CN106323286B - A kind of robot coordinate system and the transform method of three-dimensional measurement coordinate system - Google Patents
A kind of robot coordinate system and the transform method of three-dimensional measurement coordinate system Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及信息技术处理领域，更具体地，涉及一种三维测量数据到机器人运动坐标系的变换方法。The invention relates to the field of information technology processing, and more specifically, to a method for transforming three-dimensional measurement data into a robot motion coordinate system.
背景技术Background technique
智能机器人借助激光扫描仪等三维测量装置，能获取目标位置和工作环境的3维数据，从而自动规划机器人移动路径，规避环境中的障碍移动到目标位置。但实际中由于机器人运动坐标值和激光扫描仪的坐标值都是在各坐标系下得到的并不统一。因此需要先将测量得到的3维数据转换到机器人的运动坐标系下，使测量数据的3维坐标等于运动系统下的3维坐标。With the help of three-dimensional measuring devices such as laser scanners, intelligent robots can obtain three-dimensional data of the target position and working environment, thereby automatically planning the robot's movement path, avoiding obstacles in the environment and moving to the target position. However, in practice, the coordinate values of the robot motion and the laser scanner are obtained in each coordinate system and are not uniform. Therefore, it is necessary to convert the measured 3-dimensional data to the robot's motion coordinate system first, so that the 3-dimensional coordinates of the measured data are equal to the 3-dimensional coordinates of the motion system.
目前，所有的坐标转换方法都是通过在两个坐标系中找若干个公共点，然后通过建立方程组求解旋转平移参数。例如，七参数模型求解，将3个平移量、3个旋转量和1个尺度因子作为待求解的未知量，然后通过联立方程求解；十三参数模型求解，将3个旋转矩阵用一个3×3矩阵表示，则有9个未知参数，加上3个平移量和1个尺度因子合计13个未知量，然后通过联立方程求解。但将这些方法应用在智能机器人时存在以下问题：(1)难以寻找大量的公共点用于求解转换矩阵参数；(2)实际中所有的公共点是存在误差的。因此，需要一种坐标转换方法，只需要少量的公共点就能计算出坐标转换矩阵，同时能修正由于公共点误差带来的转换误差。At present, all coordinate transformation methods find several common points in the two coordinate systems, and then solve the rotation and translation parameters by establishing a system of equations. For example, to solve a seven-parameter model, 3 translations, 3 rotations, and 1 scale factor are used as unknown quantities to be solved, and then solved through simultaneous equations; to solve a thirteen-parameter model, 3 rotation matrices are used with a 3 ×3 matrix representation, there are 9 unknown parameters, plus 3 translations and 1 scale factor, a total of 13 unknowns, and then solved by simultaneous equations. But when these methods are applied to intelligent robots, there are the following problems: (1) it is difficult to find a large number of common points for solving the parameters of the transformation matrix; (2) there are errors in all common points in practice. Therefore, there is a need for a coordinate transformation method, which can calculate the coordinate transformation matrix with only a small number of common points, and can correct the transformation error caused by the common point error.
发明内容Contents of the invention
本发明为克服上述现有技术所述的公共点难以寻找，公共点存在误差等问题，提供一种机器人坐标系与三维测量坐标系的变换方法，适用于各种智能机器人运动坐标系和三维测量系统坐标系的坐标变换。In order to overcome the problems in the above-mentioned prior art that the common point is difficult to find, and there are errors in the common point, the present invention provides a transformation method between the robot coordinate system and the three-dimensional measurement coordinate system, which is applicable to various intelligent robot motion coordinate systems and three-dimensional measurement Coordinate transformation of the system coordinate system.
为解决上述技术问题，本发明的技术方案如下：In order to solve the problems of the technologies described above, the technical solution of the present invention is as follows:
一种机器人坐标系与三维测量坐标系的变换方法，所述方法包括以下步骤：A method for transforming a robot coordinate system and a three-dimensional measurement coordinate system, the method comprising the following steps:
S1：公共点坐标提取：在机器人工作环境中选定4个公共点，然后在机器人运动坐标系下和三维测量坐标系下，分别提取这4个公共点的三维空间坐标作为坐标系变换的依据；S1: Common point coordinate extraction: Select 4 common points in the robot working environment, and then extract the 3D space coordinates of these 4 common points under the robot motion coordinate system and the 3D measurement coordinate system as the basis for coordinate system transformation ;
S2：变换矩阵计算：将4个公共点划分成4个特征三角形，并建立一个标准坐标系；计算运动坐标系下和扫描坐标系下的特征三角形转换到标准坐标系的正变换矩阵和逆变换矩阵；根据正变换矩阵和逆变换矩阵，将4个公共点的扫描坐标转换到运动坐标系下，并求取每个公共点转换后的均值坐标；最后计算公共点的扫描坐标到均值坐标的旋转平移矩阵；S2: Transformation matrix calculation: Divide 4 common points into 4 characteristic triangles, and establish a standard coordinate system; calculate the forward transformation matrix and inverse transformation of the transformation of the characteristic triangles under the motion coordinate system and scanning coordinate system to the standard coordinate system matrix; according to the forward transformation matrix and the inverse transformation matrix, transform the scanning coordinates of the four common points into the motion coordinate system, and calculate the average coordinates of each common point after conversion; finally calculate the scanning coordinates of the common points to the average coordinates rotation-translation matrix;
S3：扫描数据坐标系转换：根据S2计算得到的变换矩阵，对测量系统得到的三维数据进行三维旋转和平移，使测量数据从测量系统的坐标系变换到机器人运动系统的坐标系中。S3: Scanning data coordinate system conversion: According to the transformation matrix calculated in S2, three-dimensional rotation and translation are performed on the three-dimensional data obtained by the measurement system, so that the measurement data is transformed from the coordinate system of the measurement system to the coordinate system of the robot motion system.
在一种优选的方案中，步骤S1中，公共点坐标提取具体步骤为：In a preferred solution, in step S1, the specific steps of extracting the coordinates of the public points are:
S1.1：公共点选取：在机器人工作环境中，选取4个位置不同，且绝对位置不会发生改变的角点作为公共点。S1.1: Common point selection: In the working environment of the robot, four corner points with different positions and whose absolute position will not change are selected as common points.
S1.2：公共点的运动坐标提取：通过机器人的示教器或点动控制器，将机器人的末端执行机构依次移动到4个公共点的位置，并按顺序记录4个公共点在运动坐标系下的三维空间坐标。S1.2: Motion coordinate extraction of common points: Move the end effector of the robot to the positions of the four common points in sequence through the robot’s teach pendant or jog controller, and record the motion coordinates of the four common points in sequence The three-dimensional space coordinates under the system.
S1.3：公共点的测量坐标提取：对三维测量系统测量得到的三维数据进行处理，利用角点识别方法，得到4个公共点在测量系统下的三维空间坐标。S1.3: Measurement coordinate extraction of common points: Process the 3D data measured by the 3D measurement system, and use the corner point recognition method to obtain the 3D space coordinates of the 4 common points under the measurement system.
在一种优选的方案中，步骤S2中，变换矩阵具体计算步骤为：In a preferred solution, in step S2, the specific calculation steps of the transformation matrix are:
S2.1：特征三角形划分：对4个公共点进行编号(编号为1、2、3、4)；然后抽取一个点作为特征三角形的顶点，选取另一个点与顶点连线形成参考边，最后再选取一个点与另外两点连线形成一个三角形；S2.1: Characteristic triangle division: number the 4 common points (numbered as 1, 2, 3, 4); then extract a point as the vertex of the characteristic triangle, select another point to connect with the vertex to form a reference edge, and finally Then select a point and connect the other two points to form a triangle;
S2.2：标准坐标系建立：以特征三角形的顶点作为坐标系的原点，以特征三角形参考边的方向作为X轴方向，以特征三角形平面内垂直于参考边的方向作为Y轴方向，以垂直于三角形平面的方向为Z轴方向建立一个标准坐标系；S2.2: Establishment of the standard coordinate system: take the vertex of the characteristic triangle as the origin of the coordinate system, take the direction of the reference side of the characteristic triangle as the direction of the X-axis, take the direction perpendicular to the reference side in the plane of the characteristic triangle as the direction of the Y-axis, and take the direction of the vertical Establish a standard coordinate system in the direction of the triangle plane as the Z-axis direction;
S2.3：标准坐标系变换矩阵计算：计算机器人运动坐标系和测量坐标系的特征三角形到标准坐标系的正变换矩阵和逆变换矩阵。令特征三角形三个点的坐标为：(x1,y1,z1)，(x2,y2,z2)，(x3,y3,z3)，则正变换矩阵为：S2.3: Standard coordinate system transformation matrix calculation: calculate the forward transformation matrix and inverse transformation matrix from the characteristic triangle of the robot motion coordinate system and measurement coordinate system to the standard coordinate system. Let the coordinates of the three points of the characteristic triangle be: (x 1 ,y 1 ,z 1 ), (x 2 ,y 2 ,z 2 ), (x 3 ,y 3 ,z 3 ), then the forward transformation matrix is:
式中，i＝1、2、3。逆变换矩阵为：In the formula, i=1, 2, 3. The inverse transformation matrix is:
S2.4：公共点坐标变换：将S2.3得到的测量坐标系到标准坐标系的4个正变换矩阵和机器人坐标系到标准坐标系的4个逆变换矩阵，根据特征三角形的对应关系一一对应后形成4对变换矩阵。然后，依次对测量系统下公共点的坐标乘上测量系统坐标系到标准坐标系的正变换矩阵，再乘上对应的逆变换矩阵；S2.4: Common point coordinate transformation: transform the 4 forward transformation matrices from the measurement coordinate system to the standard coordinate system obtained in S2.3 and the 4 inverse transformation matrices from the robot coordinate system to the standard coordinate system, according to the corresponding relationship of the characteristic triangle After one-to-one correspondence, 4 pairs of transformation matrices are formed. Then, the coordinates of the common points under the measurement system are multiplied by the forward transformation matrix from the measurement system coordinate system to the standard coordinate system, and then multiplied by the corresponding inverse transformation matrix;
S2.5：均值化处理：将S2.4得到的4种变换结果的坐标值进行均值计算，从而降低公共点坐标误差导致的坐标转换误差；S2.5: Averaging processing: Calculate the mean value of the coordinate values of the four transformation results obtained in S2.4, thereby reducing the coordinate conversion error caused by the common point coordinate error;
S2.6：变换矩阵计算：任意提取3个均值化处理后的公共点坐标，形成一个特征三角形，计算该特征三角形到标准坐标系的逆变换矩阵。然后在计算扫描坐标系下对应特征三角形到标准坐标系的正变换矩阵。将上述正变换矩阵和逆变换矩阵作为坐标变换矩阵组；然后将测量数据先乘上正变换矩阵，再乘上逆变换矩阵，实现测量坐标系到运动坐标系的变换。S2.6: Transformation matrix calculation: extract 3 common point coordinates after mean value processing arbitrarily to form a characteristic triangle, and calculate the inverse transformation matrix from the characteristic triangle to the standard coordinate system. Then calculate the positive transformation matrix corresponding to the characteristic triangle to the standard coordinate system in the scanning coordinate system. The above-mentioned forward transformation matrix and inverse transformation matrix are used as a coordinate transformation matrix group; then the measured data is first multiplied by the forward transformation matrix, and then multiplied by the inverse transformation matrix to realize the transformation from the measurement coordinate system to the motion coordinate system.
与现有技术相比，本发明技术方案的有益效果是：(1)本发明中需通过4个公共点，且公共点的确定方式以及坐标提取方式简单可行；(2)本发明中变换矩阵只需通过计算简单的三角函数即可得到，无需复杂的迭代计算；(3)本发明通过均值化处理方式，在一定程度上修正了公共点误差带来的变换误差。Compared with the prior art, the beneficial effects of the technical solution of the present invention are: (1) 4 common points need to be passed in the present invention, and the determination mode and the coordinate extraction mode of the common points are simple and feasible; (2) transformation matrix in the present invention It can be obtained by calculating simple trigonometric functions without complex iterative calculation; (3) the present invention corrects the transformation error caused by the common point error to a certain extent through the mean value processing method.
附图说明Description of drawings
图1为本发明机器人坐标系与三维测量坐标系变换方法的流程图。Fig. 1 is a flow chart of the transformation method between the robot coordinate system and the three-dimensional measurement coordinate system of the present invention.
图2为特征三角形到标准坐标系的变换示意图。Fig. 2 is a schematic diagram of transformation from a characteristic triangle to a standard coordinate system.
图3为扫描数据到机器人坐标系的变换示意图。Fig. 3 is a schematic diagram of transformation from scanning data to robot coordinate system.
具体实施方式Detailed ways
附图仅用于示例性说明，不能理解为对本专利的限制；The accompanying drawings are for illustrative purposes only and cannot be construed as limiting the patent;
为了更好说明本实施例，附图某些部件会有省略、放大或缩小，并不代表实际产品的尺寸；In order to better illustrate this embodiment, some parts in the drawings will be omitted, enlarged or reduced, and do not represent the size of the actual product;
对于本领域技术人员来说，附图中某些公知结构及其说明可能省略是可以理解的。For those skilled in the art, it is understandable that some well-known structures and descriptions thereof may be omitted in the drawings.
下面结合附图和实施例对本发明的技术方案做进一步的说明。The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.
实施例1Example 1
以水火弯板机器人运动坐标系和三维激光扫描仪坐标系的坐标变换为例，如图1所示，本发明方法包括以下步骤：Taking the coordinate transformation of the motion coordinate system of the water-fire bending plate robot and the coordinate system of the three-dimensional laser scanner as an example, as shown in Figure 1, the method of the present invention includes the following steps:
S1：公共点坐标提取：在机器人工作环境中选定4个公共点，然后在机器人运动坐标系下和三维测量坐标系下，分别提取这4个公共点的三维空间坐标作为坐标系变换的依据。在实例1中，公共点坐标提取具体步骤为：S1: Common point coordinate extraction: Select 4 common points in the robot working environment, and then extract the 3D space coordinates of these 4 common points under the robot motion coordinate system and the 3D measurement coordinate system as the basis for coordinate system transformation . In Example 1, the specific steps for extracting public point coordinates are:
S1.1：公共点选取：选取机器人工作平台的4个角点作为公共点。S1.1: Common point selection: Select the 4 corner points of the robot working platform as the common points.
S1.2：公共点的运动坐标提取：通过水火弯板机器人运动控制系统的点动控制按钮将机器人末端的火枪头移动到公共点的位置，并按顺序记录4个公共点在运动坐标系下的三维空间坐标。S1.2: Motion coordinate extraction of common points: Move the musket head at the end of the robot to the position of the common points through the jog control button of the motion control system of the water-fire bending plate robot, and record the 4 common points in the motion coordinate system in sequence The three-dimensional space coordinates of .
S1.3：公共点的测量坐标提取：对扫描仪测量得到的点云数据进行处理，提取工作平台4个角点的三维空间坐标。S1.3: Extraction of measurement coordinates of common points: process the point cloud data obtained by scanner measurement, and extract the three-dimensional space coordinates of the four corner points of the working platform.
S2：变换矩阵计算：将4个公共点划分成4个特征三角形，并建立一个标准坐标系；计算运动坐标系下和扫描坐标系下的特征三角形转换到标准坐标系的正变换矩阵和逆变换矩阵；根据正变换矩阵和逆变换矩阵，将4个公共点的扫描坐标转换到运动坐标系下，并求取每个公共点转换后的均值坐标；最后计算公共点的扫描坐标到均值坐标的旋转平移矩阵。具体计算步骤为：S2: Transformation matrix calculation: Divide 4 common points into 4 characteristic triangles, and establish a standard coordinate system; calculate the forward transformation matrix and inverse transformation of the transformation of the characteristic triangles under the motion coordinate system and scanning coordinate system to the standard coordinate system matrix; according to the forward transformation matrix and the inverse transformation matrix, transform the scanning coordinates of the four common points into the motion coordinate system, and calculate the average coordinates of each common point after conversion; finally calculate the scanning coordinates of the common points to the average coordinates Rotation-translation matrix. The specific calculation steps are:
S2.1：特征三角形划分：对4个公共点进行编号(编号为1、2、3、4)；然后抽取一个点作为特征三角形的顶点，选取另一个点与顶点连线形成参考边，最后再选取一个点与另外两点连线形成一个三角形；S2.1: Characteristic triangle division: number the 4 common points (numbered as 1, 2, 3, 4); then extract a point as the vertex of the characteristic triangle, select another point to connect with the vertex to form a reference edge, and finally Then select a point and connect the other two points to form a triangle;
S2.2：标准坐标系建立：以特征三角形的顶点作为坐标系的原点，以特征三角形参考边的方向作为X轴方向，以特征三角形平面内垂直于参考边的方向作为Y轴方向，以垂直于三角形平面的方向为Z轴方向建立一个标准坐标系；S2.2: Establishment of the standard coordinate system: take the vertex of the characteristic triangle as the origin of the coordinate system, take the direction of the reference side of the characteristic triangle as the direction of the X-axis, take the direction perpendicular to the reference side in the plane of the characteristic triangle as the direction of the Y-axis, and take the direction of the vertical Establish a standard coordinate system in the direction of the triangle plane as the Z-axis direction;
S2.3：标准坐标系变换矩阵计算：计算机器人运动坐标系和测量坐标系的特征三角形到标准坐标系的正变换矩阵和逆变换矩阵。令特征三角形三个点的坐标为：(x1,y1,z1)，(x2,y2,z2)，(x3,y3,z3)，则正变换矩阵为：S2.3: Standard coordinate system transformation matrix calculation: calculate the forward transformation matrix and inverse transformation matrix from the characteristic triangle of the robot motion coordinate system and measurement coordinate system to the standard coordinate system. Let the coordinates of the three points of the characteristic triangle be: (x 1 ,y 1 ,z 1 ), (x 2 ,y 2 ,z 2 ), (x 3 ,y 3 ,z 3 ), then the forward transformation matrix is:
式中，i＝1、2、3。逆变换矩阵为：In the formula, i=1, 2, 3. The inverse transformation matrix is:
具体的变换结果如图2所示。The specific transformation results are shown in Figure 2.
S2.4：公共点坐标变换：将S2.3得到的测量坐标系到标准坐标系的4个正变换矩阵和机器人坐标系到标准坐标系的4个逆变换矩阵，根据特征三角形的对应关系一一对应后形成4对变换矩阵。然后，依次对测量系统下公共点的坐标乘上测量系统坐标系到标准坐标系的正变换矩阵，再乘上对应的逆变换矩阵；S2.4: Common point coordinate transformation: transform the 4 forward transformation matrices from the measurement coordinate system to the standard coordinate system obtained in S2.3 and the 4 inverse transformation matrices from the robot coordinate system to the standard coordinate system, according to the corresponding relationship of the characteristic triangle After one-to-one correspondence, 4 pairs of transformation matrices are formed. Then, the coordinates of the common points under the measurement system are multiplied by the forward transformation matrix from the measurement system coordinate system to the standard coordinate system, and then multiplied by the corresponding inverse transformation matrix;
S2.5：均值化处理：将S2.4得到的4种变换结果的坐标值进行均值计算，从而降低公共点坐标误差导致的坐标转换误差；S2.5: Averaging processing: Calculate the mean value of the coordinate values of the four transformation results obtained in S2.4, thereby reducing the coordinate conversion error caused by the common point coordinate error;
S2.6：变换矩阵计算：任意提取3个均值化处理后的公共点坐标，形成一个特征三角形，计算该特征三角形到标准坐标系的逆变换矩阵。然后在计算扫描坐标系下对应特征三角形到标准坐标系的正变换矩阵。将上述正变换矩阵和逆变换矩阵作为坐标变换矩阵组。S2.6: Transformation matrix calculation: extract 3 common point coordinates after mean value processing arbitrarily to form a characteristic triangle, and calculate the inverse transformation matrix from the characteristic triangle to the standard coordinate system. Then calculate the positive transformation matrix corresponding to the characteristic triangle to the standard coordinate system in the scanning coordinate system. The above-mentioned forward transformation matrix and inverse transformation matrix are used as a coordinate transformation matrix group.
S3：扫描数据坐标系转换：根据S2计算得到的变换矩阵，对测量系统得到的三维数据进行三维旋转和平移，首先将测量数据先乘上坐标变换矩阵组的正变换矩阵，然后再乘上坐标变换矩阵组的逆变换矩阵，实现测量坐标系到运动坐标系的变换。使测量数据从测量系统的坐标系变换到机器人运动系统的坐标系中。具体的变换过程如图3所示。S3: Scanning data coordinate system conversion: According to the transformation matrix calculated in S2, three-dimensional rotation and translation are performed on the three-dimensional data obtained by the measurement system. First, the measurement data is multiplied by the positive transformation matrix of the coordinate transformation matrix group, and then multiplied by the coordinates The inverse transformation matrix of the transformation matrix group realizes the transformation from the measurement coordinate system to the motion coordinate system. Transform the measurement data from the coordinate system of the measurement system to the coordinate system of the robot motion system. The specific transformation process is shown in Figure 3.
附图中描述位置关系的用语仅用于示例性说明，不能理解为对本专利的限制；The terms describing the positional relationship in the drawings are only for illustrative purposes and cannot be interpreted as limitations on this patent;
显然，本发明的上述实施例仅仅是为清楚地说明本发明所作的举例，而并非是对本发明的实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式的变化或变动。这里无需也无法对所有的实施方式予以穷举。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，均应包含在本发明权利要求的保护范围之内。Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, other changes or changes in different forms can be made on the basis of the above description. It is not necessary and impossible to exhaustively list all the implementation manners here. All modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the claims of the present invention.
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| CN108692688B (en) * | 2018-04-28 | 2020-02-18 | 武汉理工大学 | A method for automatic calibration of scanner coordinate system of robot measurement-processing system |
| CN110559077B (en) * | 2018-06-05 | 2021-08-17 | 武汉联影智融医疗科技有限公司 | Coordinate system registration method, robot control method, device, equipment and medium |
| CN111351675A (en) * | 2020-03-30 | 2020-06-30 | 伯朗特机器人股份有限公司 | Industrial robot static compliance performance testing method |
| CN111409108B (en) * | 2020-04-01 | 2022-11-04 | 伯朗特机器人股份有限公司 | Industrial robot measurement coordinate system and robot instruction coordinate system conversion method |
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