”) (Gogh et al, 2003). On the other hand the inspections of surfaces which have geometries of a higher complexity like gears, sculptured surfaces etc.represents a major challenge (Goch & Tschudi, 1992; Pommer, 2002). It is to this objective that our work is directed, and consists in the development of a procedure of a procedure for modeling and inspecting complex surfaces with an aim of correcting the errors cumulated during the manufacturing phase (Portman & Shuster (1997). For this case, the ICP (Iterative Closest Point) algorithm method will be used. The iterative-closest-point (ICP) algorithm of Besl and McKay (1992) is a well-known method for registering a 3D model that minimizes the sum of squared residual errors between the set and the model, i.e. it finds a registration that is locally best in a least-squares sense (Bergevin, Laurendeau, & Poussart, 1995; Ma & Ellis, 2003). Its main goal is to find the optimal rigid transformation which will corresponds as well as possible a cloud points P to a geometrical model M, using the singular value decomposition function (SVD) (Fig.3). The parameters of the rigid transformation between the sets of points PI and PII must minimize the cost function:2Where: P is a point from PP I is a point from P associated with PiTt the rigid transformation. A rigid transformation Tt consists of the rotation matrix R and the translation vector T giving the iterative transformation Pi=R*Pi+ T (Pi will be transformed into a point Pi). This algorithm requires an initial estimate of the registration; because the computation speed and registration accuracy depend on how this initial estimate is chosen (Ma&Ellis, 2003). For this, we were mainly based on the algorithm proposed by Moron (1996) to which some changes have been made in order to make it simpler while keeping a maximum of its performances Fig. 4. In this algorithm, we have to determine the six degrees of freedom including the three for rotation and the other three for translation by ICP. Which the three dimensional translation vector has simply three parameters as T = (tx, ty, tz) T, the rotation matrix is apparently composed of nine elements which should go along with six conditions for orthonormality. A simple iterative optimization based on the least square principle can not guarantee this orthonormality (Kaneko, Kondo, & Miyamoto, 2003). Hence, ICP employs unit quaternion (q0; q1; q2; q3) for representing the rotation parameters in order to reduce this problem.The unit quaternion is used to compute a rotation about the unit vector n by an angle : , with q00 and ; q02+q12+q22+q32=1Then the rotation matrix R is defined by: The optimal motion (R; T) is computed by the unit quaternion method due to Horn (Eggert, Lorusso, & Fisher, 1997). The same method was used in the original version of ICP (Besl & Mckay, 1992). There are different analytical ways to calculate the 3D rigid motion that minimizes the sum of the squared distances between the corresponding points. In Eggert et al. (1997), four such techniques were compared and unit quaternion method was found to be robust with respect to noise, stable in presence of degenerate data and relatively (Chetverikov, Stepanov, & Krsek, 2005).3. Presentation of the algorithm Since the presentation of the I.C.P algorithm by Besl and Mckay, many variants have been introduced, which affect one or more stages of the original algorithm to try to increase its performances specially accuracy and speed, giving birth to several alternatives of I.C.P. algorithm (Kaneko et al., 2003). Some of these variants (such as Rusinkiewicz et al. (2001) expand also the abbreviation to the iterative corresponding point claiming that this would better suit the algorithm (Sablatnig & Kampel, 2002). In order, to make a choice of an algorithm, several criteria should be checked: speed, accuracy, stability, robustness, and simplicity. The importance of the one or other of those criteria depends on the use and application of the final program. The development of a complete system of inspection and quality control of manufactured parts requires the coordination of a set complex processes allowing data acquisition, their dimensional evaluation and their comparison with a reference model. For that it is essential to make profitable some conceptual knowledge relating not only to the object to be analyzed, but also to its environment. In our case, the objective of the present work consist in establishing an automation procedure for modeling and inspecting complex parts surfaces, enabling the correction of relative deviations within manufacturing parameters, then the criteria adopted are : speedy convergence, system robustness, and interface simplicity. The new algorithm can be summarized by the following procedure.1. Make a random selection of a subset of points.2. Calculate the projection of the selected points.3. Calculate the optimal rigid transformation with SVD method.4. Apply the transformation to the selected points.5. Evaluate the quality of alignment by LMS estimator.6. If alignment quality is good, calculate transformation and apply it to the whole of available points.7. Repeat the steps from 1 to 6 until convergence.The conceptual structure of our program is presented in Fig 4.We note here that the algorithm structure is very simple; it is made up of a principle program which contains a loop to carry out the iterations and another one to estimate the quality of the rigid transformation by the LMS estimator (Least Median Squares) (Rousseau & Leroy, 1987). In this program we also find three calls functions which are: the CPT function which calculates the projection of the points on the ideal model of surface in STL format (Fig.5)，the SVD function which calculates the optimal rigid transformation; and finally the RT function useful for calculating the initial rigid transformation; because as already pointed out, the algorithm requires an initial estimate solution of registration; and the computation speed and registration accuracy depend on how this initial estimate is chosen (Ma & Ellis, 2003).The STL format is generally obtained by a triangulation of an exact model using CAD software which gives a data file in STL format (Fig.6). Where a Triangular facet is defined by the co-ordinates of the three vertexes and its normal directed towards the object free side.It should be noted that, the bigger is the number of triangles in STL model the less is the approximation errors (Fig.7).The number of triangles and their distributions are function of the surface curvature and modeling tolerated error.附件1：外文资料翻译运用点算法反复自动检测齿轮箱齿轮Salim Boukebbab Hichem Bouchenitfa Hamlaoui Boughouas Jean Marc Linares摘要： 一个完整的系统的开发和制造的零部件的质量控制的一组复杂的过程，使数据采集，其尺寸的评估和比较一个参考模型，需要协调。根据定义，零件检查之间的比较，以便检查是否符合制造阶段后的测量结果和理论表面定义。从收购的过程和这些标称的表面，测量点的方式，他们“最合适”的比对方法的基础上，目前此功能的自动化。之间的标称表面和测量点（即窗体缺陷）取向阶段后，计算出的距离是必要的校正的制造参数（亨克，Summerhays，鲍德温，Cassou布朗，1999）。在工作中，一个方法的自动化控制基于使用迭代最近点（ICP）算法对准阶段的一个点云数据复杂曲面的关联。在我国的拖拉机发动机制造有关的齿齿轮工业应用。关键词：CMMs , 复曲面， ICP ，齿轮 ，制造业程序1、 绪论复杂型面的设计和制造成为一个行业现行做法。可以设想，这些表面的，直接的方法，使用计算机辅助设计（CAD）软件，或间接的方法，其中包含一个对象模型来获得其CAD模型的离散表示在治疗的基础上。这最后可以得到整个收购过程中，允许然后更快速的保障，修改，制造，自动检测，原型检查和更容易的分析（黎翁，2000年）。过去的一年，在发展过程中已覆盖了所有的自动化生产阶段，从设计到零件的检验，通过由制造。由于设计和制造复杂曲面成为一个在行业目前的做法，那么相关的部分整合的问题正在越来越感觉到。带或不带接触的三维测量机的自动化和灵活性在时间的采集和治疗的测量上已经有了显着的降低。在当前状态下的测量软件，检查的基本的表面（平面，圆柱体，圆锥体等）成为一个非常方便的做法。另一方面复杂的表面的检查仍然是一个问题，需要得以克服（塔克Kurfess，2003年）。升序复杂的零件的几何形状和降低生产成本的需要施加的更强大的工具的使用复杂的零件的表面的检查中，在组装过程中的共轭机制份（Tholath拉达克里希南，1999）为更好的服务功能的详细描述。我们的工作放在相应地，包括建立复杂的零件表面建模和检查，使在生产手段的相对偏差校正的过程。 所使用的方法是根据迭代最近点（ICP）算法，这是一个众所周知的方法，注册一个3D的点集的3D模型集和模型之间的残余误差的平方的总和最小化。这种选择是出于这种方法的鲁棒性，重要的是在此强调，没有试图去实现它在坐标测量机（CMM）的软件已经在三维的计量文献报道。 装备在我国的发动机和拖拉机厂生产的拖拉机齿轮箱齿轮的齿治疗的情况下，通过收购获得的实际面和理想的模型之间的比较的数值应用的计算上的两个侧面的齿齿轮的形式缺陷。2.问题及运算法则 他的原则三坐标测量机的软件通常包括在单独一个基本的数学模型（平面，圆柱等）相关联的每个数字化的表面。以最小化的功能的基础上的数字化的点（Mi）和理论的表面（图2）之间的距离di。 已经指出，在当前状态下的测量软件，在介绍基本的表面（平面，圆柱，圆锥等）的检查是没有问题的，最三坐标测量机正确剩余的对准偏差数值（校准手段来评估一个最佳变换T的测量点映射到相应的额定点的方式，他们“最合适”）（梵高等人，2003）。另一方面，检查表面有齿轮等提出了更高的复杂性，复杂曲面的几何形状etc.represents一个重大的挑战（九策楚迪，1992年;波默，2002年）。它是实现这一目标，我们的工作指示，在发展的一个程序的一个程序，用于建模和检查，一个目的是校正的误差累积（波特曼舒斯特（1997）在制造阶段的复杂的表面组成。在这种情况下，ICP（迭代最近点）算法的方法将被使用。迭代的最近点（ICP）算法Besl和麦基（1992）是一种公知的方法，用于登记的3D模型集和模型之间的残余误差的平方的总和最小化，例如，它找到一个注册当地最好在最小二乘意义上（Bergevin，Laurendeau，Poussart，1995年，马和埃利斯，2003）。它的主要目标是找到最佳的刚性，这将对应的转换以及云计算点P的几何模型M，利用奇异值分解函数（SVD）（图3）。2点PI和PII套之间的刚体变换的参数必须最大限度地降低成本的功能：其中：P是I是一个点从P点从PP“与PiTt刚体变换。一个的刚体变换TT的旋转矩阵R和平移向量T提供的迭代转变PI“= R* PI+T（曹丕”将被改造成一个点Pi“）。该算法需要一个初始估计登记手续;因为计算速度和配准精度取决于这个初步估计被选中（马和埃利斯，2003）。对于这一点，我们主要是基于伦（1996）所提出的算法，其中一些已经作了修改，以便使其更简单，同时保持其性能最大。图4。在该算法中，我们要确定的六个自由度，包括三个旋转和其他三个翻译ICP。哪个的三维平移向量具有简单的三个参数，T=（TX，TY与tz）T中，显然是由9个元素应随着六个条件正交性去旋转矩阵。一个简单的迭代优化的最小二乘原理的基础上，不能保证这一点的正交性（金子，近藤，与宫本，2003年）。因此，ICP采用四元数（q0，q1，q2，q3）为代表的旋转参数，以减少这个问题。单位四元数被用来计算单位矢量n的角度的旋转约：，其中q0 0和q02+ q12+ q22+ q32 =1;然后旋转矩阵R被定义为： 最佳运动（RT）计算的单位四元数法由于喇叭（艾格特，Lorusso医师与其与Fisher，1997）。用同样的方法在原有版本的ICP（BESL麦凯，1992年）。有不同的分析方法来计算的对应点之间的距离的平方的总和最小化的3D刚体运动。在艾格特等。 （1997年），四等技术进行了比较，发现四元数法是强大的，对于噪声，稳定中存在的退化数据和相对“（切特韦里科夫，斯捷潘诺夫，Krsek的，2005年）。3.算法的介绍自ICP算法Besl和麦凯的介绍后，有很多种说法被介绍，从而影响一个或多个阶段，对原有算法设法提高其性能特别的精度和速度，分娩的ICP几种选择算法（Kaneko等人，2003年）。这些变体中的一些（如Rusinkiewicz等人（2001）的扩大也缩写迭代声称，这将更好地适应的的算法（SablatnigKampel，2002）的对应点。为了使选择的算法，有几个标准，应检查：速度，精度，稳定性，鲁棒性和简单。这些标准的一个或其他的重要性取决于最终的程序的使用和应用。一组复杂的过程，使数据采集，其尺寸的评估和比较一个参考模型，一个完整的系统制造的零部件的检测和质量控制的发展需要协调。为此，它是必不可少的，使有利可图的一些概念方面的知识，不仅要分析的对象，但也给它的环境。在我们的例子中，目前的工作目标包括建立一个自动化过程进行建模和检查复杂的零件表面，使制造参数内的相对偏差修正，然后采用的标准是：收敛速度快，系统的可靠性，界面简洁明了。新算法可以概括为以下步骤：1 一个随机选择的一个子集点。2 计算的选定点的投影3 计算出最佳的刚性变换与SVD方法。4 应用转型到选定的点。5 评估LMS估计质量的对齐方式。6 如果对齐质量好，计算转型，并把它应用到整个可用点。7 重复步骤1到6，直到收敛。我们的计划是在图4的概念结构。我们注意到，该算法的结构非常简单，它是由一个原则方案，其中包含一个循环进行迭代和另一个估计质量的刚体变换估计的LMS（最小中位数平方）（卢梭乐华，1987）。在这个程序中，我们也发现三个电话功能分别是：计算上的点的投影表面的理想模型的STL格式（图5），计算最佳的刚性变换的SVD功能，CPT功能，最后是RT功能，可用于计算初始刚体变换，因为正如已经指出的，该算法需要注册一个初步的估算解决方案;和运算速度和配准精度取决于这个初步估计被选中（马和埃利斯，2003）。 STL格式通常是通过三角测量的精确模型使用CAD软件，该软件提供了一个数据文件中的STL格式（图6）。凡三角刻面所定义的坐标的三个顶点和其正常朝向的对象自由侧。 应当指出的是，STL模型的越少，是近似误差（图7）的三角形的数量越大。 三角形的数量及其分布的表面曲率和建模允许误差的功能。
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