WO2021179460A1 - 一种基于标准球的激光出光方向标定方法 - Google Patents

一种基于标准球的激光出光方向标定方法 Download PDF

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WO2021179460A1
WO2021179460A1 PCT/CN2020/095989 CN2020095989W WO2021179460A1 WO 2021179460 A1 WO2021179460 A1 WO 2021179460A1 CN 2020095989 W CN2020095989 W CN 2020095989W WO 2021179460 A1 WO2021179460 A1 WO 2021179460A1
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laser light
coordinate system
spherical
machine tool
standard
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French (fr)
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李文龙
寇猛
王刚
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华中科技大学
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
    • B23Q17/00—Arrangements for observing, indicating or measuring on machine tools
    • B23Q17/24—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves
    • B23Q17/2428—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves for measuring existing positions of tools or workpieces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/02—Measuring arrangements characterised by the use of optical techniques for measuring length, width or thickness
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • G01B21/042—Calibration or calibration artifacts

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  • the present invention belongs to the technical field related to online measurement, and more specifically, relates to a non-contact online measurement method, in particular to a method for calibrating the direction of laser light emission based on a standard sphere.
  • the traditional measurement method is the three-coordinate measuring method.
  • the three-coordinate measuring instrument is operated in a fully enclosed measurement environment.
  • the contact detection method requires cumbersome detection route design and collision simulation inspection, which causes the detection time to be longer than the processing time.
  • the long-term status quo has seriously affected the production efficiency.
  • the parts may be transferred many times and clamped repeatedly, which causes accumulation of errors, hidden quality problems, slow measurement speed, and low measurement efficiency.
  • non-contact online measurement technology is fast, accurate, and can effectively compensate for the contact type. Problems such as difficulty in online measurement path planning and easy interference have received widespread attention.
  • non-contact measurement sensors can be divided into one-dimensional measurement sensors, two-dimensional measurement sensors, and three-dimensional measurement sensors.
  • laser displacement sensor measurement has the advantages of high measurement accuracy, high efficiency, and low cost. Occupies a large number of online measurement fields.
  • the laser displacement sensor is usually installed on the Z axis of the CNC machine tool. Since the data measured by the laser displacement sensor is a one-dimensional measurement value, the measurement value of the laser displacement sensor needs to be converted from its sensor measurement coordinate system to the machine tool coordinate system during the measurement process. In order to ensure the measurement accuracy of the system and the normal operation of the laser displacement sensor, it is necessary to rotate the sensor to ensure the tilt during the measurement process. The angle is controlled within a certain range.
  • the laser displacement sensor is installed on the spindle of the machine tool and its light is parallel to the Z axis; among them, Lu of Zhejiang University Ke Qing et al. proposed a laser light direction calibration method based on a multi-directional calibration block.
  • This method constructs a quadratic equation by scanning two planes, and then obtains the laser light direction vector by solving the quadratic equation, but this method obtains
  • This method needs to rotate the calibration surface to be perpendicular to the laser light emitting direction each time, and the operation is cumbersome. Therefore, how to quickly calibrate the light emitting direction of the laser displacement sensor needs to be solved urgently.
  • the present invention provides a calibration method for laser light emission direction based on standard spheres, which is based on scanning and measuring a standard sphere with a known diameter to solve the laser light emission direction and the spherical coordinate points of the standard sphere.
  • the calibration method can quickly and accurately realize the calibration of the laser sensor light direction in the online measurement system, and realize the fast and dynamic combination of the three-dimensional coordinate points of the machine tool and the distance value measured by the sensor, which greatly improves the efficiency of acquiring the online measurement point cloud data. It is of great significance to realize the integration of "processing-measurement" of typical parts.
  • the present invention provides a calibration method of laser light emission direction based on a standard sphere, the method includes the following steps:
  • the laser displacement sensor is set on the machine tool spindle, and the standard ball is fixed on the worktable at the same time.
  • the machine tool spindle drives the laser displacement sensor to scan and measure the upper surface of the standard ball, so as to obtain the machine tool coordinates and the corresponding
  • the sensor measures the distance value in one dimension
  • step S2 combines and transforms the original data obtained in step S1 into a spherical coordinate system, and constructs a nonlinear equation system about spherical coordinates and light emission direction based on the transformed data, and the transformed data satisfies the spherical constraint equation;
  • S3 converts the solution of the nonlinear equations into the least squares optimization of the new function ⁇ (x), and then uses the Levenberg-Marquardt iterative optimization algorithm to solve the new function ⁇ (x), thereby obtaining the laser light direction and the sphere The coordinates of the heart position.
  • the surface features of the standard sphere are within the measurement range of the laser displacement sensor; during scanning measurement, the angle between the laser light emission direction and the spherical normal of the standard sphere is less than 30°.
  • combining and transforming the original data obtained in step S1 into a spherical coordinate system includes the following steps: firstly, respectively establishing a machine tool coordinate system, a spherical coordinate system, and a sensor coordinate system; then, transforming the original data into the machine tool coordinates After the system is set, the coordinate conversion is finally converted to the spherical coordinate system.
  • the points measured by scanning are discrete points on the spherical surface in the spherical coordinate system, and the discrete points satisfy the spherical constraint equation, and the spherical constraint equation is constructed from the obtained discrete points, and then the multiple spherical constraint equations obtained are combined into the Non-linear equations.
  • f(X) is a system of nonlinear equations.
  • the number of equations in the nonlinear equation group is not less than six.
  • the diameter of the standard ball is preferably 50 mm.
  • the laser displacement sensor is a point laser sensor.
  • the standard ball-based laser light emission direction calibration method provided by the present invention mainly has the following beneficial effects:
  • the present invention introduces the parameters of the laser light emitting direction, and improves the measurement accuracy of the laser displacement sensor on-line measurement through the mentioned ball calibration method.
  • the present invention overcomes the cumbersome operation and low efficiency of other calibration methods; the method mentioned in the present invention does not need to adjust the posture of the calibration object multiple times, and can achieve rapid and high-precision laser light emission direction calibration.
  • the present invention converts the difficult-to-solve nonlinear equation system into the least squares optimization problem of the new function, which greatly simplifies the difficulty of solving the problem and improves the speed.
  • the present invention uses the Levenberg-Marquardt iterative optimization algorithm to optimize the sphere center coordinates and the laser light emitting direction, and through the iterative parameter adjustment, the laser light emitting direction is quickly solved.
  • Fig. 1 is a schematic flow chart of a method for calibrating the direction of laser light emission based on a standard sphere provided by the present invention
  • Fig. 2 is a flow chart of the Levenberg-Marquardt algorithm involved in the calibration method of laser light emission direction based on the standard sphere in Fig. 1;
  • FIG. 3 is a schematic diagram of the calibration of the laser displacement sensor on-line measurement system involved in the standard ball-based laser light direction calibration method in FIG. 1;
  • FIG. 4 is a schematic diagram of three coordinate systems involved in the calibration method of laser light emission direction based on the standard sphere in FIG. 1;
  • Fig. 5 is a schematic model diagram of the calibration method of laser light emission direction based on the standard sphere in Fig. 1;
  • Fig. 6 is a flow chart of the Levenberg-Marquardt iterative optimization algorithm for solving nonlinear equations involved in the standard sphere-based laser light direction calibration method in Fig. 1;
  • Fig. 7 is a schematic diagram of the process flow of the laser displacement sensor on-line measurement system in Fig. 2 for direction calibration and parts detection.
  • the standard ball-based laser light emission direction calibration method provided by the present invention mainly includes the following steps:
  • Step 1 Set the laser displacement sensor on the machine tool spindle of the machine tool, and at the same time fix the standard ball on the worktable of the machine tool.
  • the machine tool spindle drives the laser displacement sensor to scan and measure the upper surface of the standard ball, thereby Obtain the coordinates of the machine tool and the corresponding one-dimensional measurement distance value of the sensor.
  • a laser displacement sensor online measurement system includes a machine tool spindle 100, a tool holder fixture 101, a worktable 103, a microprocessor 106, a laser displacement sensor 105 mounted on the tool holder fixture 101, and an installation The standard ball 102 and the part to be tested 104 on the worktable 103.
  • the laser displacement sensor 105 is connected to the machine tool spindle 100 through the tool holder clamp 101.
  • the machine tool spindle 100 is located above the work table 103, and an operating space for clamping the part to be tested 104 and performing measurement calibration is formed between the work table 103 and the machine tool spindle 100.
  • the tool holder clamp 101 is connected to The machine tool spindle 100 is accommodated in the operating space.
  • the part to be tested 104 and the standard ball 102 are respectively fixed on the worktable 103. During the calibration process of the laser displacement sensor 105, it is not necessary to repeatedly adjust the position and posture of the standard ball 102. .
  • the laser displacement sensor 105 is installed on the tool holder holder 101. During calibration, the laser displacement sensor 105 is separated from the standard ball 102 by a certain distance. The laser displacement sensor can be moved up and down through the machine tool spindle 100. The sensor 105 is used to ensure that the surface features of the standard ball 102 are within the measurement range of the laser displacement sensor 105.
  • the laser displacement sensor is a point laser sensor; when the laser displacement sensor is triggered by PLC, the PLC realizes the closing and disconnection of the machine tool relay, and an external circuit provides a high level of +5V to trigger the laser displacement sensor Measurement.
  • Step 2 Combine and convert the original data obtained in Step 1 to a spherical coordinate system, and construct a nonlinear equation system about spherical coordinates and light emitting direction based on the multiple converted data, and the converted data satisfy the spherical constraint equation.
  • the coordinate conversion of the original data mainly includes the following steps: First, establish three coordinate systems, namely the machine coordinate system, the spherical coordinate system and the sensor coordinate system; The data undergoes coordinate conversion. First, the collected raw data is converted to the machine coordinate system, and then the coordinate conversion is finally converted to the spherical coordinate system.
  • the coordinate system established in this embodiment includes a machine tool coordinate system ⁇ M ⁇ , a sensor coordinate system ⁇ S ⁇ , and a spherical coordinate system ⁇ B ⁇ ;
  • the machine tool coordinate system its origin is at the machine tool x, y, z axis, the encoder is at the zero position and the sensor In the initial posture, the point where the measuring distance is 0, the directions of the three coordinate axes are consistent with the directions of the X, Y, and Z axes of the machine tool, and the coordinate origin does not change with the movement of each axis during the measurement process.
  • Sensor coordinate system The laser displacement sensor is fixed on the spindle of the machine tool, and is fixedly connected to the spindle of the machine tool.
  • Its origin p So is located at the point where the laser displacement sensor is in the initial posture and the measuring distance is 0.
  • the direction is the same as the direction of the machine coordinate system.
  • Spherical coordinate system Fix the standard sphere with radius R on the machine tool table. Its surface is a standard spherical surface.
  • the spherical coordinate system that defines the standard sphere is ⁇ B ⁇ , and its origin p Bo is at the center point of the calibration sphere.
  • the direction of the coordinate system is the same.
  • the light emitting direction of the laser displacement sensor at the initial pose is t 1 , and the measured value is d 1 at this time.
  • the obtained nonlinear equation group is based on the fact that when the number of nonlinear equation groups is greater than 6, the equation group is an overdetermined equation group and can be optimally solved.
  • the number of equations in the nonlinear equation group is not less than 6, preferably 50.
  • Step 3 Convert the solution of the nonlinear equations to the least squares optimization of the new function ⁇ (x), and then use the Levenberg-Marquardt iterative optimization algorithm to solve the new function ⁇ (x), thereby obtaining the laser light direction And the coordinates of the center of the sphere.
  • the steps of solving the nonlinear equation system include:
  • the laser displacement sensor calibration is mainly used to determine the direction of light emission of the sensor, so that the measured value of the sensor can be well converted to the machine tool coordinate system;
  • the diameter of the standard ball is greater than or equal to 50mm, preferably 50mm;
  • the light output direction of the laser displacement sensor roughly passes through the center of the sphere;
  • the adopted machine tool is preferably a semi-closed loop or a fully closed loop machine with a positioning accuracy better than 0.03 mm.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

一种基于标准球的激光出光方向标定方法，包括以下步骤：S1将激光位移传感器（105）安装在机床主轴（100）上，同时将标准球（102）固定在工作台（103）上，机床主轴（100）带动激光位移传感器（105）对标准球（102）的上表面进行扫描测量，从而获取机床坐标和对应的传感器一维测量距离值；S2将得到的原始数据结合并转换到球坐标系下，并基于转换得到的数据构造关于球形坐标和出光方向的非线性方程组；S3将非线性方程组的求解转换为新函数φ(x)的最小二乘优化，进而采用Levenberg-Marquardt迭代优化算法对新函数φ(x)进行求解，由此得到激光出光方向及球心位置坐标。这种方法提高了效率，适用性较强。

Description

一种基于标准球的激光出光方向标定方法 【技术领域】
本发明属于在线测量相关技术领域，更具体地，涉及非接触式在线测量方法，尤其涉及一种基于标准球的激光出光方向标定方法。
【背景技术】
随着制造业的快速发展，航空航天领域的飞机结构件与导弹弹体结构件等大型复杂薄壁零件的加工要求越来越高，该类零件往往尺寸规格及加工特征多，极易发生变形，很难保证其加工精度。传统测量方法为三坐标测量法，三坐标测量仪是在全封闭式的测量环境中运行的，其接触式的检测方法需要进行繁琐的检测路线设计及碰撞仿真检查，造成检测时间比加工时间还要长的现状，严重影响了生产效率，同时零件也可能会多次中转，反复装夹，这就造成误差累积，存在质量隐患，测量速度慢，测量效率低。
近年来，随着制造技术的智能化水平不断提高，接触式和非接触式在线检测领域有了长足的发展，其中非接触式在线测量技术以其速度快、精度高、可有效地弥补接触式在线测量路径规划困难、易干涉等问题受到广泛关注。根据所得到测量数据的维数，非接触式测量传感器可以分为一维测量传感器、二维测量传感器、三维测量传感器，其中，激光位移传感器测量以其测量精度高、效率高、成本低等优势占据了大量在线测量领域。
激光位移传感器通常安装在CNC机床的Z轴上，由于激光位移传感器测得数据为一维测量值，因此在测量过程中需要将激光位移传感器的测量值从其传感器测量坐标系转换到机床坐标系下，实现了激光位移传感器与机床坐标的实时结合，且为了保证系统的测量精度以及激光位移传感器的正常工作，在测量多个不同倾斜角度的特征时需要旋转传感器以保证在测量过程中把倾斜角控制在一定范围内。
如此将涉及到安装后传感器出光方向标定的问题，然后目前很多研究工作并没有考虑传感器出光方向的问题，默认激光位移传感器安装在机床主轴上之后其出射光线与Z轴平行；其中，浙江大学卢科青等人提出了一种基于多向标定块的激光出光方向标定方法，该方法通过扫描两个平面构建二次方程，继而通过求解二次方程求得激光出光方向矢量，但是该方法求得出光方向为两个，且该方法需要每次旋转标定面至垂直于激光出光方向，操作繁琐，所以如何快速实现激光位移传感器的出光方向标定亟需解决。
【发明内容】
针对现有技术的以上缺陷或改进需求，本发明提供了一种基于标准球的激光出光方向标定方法，其基于扫描测量已知直径的标准球，求解激光出光方向和标准球的球形坐标点。所述标定方法能够快速、准确地实现在线测量系统中激光传感器出光方向的标定，并实现机床三维坐标点和传感器测量距离值的快速动态结合，大大地提高了在线测量点云数据的获取效率，对实现典型零件的“加工-测量”一体化具有重要意义。
为实现上述目的，本发明提供了一种基于标准球的激光出光方向标定方法，所述方法包括以下步骤：
S1将激光位移传感器设置在机床主轴上，同时将标准球固定在工作台上，所述机床主轴带动所述激光位移传感器对所述标准球的上表面进行扫描测量，从而获取机床坐标和对应的传感器一维测量距离值；
S2将步骤S1得到的原始数据结合并转换到球坐标系下，并基于转换得到的数据构造关于球形坐标和出光方向的非线性方程组，转换得到的数据满足球面约束方程；
S3将所述非线性方程组的求解转换为新函数φ(x)的最小二乘优化，进而采用Levenberg-Marquardt迭代优化算法对新函数φ(x)进行求解，由此得 到激光出光方向及球心位置坐标。
进一步地，所述标准球的表面特征在所述激光位移传感器的测量范围内；扫描测量时，激光出光方向与标准球的球面法矢之间的夹角小于30°。
进一步地，将步骤S1得到的原始数据结合并转换到球坐标系包括以下步骤：首先，分别建立机床坐标系、球坐标系及传感器坐标系；接着，将所述原始数据转换到所述机床坐标系下后，再将经过坐标转换最终转换到所述球坐标系下。
进一步地，传感器坐标系的原点p So位于激光位移传感器处于初始姿态时、测量距离为0的点，传感器坐标系原点在机床坐标系下的坐标为 Mp So＝[ Mx So  My So  Mz So] T；球坐标系的原点p Bo位于标定球球心点，p Bo在机床坐标系下的坐标为 Mp Bo＝[ Mx Bo  My Bo  Mz Bo] T。
进一步地，扫描测量到的点为球坐标系下的球面上的离散点，该离散点满足球面约束方程，以得到的离散点构建球面约束方程，再将得到的多个球面约束方程组成所述非线性方程组。
进一步地，
Figure PCTCN2020095989-appb-000001
f(X)为非线性方程组。
进一步地，采用Levenberg-Marquardt迭代优化算法对新函数φ(x)进行求解包括以下步骤：
(1)定义新函数φ(X)的梯度函数为
Figure PCTCN2020095989-appb-000002
并将梯度函数在X k进行泰勒展开，得到
Figure PCTCN2020095989-appb-000003
(2)将泰勒展开式U k(X)代入梯度函数g(X)中，得到：
Figure PCTCN2020095989-appb-000004
并求得下次迭代参数：
Figure PCTCN2020095989-appb-000005
继而得到 Levenberg-Marquardt迭代矩阵G(X)为：
Figure PCTCN2020095989-appb-000006
(3)初始值定义为X 0＝[0 0 0 0 -π]，阻尼系数μ 0＝10和放大系数β＝9，定义迭代变量k＝0和收敛标准ε＝0.001；
(4)求解f(X 0)和φ(X 0)的值；
(5)计算Jacobi矩阵
Figure PCTCN2020095989-appb-000007
和
Figure PCTCN2020095989-appb-000008
的值，如果
Figure PCTCN2020095989-appb-000009
停止迭代，求解结果为X k，否则转至步骤(6)；
(6)计算迭代Levenberg-Marquardt的迭代矩阵
Figure PCTCN2020095989-appb-000010
和迭代变量
Figure PCTCN2020095989-appb-000011
(7)求解f(X k+1)和φ(X k+1)的值，如果φ(X k+1)＜φ(X k)，阻尼系数μ k+1＝μ kβ，并跳转至步骤(6)；如果φ(X k+1)＞φ(X k)，阻尼系数μ k+1＝μ k/β，并跳转至步骤(5)。
进一步地，所述非线性方程组中方程数量不小于6个。
进一步地，所述标准球直径优选为50mm。
进一步地，所述激光位移传感器为点激光传感器。
总体而言，通过本发明所构思的以上技术方案与现有技术相比，本发明提供的基于标准球的激光出光方向标定方法主要具有以下有益效果：
1.本发明引入了激光出光方向参数，通过提到的球标定法提高了激光位移传感器在线测量的测量精度。
2.本发明克服了其他标定方法操作繁琐，效率偏低的缺陷；利用本发明提及的方法，无需多次调整标定物位姿，可实现快速和高精度的激光出光方向标定。
3.本发明通过问题转换，将难以求解的非线性方程组转换为了新函数 的最小二乘优化问题，大大简化了问题的求解难度，提高了速度。
4.本发明通过Levenberg-Marquardt迭代优化算法对球心坐标和激光出光方向进行优化求解，通过迭代参数的调整，实现了激光出光方向的快速求解。
【附图说明】
图1是本发明提供的基于标准球的激光出光方向标定方法的流程示意图；
图2是图1中的基于标准球的激光出光方向标定方法涉及的Levenberg-Marquardt算法流程图；
图3是图1中的基于标准球的激光出光方向标定方法涉及的激光位移传感器在线测量系统的标定示意图；
图4是图1中的基于标准球的激光出光方向标定方法涉及的三个坐标系的示意图；
图5是图1中的基于标准球的激光出光方向标定方法的原理模型图；
图6是图1中的基于标准球的激光出光方向标定方法涉及的用于求解非线性方程组的Levenberg-Marquardt迭代优化算法流程图；
图7是图2中的激光位移传感器在线测量系统进行方向标定和零件检测的流程示意图。
在所有附图中，相同的附图标记用来表示相同的元件或结构，其中：100-机床主轴，101-刀柄夹具，102-标准球，103-工作台，104-待测零件，105-激光位移传感器，106-微处理器。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可 以相互组合。
请参阅图1、图2及图3，本发明提供的基于标准球的激光出光方向标定方法，所述标定方法主要包括以下步骤：
步骤一，将激光位移传感器设置在机床的机床主轴上，同时将标准球固定在机床的工作台上，所述机床主轴带动所述激光位移传感器对所述标准球的上表面进行扫描测量，从而获取机床坐标和对应的传感器一维测量距离值。
具体地，提供激光位移传感器在线测量系统，所述系统包括机床主轴100、刀柄夹具101、工作台103、微处理器106、安装在所述刀柄夹具101上的激光位移传感器105、以及安装在所述工作台103上的标准球102及待测零件104。所述激光位移传感器105通过所述刀柄夹具101连接于所述机床主轴100。
所述机床主轴100位于所述工作台103上方，所述工作台103与所述机床主轴100之间形成有用于装夹待测零件104和进行测量标定的操作空间，所述刀柄夹具101与所述机床主轴100均容置于所述操作空间内。本实施方式中，所述待测零件104及所述标准球102分别固定在所述工作台103上，在所述激光位移传感器105的标定过程中，不必反复调整所述标准球102的位姿。
所述激光位移传感器105安装在所述刀柄夹具101上，在标定时所述激光位移传感器105与所述标准球102之间相隔一定距离，通过所述机床主轴100可以上下移动所述激光位移传感器105，以用于保证所述标准球102的表面特征在所述激光位移传感器105的测量范围内。
对所述标准球进行的扫描测量具体包括以下步骤：首先，通过刀柄夹具101将所述激光位移传感器105安装在所述机床主轴100上，所述微处理器106(计算机)采用PLC触发所述激光位移传感器105进行采点。其中，根据传感器的三角测量原理，为了保证传感器测量精度，采点时尽量 保证激光出光方向与球面法矢之间的夹角小于30°，且将机床坐标p Mi＝(x i,y i,z i)和对应的传感器一维测量距离值d i输出。
本实施方式中，所述激光位移传感器为点激光传感器；采用PLC触发所述激光位移传感器时，PLC实现机床继电器的闭合与断开，通过外接电路提供+5V的高电平来触发激光位移传感器的测量。
步骤二，将步骤一得到的原始数据结合并转换到球坐标系下，并基于多个转换得到的数据构造关于球形坐标和出光方向的非线性方程组，转换得到的数据满足球面约束方程。
具体地，请参阅图4及图5，原始数据的坐标转换主要包括以下步骤：首先，建立三个坐标系，分别为机床坐标系、球坐标系及传感器坐标系；之后，将采集到的原始数据进行坐标转换，先将采集到的原始数据转换到机床坐标系下，然后再经过坐标转换最终转换到球坐标系下。
本实施方式建立的坐标系包括机床坐标系{M}、传感器坐标系{S}和球坐标系{B}；机床坐标系：其原点位于机床x,y,z轴编码器处于零位且传感器初始姿态时、测量距离为0的点，三个坐标轴的方向与机床X、Y、Z三轴的方向一致，坐标原点在测量过程中不随各轴的运动而发生改变。传感器坐标系：激光位移传感器固定在机床主轴上，与机床主轴固连，其原点p So位于激光位移传感器处于初始姿态时、测量距离为0的点，方向与机床坐标系方向相同。对于三轴数控铣床，传感器坐标系原点相对机床坐标系原点在x、y、z方向的偏移量可以直接从数控系统中读出，传感器坐标系原点在机床坐标系下的坐标为 Mp So＝[ Mx So  My So  Mz So] T。球坐标系：将半径为R的标准球固定在机床工作台上，其表面为标准球面，定义标准球的球坐标系为{B}，其原点p Bo位于标定球球心点，方向与机床坐标系方向相同，p Bo在机床坐标系下的坐标为 Mp Bo＝[ Mx Bo  My Bo  Mz Bo] T。
定义激光出光方向为t＝[l m n] T，易得激光光束与球面交点p Mi在机床坐标系下，可表示为 Mp Mi＝d it+ Mp Soi，进而转换到球面坐标系下为 Bp Mi＝d it+ Mp Soi- Mp Bo。
初始位姿时激光位移传感器出光方向为t 1，此时测量值为d 1，传感器坐标系的原点在机床坐标系下可表示为 Mp S1＝[ Mx S1  My S1  Mz S1] T，所以球面点 Bp M1＝[ Bx M1  By M1  Bz M1] T在球坐标系中可以表示为 Bp M1＝d 1t+ Mp S1- Mp Bo，该点满足球面方程 Bp Mi T Bp Mi＝R 2。
非线性方程组的构造包括以下子步骤：首先，采集到的测量点为球坐标系下的球面上的离散点，该离散点满足球面约束方程 Bp Mi T Bp Mi＝R 2；接着以离散点构建球面约束方程f i(X)，该方程为非线性方程；之后，将得到的多个球面约束方程组成一个非线性方程组f(X)。
构造的非线性方程组为：
Figure PCTCN2020095989-appb-000012
需要对得到的非线性方程组进行降维，激光出光方向t＝[l m n] T为单位矢量，则t Tt＝1，因此可以用
Figure PCTCN2020095989-appb-000013
代替，具体代替方案如下式：
Figure PCTCN2020095989-appb-000014
进而非线性方程组可以化为：
Figure PCTCN2020095989-appb-000015
得到的非线性方程组，基于非线性方程组数量大于6时，该方程组为超定方程组，可以进行优化求解。本实施方式中，所述非线性方程组中方程数量不小于6个，优选地为50个。
步骤三，将所述非线性方程组的求解转换为新函数φ(x)的最小二乘优化，进而采用Levenberg-Marquardt迭代优化算法对新函数φ(x)进行求解，由此得到激光出光方向及球心位置坐标。
请参阅图6及图7，具体地，求解所述非线性方程组的步骤包括：
(1)将参数 Mx Bo, My Bo, Mz Bo,θ,
Figure PCTCN2020095989-appb-000016
用矩阵X代替，上述得到的非线性方程组可转化为：
Figure PCTCN2020095989-appb-000017
(2)定义新函数φ(X)，
Figure PCTCN2020095989-appb-000018
至此非线性方程组的求解问题可以转换为求解非线性最小二乘问题，最小值即为非线性方程组的解。
(3)定义新函数φ(X)的梯度函数为
Figure PCTCN2020095989-appb-000019
并将梯度函数在X k进行泰勒展开，得到
Figure PCTCN2020095989-appb-000020
(4)将泰勒展开式U k(X)代入梯度函数g(X)中，得到：
Figure PCTCN2020095989-appb-000021
进而求得下次迭代参数：
Figure PCTCN2020095989-appb-000022
至此非线性方程组的求解问题已经转换为非线性最小二乘优化求解的问题，通过迭代优化算法 等即可对该问题进行求解。
(5)基于得到的下次迭代参数得到Gauss-Newton迭代矩阵G(X)为
Figure PCTCN2020095989-appb-000023
由于该迭代矩阵G(X)为奇异矩阵，无法运算，而Levenberg-Marquardt算法引入了阻尼参数μ来避免矩阵奇异的问题，Levenberg-Marquardt的迭代矩阵为：
G(X k)＝G(X k)+μ kI。
(6)初始值定义为X 0＝[0 0 0 0 -π]，定义阻尼系数μ 0＝10和放大系数β＝9，定义迭代变量k＝0和收敛标准ε＝0.001。
(7)求解f(X 0)和φ(X 0)的值。
(8)计算Jacobi矩阵
Figure PCTCN2020095989-appb-000024
和
Figure PCTCN2020095989-appb-000025
的值，如果
Figure PCTCN2020095989-appb-000026
停止迭代，求解结果为X k，否则转至步骤(9)。
(9)计算迭代Levenberg-Marquardt的迭代矩阵
Figure PCTCN2020095989-appb-000027
和迭代变量
Figure PCTCN2020095989-appb-000028
(10)求解f(X k+1)和φ(X k+1)的值，如果φ(X k+1)＜φ(X k)，阻尼系数μ k+1＝μ kβ，并跳转至步骤(9)；如果φ(X k+1)＞φ(X k)，阻尼系数μ k+1＝μ k/β，并跳转至步骤(8)。
本实施方式中，激光位移传感器标定主要用于确定传感器的出光方向，以便能够很好地将传感器的测量数值转换到机床坐标系下；所述标准球的直径大于等于50mm，优选为50mm；所述激光位移传感器的出光方向大致通过球心；采用的机床优选为定位精度优于0.03mm的半闭环或全闭环机床。
本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已， 并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种基于标准球的激光出光方向标定方法，其特征在于，该方法包括以下步骤：
    S1将激光位移传感器安装在机床主轴上，同时将标准球固定在工作台上，所述机床主轴带动所述激光位移传感器对所述标准球的上表面进行扫描测量，从而获取机床坐标和对应的传感器一维测量距离值；
    S2将步骤S1得到的原始数据结合并转换到球坐标系下，并基于转换得到的数据构造关于球形坐标和出光方向的非线性方程组，转换得到的数据满足球面约束方程；
    S3将所述非线性方程组的求解转换为新函数φ(x)的最小二乘优化，进而采用Levenberg-Marquardt迭代优化算法对新函数φ(x)进行求解，由此得到激光出光方向及球心位置坐标。
  2. 如权利要求1所述的基于标准球的激光出光方向标定方法，其特征在于：所述标准球的表面特征在所述激光位移传感器的测量范围内；扫描测量时，激光出光方向与标准球的球面法矢之间的夹角小于30°。
  3. 如权利要求1所述的基于标准球的激光出光方向标定方法，其特征在于：将步骤S1得到的原始数据结合并转换到球坐标系包括以下步骤：首先，分别建立机床坐标系、球坐标系及传感器坐标系；接着，将所述原始数据转换到所述机床坐标系下后，再将经过坐标转换最终转换到所述球坐标系下。
  4. 如权利要求3所述的基于标准球的激光出光方向标定方法，其特征在于：传感器坐标系的原点p So位于激光位移传感器处于初始姿态时、测量距离为0的点，传感器坐标系原点在机床坐标系下的坐标为 Mp So＝[ Mx So  My So  Mz So] T；球坐标系的原点p Bo位于标定球球心点，p Bo在机 床坐标系下的坐标为 Mp Bo＝[ Mx Bo  My Bo  Mz Bo] T。
  5. 如权利要求3所述的基于标准球的激光出光方向标定方法，其特征在于：扫描测量到的点为球坐标系下的球面上的离散点，该离散点满足球面约束方程，以得到的离散点构建球面约束方程，再将得到的多个球面约束方程组成所述非线性方程组。
  6. 如权利要求1所述的基于标准球的激光出光方向标定方法，其特征在于：
    Figure PCTCN2020095989-appb-100001
    f(X)为非线性方程组。
  7. 如权利要求6所述的基于标准球的激光出光方向标定方法，其特征在于：采用Levenberg-Marquardt迭代优化算法对新函数φ(x)进行求解包括以下步骤：
    (1)定义新函数φ(X)的梯度函数为
    Figure PCTCN2020095989-appb-100002
    并将梯度函数在X k进行泰勒展开，得到
    Figure PCTCN2020095989-appb-100003
    (2)将泰勒展开式U k(X)代入梯度函数g(X)中，得到：
    Figure PCTCN2020095989-appb-100004
    并求得下次迭代参数：
    Figure PCTCN2020095989-appb-100005
    继而得到Levenberg-Marquardt迭代矩阵G(X)为：
    Figure PCTCN2020095989-appb-100006
    (3)初始值定义为X 0＝[0 0 0 0 -π]，阻尼系数μ 0＝10和放大系数β＝9，定义迭代变量k＝0和收敛标准ε＝0.001；
    (4)求解f(X 0)和φ(X 0)的值；
    (5)计算Jacobi矩阵
    Figure PCTCN2020095989-appb-100007
    和
    Figure PCTCN2020095989-appb-100008
    的值，如果
    Figure PCTCN2020095989-appb-100009
    停止迭代，求解结果为X k，否则转至步骤(6)；
    (6)计算迭代Levenberg-Marquardt的迭代矩阵
    Figure PCTCN2020095989-appb-100010
    和迭代变量
    Figure PCTCN2020095989-appb-100011
    (7)求解f(X k+1)和φ(X k+1)的值，如果φ(X k+1)＜φX k)，阻尼系数μ k+1＝μ kβ，并跳转至步骤(6)；如果φ(X k+1)＞φX k)，阻尼系数μ k+1＝μ k/β，并跳转至步骤(5)。
  8. 如权利要求1-7任一项所述的基于标准球的激光出光方向标定方法，其特征在于：所述非线性方程组中方程数量不小于6个。
  9. 如权利要求1-7任一项所述的基于标准球的激光出光方向标定方法，其特征在于：所述标准球的直径大于等于50mm。
  10. 如权利要求1-7任一项所述的基于标准球的激光出光方向标定方法，其特征在于：所述激光位移传感器为点激光传感器。
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