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CN107738254A - The conversion scaling method and system of a kind of mechanical arm coordinate system - Google Patents

The conversion scaling method and system of a kind of mechanical arm coordinate system Download PDF

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CN107738254A
CN107738254A CN201710743278.1A CN201710743278A CN107738254A CN 107738254 A CN107738254 A CN 107738254A CN 201710743278 A CN201710743278 A CN 201710743278A CN 107738254 A CN107738254 A CN 107738254A
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coordinate system
coordinate
center
manipulator
measurement reference
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CN107738254B (en
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杨聚庆
董登峰
周维虎
劳达宝
纪荣祎
张滋黎
袁江
石俊凯
王岩庆
范百兴
王国名
程智
朱志忠
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Institute of Microelectronics of CAS
Aerospace Information Research Institute of CAS
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration

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  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Mathematical Physics (AREA)
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  • Computer Vision & Pattern Recognition (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Length Measuring Devices By Optical Means (AREA)
  • Manipulator (AREA)
  • Numerical Control (AREA)

Abstract

本发明提供一种机械臂坐标系的转换标定方法与系统，所述方法包括：S1，基于目标机械臂工作范围内布置的跟踪测量装置，利用末端坐标系平移运动法，获取末端工具坐标系相对测量参考坐标系的坐标旋转变换关系；S2，利用基于所述末端工具坐标系的单轴旋转法和相对机械臂基坐标系的运动学变换，获取所述末端工具坐标系相对所述机械臂基坐标系的坐标齐次变换关系；S3，基于选定标定采样点的坐标，分别利用多点重心求解法、重心化处理法和罗德里格矩阵变换求解法，获取所述机械臂基坐标系与所述测量参考坐标系的坐标齐次变换关系。本发明标定流程简单，标定算法无迭代过程，能够有效减少坐标系标定耗时，提高坐标系标定精度。

The present invention provides a method and system for converting and calibrating a manipulator coordinate system. The method includes: S1, based on the tracking and measuring device arranged within the working range of the target manipulator, using the translational motion method of the end coordinate system to obtain the relative position of the end tool coordinate system. Measuring the coordinate rotation transformation relationship of the reference coordinate system; S2, using the single-axis rotation method based on the end tool coordinate system and the kinematic transformation relative to the base coordinate system of the manipulator to obtain Coordinate homogeneous transformation relationship of the coordinate system; S3, based on the coordinates of the selected calibration sampling points, respectively use the multi-point center of gravity solution method, the center of gravity processing method and the Rodrigue matrix transformation solution method to obtain the base coordinate system of the manipulator and Coordinate homogeneous transformation relationship of the measurement reference coordinate system. The calibration process of the invention is simple, and the calibration algorithm has no iterative process, which can effectively reduce the time-consuming calibration of the coordinate system and improve the calibration accuracy of the coordinate system.

Description

一种机械臂坐标系的转换标定方法与系统A method and system for converting and calibrating a manipulator coordinate system

技术领域technical field

本发明涉及机器人控制与应用技术领域，更具体地，涉及一种机械臂坐标系的转换标定方法与系统。The present invention relates to the technical field of robot control and application, and more specifically, to a method and system for converting and calibrating a mechanical arm coordinate system.

背景技术Background technique

工业机械臂通常采用工具坐标系表示末端工具的工具中心点(Tool CenterPoint,TCP)位置及末端工具的姿态。机械臂末端工具的位姿控制取决于相对于基坐标系的机器人运动学变换关系。但在外部测量过程中，末端工具位姿测量值是相对于测量参考坐标系，必须进行测量参考坐标系与机械臂相关坐标系的转换标定，获取机械臂末端工具坐标系和机械臂基坐标系的全局定位，从而能够进一步实现机械臂末端工具位姿的引导与补偿修正。Industrial manipulators usually use the tool coordinate system to represent the position of the Tool Center Point (TCP) of the end tool and the attitude of the end tool. The pose control of the tool at the end of the manipulator depends on the kinematic transformation relationship of the robot relative to the base coordinate system. However, in the external measurement process, the measured value of the end tool pose is relative to the measurement reference coordinate system, and the conversion calibration between the measurement reference coordinate system and the relevant coordinate system of the manipulator must be carried out to obtain the end tool coordinate system of the manipulator and the base coordinate system of the manipulator The global positioning of the robot can further realize the guidance and compensation correction of the tool pose at the end of the manipulator.

目前机械臂坐标系与外部参考坐标系转换标定常采用的一种方法为单轴旋转运动法。单轴旋转运动法通过3次单轴周期旋转，结合空间几何矢量和坐标系变换方程进行求解，末端工具坐标系平移向量取决于空间交叉点单点测量精度，且没有考虑当前末端工具TCP点相对基坐标系的位置误差，因此不能保证坐标系标定精度的可靠性。At present, a method commonly used for conversion and calibration of the manipulator coordinate system and the external reference coordinate system is the single-axis rotation motion method. The single-axis rotation motion method uses three single-axis periodic rotations, combined with the space geometry vector and the coordinate system transformation equation to solve the problem. The translation vector of the end tool coordinate system depends on the measurement accuracy of the single point of the spatial intersection point, and does not consider the relative position of the current end tool TCP point. The position error of the base coordinate system, so the reliability of the calibration accuracy of the coordinate system cannot be guaranteed.

发明内容Contents of the invention

为了克服上述问题或者至少部分地解决上述问题，本发明提供一种机械臂坐标系的转换标定方法与系统，以达到有效减少坐标系标定耗时及提高坐标系标定精度的目的。In order to overcome the above problems or at least partially solve the above problems, the present invention provides a method and system for converting and calibrating the coordinate system of a manipulator, so as to effectively reduce the time-consuming and improve the calibration accuracy of the coordinate system.

一方面，本发明提供一种机械臂坐标系的转换标定方法，包括：S1，基于目标机械臂工作范围内布置的跟踪测量装置，利用末端坐标系平移运动法，获取末端工具坐标系相对测量参考坐标系的坐标旋转变换关系；S2，利用基于所述末端工具坐标系的单轴旋转法和相对机械臂基坐标系的运动学变换，获取所述末端工具坐标系相对所述机械臂基坐标系的坐标齐次变换关系；S3，基于选定标定采样点的坐标，分别利用多点重心求解法、重心化处理法和罗德里格矩阵变换求解法，获取所述机械臂基坐标系与所述测量参考坐标系的坐标齐次变换关系。On the one hand, the present invention provides a method for converting and calibrating the coordinate system of the manipulator, including: S1, based on the tracking and measuring device arranged within the working range of the target manipulator, using the translational movement method of the end coordinate system to obtain the relative measurement reference of the end tool coordinate system The coordinate rotation transformation relationship of the coordinate system; S2, using the single-axis rotation method based on the end tool coordinate system and the kinematic transformation relative to the base coordinate system of the manipulator, to obtain the coordinate system of the end tool relative to the base coordinate system of the manipulator Coordinate homogeneous transformation relationship; S3, based on the coordinates of the selected calibration sampling points, respectively use the multi-point center of gravity solution method, the center of gravity processing method and the Rodrigue matrix transformation solution method to obtain the base coordinate system of the manipulator and the described Coordinate homogeneous transformation relationship of the measurement reference coordinate system.

其中，步骤S1中所述利用末端坐标系平移运动法，获取末端工具坐标系相对测量参考坐标系的坐标旋转变换关系的步骤进一步包括：通过测量所述目标机械臂的末端工具沿所述末端工具坐标系各方向轴平移运动时，所述末端工具坐标系的原点坐标和平移位移矢量，计算所述末端工具坐标系在所述测量参考坐标系下的单位分量。Wherein, the step of obtaining the coordinate rotation transformation relationship of the end tool coordinate system relative to the measurement reference coordinate system by using the end coordinate system translation motion method described in step S1 further includes: by measuring the end tool of the target mechanical arm along the end tool When the axes in each direction of the coordinate system move in translation, the origin coordinates and translational displacement vectors of the end tool coordinate system are used to calculate the unit components of the end tool coordinate system under the measurement reference coordinate system.

其中，所述S2的步骤进一步包括：拟合获取所述目标机械臂1轴和6轴的轴旋转圆周半径，计算两旋转圆周交点相对于所述测量参考坐标系的坐标在各所述单位分量上的投影，并利用空间矢量几何关系，获取末端工具坐标系相对所述机械臂基坐标系的坐标齐次变换关系。Wherein, the step of S2 further includes: fitting and obtaining the radii of the rotation circles of the 1st and 6th axes of the target manipulator, and calculating the coordinates of the intersection of the two rotation circles relative to the coordinates of the measurement reference coordinate system in each of the unit components and using the space vector geometric relationship to obtain the coordinate homogeneous transformation relationship of the end tool coordinate system relative to the base coordinate system of the manipulator.

其中，所述S3的步骤进一步包括：S31，利用多点重心求解法，分别计算所述标定采样点相对所述机械臂基坐标系和所述测量参考坐标系的重心坐标；S32，分别基于所述标定采样点相对所述机械臂基坐标系以及所述测量参考坐标系的重心坐标和标定采样点坐标，对所述标定采样点进行重心化处理，分别获取所述标定采样点相对所述机械臂基坐标系和所述测量参考坐标系的重心化坐标；S33，利用罗德里格矩阵形式，表示所述标定采样点相对所述机械臂基坐标系与所述测量参考坐标系的重心化坐标变换方程；S34，利用特征值带入法求解所述重心化坐标变换方程，获取所述机械臂基坐标系相对所述测量参考坐标系的变换矩阵。Wherein, the step of S3 further includes: S31, using the multi-point center of gravity solution method, respectively calculating the center of gravity coordinates of the calibration sampling points relative to the base coordinate system of the manipulator and the measurement reference coordinate system; The center of gravity coordinates of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system and the coordinates of the calibration sampling point are carried out to the center of gravity of the calibration sampling point, and the coordinates of the calibration sampling point relative to the mechanical arm are respectively obtained. The barycentric coordinates of the arm base coordinate system and the measurement reference coordinate system; S33, using the Rodrigue matrix form to represent the barycentric coordinates of the calibration sampling point relative to the manipulator base coordinate system and the measurement reference coordinate system Transformation equation; S34, using the eigenvalue bring-in method to solve the barycentric coordinate transformation equation, and obtain a transformation matrix of the base coordinate system of the manipulator relative to the measurement reference coordinate system.

其中，所述S32的步骤进一步包括：S321，将所述机械臂基坐标系中的标定采样点坐标矩阵与标定采样点的重心坐标矩阵相减，获取所述标定采样点相对所述机械臂基坐标系的重心化坐标；S322，将所述测量参考坐标系中的标定采样点坐标矩阵与标定采样点的重心坐标矩阵相减，获取所述标定采样点相对所述测量参考坐标系的重心化坐标。Wherein, the step of S32 further includes: S321, subtracting the calibration sampling point coordinate matrix in the base coordinate system of the manipulator from the center-of-gravity coordinate matrix of the calibration sampling point to obtain The barycentric coordinates of the coordinate system; S322, subtracting the coordinate matrix of the calibration sampling points in the measurement reference coordinate system from the barycentric coordinate matrix of the calibration sampling points to obtain the barycentricity of the calibration sampling points relative to the measurement reference coordinate system coordinate.

其中，所述S33的步骤进一步包括：S331，基于标定采样点相对机械臂基坐标系和测量参考坐标系的重心化坐标维数要求，设定相应维数的罗德里格反对称矩阵；S332，基于所述罗德里格反对称矩阵，将机械臂基坐标系相对测量参考坐标系的旋转分量变换矩阵等效变换为罗德里格矩阵形式；S333，基于罗德里格矩阵形式的所述旋转分量变换矩阵，将所述标定采样点相对所述机械臂基坐标系与所述测量参考坐标系的重心化坐标变换方程等效变换为包含所述罗德里格反对称矩阵的方程形式。Wherein, the step of S33 further includes: S331, based on the barycentric coordinate dimension requirements of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system, setting the Rodrigue antisymmetric matrix of the corresponding dimension; S332, Based on the Rodrigue antisymmetric matrix, equivalently transform the rotation component transformation matrix of the base coordinate system of the manipulator relative to the measurement reference coordinate system into a Rodrigue matrix form; S333, transform the rotation component based on the Rodrigue matrix form matrix, which equivalently transforms the barycentric coordinate transformation equation of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system into an equation form including the Rodrigue anti-symmetric matrix.

其中，步骤S1中所述跟踪测量装置按如下步骤进行布置：在所述目标机械臂工作范围内架设激光跟踪测量装置；在所述目标机械臂的末端工具上固定激光反射靶球，并使所述激光反射靶球处于所述激光跟踪测量装置的工作范围。Wherein, the tracking and measuring device in step S1 is arranged according to the following steps: set up a laser tracking and measuring device within the working range of the target manipulator; fix the laser reflection target ball on the end tool of the target manipulator, and make the The laser reflection target ball is within the working range of the laser tracking and measuring device.

其中，所述两旋转圆周交点为初始位型所述激光反射靶球的中心；通过计算所述激光反射靶球的中心坐标在各所述单位分量上的投影，并利用空间矢量几何关系，获取所述激光反射靶球的中心相对所述末端工具坐标系的坐标如下：Wherein, the intersection point of the two rotating circles is the center of the laser reflection target ball in the initial configuration; by calculating the projection of the center coordinates of the laser reflection target ball on each of the unit components, and using the space vector geometric relationship, to obtain The coordinates of the center of the laser reflection target sphere relative to the end tool coordinate system are as follows:

式中，表示激光反射靶球中心相对末端工具坐标系的坐标，xEto、yEto和zEto分别表示激光反射靶球中心相对末端工具坐标系的xE轴、yE轴和zE轴的坐标分量，表示6轴旋转中心相对激光反射靶球中心的位置矢量，其模长等于所述6轴的拟合半径值，和分别表示末端工具坐标系在测量参考坐标系下xE轴和yE轴的单位分量，R1表示所述1轴的拟合半径值，xBeo表示末端工具坐标系原点在初始位型时相对机械臂基坐标系xB轴的分量。In the formula, Represent the coordinates of the center of the laser reflection target sphere relative to the end tool coordinate system, x Eto , y Eto and z Eto represent the coordinate components of the x E axis, y E axis and z E axis of the center of the laser reflection target sphere relative to the end tool coordinate system, Indicates the position vector of the 6-axis rotation center relative to the laser reflection target ball center, and its modulus length is equal to the fitting radius value of the 6-axis, with represent the unit components of the x E axis and y E axis of the end tool coordinate system in the measurement reference coordinate system, R 1 represents the fitting radius value of the 1 axis, and x Beo represents that the origin of the end tool coordinate system is relative to The component of the x- B axis of the base coordinate system of the manipulator.

其中，选取所述激光跟踪测量装置的测量坐标系作为所述测量参考坐标系。Wherein, the measurement coordinate system of the laser tracking measurement device is selected as the measurement reference coordinate system.

另一方面，本发明提供一种机械臂坐标系的转换标定系统，包括：至少一个存储器、至少一个处理器、通信接口和总线；所述存储器、所述处理器和所述通信接口通过所述总线完成相互间的通信，所述通信接口用于所述转换标定设备与坐标测量设备之间的信息传输；所述存储器中存储有可在所述处理器上运行的计算机程序，所述处理器执行所述程序时实现如如上所述的机械臂坐标系的转换标定方法。On the other hand, the present invention provides a conversion and calibration system of a mechanical arm coordinate system, comprising: at least one memory, at least one processor, a communication interface, and a bus; the memory, the processor, and the communication interface communicate through the The bus completes the mutual communication, and the communication interface is used for the information transmission between the conversion and calibration equipment and the coordinate measuring equipment; the computer program that can run on the processor is stored in the memory, and the processor When the program is executed, the method for transforming and calibrating the coordinate system of the manipulator as described above is realized.

本发明提供的一种机械臂坐标系的转换标定方法与系统，通过采用直线运动与旋转运动相结合的方式改进单轴旋转运动法的坐标系矢量方向标定，同时采用多点重心采样和罗德里格算法进行坐标系转换方程求解，标定流程简单，便于现场操作，标定算法无迭代过程，能够有效减少坐标系标定耗时，提高坐标系标定精度。The method and system for converting and calibrating the coordinate system of a manipulator provided by the present invention improve the coordinate system vector direction calibration of the single-axis rotary motion method by adopting the combination of linear motion and rotary motion, and simultaneously adopt multi-point center of gravity sampling and Rodri The grid algorithm is used to solve the coordinate system conversion equation. The calibration process is simple and convenient for on-site operation. The calibration algorithm has no iterative process, which can effectively reduce the time-consuming of coordinate system calibration and improve the accuracy of coordinate system calibration.

附图说明Description of drawings

图1为本发明实施例一种机械臂空间坐标系转换标定的布置示意图；Fig. 1 is a schematic diagram of the layout of a manipulator space coordinate system transformation and calibration according to an embodiment of the present invention;

图2为本发明实施例一种机械臂坐标系的转换标定方法的流程图；Fig. 2 is a flow chart of a method for converting and calibrating a manipulator coordinate system according to an embodiment of the present invention;

图3为本发明实施例一种获取机械臂基坐标系与测量参考坐标系的坐标变换关系的处理过程流程图；Fig. 3 is a flow chart of the process of obtaining the coordinate transformation relationship between the base coordinate system of the manipulator and the measurement reference coordinate system according to an embodiment of the present invention;

图4为本发明实施例一种对标定采样点进行重心化处理的处理过程流程图；Fig. 4 is a kind of flow chart of the process of centering the calibration sampling point according to the embodiment of the present invention;

图5为本发明实施例一种获取标定采样点相对机械臂基坐标系和测量参考坐标系的重心化坐标变换方程的处理过程流程图；Fig. 5 is a flow chart of the process of obtaining the barycentric coordinate transformation equation of the calibrated sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system according to an embodiment of the present invention;

图6为本发明实施例一种机械臂坐标系的转换标定系统的结构框图。FIG. 6 is a structural block diagram of a system for converting and calibrating a manipulator coordinate system according to an embodiment of the present invention.

具体实施方式detailed description

为使本发明的目的、技术方案和优点更加清楚，下面将结合本发明实施例中的附图，对本发明中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明的一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动的前提下所获得的所有其他实施例，都属于本发明保护的范围。In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are the embodiment of the present invention. Some, but not all, embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

作为本发明实施例的一个方面，本实施例提供一种机械臂坐标系的转换标定方法，参考图1，为本发明实施例一种机械臂空间坐标系转换标定的布置示意图。在进行目标机械臂坐标系转换标定装置的布置时，首先在所述目标机械臂工作范围内架设激光跟踪测量装置；然后在所述目标机械臂的末端工具上固定激光反射靶球，并使所述激光反射靶球处于所述激光跟踪测量装置的工作范围。As an aspect of the embodiment of the present invention, this embodiment provides a method for transforming and calibrating the coordinate system of a manipulator. Referring to FIG. 1 , it is a schematic diagram of an arrangement for transforming and calibrating a space coordinate system of a manipulator according to an embodiment of the present invention. When arranging the target manipulator coordinate system conversion calibration device, first set up a laser tracking measurement device within the working range of the target manipulator; then fix the laser reflection target ball on the end tool of the target manipulator, and make the target manipulator The laser reflection target ball is within the working range of the laser tracking and measuring device.

可以理解为，在进行目标机械臂坐标系转换标定之前，首先在目标机械臂工作区域附近设立系统全局测量控制站，架设激光跟踪测量装置，如激光跟踪仪。在目标机械臂末端工具固定激光反射靶球，保证该激光反射靶球处于激光跟踪仪的工作范围内，并建立如图1所示的空间坐标系。选取外部测量参考坐标系作为基准坐标系。在一个实施例中，选取所述激光跟踪测量装置的测量坐标系作为所述测量参考坐标系。如选取激光跟踪仪的测量坐标系作为测量参考坐标系。It can be understood that, before carrying out conversion and calibration of the coordinate system of the target manipulator, a system global measurement and control station is first set up near the working area of the target manipulator, and a laser tracking measurement device, such as a laser tracker, is set up. Fix the laser reflective target ball at the end of the target manipulator to ensure that the laser reflective target ball is within the working range of the laser tracker, and establish the spatial coordinate system shown in Figure 1. Select the external survey reference frame as the datum frame. In one embodiment, the measurement coordinate system of the laser tracking measurement device is selected as the measurement reference coordinate system. For example, the measurement coordinate system of the laser tracker is selected as the measurement reference coordinate system.

参考图2，为本发明实施例一种机械臂坐标系的转换标定方法的流程图，包括：Referring to FIG. 2 , it is a flowchart of a method for converting and calibrating a mechanical arm coordinate system according to an embodiment of the present invention, including:

S1，基于目标机械臂工作范围内布置的跟踪测量装置，利用末端坐标系平移运动法，获取末端工具坐标系相对测量参考坐标系的坐标旋转变换关系；S1, based on the tracking and measuring device arranged within the working range of the target manipulator, using the translational motion method of the end coordinate system to obtain the coordinate rotation transformation relationship of the end tool coordinate system relative to the measurement reference coordinate system;

S2，利用基于所述末端工具坐标系的单轴旋转法和相对机械臂基坐标系的运动学变换，获取所述末端工具坐标系相对所述机械臂基坐标系的坐标齐次变换关系；S2, using the single-axis rotation method based on the end tool coordinate system and the kinematic transformation relative to the base coordinate system of the manipulator to obtain a coordinate homogeneous transformation relationship of the end tool coordinate system relative to the base coordinate system of the manipulator;

S3，基于选定标定采样点的坐标，分别利用多点重心求解法、重心化处理法和罗德里格矩阵变换求解法，获取所述机械臂基坐标系与所述测量参考坐标系的坐标齐次变换关系。S3, based on the coordinates of the selected calibration sampling points, respectively use the multi-point center of gravity solution method, the center of gravity processing method and the Rodrigue matrix transformation solution method to obtain the coordinate alignment between the base coordinate system of the manipulator and the measurement reference coordinate system transformation relationship.

步骤S1可以理解为，为了进行目标机械臂各相关坐标系之间的相互转换标定，事先在目标机械臂工作范围内布置对目标机械臂末端工具的跟踪测量装置，便于对所述末端工具进行坐标值的测量。选定末端工具坐标系和测量参考坐标系，通过驱动末端工具在末端工具坐标系各方向轴上作平移运动，分别对末端工具坐标系和测量参考坐标系进行标定，并根据标定结果获取末端工具坐标系相对测量参考坐标系的坐标旋转变换关系。Step S1 can be understood as, in order to carry out the mutual conversion and calibration between the relevant coordinate systems of the target manipulator, a tracking and measuring device for the end tool of the target manipulator is arranged in advance within the working range of the target manipulator, so as to facilitate the coordinate measurement of the end tool value measurement. Select the end tool coordinate system and the measurement reference coordinate system, and calibrate the end tool coordinate system and the measurement reference coordinate system respectively by driving the end tool to perform translational movement on each direction axis of the end tool coordinate system, and obtain the end tool according to the calibration results The coordinate rotation transformation relationship of the coordinate system relative to the measurement reference coordinate system.

其中可选的，步骤S1中所述利用末端坐标系平移运动法，获取末端工具坐标系相对测量参考坐标系的坐标旋转变换关系的步骤进一步包括：Optionally, the step of obtaining the coordinate rotation transformation relationship of the end tool coordinate system relative to the measurement reference coordinate system by using the translational motion method of the end coordinate system described in step S1 further includes:

通过测量所述目标机械臂的末端工具沿所述末端工具坐标系各方向轴平移运动时，所述末端工具坐标系的原点坐标和平移位移矢量，计算所述末端工具坐标系在所述测量参考坐标系下的单位分量。By measuring the origin coordinates and translational displacement vectors of the end tool coordinate system when the end tool of the target mechanical arm is moving in translation along each direction axis of the end tool coordinate system, the calculation of the end tool coordinate system in the measurement Unit components in the reference coordinate system.

可以理解为，在上述实施例的基础上，选取末端工具坐标系方位与末端法兰坐标系一致，激光反射靶球中心作为末端工具坐标系的原点。将机械臂调整到初始位型，进行末端工具坐标系初始标定。It can be understood that, on the basis of the above embodiments, the orientation of the end tool coordinate system is selected to be consistent with the end flange coordinate system, and the center of the laser reflection target sphere is used as the origin of the end tool coordinate system. Adjust the manipulator to the initial configuration, and perform the initial calibration of the end tool coordinate system.

采用末端坐标系平移运动法，以末端法兰坐标系为参考进行xE轴、yE轴和zE轴方向上的平移运动，测量激光反射靶球中心坐标和平移位移矢量，并据此分别计算末端工具坐标系在测量参考坐标系下的各单位分量和由该单位分量表示末端工具坐标系相对测量参考坐标系的坐标旋转变换关系。Using the translational movement method of the end coordinate system, the translational movement in the directions of x E axis, y E axis and z E axis is carried out with the end flange coordinate system as a reference, and the center coordinate and translation displacement vector of the laser reflection target are measured, and based on this Calculate the unit components of the end tool coordinate system in the measurement reference coordinate system separately with The unit component represents the coordinate rotation transformation relation of the end tool coordinate system relative to the measurement reference coordinate system.

步骤S2可以理解为，通过驱动目标机械臂做相对于末端工具坐标系的单轴旋转运动，并利用末端工具坐标系相对机械臂基坐标系的运动学变换，分别对末端工具坐标系和机械臂基坐标系进行坐标标定。根据该坐标标定结果，齐次化计算激光反射靶球中心坐标在机械臂基坐标系下的坐标变换关系如下：Step S2 can be understood as, by driving the target manipulator to perform a single-axis rotational movement relative to the end tool coordinate system, and using the kinematic transformation of the end tool coordinate system relative to the base coordinate system of the manipulator, respectively transforming the end tool coordinate system and the manipulator Base coordinate system for coordinate calibration. According to the coordinate calibration results, the homogeneous calculation of the coordinate transformation relationship of the center coordinates of the laser reflection target ball in the base coordinate system of the manipulator is as follows:

式中，表示激光反射靶球中心相对机械臂基坐标系的坐标，xBto、yBto和zBto分别表示激光反射靶球中心相对机械臂基坐标系的xB轴、yB轴和zB轴的坐标分量，表示末端工具坐标系相对机械臂基坐标系的齐次变换矩阵，表示激光反射靶球中心相对末端工具坐标系的坐标，xEto、yEto和zEto分别表示激光反射靶球中心相对末端工具坐标系的xE轴、yE轴和zE轴的坐标分量。In the formula, Indicates the coordinates of the center of the laser reflection target sphere relative to the base coordinate system of the manipulator, x Bto , y Bto and z Bto respectively denote the coordinates of the center of the laser reflection target sphere relative to the x B axis, y B axis and z B axis of the base coordinate system of the manipulator weight, Indicates the homogeneous transformation matrix of the end tool coordinate system relative to the base coordinate system of the manipulator, Indicates the coordinates of the center of the laser reflection target sphere relative to the end tool coordinate system, and x Eto , y Eto and z Eto represent the coordinate components of the x E axis, y E axis and z E axis of the center of the laser reflection target sphere relative to the end tool coordinate system, respectively.

其中可选的，所述S2的步骤进一步包括：拟合获取所述目标机械臂1轴和6轴的轴旋转圆周半径，计算两旋转圆周交点相对于所述测量参考坐标系坐标在各所述单位分量上的投影，并利用空间矢量几何关系，获取末端工具坐标系相对所述机械臂基坐标系的坐标齐次变换关系。Optionally, the step of S2 further includes: fitting and obtaining the radii of the rotation circles of the 1st and 6th axes of the target manipulator, and calculating the intersection point of the two rotation circles relative to the coordinates of the measurement reference coordinate system at each The projection on the unit component, and using the space vector geometric relationship, obtains the coordinate homogeneous transformation relationship of the end tool coordinate system relative to the base coordinate system of the manipulator.

可以理解为，采用单轴旋转法，分别单独旋转如图1所示的目标机械臂的1轴和6轴。拟合获取两轴旋转圆周半径，获取两轴旋转圆周的交点，测量该交点相对测量参考坐标系的坐标向量，并分别计算该坐标向量在上述步骤中单位分量和上的投影。然后根据末端工具和激光跟踪仪的空间位置关系及各坐标几何矢量关系，列写末端工具坐标系与测量参考坐标系下的几何关系方程，获取末端工具坐标系与测量参考坐标系的坐标变换关系。It can be understood that the 1-axis and 6-axis of the target robot arm as shown in FIG. 1 are separately rotated by using the single-axis rotation method. Fit to obtain the radius of the two-axis rotation circle, obtain the intersection point of the two-axis rotation circle, measure the coordinate vector of the intersection point relative to the measurement reference coordinate system, and calculate the unit component of the coordinate vector in the above steps with projection on . Then, according to the spatial position relationship between the end tool and the laser tracker and the geometric vector relationship of each coordinate, write the geometric relationship equation between the end tool coordinate system and the measurement reference coordinate system, and obtain the coordinate transformation relationship between the end tool coordinate system and the measurement reference coordinate system .

其中可选的，所述两旋转圆周交点为初始位型所述激光反射靶球的中心；通过计算所述激光反射靶球的中心坐标在各所述单位分量上的投影，并利用空间矢量几何关系，获取所述激光反射靶球的中心相对所述末端工具坐标系的坐标如下：Optionally, the intersection point of the two rotating circles is the center of the laser reflection target sphere in the initial configuration; by calculating the projection of the center coordinates of the laser reflection target sphere on each of the unit components, and using space vector geometry relationship, the coordinates of the center of the laser reflection target sphere relative to the end tool coordinate system are obtained as follows:

式中，表示激光反射靶球中心相对末端工具坐标系的坐标，xEto、yEto和zEto分别表示激光反射靶球中心相对末端工具坐标系的xE轴、yE轴和zE轴的坐标分量，表示6轴旋转中心相对激光反射靶球中心的位置矢量，其模长等于所述6轴的拟合半径值，和分别表示末端工具坐标系在测量参考坐标系下xE轴和yE轴的单位分量，R1表示所述1轴的拟合半径值，xBeo表示末端工具坐标系原点在初始位型时相对机械臂基坐标系xB轴的分量。In the formula, Represent the coordinates of the center of the laser reflection target sphere relative to the end tool coordinate system, x Eto , y Eto and z Eto represent the coordinate components of the x E axis, y E axis and z E axis of the center of the laser reflection target sphere relative to the end tool coordinate system, Indicates the position vector of the 6-axis rotation center relative to the laser reflection target ball center, and its modulus length is equal to the fitting radius value of the 6-axis, with represent the unit components of the x E axis and y E axis of the end tool coordinate system in the measurement reference coordinate system, R 1 represents the fitting radius value of the 1 axis, and x Beo represents that the origin of the end tool coordinate system is relative to The component of the x- B axis of the base coordinate system of the manipulator.

可以理解为，采用单轴旋转法，分别单独旋转图1中的1轴和6轴，拟合获取轴旋转圆周半径R1和R6，交点即为初始位型激光反射靶球中心Pto。设Pto在测量参考坐标系下的坐标为Pto R＝(xRto,yRto,zRto)T，则分别计算Pto R在和上的投影，同时利用空间几何关系，获取激光反射靶球中心在当前位型下相对末端工具坐标系的坐标如下：It can be understood that, using the single-axis rotation method, the 1st axis and 6th axis in Figure 1 are rotated separately, and the radii R 1 and R 6 of the axis rotation circle are obtained by fitting, and the intersection point is the center P to of the initial laser reflection target sphere. Let the coordinates of P to in the measurement reference coordinate system be P to R ＝(x Rto ,y Rto ,z Rto ) T , then calculate P to R in with At the same time, using the spatial geometric relationship, the coordinates of the center of the laser reflection target ball in the current configuration relative to the end tool coordinate system are obtained as follows:

式中，表示激光反射靶球中心相对末端工具坐标系的坐标，xEto、yEto和zEto分别表示激光反射靶球中心相对末端工具坐标系的xE轴、yE轴和zE轴的坐标分量，表示6轴旋转中心相对激光反射靶球中心的位置矢量，其模长等于机械臂6轴的拟合半径R6，和分别表示末端工具坐标系在测量参考坐标系下xE轴和yE轴的单位分量，R1表示机械臂1轴的拟合半径，xBeo表示末端工具坐标系原点在初始位型时相对机械臂基坐标系xB轴的坐标分量。In the formula, Represent the coordinates of the center of the laser reflection target sphere relative to the end tool coordinate system, x Eto , y Eto and z Eto represent the coordinate components of the x E axis, y E axis and z E axis of the center of the laser reflection target sphere relative to the end tool coordinate system, Indicates the position vector of the 6-axis rotation center relative to the center of the laser reflection target ball, and its modulus length is equal to the fitting radius R 6 of the 6-axis of the manipulator, with Respectively represent the unit components of the end tool coordinate system in the measurement reference coordinate system x E axis and y E axis, R 1 represents the fitting radius of the first axis of the manipulator, x Beo represents the relative mechanical position of the end tool coordinate system origin in the initial configuration The coordinate component of the x- B axis of the arm base coordinate system.

本实施例以激光跟踪测量装置坐标系作为外部测量参考坐标系，在目标机械臂末端上安装激光反射靶球，采用机械臂末端直线运动和旋转运动结合确定坐标系方位，精确测定激光反射靶球中心点，即机械臂末端工具坐标系相对于机械臂基坐标系的坐标位置，标定精度高。In this embodiment, the coordinate system of the laser tracking and measuring device is used as the external measurement reference coordinate system, and a laser reflective target ball is installed on the end of the target mechanical arm, and a combination of linear motion and rotational motion at the end of the mechanical arm is used to determine the orientation of the coordinate system to accurately measure the laser reflective target ball The center point, that is, the coordinate position of the tool coordinate system at the end of the manipulator relative to the base coordinate system of the manipulator, has high calibration accuracy.

步骤S3可以理解为，为了获取机械臂基坐标系和测量参考坐标系的坐标变换关系，事先选定指定数量的标定采样点，并分别测量各标定采样点相对机械臂基坐标系和测量参考坐标系的坐标。根据这些坐标值，利用多点重心法，分别计算机械臂基坐标系和测量参考坐标系下各标定采样点的重心，并对各标定采样点进行相对机械臂基坐标系和测量参考坐标系的重心化处理，获取重心化坐标下机械臂基坐标系和测量参考坐标系的坐标变换关系。Step S3 can be understood as, in order to obtain the coordinate transformation relationship between the base coordinate system of the manipulator and the measurement reference coordinate system, select a specified number of calibration sampling points in advance, and measure the relative coordinates of each calibration sampling point to the base coordinate system of the manipulator and the measurement reference coordinate system. system coordinates. According to these coordinate values, use the multi-point center of gravity method to calculate the center of gravity of each calibration sampling point in the base coordinate system of the manipulator and the measurement reference coordinate system, and carry out the calculation of each calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system. Center of gravity processing, to obtain the coordinate transformation relationship between the base coordinate system of the manipulator and the measurement reference coordinate system under the center of gravity coordinates.

然后按照罗德里格矩阵形式，将重心化坐标下机械臂基坐标系相对测量参考坐标系的变换矩阵表示为罗德里格形式，并通过求解罗德里格形式的机械臂基坐标系和测量参考坐标系的坐标变换方程式，获取机械臂基坐标系相对测量参考坐标系的变换矩阵。最后基于该变换矩阵，获取机械臂基坐标系相对测量参考坐标系的坐标变换关系。Then, according to the form of the Rodrigue matrix, the transformation matrix of the manipulator base coordinate system relative to the measurement reference coordinate system in the barycentric coordinates is expressed as the Rodrigue form, and by solving the Rodrigue form of the manipulator base coordinate system and the measurement reference coordinate The coordinate transformation equation of the system can obtain the transformation matrix of the base coordinate system of the manipulator relative to the measurement reference coordinate system. Finally, based on the transformation matrix, the coordinate transformation relationship between the base coordinate system of the manipulator and the measurement reference coordinate system is obtained.

本发明实施例提供的一种机械臂坐标系的转换标定方法，采用激光跟踪测量装置，进行机械臂基坐标系、末端工具坐标系与外部测量参考坐标系的转换标定。通过采用机械臂末端直线运动和旋转运动，实现末端工具坐标系与测量参考坐标系的转换标定；通过采用重心法和罗德里格变换矩阵，实现机械臂基坐标系与测量参考坐标系的转换标定，标定流程简单，标定算法无迭代过程，能够有效减少坐标系标定耗时，提高坐标系标定精度。The embodiment of the present invention provides a conversion and calibration method of a manipulator coordinate system, which uses a laser tracking measurement device to perform conversion and calibration of the manipulator base coordinate system, end tool coordinate system and external measurement reference coordinate system. By adopting the linear motion and rotational motion of the end of the manipulator, the conversion calibration of the end tool coordinate system and the measurement reference coordinate system is realized; by using the center of gravity method and the Rodrigue transformation matrix, the conversion calibration of the base coordinate system of the manipulator and the measurement reference coordinate system is realized. , the calibration process is simple, and the calibration algorithm has no iterative process, which can effectively reduce the time-consuming of coordinate system calibration and improve the accuracy of coordinate system calibration.

在另一个实施例中，所述S3的进一步处理步骤参考图3，为本发明实施例一种获取机械臂基坐标系与测量参考坐标系的坐标变换关系的处理过程流程图，包括：In another embodiment, the further processing steps of S3 refer to FIG. 3 , which is a flowchart of a processing process for obtaining the coordinate transformation relationship between the base coordinate system of the manipulator and the measurement reference coordinate system according to an embodiment of the present invention, including:

S31，利用多点重心求解法，分别计算所述标定采样点相对所述机械臂基坐标系和所述测量参考坐标系的重心坐标；S31. Using a multi-point center-of-gravity solution method, respectively calculate the center-of-gravity coordinates of the calibration sampling points relative to the base coordinate system of the manipulator and the measurement reference coordinate system;

S32，分别基于所述标定采样点相对所述机械臂基坐标系以及所述测量参考坐标系的重心坐标和标定采样点坐标，对所述标定采样点进行重心化处理，分别获取所述标定采样点相对所述机械臂基坐标系和所述测量参考坐标系的重心化坐标；S32. Based on the coordinates of the center of gravity of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system and the coordinates of the calibration sampling point, respectively, perform barycentric processing on the calibration sampling points, and obtain the calibration samples respectively. The barycentric coordinates of the point relative to the base coordinate system of the manipulator and the measurement reference coordinate system;

S33，利用罗德里格矩阵形式，表示所述标定采样点相对所述机械臂基坐标系与所述测量参考坐标系的重心化坐标变换方程；S33, expressing a barycentric coordinate transformation equation of the calibration sampling point with respect to the base coordinate system of the manipulator and the measurement reference coordinate system in the form of a Rodrigue matrix;

S34，利用特征值带入法求解所述重心化坐标变换方程，获取所述机械臂基坐标系相对所述测量参考坐标系的变换矩阵。S34. Using the eigenvalue bringing-in method to solve the barycentric coordinate transformation equation, and obtain a transformation matrix of the base coordinate system of the manipulator relative to the measurement reference coordinate system.

步骤S31可以理解为，本实施例进行标定点的采样与空间变换。首先建立机械臂基坐标系与测量参考坐标系的变换关系，可表示如下：Step S31 can be understood as, this embodiment performs sampling and space transformation of the calibration points. First, establish the transformation relationship between the base coordinate system of the manipulator and the measurement reference coordinate system, which can be expressed as follows:

式中，和分别表示激光反射靶球中心在标定点位相对机械臂基坐标系和测量参考坐标系的齐次坐标，xBto、yBto和zBto分别表示激光反射靶球中心相对机械臂基坐标系的xB轴、yB轴和zB轴的坐标分量，xRto、yRto和zRto分别表示激光反射靶球中心相对测量参考坐标系的xR轴、yR轴和zR轴的坐标分量，表示测量参考坐标系相对机械臂基坐标系的齐次变换矩阵，表示的旋转分量，ΔPR表示相对的坐标偏置分量，ΔxR、ΔyR和ΔzR分别表示相对在xR轴、yR轴和zR轴的坐标偏置分量。In the formula, with Respectively represent the homogeneous coordinates of the center of the laser reflection target ball relative to the base coordinate system of the manipulator and the measurement reference coordinate system at the calibration point, x Bto , y Bto and z Bto respectively represent the x of the center of the laser reflection target ball relative to the base coordinate system of the manipulator The coordinate components of B axis, y B axis and z B axis, x Rto , y Rto and z Rto respectively represent the coordinate components of the x R axis, y R axis and z R axis of the laser reflection target ball center relative to the measurement reference coordinate system, Indicates the homogeneous transformation matrix of the measurement reference coordinate system relative to the base coordinate system of the manipulator, express The rotational component of , ΔP R represents relatively The coordinate offset components of , Δx R , Δy R and Δz R represent respectively relatively Coordinate offset components on the x R axis, y R axis, and z R axis.

在一个实施例中，所述方法在所述S31的步骤之前还包括：在所述目标机械臂的工作范围内选定指定数量的标定采样点。In one embodiment, before the step of S31, the method further includes: selecting a specified number of calibration sampling points within the working range of the target robotic arm.

可以理解为，采用z-y-x欧拉角表示坐标旋转矩阵依次选取n个激光反射靶球定标采样点作为标定采样点，获取各标定采样点对应的机械臂基坐标系坐标和测量参考坐标系坐标。采用多点重心法，分别计算标定采样点相对机械臂基坐标系和测量参考坐标系的重心坐标如下：It can be understood that the coordinate rotation matrix is represented by the zyx Euler angle Select n laser reflection target ball calibration sampling points in turn as the calibration sampling points, and obtain the coordinates of the base coordinate system of the manipulator and the coordinates of the measurement reference coordinate system corresponding to each calibration sampling point. Using the multi-point center of gravity method, calculate the coordinates of the center of gravity of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system as follows:

式中，和分别表示标定采样点相对机械臂基坐标系和测量参考坐标系的重心坐标，xBg、yBg和zBg分别表示标定采样点相对机械臂基坐标系的xB轴、yB轴和zB轴的重心坐标分量，xRg、yRg和zRg分别表示标定采样点相对测量参考坐标系的xR轴、yR轴和zR轴的重心坐标分量，xBtoi、yBtoi和zBtoi分别表示第i个标定采样点相对机械臂基坐标系的xB轴、yB轴和zB轴的坐标分量，xRtoi、yRtoi和zRtoi分别表示第i个标定采样点相对测量参考坐标系的xR轴、yR轴和zR轴的坐标分量，n表示标定采样点的总个数。In the formula, with Respectively represent the coordinates of the center of gravity of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system, x Bg , y Bg and z Bg respectively represent the x B axis, yB axis and z B axis of the calibration sampling point relative to the base coordinate system of the manipulator x Rg , y Rg and z Rg represent the barycentric coordinate components of the calibration sampling point relative to the x R axis, y R axis and z R axis of the measurement reference coordinate system, and x Btoi , y Btoi and z Btoi respectively represent x Rtoi , y Rtoi and z Rtoi respectively represent the x of the i-th calibration sampling point relative to the measurement reference coordinate system Coordinate components of the R axis, y R axis, and z R axis, and n represents the total number of calibration sampling points.

步骤S32可以理解为，对于上述步骤获取的各标定采样点对应的机械臂基坐标系坐标和测量参考坐标系坐标，以及标定采样点相对机械臂基坐标系和测量参考坐标系的重心坐标，利于其分别对于机械臂基坐标系坐标和测量参考坐标系下的标定采样点进行重心化处理。所述的重心化处理指计算标定采样点坐标相对重心坐标的变化关系。Step S32 can be understood as, for the coordinates of the base coordinate system of the manipulator and the coordinates of the measurement reference coordinate system corresponding to each calibration sampling point obtained in the above steps, and the coordinates of the center of gravity of the calibration sampling points relative to the base coordinate system of the manipulator and the measurement reference coordinate system, it is beneficial to It respectively performs barycentric processing on the coordinates of the base coordinate system of the manipulator and the calibration sampling points in the measurement reference coordinate system. The barycentric processing refers to calculating the change relationship of the calibration sampling point coordinates relative to the barycentric coordinates.

即利用标定采样点相对机械臂基坐标系的坐标和重心坐标，进行重心化处理，获取标定采样点相对机械臂基坐标系的重心化坐标；利用标定采样点相对测量参考坐标系的坐标和重心坐标，进行重心化处理，获取标定采样点相对测量参考坐标系的重心化坐标。That is, use the coordinates and center of gravity coordinates of the calibrated sampling points relative to the base coordinate system of the manipulator to perform barycentric processing to obtain the barycentric coordinates of the calibrated sampling points relative to the base coordinate system of the manipulator; use the coordinates and center of gravity of the calibrated sampling points relative to the measurement reference coordinate system Coordinates, perform barycentric processing, and obtain the barycentric coordinates of the calibration sampling point relative to the measurement reference coordinate system.

其中可选的，所述S32的进一步处理步骤参考图4，为本发明实施例一种对标定采样点进行重心化处理的处理过程流程图，包括：S321，将所述机械臂基坐标系中的标定采样点坐标矩阵与标定采样点的重心坐标矩阵相减，获取所述标定采样点相对所述机械臂基坐标系的重心化坐标；S322，将所述测量参考坐标系中的标定采样点坐标矩阵与标定采样点的重心坐标矩阵相减，获取所述标定采样点相对所述测量参考坐标系的重心化坐标。Optionally, the further processing steps of S32 refer to FIG. 4 , which is a flowchart of a processing process for centering processing of calibration sampling points in an embodiment of the present invention, including: Subtract the calibration sampling point coordinate matrix of the calibration sampling point from the barycentric coordinate matrix of the calibration sampling point to obtain the barycentric coordinates of the calibration sampling point relative to the base coordinate system of the manipulator; S322, the calibration sampling point in the measurement reference coordinate system The coordinate matrix is subtracted from the barycentric coordinate matrix of the calibration sampling point to obtain the barycentric coordinates of the calibration sampling point relative to the measurement reference coordinate system.

可以理解为，针对标定采样点在机械臂基坐标系坐标和测量参考坐标系下的坐标，对上述步骤中每一个标定采样点，分别在机械臂基坐标系坐标和测量参考坐标系下按下式进行重心化处理：It can be understood that, for the coordinates of the calibration sampling point in the coordinate system of the base coordinate system of the manipulator and the coordinate system of the measurement reference coordinate system, for each calibration sampling point in the above steps, press the The center of gravity is processed as follows:

式中，和分别表示第i个标定采样点相对机械臂基坐标系和测量参考坐标系的重心化坐标，和分别表示第i个标定采样点相对机械臂基坐标系和测量参考坐标系的坐标，和分别表示标定采样点相对机械臂基坐标系和测量参考坐标系的重心坐标，xgBtoi、ygBtoi和zgBtoi分别表示第i个标定采样点相对机械臂基坐标系的xB轴、yB轴和zB轴的重心化坐标分量，xgRtoi、ygRtoi和zgRtoi分别表示第i个标定采样点相对测量参考坐标系的xR轴、yR轴和zR轴的重心化坐标分量，xBg、yBg和zBg分别表示标定采样点相对机械臂基坐标系的xB轴、yB轴和zB轴的重心坐标分量，xRg、yRg和zRg分别表示标定采样点相对测量参考坐标系的xR轴、yR轴和zR轴的重心坐标分量，xBtoi、yBtoi和zBtoi分别表示第i个标定采样点相对机械臂基坐标系的xB轴、yB轴和zB轴的坐标分量，xRtoi、yRtoi和zRtoi分别表示第i个标定采样点相对测量参考坐标系的xR轴、yR轴和zR轴的坐标分量。In the formula, with Represent the barycentric coordinates of the i-th calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system, respectively, with respectively represent the coordinates of the i-th calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system, with Respectively represent the coordinates of the center of gravity of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system, x gBtoi , y gBtoi and z gBtoi respectively represent the x B axis, yB axis and The barycentric coordinate components of the z B axis, x gRtoi , y gRtoi and z gRtoi respectively represent the barycentric coordinate components of the i-th calibration sampling point relative to the x R axis, y R axis and z R axis of the measurement reference coordinate system, x Bg , y Bg and z Bg respectively represent the barycentric coordinate components of the calibration sampling point relative to the x B axis, yB axis and z B axis of the base coordinate system of the manipulator, and x Rg , y Rg and z Rg represent the calibration sampling point relative to the measurement reference coordinates x Btoi , y Btoi and z Btoi represent the x B axis, yB axis and z Btoi of the i - th calibration sampling point relative to the base coordinate system of the manipulator x Rtoi , y Rtoi and z Rtoi represent the coordinate components of the i-th calibration sampling point relative to the x R axis, y R axis and z R axis of the measurement reference coordinate system, respectively.

各标定采样点坐标重心化处理后，机械臂基坐标系和测量参考坐标系中的标定采样点坐标值消去了偏移量关系，对应的旋转变换关系转化为：After the center of gravity processing of the coordinates of each calibration sampling point, the coordinate values of the calibration sampling points in the base coordinate system of the manipulator and the measurement reference coordinate system have eliminated the offset relationship, and the corresponding rotation transformation relationship is transformed into:

式中，xgBtoi、ygBtoi和zgBtoi分别表示第i个标定采样点相对机械臂基坐标系的xB轴、yB轴和zB轴的重心化坐标分量，xgRtoi、ygRtoi和zgRtoi分别表示第i个标定采样点相对测量参考坐标系的xR轴、yR轴和zR轴的重心化坐标分量，表示测量参考坐标系相对机械臂基坐标系的齐次变换矩阵的旋转分量。In the formula, x gBtoi , y gBtoi and z gBtoi represent the barycentric coordinate components of the i-th calibration sampling point relative to the x B axis, yB axis and z B axis of the base coordinate system of the manipulator, and x gRtoi , y gRtoi and z gRtoi Represent the barycentric coordinate components of the i-th calibration sampling point relative to the x R axis, y R axis and z R axis of the measurement reference coordinate system, Represents the rotation component of the homogeneous transformation matrix of the measurement reference frame relative to the base coordinate system of the manipulator.

于是可得激光反射靶球中心在标定点位的机械臂基坐标系坐标相对测量参考坐标系坐标的偏置分量如下：Therefore, the offset component of the coordinates of the base coordinate system of the manipulator relative to the coordinates of the measurement reference coordinate system with the center of the laser reflection target at the calibration point is as follows:

式中，ΔPR表示激光反射靶球中心在标定点位的机械臂基坐标系坐标相对测量参考坐标系坐标的偏置分量，ΔxR、ΔyR和ΔzR分别表示相对在xR轴、yR轴和zR轴的坐标偏置分量，xBto、yBto和zBto分别表示激光反射靶球中心相对机械臂基坐标系的xB轴、yB轴和zB轴的坐标分量，xRto、yRto和zRto分别表示激光反射靶球中心相对测量参考坐标系的xR轴、yR轴和zR轴的坐标分量，表示测量参考坐标系相对机械臂基坐标系的齐次变换矩阵的旋转分量。In the formula, ΔP R represents the offset component of the coordinates of the base coordinate system of the manipulator at the calibration point relative to the coordinates of the measurement reference coordinate system at the center of the laser reflection target ball, and Δx R , Δy R and Δz R represent relatively The coordinate offset components of the x R axis, y R axis and z R axis, x Bto , y Bto and z Bto respectively represent the x B axis, y B axis and z B axis of the center of the laser reflection target ball relative to the base coordinate system of the manipulator The coordinate components of axis, x Rto , y Rto and z Rto respectively represent the coordinate components of the x R axis, y R axis and z R axis of the center of the laser reflection target sphere relative to the measurement reference coordinate system, Represents the rotation component of the homogeneous transformation matrix of the measurement reference frame relative to the base coordinate system of the manipulator.

步骤S33可以理解为，对于上述步骤获取的各标定采样点坐标重心化处理后，机械臂基坐标系和测量参考坐标系对应的旋转变换关系式，将其中的旋转变换矩阵表示成罗德里格矩阵形式，相应的，该旋转变换关系式转换为罗德里格形式的旋转变换关系式。Step S33 can be understood as, after the barycentric processing of the coordinates of each calibration sampling point obtained in the above steps, the rotation transformation relationship corresponding to the base coordinate system of the manipulator and the measurement reference coordinate system, the rotation transformation matrix is expressed as a Rodrigue matrix Correspondingly, the rotation transformation relation is transformed into a rotation transformation relation of Rodrigue's form.

其中可选的，所述S33的进一步处理步骤参考图5，为本发明实施例一种获取标定采样点相对机械臂基坐标系和测量参考坐标系的重心化坐标变换方程的处理过程流程图，包括：Optionally, refer to FIG. 5 for the further processing steps of S33, which is a flowchart of a processing process for obtaining the barycentric coordinate transformation equation of the calibrated sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system according to an embodiment of the present invention. include:

S331，基于标定采样点相对机械臂基坐标系和测量参考坐标系的重心化坐标维数要求，设定相应维数的罗德里格反对称矩阵。S331. Based on the barycentric coordinate dimension requirement of the calibration sampling point relative to the base coordinate system of the manipulator and the measurement reference coordinate system, set a Rodrigue anti-symmetric matrix of corresponding dimension.

可以理解为，基于上述实施例，标定采样点相对机械臂基坐标系和测量参考坐标系的重心化坐标均为三维坐标形式，因此设定罗德里格反对称矩阵L如下：It can be understood that, based on the above-mentioned embodiment, the barycentric coordinates of the calibration sampling points relative to the base coordinate system of the manipulator and the measurement reference coordinate system are all in the form of three-dimensional coordinates, so the Rodrigue antisymmetric matrix L is set as follows:

式中，a、b和c均表示罗德里格参数。In the formula, a, b and c all represent Rodrigue parameters.

S332，基于所述罗德里格反对称矩阵，将机械臂基坐标系相对测量参考坐标系的旋转分量变换矩阵等效变换为罗德里格矩阵形式。S332. Based on the Rodriguez antisymmetric matrix, equivalently transform the rotation component transformation matrix of the manipulator base coordinate system relative to the measurement reference coordinate system into a Rodrigue matrix form.

可以理解为，对于上述步骤设定的罗德里格反对称矩阵L，根据矩阵初等变换规则，将机械臂基坐标系相对测量参考坐标系的旋转分量变换矩阵表示为罗德里格矩阵形式如下：It can be understood that, for the Rodrigue anti-symmetric matrix L set in the above steps, according to the matrix elementary transformation rules, the transformation matrix of the rotation component of the manipulator base coordinate system relative to the measurement reference coordinate system is expressed as a Rodrigue matrix in the following form:

式中，表示机械臂基坐标系相对测量参考坐标系的旋转分量变换矩阵，E表示单位矩阵，L表示罗德里格反对称矩阵。In the formula, Indicates the rotation component transformation matrix of the base coordinate system of the manipulator relative to the measurement reference coordinate system, E indicates the identity matrix, and L indicates the Rodrigue anti-symmetric matrix.

S333，基于罗德里格矩阵形式的所述旋转分量变换矩阵，将所述标定采样点相对所述机械臂基坐标系与所述测量参考坐标系的重心化坐标变换方程等效变换为包含所述罗德里格反对称矩阵的方程形式。S333. Based on the rotation component transformation matrix in the form of a Rodrigue matrix, equivalently transform the barycentric coordinate transformation equation of the calibration sampling point relative to the manipulator base coordinate system and the measurement reference coordinate system to include the Equational form of Rodriguez antisymmetric matrices.

可以理解为，根据上述实施例可知，各标定采样点坐标重心化处理后，机械臂基坐标系和测量参考坐标系中的标定采样点坐标值消去了偏移量关系，因此可将上述对应的旋转变换关系式等效变换为如下形式：It can be understood that, according to the above-mentioned embodiment, after the center of gravity processing of the coordinates of each calibration sampling point, the coordinate values of the calibration sampling points in the base coordinate system of the manipulator and the measurement reference coordinate system have eliminated the offset relationship, so the above-mentioned corresponding The equivalent transformation of the rotation transformation relation is as follows:

式中，E表示单位矩阵，L表示罗德里格反对称矩阵，(xgBtoi，ygBtoi,zgBtoi)T表示标定采样点相对机械臂基坐标系的重心化坐标，(xgRtoi，ygRtoi,zgRtoi)T表示标定采样点相对测量参考坐标系的重心化坐标。In the formula, E represents the identity matrix, L represents the Rodrigue anti-symmetric matrix, (x gBtoi , y gBtoi , z gBtoi ) T represents the barycentric coordinates of the calibration sampling point relative to the base coordinate system of the manipulator, (x gRtoi , y gRtoi , z gRtoi ) T represents the barycentric coordinates of the calibration sampling point relative to the measurement reference coordinate system.

步骤S34可以理解为，对于上述步骤获取的包含罗德里格反对称矩阵的重心化坐标变换方程组，根据方程组维数，选取相应个数的标定采样点，将这些采样点的坐标值带入该方程组，例如根据上述实施例，选取三个标定采样特值点。然后采用最小二乘法等求解方法，求解方程组，获取测量参考坐标系相对机械臂基坐标系的旋转分量变换矩阵并据此获取测量参考坐标系相对机械臂基坐标系的变换矩阵 Step S34 can be understood as, for the barycentric coordinate transformation equations including the Rodrigue antisymmetric matrix obtained in the above steps, according to the dimension of the equations, select the corresponding number of calibration sampling points, and bring the coordinate values of these sampling points into For the equation set, for example, according to the above-mentioned embodiment, three calibration sampling characteristic value points are selected. Then use the least square method and other solving methods to solve the equations to obtain the transformation matrix of the rotation component of the measurement reference coordinate system relative to the base coordinate system of the manipulator And based on this, obtain the transformation matrix of the measurement reference coordinate system relative to the base coordinate system of the manipulator

本发明实施例提供的一种机械臂坐标系的转换标定方法，通过选择多个标定采样点，应用重心法进行末端工具测量点标定，有效减少机械臂末端位姿误差和测量误差的影响；同时基于罗德里格变换矩阵实现坐标系变换方程的快速精确求解，无需迭代运算即可得到机械臂基坐标系相对测量参考坐标系的变换矩阵，能够有效提高系统运行速度，减少变换标定耗时，提高标定精度。The embodiment of the present invention provides a method for converting and calibrating the coordinate system of the manipulator. By selecting a plurality of calibration sampling points and using the center of gravity method to calibrate the measurement point of the end tool, the influence of the pose error and measurement error at the end of the manipulator is effectively reduced; at the same time Based on the Rodrigue transformation matrix, the coordinate system transformation equation can be quickly and accurately solved, and the transformation matrix of the base coordinate system of the manipulator relative to the measurement reference coordinate system can be obtained without iterative operations, which can effectively improve the system operating speed, reduce the time-consuming transformation and calibration, and improve Calibration accuracy.

作为本发明实施例的另一个方面，本实施例提供一种机械臂坐标系的转换标定系统，参考图6，为本发明实施例一种机械臂坐标系的转换标定系统的结构框图，包括：至少一个存储器1、至少一个处理器2、通信接口3和总线4。As another aspect of the embodiment of the present invention, this embodiment provides a conversion and calibration system of a manipulator coordinate system. Referring to FIG. 6 , it is a structural block diagram of a conversion and calibration system of a manipulator coordinate system according to an embodiment of the present invention, including: At least one memory 1 , at least one processor 2 , communication interface 3 and bus 4 .

其中，存储器1、处理器2和通信接口3通过总线4完成相互间的通信，通信接口3用于所述转换标定系统与坐标测量设备之间的信息传输；存储器1中存储有可在处理器2上运行的计算机程序，处理器2执行所述程序时实现如上述实施例所述的机械臂坐标系的转换标定方法。Wherein, the memory 1, the processor 2 and the communication interface 3 complete mutual communication through the bus 4, and the communication interface 3 is used for information transmission between the conversion calibration system and the coordinate measuring equipment; 2, when the processor 2 executes the program, it realizes the method for transforming and calibrating the coordinate system of the manipulator as described in the above-mentioned embodiment.

可以理解为，所述的机械臂坐标系的转换标定系统中至少包含存储器1、处理器2、通信接口3和总线4，且存储器1、处理器2和通信接口3通过总线4形成相互之间的通信连接，并可完成相互间的通信。It can be understood that the conversion and calibration system of the manipulator coordinate system includes at least a memory 1, a processor 2, a communication interface 3 and a bus 4, and the memory 1, the processor 2 and the communication interface 3 form a mutual relationship through the bus 4. The communication connection, and can complete the communication between each other.

通信接口3实现机械臂坐标系的转换标定系统与标定点坐标测量设备之间的通信连接，并可完成相互间信息传输，如通过通信接口3获取标定点坐标测量设备测定的标定点相对测量参考坐标系的坐标值等。The communication interface 3 realizes the communication connection between the conversion calibration system of the manipulator coordinate system and the coordinate measuring equipment of the calibration point, and can complete the mutual information transmission, such as obtaining the relative measurement reference of the calibration point determined by the coordinate measuring equipment of the calibration point through the communication interface 3 Coordinate values of the coordinate system, etc.

系统运行时，处理器2调用存储器1中的程序指令，以执行上述各方法实施例所提供的方法的全部或部分步骤，例如包括：基于目标机械臂工作范围内布置的跟踪测量装置，利用末端坐标系平移运动法和单轴旋转法，获取末端工具坐标系与测量参考坐标系的坐标变换关系。以及通过测量所述目标机械臂的末端工具沿所述末端工具坐标系各方向轴平移运动时，所述末端工具坐标系的原点坐标和平移位移矢量，计算所述末端工具坐标系在所述测量参考坐标系下的单位分量；拟合获取所述目标机械臂1轴和6轴的轴旋转圆周半径，计算两旋转圆周交点的测量参考坐标系坐标在各所述单位分量上的投影，并利用空间几何关系，获取末端工具坐标系与测量参考坐标系的坐标变换关系等。When the system is running, the processor 2 calls the program instructions in the memory 1 to execute all or part of the steps of the methods provided by the above method embodiments, for example, including: based on the tracking and measuring device arranged within the working range of the target manipulator, using the terminal The coordinate system translation motion method and the single-axis rotation method obtain the coordinate transformation relationship between the end tool coordinate system and the measurement reference coordinate system. and by measuring the origin coordinates and translational displacement vectors of the end tool coordinate system when the end tool of the target mechanical arm is moving in translation along each direction axis of the end tool coordinate system, calculating the position of the end tool coordinate system in the Measuring the unit components in the reference coordinate system; fitting and obtaining the radii of the rotation circles of the 1st and 6th axes of the target manipulator, calculating the projection of the coordinates of the measurement reference coordinate system at the intersection of the two rotation circles on each of the unit components, and Using the spatial geometric relationship, the coordinate transformation relationship between the end tool coordinate system and the measurement reference coordinate system is obtained.

本发明又一个实施例中，提供一种非暂态计算机可读存储介质，所述非暂态计算机可读存储介质存储计算机指令，所述计算机指令使所述计算机执行如上述实施例所述的机械臂坐标系的转换标定方法。In yet another embodiment of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method described in the above-mentioned embodiments. The conversion and calibration method of the coordinate system of the manipulator.

可以理解为，实现上述方法实施例的全部或部分步骤可以通过程序指令相关的硬件来完成，前述的程序可以存储于一计算机可读取存储介质中，该程序在执行时，执行包括上述方法实施例的步骤；而前述的存储介质包括：ROM、RAM、磁碟或者光盘等各种可以存储程序代码的介质。It can be understood that all or part of the steps for realizing the above-mentioned method embodiments can be completed by program instructions related hardware, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, the execution includes the implementation of the above-mentioned method The steps of the example; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other various media that can store program codes.

以上所描述的机械臂坐标系的转换标定系统的实施例仅仅是示意性的，其中作为分离部件说明的单元可以是或者也可以不是物理上分开的，既可以位于一个地方，或者也可以分布到不同网络单元上。可以根据实际需要选择其中的部分或者全部模块来实现本实施例方案的目的。本领域普通技术人员在不付出创造性的劳动的情况下，即可以理解并实施。The embodiment of the conversion and calibration system of the manipulator coordinate system described above is only illustrative, and the units described as separate components may or may not be physically separated, and may be located in one place or distributed to on different network elements. Part or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. It can be understood and implemented by those skilled in the art without any creative effort.

通过以上实施方式的描述，本领域的技术人员可以清楚地了解，各实施方式可借助软件加必需的通用硬件平台的方式来实现，当然也可以通过硬件。基于这样的理解，上述技术方案本质上或者说对现有技术做出贡献的部分可以以软件产品的形式体现出来，该计算机软件产品可以存储在计算机可读存储介质中，如ROM/RAM、磁碟、光盘等，包括若干指令，用以使得一台计算机设备(如个人计算机，服务器，或者网络设备等)执行上述各方法实施例或者方法实施例的某些部分所述的方法。Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general-purpose hardware platform, and of course also by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the prior art can be embodied in the form of software products, and the computer software products can be stored in computer-readable storage media, such as ROM/RAM, magnetic Discs, optical discs, etc., include several instructions for making a computer device (such as a personal computer, server, or network device, etc.) execute the methods described in the above method embodiments or some parts of the method embodiments.

本发明实施例提供的一种机械臂坐标系的转换标定系统和一种非暂态计算机可读存储介质，通过采用直线运动与旋转运动相结合的方式改进单轴旋转运动法的坐标系矢量方向标定，同时采用多点重心采样和罗德里格算法进行坐标系转换方程求解，标定流程简单，便于现场操作，标定算法无迭代过程，能够有效减少坐标系标定耗时，提高坐标系标定精度。The embodiments of the present invention provide a conversion and calibration system of a mechanical arm coordinate system and a non-transitory computer-readable storage medium, which improve the vector direction of the coordinate system of the single-axis rotary motion method by using a combination of linear motion and rotary motion Calibration, while using multi-point center of gravity sampling and Rodrigue algorithm to solve the coordinate system conversion equation, the calibration process is simple, easy to operate on site, and the calibration algorithm has no iterative process, which can effectively reduce the time-consuming of coordinate system calibration and improve the accuracy of coordinate system calibration.

综上，本发明提供的一种机械臂坐标系的转换标定方法与系统，能够可靠实现机械臂基坐标系、末端工具坐标系与外部测量参考坐标系之间的相互转换；具有标定流程简单、便于现场操作和算法无迭代过程的特点，能够有效减小测量过程与系统误差的影响，提高标定精度，且能够有效减少标定环节和耗时，提高标定效率；可用于高精度快速在线标定，同时适用于多机械臂装置的同步标定和其他测量仪器标定。To sum up, the method and system for converting and calibrating the coordinate system of the manipulator provided by the present invention can reliably realize the mutual conversion between the base coordinate system of the manipulator, the end tool coordinate system and the external measurement reference coordinate system; the calibration process is simple, It is convenient for on-site operation and the algorithm has no iterative process, which can effectively reduce the influence of measurement process and system errors, improve calibration accuracy, and can effectively reduce calibration links and time-consuming, and improve calibration efficiency; it can be used for high-precision and fast online calibration, and at the same time Suitable for simultaneous calibration of multi-manipulator devices and calibration of other measuring instruments.

最后应说明的是：以上实施例仅用以说明本发明的技术方案，而非对其限制；尽管参照前述实施例对本发明进行了详细的说明，本领域的技术人员应当理解：其依然可以对前述各实施例所记载的技术方案进行修改，或者对其中部分技术特征进行等同替换；而这些修改或者替换，并不使相应技术方案的本质脱离本发明各实施例技术方案的精神和范围。Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it still can The technical solutions described in the foregoing embodiments are modified, or some of the technical features are replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims (10)

  1. A kind of 1. conversion scaling method of mechanical arm coordinate system, it is characterised in that including：
    S1, based on the tracking measurement device arranged in target mechanical arm working range, using ending coordinates system translational motion method, obtain Take the Rotating Transition of Coordinate relation of end-of-arm tooling coordinate system relative measurement reference frame；
    S2, become using the kinematics of the single-shaft-rotation method based on the end-of-arm tooling coordinate system and relative mechanical arm basis coordinates system Change, obtain the coordinate homogeneous transformation relation of the relatively described mechanical arm basis coordinates system of the end-of-arm tooling coordinate system；
    S3, based on the coordinate of selected demarcation sampled point, it is utilized respectively multiple spot center of gravity solving method, center of gravity facture and Rodrigo Matrixing solving method, obtain the mechanical arm basis coordinates system and the coordinate homogeneous transformation relation of the measurement reference frame.
  2. 2. according to the method for claim 1, it is characterised in that the translational motion of ending coordinates system is utilized described in step S1 Method, obtain end-of-arm tooling coordinate system relative measurement reference frame Rotating Transition of Coordinate relation the step of further comprise：
    By measuring the end-of-arm tooling of the target mechanical arm along during the end-of-arm tooling coordinate system all directions axle translational motion, institute The origin and translational displacement vector of end-of-arm tooling coordinate system are stated, calculates the end-of-arm tooling coordinate system in the measurement reference Identity component under coordinate system.
  3. 3. according to the method for claim 2, it is characterised in that further comprise the step of the S2：
    Fitting obtains the axle rotation round radius of the axle of target mechanical arm 1 and 6 axles, calculates two rotation round intersection points relative to institute Projection of the coordinate of measurement reference frame on each identity component, and utilization space vector geometrical relationship are stated, obtains end The coordinate homogeneous transformation relation of the relatively described mechanical arm basis coordinates system of ending tool coordinate system.
  4. 4. according to the method for claim 1, it is characterised in that further comprise the step of the S3：
    S31, using multiple spot center of gravity solving method, the relatively described mechanical arm basis coordinates system of the demarcation sampled point and described is calculated respectively Measure the barycentric coodinates of reference frame；
    S32, it is based respectively on the relatively described mechanical arm basis coordinates system of the demarcation sampled point and the measurement reference frame Barycentric coodinates and demarcation sample point coordinate, center of gravity processing is carried out to the demarcation sampled point, obtains the demarcation sampling respectively The center of gravity coordinate of the relatively described mechanical arm basis coordinates system of point and the measurement reference frame；
    S33, using Roderick matrix form, represent the demarcation relatively described mechanical arm basis coordinates system of sampled point and the survey Measure the center of gravity coordinate transformation equation of reference frame；
    S34, bring method into using characteristic value and solve the center of gravity coordinate transformation equation, it is relative to obtain the mechanical arm basis coordinates system The transformation matrix of the measurement reference frame.
  5. 5. according to the method for claim 4, it is characterised in that further comprise the step of the S32：
    S321, by the barycentric coodinates matrix of the demarcation sample point coordinate matrix in the mechanical arm basis coordinates system and demarcation sampled point Subtract each other, obtain the center of gravity coordinate of the demarcation relatively described mechanical arm basis coordinates system of sampled point；
    S322, by the barycentric coodinates matrix of demarcation sample point coordinate matrix and demarcation sampled point in the measurement reference frame Subtract each other, obtain the center of gravity coordinate of the relatively described measurement reference frame of the demarcation sampled point.
  6. 6. according to the method for claim 4, it is characterised in that further comprise the step of the S33：
    S331, wanted based on demarcation sampled point relative mechanical arm basis coordinates system and the center of gravity coordinate dimension for measuring reference frame Ask, set Rodrigo's antisymmetric matrix of corresponding dimension；
    S332, based on Rodrigo's antisymmetric matrix, by the rotation of mechanical arm basis coordinates system relative measurement reference frame Component transformation matrix equivalent transformation is Roderick matrix form；
    S333, the rotational component transformation matrix based on Roderick matrix form are relatively described by the demarcation sampled point Mechanical arm basis coordinates system and the center of gravity coordinate transformation equation equivalent transformation of the measurement reference frame are to include the Luo De The equation form of league (unit of length) antisymmetric matrix.
  7. 7. according to the method for claim 3, it is characterised in that tracking measurement device enters as follows described in step S1 Row arrangement：
    Laser tracking measurement device is set up in the target mechanical arm working range；
    Fixed laser reflects target ball on the end-of-arm tooling of the target mechanical arm, and the laser reflection target ball is in described The working range of laser tracking measurement device.
  8. 8. according to the method for claim 7, it is characterised in that the two rotation rounds intersection point is laser described in initial bit-type Reflect the center of target ball；
    By calculating projection of the centre coordinate of the laser reflection target ball on each identity component, and utilization space vector Geometrical relationship, the coordinate for obtaining the relatively described end-of-arm tooling coordinate system in center of the laser reflection target ball are as follows：
    In formula,Represent the coordinate of laser reflection target ball center opposing end portions tool coordinates system, xEto、yEtoAnd zEtoRepresent respectively The x of laser reflection target ball center opposing end portions tool coordinates systemEAxle, yEAxle and zEThe coordinate components of axle,Represent that 6 axles rotate The position vector of center relative laser reflecting target ball center, its mould length are equal to the fit radius value of 6 axle,WithRespectively Represent end-of-arm tooling coordinate system x in the case where measuring reference frameEAxle and yEThe identity component of axle, R1Represent the fitting half of 1 axle Footpath is worth, xBeoRepresent end-of-arm tooling coordinate origin in initial bit-type phase to mechanical arm basis coordinates system xBThe component of axle.
  9. 9. according to the method for claim 7, it is characterised in that choose the measuring coordinate system of the laser tracking measurement device As the measurement reference frame.
  10. A kind of 10. conversion calibration system of mechanical arm coordinate system, it is characterised in that including：It is at least one memory, at least one Processor, communication interface and bus；
    The memory, the processor and the communication interface complete mutual communication, the communication by the bus The information transfer that interface is used between the conversion calibration facility and coordinate measurment instrument；
    The computer program that can be run on the processor, the computing device described program are stored with the memory In Shi Shixian such as claim 1 to 9 it is any as described in method.
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