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CN110370272B - A Robot TCP Calibration System Based on Vertical Reflection - Google Patents

A Robot TCP Calibration System Based on Vertical Reflection Download PDF

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CN110370272B
CN110370272B CN201910539099.5A CN201910539099A CN110370272B CN 110370272 B CN110370272 B CN 110370272B CN 201910539099 A CN201910539099 A CN 201910539099A CN 110370272 B CN110370272 B CN 110370272B
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唐倩
李志航
周浩
李代杨
刘联超
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Chongqing University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B25J19/0095—Means or methods for testing manipulators
    • 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
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    • B25J9/1692—Calibration of manipulator

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Abstract

本发明公开了一种基于垂直反射的机器人TCP标定系统，以双目视觉系统、机器人和作业工具结合作业，以平面镜作为辅助工具，利用机器人运动学和空间坐标变换的关系，对空间固定点进行多次测量，确立出手眼关系，在对作业工具的末端圆形靶点进行检测，通过坐标变换关系以及平面镜成像对称性的特点，以完成TCP的标定。本发明的TCP标定系统，本系统区别于接触式标定系统，无碰撞风险，安全系数高。

Figure 201910539099

The invention discloses a robot TCP calibration system based on vertical reflection, which combines a binocular vision system, a robot and a working tool, uses a plane mirror as an auxiliary tool, and uses the relationship between robot kinematics and spatial coordinate transformation to perform a fixed point in space. After multiple measurements, the hand-eye relationship is established, and the circular target at the end of the work tool is detected. Through the coordinate transformation relationship and the characteristics of plane mirror imaging symmetry, the TCP calibration is completed. The TCP calibration system of the present invention is different from the contact calibration system, has no collision risk, and has a high safety factor.

Figure 201910539099

Description

一种基于垂直反射的机器人TCP标定系统A Robot TCP Calibration System Based on Vertical Reflection

技术领域technical field

本发明涉及智能制造领域，特别是涉及一种基于垂直反射的机器人TCP标定系统。The invention relates to the field of intelligent manufacturing, in particular to a robot TCP calibration system based on vertical reflection.

背景技术Background technique

在工业4.0的背景下，双目视觉系统辅助机器人自主作业已成常态。以焊接为例，双目视觉系统可以对焊缝进行实时追踪识别，有助于提高焊接质量和焊接效率。作业工具的作业点(TCP)的标定精度直接影响实际的作业质量。而传统的示教接触式TCP标定方法存在低效、碰撞等问题，已不能满足当前作业需求，低成本、高效、安全的标定方法对工业生产具有重要意义。In the context of Industry 4.0, it has become the norm for binocular vision systems to assist robots in autonomous operation. Taking welding as an example, the binocular vision system can track and identify the welding seam in real time, which helps to improve the welding quality and welding efficiency. The calibration accuracy of the working point (TCP) of the working tool directly affects the actual working quality. However, the traditional teaching and contact TCP calibration method has problems such as inefficiency and collision, and can no longer meet the current operation needs. The low-cost, efficient and safe calibration method is of great significance to industrial production.

因此本领域技术人员致力于开发一种安全系数高的基于垂直反射的机器人 TCP标定系统。Therefore, those skilled in the art are devoted to developing a vertical reflection-based robot TCP calibration system with high safety factor.

发明内容SUMMARY OF THE INVENTION

有鉴于现有技术的上述缺陷，本发明所要解决的技术问题是提供一种安全系数高的基于垂直反射的机器人TCP系统。In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is to provide a vertical reflection-based robot TCP system with a high safety factor.

为实现上述目的，本发明提供了一种基于垂直反射的机器人TCP标定系统，包括机器人、平面镜和双目视觉系统，所述双目视觉系统包括两台摄像机，两台所述摄像机分别设置在所述机器人的末端两侧，所述平面镜设置在所述双目视觉系统的摄像范围内。In order to achieve the above object, the present invention provides a robot TCP calibration system based on vertical reflection, including a robot, a plane mirror and a binocular vision system, the binocular vision system includes two cameras, and the two cameras are respectively arranged in the On both sides of the end of the robot, the plane mirror is arranged within the imaging range of the binocular vision system.

较佳的，两台所述摄像机通过连接支架固定在作业工具上，两台所述摄像机分别固定设置在所述连接支架的两端。Preferably, the two cameras are fixed on the working tool through a connecting bracket, and the two cameras are respectively fixed on both ends of the connecting bracket.

较佳的，还包括逻辑运算模块和数据采集模块，所述数据采集模块设置在所述逻辑运算模块和双目视觉系统之间，所述数据采集模块用于采集双目视觉系统测量的测量值，所述数据采集模块将采集到的数据传送给所述逻辑运算模块。Preferably, it also includes a logic operation module and a data collection module, the data collection module is arranged between the logic operation module and the binocular vision system, and the data collection module is used to collect the measurement values measured by the binocular vision system. , the data collection module transmits the collected data to the logic operation module.

较佳的，所述逻辑运算模块包括人眼关系逻辑运算模块和TCP标定逻辑运算模块，所述人眼关系逻辑运算模块通过机器人运动学和空间坐标变换来确定双目视觉系统坐标系{C}相对于机器人末端坐标系{E}的变换矩阵

Figure GDA0003077444840000021
Figure GDA0003077444840000022
为机器人手眼关系；所述TCP标定逻辑运算模块通过求得的机器人手眼关系
Figure GDA0003077444840000023
来完成作业工具末端TCP的标定。Preferably, the logic operation module includes a human-eye relationship logic operation module and a TCP calibration logic operation module, and the human-eye relationship logic operation module determines the binocular vision system coordinate system {C} through robot kinematics and spatial coordinate transformation. Transformation matrix relative to the robot end coordinate system {E}
Figure GDA0003077444840000021
Figure GDA0003077444840000022
is the robot hand-eye relationship; the robot hand-eye relationship obtained by the TCP calibration logic operation module
Figure GDA0003077444840000023
To complete the calibration of the TCP at the end of the work tool.

较佳的，确定所述机器人手眼关系

Figure GDA0003077444840000024
流程如下：Preferably, determine the hand-eye relationship of the robot
Figure GDA0003077444840000024
The process is as follows:

(S101)建立机器人手眼关系为

Figure GDA0003077444840000025
其中，RC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的旋转矩阵且为定值；TC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的平移向量且为定值；(S101) The robot hand-eye relationship is established as
Figure GDA0003077444840000025
Among them, RC is the rotation matrix of the transformation between the robot end coordinate system {E} and the binocular vision system coordinate system { C } and is a fixed value; T C is the robot end coordinate system {E} and the binocular vision system coordinate system {C } Converted translation vector and is a fixed value;

(S102)在工作平台上设置第一圆形靶点，第一圆形靶点为固定点，所述机器人末端姿态保持不变，所述机器人做线性运动，所述机器人末端依次运动到多个位置并对所述第一圆形靶点进行测量；(S102) A first circular target point is set on the working platform, the first circular target point is a fixed point, the posture of the end of the robot remains unchanged, the robot performs linear motion, and the end of the robot moves to multiple position and measure the first circular target;

(S103)依次控制所述机器人做变位姿运动到多个位置并在双目视觉系统坐标系{C}下对所述第一圆形靶点进行测量；(S103) Controlling the robot to move to multiple positions in sequence and to measure the first circular target point in the binocular vision system coordinate system {C};

(S104)将步骤(S102)和步骤(S103)对所述第一圆形靶点的测量值通过机器人运动学和空间坐标变换的关系计算得出RC和TC，即标定出机器人手眼关系

Figure GDA0003077444840000031
(S104) Calculate the measured value of the first circular target point in steps (S102) and (S103) through the relationship between robot kinematics and spatial coordinate transformation to obtain R C and T C , that is, the robot hand-eye relationship is calibrated
Figure GDA0003077444840000031

较佳的，所述人眼关系逻辑运算模块中的机器人运动学和空间坐标变换逻辑运算包括：Preferably, the robot kinematics and spatial coordinate transformation logic operations in the human-eye relationship logic operation module include:

(B1)建立机器人末端坐标系{E}相对于机器人基坐标{B}的变换矩阵

Figure GDA0003077444840000032
其中，R为机器人基坐标{B}和机器人末端坐标系{E}转换的旋转矩阵，由于所述机器人做线性运动过程中，机器人末端姿态是保持不变的，即R 不变，R为定值；T为机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量；(B1) Establish the transformation matrix of the robot end coordinate system {E} relative to the robot base coordinate {B}
Figure GDA0003077444840000032
Among them, R is the rotation matrix of the transformation between the robot base coordinate {B} and the robot end coordinate system {E}. Since the robot does a linear motion, the robot end posture remains unchanged, that is, R is unchanged, and R is a fixed value; T is the translation vector transformed between the robot base coordinate {B} and the robot end coordinate system {E};

由坐标转换公式可得：It can be obtained from the coordinate conversion formula:

Figure GDA0003077444840000033
Figure GDA0003077444840000033

展开得到：Expand to get:

Figure GDA0003077444840000034
Figure GDA0003077444840000034

Pc的坐标值可由双目视觉系统测量得到；The coordinate value of P c can be measured by the binocular vision system;

其中，Pc为所述第一圆形靶点在双目视觉系统坐标系{C}下的坐标；Wherein, P c is the coordinate of the first circular target point in the binocular vision system coordinate system {C};

Pb为所述第一圆形靶点在机器人基坐标{B}下的坐标，Pb为定值；P b is the coordinate of the first circular target point under the robot base coordinate {B}, and P b is a fixed value;

Figure GDA0003077444840000035
和
Figure GDA0003077444840000036
分别为Pc和Pb转换的转置矩阵；
Figure GDA0003077444840000035
and
Figure GDA0003077444840000036
are the transposed matrices of P c and P b transformations, respectively;

(B2)由于在步骤(S102)中，所述机器人末端姿态保持不变，所述机器人末端依次运动到多个位置，选取两个位置，在双目视觉系统坐标系{C}下得到第一圆形靶点的测量值

Figure GDA0003077444840000037
和
Figure GDA0003077444840000038
分别代入公式(a1)，可以建立以下方程：(B2) Since in step (S102), the posture of the end of the robot remains unchanged, the end of the robot moves to multiple positions in turn, selects two positions, and obtains the first position in the binocular vision system coordinate system {C} Measured values for circular targets
Figure GDA0003077444840000037
and
Figure GDA0003077444840000038
Substituting into formula (a1) respectively, the following equations can be established:

Figure GDA0003077444840000041
Figure GDA0003077444840000041

两式相减可得：Subtract the two formulas to get:

Figure GDA0003077444840000042
Figure GDA0003077444840000042

因为R为正交矩阵，上式可变为：Because R is an orthogonal matrix, the above formula can be changed to:

Figure GDA0003077444840000043
Figure GDA0003077444840000043

依次进行四次测量所述第一圆形靶点在双目视觉系统坐标系{C}下不同的位置参数，得到第一圆形靶点的测量值

Figure GDA0003077444840000044
和
Figure GDA0003077444840000045
并代公式(a2)中，可得：Measure the different position parameters of the first circular target point in the binocular vision system coordinate system {C} four times in turn to obtain the measurement value of the first circular target point
Figure GDA0003077444840000044
and
Figure GDA0003077444840000045
Substituting into formula (a2), we can get:

Figure GDA0003077444840000046
Figure GDA0003077444840000046

即RcA＝b；That is, R c A = b;

可得出，

Figure GDA0003077444840000047
It can be concluded that,
Figure GDA0003077444840000047

b＝RT[T1-T2 T2-T3 T3-T4]；b=RT [ T 1 -T 2 T 2 -T 3 T 3 -T 4 ];

利用矩阵奇异值分解求解可得RC；R C can be obtained by solving the matrix singular value decomposition;

其中，

Figure GDA0003077444840000048
和
Figure GDA0003077444840000049
分别为第一圆形靶点在双目视觉系统坐标系{C} 下的坐标；
Figure GDA00030774448400000410
和
Figure GDA00030774448400000411
分别为
Figure GDA00030774448400000412
和
Figure GDA00030774448400000413
的转置矩阵；in,
Figure GDA0003077444840000048
and
Figure GDA0003077444840000049
are the coordinates of the first circular target point in the binocular vision system coordinate system {C};
Figure GDA00030774448400000410
and
Figure GDA00030774448400000411
respectively
Figure GDA00030774448400000412
and
Figure GDA00030774448400000413
The transposed matrix of ;

T1、T2、T3和T4分别为所述机器人运动时不同位置下机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量；T 1 , T 2 , T 3 and T 4 are respectively translation vectors converted from the robot base coordinate {B} and the robot end coordinate system {E} at different positions when the robot moves;

(B3)由于在步骤(S103)中，所述第一圆形靶点在双目视觉系统坐标系 {C}下的坐标值随着机器人做变位姿运动变化而变化，选取两个移动位置，得到第一圆形靶点的测量值

Figure GDA00030774448400000414
和
Figure GDA00030774448400000415
建立以下方程：(B3) Since in step (S103), the coordinate value of the first circular target point in the binocular vision system coordinate system {C} changes as the robot moves to change the pose, select two moving positions , get the measured value of the first circular target
Figure GDA00030774448400000414
and
Figure GDA00030774448400000415
Build the following equations:

Figure GDA0003077444840000051
Figure GDA0003077444840000051

两式相减，可得：Subtracting the two equations, we get:

Figure GDA0003077444840000052
Figure GDA0003077444840000052

Figure GDA0003077444840000053
的值可以由双目视觉系统测得，将上述已经求得的RC代入式中，求得TC，标定出手眼关系
Figure GDA0003077444840000054
Figure GDA0003077444840000053
The value of can be measured by the binocular vision system. Substitute the obtained RC into the formula to obtain TC, and calibrate the hand - eye relationship.
Figure GDA0003077444840000054

其中，R11和R22分别为所述机器人变位姿运动时不同位置下机器人基坐标{B}和机器人末端坐标系{E}转换的旋转矩阵；Wherein, R 11 and R 22 are respectively the rotation matrices converted from the robot base coordinate {B} and the robot end coordinate system {E} at different positions when the robot moves in a variable pose;

T11和T22分别为所述机器人变位姿运动时不同位置下机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量； T11 and T22 are respectively the translation vectors converted from the robot base coordinate {B} and the robot end coordinate system {E} under different positions when the robot moves in a variable pose;

Figure GDA0003077444840000055
和
Figure GDA0003077444840000056
分别为第一圆形靶点在双目视觉系统坐标系{C}下的坐标；
Figure GDA0003077444840000057
和
Figure GDA0003077444840000058
分别为
Figure GDA0003077444840000059
和
Figure GDA00030774448400000510
的转置矩阵。
Figure GDA0003077444840000055
and
Figure GDA0003077444840000056
are the coordinates of the first circular target point in the binocular vision system coordinate system {C};
Figure GDA0003077444840000057
and
Figure GDA0003077444840000058
respectively
Figure GDA0003077444840000059
and
Figure GDA00030774448400000510
The transposed matrix of .

较佳的，作业工具末端的TCP标定的流程包括：Preferably, the TCP calibration process at the end of the work tool includes:

将平面镜放置在工作平台上，将第二圆形靶点粘贴于所述机器人末端的作业工具末端处，控制所述机器人将所述第二圆形靶点设置于所述平面镜上方，保持机器人末端垂直于所述平面镜。Place the plane mirror on the working platform, paste the second circular target point on the end of the working tool at the end of the robot, control the robot to set the second circular target point above the plane mirror, and keep the end of the robot perpendicular to the plane mirror.

较佳的，所述TCP标定逻辑运算模块的逻辑运算包括：Preferably, the logic operation of the TCP calibration logic operation module includes:

所述作业工具末端上的第二圆形靶点在所述平面镜里的点为投影点，通过双目视觉系统测得投影点在双目视觉系统坐标系{C}中的值，通过

Figure GDA00030774448400000511
可求得投影点在机器人末端坐标系{E}的值(x',y',z')；假设第二圆形靶点在机器人末端坐标系{E}的值为(x,y,z)；由垂直关系可得x＝x'，y＝y'；在所述工作平台上选取对称点，先求得对称点在机器人末端坐标系{E}下的Z轴坐标值zm，根据对称性可得z＝z'-2×(z'-zm)，最后求得第二圆形靶点在机器人末端坐标系{E}下的值，完成TCP的标定。The point of the second circular target point on the end of the working tool in the plane mirror is the projection point, and the value of the projection point in the coordinate system {C} of the binocular vision system is measured by the binocular vision system.
Figure GDA00030774448400000511
The value (x', y', z') of the projection point in the coordinate system {E} of the robot end can be obtained; assuming that the value of the second circular target point in the coordinate system {E} of the robot end is (x, y, z ); can obtain x=x', y=y' from the vertical relationship; Select the symmetrical point on the working platform, first obtain the Z-axis coordinate value zm of the symmetrical point under the robot end coordinate system { E}, according to The symmetry can be obtained as z=z'-2×(z'-z m ), and finally the value of the second circular target point in the robot end coordinate system {E} is obtained to complete the calibration of the TCP.

较佳的，还包括控制装置，所述机器人、所述逻辑运算模块、所述数据采集模块、所述机器人和所述双目视觉系统均与所述控制装置连接。Preferably, it also includes a control device, and the robot, the logic operation module, the data acquisition module, the robot and the binocular vision system are all connected to the control device.

本发明的有益效果是：本发明的基于垂直反射的机器人TCP标定系统，无需额外的辅助标定设备，仅需要一面镜子，成本低廉，操作方便；本系统区别于接触式标定系统，无碰撞风险，安全系数高；仅需要控制机器人做四次运动即可完成TCP标定，实现了对TCP的快速精确标定,可满足实际工业生产中机器人末端工具参数的标定需求。The beneficial effects of the present invention are as follows: the robot TCP calibration system based on vertical reflection of the present invention does not require additional auxiliary calibration equipment, but only needs a mirror, with low cost and convenient operation; The safety factor is high; it only needs to control the robot to do four movements to complete the TCP calibration, which realizes the rapid and accurate calibration of the TCP, and can meet the calibration requirements of the robot end tool parameters in actual industrial production.

附图说明Description of drawings

图1是本发明一具体实施方式基于垂直反射的机器人TCP标定系统的结构示意图。FIG. 1 is a schematic structural diagram of a robot TCP calibration system based on vertical reflection according to a specific embodiment of the present invention.

图2是图1的模块图。FIG. 2 is a block diagram of FIG. 1 .

具体实施方式Detailed ways

下面结合附图和实施例对本发明作进一步说明：Below in conjunction with accompanying drawing and embodiment, the present invention will be further described:

如图1所示，本发明实施例公开了一种基于垂直反射的机器人TCP标定方法，包括以下步骤：As shown in FIG. 1 , an embodiment of the present invention discloses a method for calibrating a robot TCP based on vertical reflection, which includes the following steps:

(S1)在双目视觉系统上建立双目视觉系统坐标系{C}；在机器人末端6建立机器人末端坐标系{E}，确定双目视觉系统坐标系{C}相对于机器人末端坐标系{E}的变换矩阵

Figure GDA0003077444840000061
Figure GDA0003077444840000062
为机器人手眼关系。(S1) Establish the binocular vision system coordinate system {C} on the binocular vision system; establish the robot end coordinate system {E} at the robot end 6, and determine the binocular vision system coordinate system {C} relative to the robot end coordinate system { The transformation matrix of E}
Figure GDA0003077444840000061
Figure GDA0003077444840000062
Hand-eye relationship for the robot.

在本实施例中，在步骤(S1)中，具体步骤为：In this embodiment, in step (S1), the specific steps are:

(S101)确立机器人手眼关系为

Figure GDA0003077444840000063
其中，RC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的旋转矩阵且为定值；TC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的平移向量且为定值；在其他实施例中，双目视觉系统坐标系{C}是以双目视觉系统中的一个摄像机2建立的。(S101) Establish the robot hand-eye relationship as
Figure GDA0003077444840000063
Among them, RC is the rotation matrix of the transformation between the robot end coordinate system {E} and the binocular vision system coordinate system { C } and is a fixed value; T C is the robot end coordinate system {E} and the binocular vision system coordinate system {C } The transformed translation vector is a fixed value; in other embodiments, the binocular vision system coordinate system {C} is established with a camera 2 in the binocular vision system.

(S102)在工作平台上设置第一圆形靶点P，第一圆形靶点P为固定点，机器人末端6姿态保持不变，机器人1做线性运动，机器人末端6依次运动到多个位置并在双目视觉系统坐标系{C}下对第一圆形靶点P进行测量；在本实施例中，第一圆形靶点P在工作平台上是固定不动的，控制机器人进行变位姿运动，双目视觉系统坐标系{C}也是变化的，不同位置上的双目视觉系统坐标系{C}是不同的，进而第一圆形靶点P的坐标值也是不同的。(S102) A first circular target point P is set on the working platform, the first circular target point P is a fixed point, the posture of the robot end 6 remains unchanged, the robot 1 performs linear motion, and the robot end 6 moves to multiple positions in sequence And measure the first circular target point P under the binocular vision system coordinate system {C}; in this embodiment, the first circular target point P is fixed on the working platform, and the robot is controlled to change. The pose movement, the binocular vision system coordinate system {C} also changes, the binocular vision system coordinate system {C} at different positions is different, and the coordinate value of the first circular target point P is also different.

(S103)依次控制机器人1做变位姿运动到多个位置并在双目视觉系统坐标系{C}下对第一圆形靶点P进行测量。在本实施例中，机器人1的姿态和位置都会发生变化。(S103) Controlling the robot 1 to move to a plurality of positions in sequence and to measure the first circular target point P in the binocular vision system coordinate system {C}. In this embodiment, the posture and position of the robot 1 will change.

(S104)将步骤(S102)和步骤(S103)对第一圆形靶点P的测量值通过机器人运动学和空间坐标变换的关系计算得出RC和TC，标定出手眼关系

Figure GDA0003077444840000071
(S104) Calculate the measured value of the first circular target point P in steps (S102) and (S103) through the relationship between robot kinematics and spatial coordinate transformation to obtain RC and TC, and calibrate the hand - eye relationship
Figure GDA0003077444840000071

在本实施例中，在步骤(S104)中，具体包括以下步骤：In this embodiment, in step (S104), the following steps are specifically included:

(B1)由坐标转换公式可得：(B1) can be obtained from the coordinate conversion formula:

Figure GDA0003077444840000072
Figure GDA0003077444840000072

展开得到：Expand to get:

Figure GDA0003077444840000073
Figure GDA0003077444840000073

Pc的坐标值可由双目视觉系统测量得到；The coordinate value of P c can be measured by the binocular vision system;

其中，Pc为第一圆形靶点P在双目视觉系统坐标系{C}下的坐标；Wherein, P c is the coordinate of the first circular target point P in the binocular vision system coordinate system {C};

Pb为第一圆形靶点P在机器人基坐标{B}下的坐标，Pb为定值；P b is the coordinate of the first circular target point P under the robot base coordinate {B}, and P b is a fixed value;

Figure GDA0003077444840000081
和
Figure GDA0003077444840000082
分别为Pc和Pb转换的转置矩阵。
Figure GDA0003077444840000081
and
Figure GDA0003077444840000082
are the transposed matrices of the P c and P b transformations, respectively.

建立机器人末端坐标系{E}相对于机器人基坐标{B}的变换矩阵

Figure GDA0003077444840000083
其中，R为机器人基坐标{B}和机器人末端坐标系{E}转换的旋转矩阵，由于机器人1做线性运动过程中，机器人末端6姿态是保持不变的，即R不变，R为定值； T为机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量。Establish the transformation matrix of the robot end coordinate system {E} relative to the robot base coordinate {B}
Figure GDA0003077444840000083
Among them, R is the rotation matrix of the transformation between the robot base coordinate {B} and the robot end coordinate system {E}. Since the robot 1 performs linear motion, the robot end 6 posture remains unchanged, that is, R remains unchanged, and R is a fixed value; T is the translation vector transformed between the robot base coordinate {B} and the robot end coordinate system {E}.

(B2)由于在步骤(S102)中，所述机器人末端6姿态保持不变，所述机器人末端6依次运动到多个位置，选取两个位置，在双目视觉系统坐标系{C}下得到第一圆形靶点(P)的测量值

Figure GDA0003077444840000084
和
Figure GDA0003077444840000085
分别代入公式(a1)，可以建立以下方程：(B2) Since in step (S102), the posture of the robot end 6 remains unchanged, the robot end 6 moves to multiple positions in turn, selects two positions, and obtains in the binocular vision system coordinate system {C} Measured value of the first circular target point (P)
Figure GDA0003077444840000084
and
Figure GDA0003077444840000085
Substituting into formula (a1) respectively, the following equations can be established:

Figure GDA0003077444840000086
Figure GDA0003077444840000086

两式相减可得：Subtract the two formulas to get:

Figure GDA0003077444840000087
Figure GDA0003077444840000087

因为R为正交矩阵，上式可变为：Because R is an orthogonal matrix, the above formula can be changed to:

Figure GDA0003077444840000088
Figure GDA0003077444840000088

依次进行四次测量所述第一圆形靶点P在双目视觉系统坐标系{C}下不同的位置参数，得到第一圆形靶点P的测量值

Figure GDA0003077444840000089
和
Figure GDA00030774448400000810
并代公式(a2) 中，可得：Measure the different position parameters of the first circular target point P in the binocular vision system coordinate system {C} four times in turn to obtain the measured value of the first circular target point P
Figure GDA0003077444840000089
and
Figure GDA00030774448400000810
Substituting into formula (a2), we can get:

Figure GDA00030774448400000811
Figure GDA00030774448400000811

即RcA＝b；That is, R c A = b;

可得出，

Figure GDA0003077444840000091
It can be concluded that,
Figure GDA0003077444840000091

b＝RT[T1-T2 T2-T3 T3-T4]；b=RT [ T 1 -T 2 T 2 -T 3 T 3 -T 4 ];

利用矩阵奇异值分解求解可得RC；R C can be obtained by solving the matrix singular value decomposition;

其中，

Figure GDA0003077444840000092
和
Figure GDA0003077444840000093
分别为第一圆形靶点P在双目视觉系统坐标系 {C}下的坐标；
Figure GDA0003077444840000094
和
Figure GDA0003077444840000095
分别为
Figure GDA0003077444840000096
和
Figure GDA0003077444840000097
的转置矩阵；in,
Figure GDA0003077444840000092
and
Figure GDA0003077444840000093
are the coordinates of the first circular target point P in the binocular vision system coordinate system {C};
Figure GDA0003077444840000094
and
Figure GDA0003077444840000095
respectively
Figure GDA0003077444840000096
and
Figure GDA0003077444840000097
The transposed matrix of ;

T1、T2、T3和T4分别为所述机器人1运动时不同位置下机器人基坐标{B} 和机器人末端坐标系{E}转换的平移向量。T1、T2、T3和T4分别为在测量

Figure GDA0003077444840000098
Figure GDA0003077444840000099
和
Figure GDA00030774448400000910
坐标值时机器人所处运动状态下机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量。T 1 , T 2 , T 3 and T 4 are respectively translation vectors converted from the robot base coordinate {B} and the robot end coordinate system {E} at different positions when the robot 1 moves. T 1 , T 2 , T 3 and T 4 are measured at
Figure GDA0003077444840000098
Figure GDA0003077444840000099
and
Figure GDA00030774448400000910
The coordinate value is the translation vector converted from the robot base coordinate {B} and the robot end coordinate system {E} in the motion state of the robot.

(B3)由于在步骤(S103)中，第一圆形靶点P在双目视觉系统坐标系{C} 下的坐标值随着机器人做变位姿运动变化而变化，选取两个移动位置，得到第一圆形靶点(P)的测量值

Figure GDA00030774448400000911
和
Figure GDA00030774448400000912
建立以下方程：(B3) Since in step (S103), the coordinate value of the first circular target point P in the binocular vision system coordinate system {C} changes with the change of the robot's pose-changing motion, select two moving positions, Obtain the measurement of the first circular target point (P)
Figure GDA00030774448400000911
and
Figure GDA00030774448400000912
Build the following equations:

Figure GDA00030774448400000916
Figure GDA00030774448400000916

两式相减，可得：Subtracting the two equations, we get:

Figure GDA00030774448400000913
Figure GDA00030774448400000913

Figure GDA00030774448400000914
的值可以由双目视觉系统测得，将上述已经求得的RC代入式中，求得TC，标定出手眼关系：
Figure GDA00030774448400000915
Figure GDA00030774448400000914
The value of can be measured by the binocular vision system. Substitute the obtained RC into the formula to obtain TC, and calibrate the hand - eye relationship:
Figure GDA00030774448400000915

其中，R11和R22分别为所述机器人变位姿运动时不同位置下机器人基坐标 {B}和机器人末端坐标系{E}转换的旋转矩阵；R11和R22分别为在测量

Figure GDA00030774448400000917
和
Figure GDA0003077444840000101
坐标值时机器人所处运动状态下机器人基坐标{B}和机器人末端坐标系{E} 转换的旋转矩阵；Wherein, R 11 and R 22 are the rotation matrices converted from the robot base coordinate {B} and the robot end coordinate system {E} at different positions when the robot moves with changing poses; R 11 and R 22 are the rotation matrices during the measurement
Figure GDA00030774448400000917
and
Figure GDA0003077444840000101
The coordinate value is the rotation matrix of the transformation between the robot base coordinate {B} and the robot end coordinate system {E} in the motion state of the robot;

T11和T22分别为所述机器人变位姿运动时不同位置下机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量；T11和T22分别为在测量

Figure GDA0003077444840000102
和
Figure GDA0003077444840000103
坐标值时机器人所处运动状态下机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量； T11 and T22 are respectively the translation vectors converted from the robot base coordinate {B} and the robot end coordinate system {E} at different positions when the robot moves with variable poses; T11 and T22 are respectively in the measurement
Figure GDA0003077444840000102
and
Figure GDA0003077444840000103
The coordinate value is the translation vector of the transformation between the robot base coordinate {B} and the robot end coordinate system {E} in the motion state of the robot;

Figure GDA0003077444840000104
和
Figure GDA0003077444840000105
分别为第一圆形靶点P在双目视觉系统坐标系{C}下的坐标；
Figure GDA0003077444840000106
和
Figure GDA0003077444840000107
分别为
Figure GDA0003077444840000108
和
Figure GDA0003077444840000109
的转置矩阵。
Figure GDA0003077444840000104
and
Figure GDA0003077444840000105
are the coordinates of the first circular target point P in the binocular vision system coordinate system {C};
Figure GDA0003077444840000106
and
Figure GDA0003077444840000107
respectively
Figure GDA0003077444840000108
and
Figure GDA0003077444840000109
The transposed matrix of .

在本实施例中，由于双目视觉系统坐标系{C}随着机器人做变位姿运动变化而变化，因此两次选取并测量第一圆形靶点P的双目视觉系统坐标系{C}不同，由于第一圆形靶点P是固定不动的，因此第一圆形靶点P在不同的双目视觉系统坐标系{C}下坐标值也不同。In this embodiment, since the coordinate system {C} of the binocular vision system changes as the robot performs the pose-changing motion, the coordinate system {C of the binocular vision system of the first circular target point P is selected and measured twice. } Different, since the first circular target point P is fixed, the coordinate values of the first circular target point P under different binocular vision system coordinate systems {C} are also different.

(S2)将平面镜3放置在工作平台上，将第二圆形靶点Pa粘贴于机器人末端6的作业工具5末端处，控制机器人1将第二圆形靶点Pa设置于平面镜3上方，保持机器人末端6垂直于平面镜3，作业工具5末端上的第二圆形靶点Pa在平面镜3里的点为投影点P'a，通过双目视觉系统测得投影点P'a在双目视觉系统坐标系{C}中的值，通过

Figure GDA00030774448400001010
可求得投影点P'a在机器人末端坐标系{E}的值 (x',y',z')；然后根据平面镜3的镜面对称计算出第二圆形靶点Pa在机器人末端坐标系{E}下的值，完成TCP的标定。(S2) Place the plane mirror 3 on the working platform, paste the second circular target point Pa on the end of the working tool 5 of the robot end 6, control the robot 1 to set the second circular target point Pa above the plane mirror 3 , keep the robot end 6 perpendicular to the plane mirror 3, the point of the second circular target point P a on the end of the working tool 5 in the plane mirror 3 is the projection point P' a , and the projection point P' a is measured by the binocular vision system at The value in the binocular vision system coordinate system {C}, via
Figure GDA00030774448400001010
The value (x', y', z') of the projection point P' a in the coordinate system {E} of the robot end can be obtained; then the coordinates of the second circular target point P a at the end of the robot are calculated according to the mirror symmetry of the plane mirror 3 Set the value under {E} to complete the TCP calibration.

在本实施例中，在步骤(S2)中，然后根据所述平面镜3的镜面对称计算出第二圆形靶点Pa在机器人末端坐标系{E}下的值，具体步骤包括：In this embodiment, in step (S2), the value of the second circular target point Pa in the robot end coordinate system {E} is then calculated according to the mirror symmetry of the plane mirror 3, and the specific steps include:

假设第二圆形靶点Pa在机器人末端坐标系{E}的值为(x,y,z)；由垂直关系可得x＝x'，y＝y'；在所述工作平台上选取对称点Pm，先求得对称点Pm在机器人末端坐标系{E}下的Z轴坐标值zm，根据对称性可得z＝z'-2×(z'-zm)，最后求得点Pa在机器人末端坐标系{E}下的值。在某些实施例中，对称点Pm设置在第一圆形靶点P处，对称点Pm即为第一圆形靶点P,在其他实施例中，对称点 Pm也可以是在工作平台上第一圆形靶点P之外的点。Assume that the value of the second circular target point P a in the robot end coordinate system {E} is (x, y, z); from the vertical relationship, x=x', y=y'; Symmetric point P m , first obtain the Z-axis coordinate value z m of the symmetrical point P m in the robot end coordinate system {E}, according to the symmetry, z=z'-2×(z'-z m ) can be obtained, and finally Find the value of point P a in the robot end coordinate system {E}. In some embodiments, the symmetric point P m is set at the first circular target point P, and the symmetric point P m is the first circular target point P. In other embodiments, the symmetric point P m can also be at Points other than the first circular target point P on the working platform.

在某些实施例中，作业工具5例如为焊枪或其他工具，在此不作限定。In some embodiments, the working tool 5 is, for example, a welding gun or other tools, which is not limited herein.

如图1和图2所示，本发明实施例还公开了本发明实施例公开了一种基于垂直反射的机器人TCP标定系统，包括机器人1、平面镜3和双目视觉系统，双目视觉系统包括两台摄像机2，两台摄像机2分别设置在机器人1的末端两侧，平面镜3设置在双目视觉系统的摄像范围内。As shown in FIG. 1 and FIG. 2 , an embodiment of the present invention also discloses a robot TCP calibration system based on vertical reflection, including a robot 1, a plane mirror 3 and a binocular vision system. The binocular vision system includes Two cameras 2 are arranged on both sides of the end of the robot 1 respectively, and the plane mirror 3 is arranged within the imaging range of the binocular vision system.

在本实施例中，两台摄像机2通过连接支架4固定在作业工具5上，两台摄像机2分别固定设置在连接支架4的两端。在本实施例中，作业工具5安装在机器人末端6上。在本实施例中，连接支架4为圆盘状，摄像机2嵌入连接支架4上的安装槽中，以使得摄像机2能被固定在连接支架4上。在某些实施例中，连接支架4与作业工具5一体制成。在其他实施例中，两台摄像机2通过连接支架4固定在机器人1上，两台摄像机2分别固定设置在连接支架4的两端。In this embodiment, the two cameras 2 are fixed on the working tool 5 through the connecting bracket 4 , and the two cameras 2 are respectively fixed on both ends of the connecting bracket 4 . In this embodiment, the work tool 5 is mounted on the robot end 6 . In this embodiment, the connecting bracket 4 is in the shape of a disc, and the camera 2 is embedded in the mounting groove on the connecting bracket 4 , so that the camera 2 can be fixed on the connecting bracket 4 . In some embodiments, the connecting bracket 4 is made in one piece with the working tool 5 . In other embodiments, the two cameras 2 are fixed on the robot 1 through the connecting bracket 4 , and the two cameras 2 are respectively fixed on both ends of the connecting bracket 4 .

在本实施例中，还包括逻辑运算模块和数据采集模块，数据采集模块设置在逻辑运算模块和双目视觉系统之间，数据采集模块用于采集双目视觉系统测量的测量值，数据采集模块将采集到的数据传送给逻辑运算模块。数据采集模块用于采集双目视觉系统的测量值信号，并将测量值信号传送到逻辑运算模块进行计算。In this embodiment, it also includes a logic operation module and a data acquisition module. The data acquisition module is arranged between the logic operation module and the binocular vision system. The data acquisition module is used to collect the measured values measured by the binocular vision system. The data acquisition module Send the collected data to the logic operation module. The data acquisition module is used to collect the measured value signal of the binocular vision system, and transmit the measured value signal to the logic operation module for calculation.

在本实施例中，逻辑运算模块包括人眼关系逻辑运算模块和TCP标定逻辑运算模块，人眼关系逻辑运算模块通过机器人运动学和空间坐标变换来确定双目视觉系统坐标系{C}相对于机器人末端坐标系{E}的变换矩阵

Figure GDA0003077444840000121
Figure GDA0003077444840000122
为机器人手眼关系；TCP标定逻辑运算模块通过求得的机器人手眼关系
Figure GDA0003077444840000123
来完成作业工具5末端TCP的标定。In this embodiment, the logic operation module includes a human-eye relationship logic operation module and a TCP calibration logic operation module, and the human-eye relationship logic operation module determines, through robot kinematics and spatial coordinate transformation, relative to the binocular vision system coordinate system {C} relative to Transformation matrix of robot end coordinate system {E}
Figure GDA0003077444840000121
Figure GDA0003077444840000122
is the robot hand-eye relationship; the robot hand-eye relationship obtained by the TCP calibration logic operation module
Figure GDA0003077444840000123
To complete the calibration of the TCP at the end of the work tool 5.

在本实施例中，还包括控制装置，机器人1、逻辑运算模块、数据采集模块、机器人1和双目视觉系统均与控制装置连接。控制模块用于驱动各个操作步骤中机器人的运动、数据采集模块的启动，双目视觉系统测量以及逻辑运算模块的运算等装置的操作。In this embodiment, a control device is also included, and the robot 1 , the logic operation module, the data acquisition module, the robot 1 and the binocular vision system are all connected to the control device. The control module is used to drive the motion of the robot in each operation step, the startup of the data acquisition module, the measurement of the binocular vision system, and the operation of the logic operation module.

在本实施例中，确定机器人手眼关系

Figure GDA0003077444840000124
流程如下：In this embodiment, the robot hand-eye relationship is determined
Figure GDA0003077444840000124
The process is as follows:

(S1)在双目视觉系统上建立双目视觉系统坐标系{C}；在机器人末端6建立机器人末端坐标系{E}，确定双目视觉系统坐标系{C}相对于机器人末端坐标系{E}的变换矩阵

Figure GDA0003077444840000125
Figure GDA0003077444840000126
为机器人手眼关系。(S1) Establish the binocular vision system coordinate system {C} on the binocular vision system; establish the robot end coordinate system {E} at the robot end 6, and determine the binocular vision system coordinate system {C} relative to the robot end coordinate system { The transformation matrix of E}
Figure GDA0003077444840000125
Figure GDA0003077444840000126
Hand-eye relationship for the robot.

在步骤(S1)中，具体包括如下步骤：In step (S1), it specifically includes the following steps:

(S101)建立机器人手眼关系为

Figure GDA0003077444840000127
其中，RC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的旋转矩阵且为定值；TC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的平移向量且为定值；在其他实施例中，双目视觉系统坐标系{C}是以双目视觉系统中的一个摄像机2建立的。(S101) The robot hand-eye relationship is established as
Figure GDA0003077444840000127
Among them, RC is the rotation matrix of the transformation between the robot end coordinate system {E} and the binocular vision system coordinate system { C } and is a fixed value; T C is the robot end coordinate system {E} and the binocular vision system coordinate system {C } The transformed translation vector is a fixed value; in other embodiments, the binocular vision system coordinate system {C} is established with a camera 2 in the binocular vision system.

(S102)在工作平台上设置第一圆形靶点P，第一圆形靶点为固定点，机器人末端6姿态保持不变，机器人1做线性运动，机器人末端6依次运动到多个位置并对第一圆形靶点P进行测量；在本实施例中，第一圆形靶点P在工作平台上是固定不动的，控制机器人进行变位姿运动，双目视觉系统坐标系{C}也是变化的，不同位置上的双目视觉系统坐标系{C}是不同的，进而第一圆形靶点P 的坐标值也是不同的。(S102) A first circular target point P is set on the working platform, the first circular target point is a fixed point, the posture of the robot end 6 remains unchanged, the robot 1 performs linear motion, and the robot end 6 moves to multiple positions in sequence and Measure the first circular target point P; in this embodiment, the first circular target point P is fixed on the working platform, and the robot is controlled to perform position-changing motion, and the coordinate system of the binocular vision system {C } is also changed, the coordinate system {C} of the binocular vision system at different positions is different, and the coordinate value of the first circular target point P is also different.

(S103)依次控制机器人1做变位姿运动到多个位置并在双目视觉系统坐标系{C}下对第一圆形靶点P进行测量；在本实施例中，机器人1的姿态和位置都会发生变化。(S103) Controlling the robot 1 to move to a plurality of positions in sequence and to measure the first circular target point P in the binocular vision system coordinate system {C}; in this embodiment, the posture of the robot 1 and the The location will change.

(S104)将步骤(S102)和步骤(S103)对第一圆形靶点P的测量值通过机器人运动学和空间坐标变换的关系计算得出RC和TC，即标定出机器人手眼关系

Figure GDA0003077444840000131
(S104) Calculate the measured value of the first circular target point P in steps (S102) and (S103) through the relationship between robot kinematics and spatial coordinate transformation to obtain R C and T C , that is, the robot hand-eye relationship is calibrated
Figure GDA0003077444840000131

在本实施例中，人眼关系逻辑运算模块中的机器人运动学和空间坐标变换逻辑运算包括：In this embodiment, the robot kinematics and spatial coordinate transformation logic operations in the human-eye relationship logic operation module include:

(B1)建立机器人末端坐标系{E}相对于机器人基坐标{B}的变换矩阵

Figure GDA0003077444840000132
其中，R为机器人基坐标{B}和机器人末端坐标系{E}转换的旋转矩阵，由于机器人1做线性运动过程中，机器人末端6姿态是保持不变的，即R 不变，R为定值；T为机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量；(B1) Establish the transformation matrix of the robot end coordinate system {E} relative to the robot base coordinate {B}
Figure GDA0003077444840000132
Among them, R is the rotation matrix of the transformation between the robot base coordinate {B} and the robot end coordinate system {E}. Since the robot end 6 is in the process of linear motion, the attitude of the robot end 6 remains unchanged, that is, R is unchanged, and R is a fixed value; T is the translation vector transformed between the robot base coordinate {B} and the robot end coordinate system {E};

由坐标转换公式可得：It can be obtained from the coordinate conversion formula:

Figure GDA0003077444840000133
Figure GDA0003077444840000133

展开得到：Expand to get:

Figure GDA0003077444840000134
Figure GDA0003077444840000134

Pc的坐标值可由双目视觉系统测量得到；The coordinate value of P c can be measured by the binocular vision system;

其中，Pc为第一圆形靶点P在双目视觉系统坐标系{C}下的坐标；Wherein, P c is the coordinate of the first circular target point P in the binocular vision system coordinate system {C};

Pb为第一圆形靶点P在机器人基坐标{B}下的坐标，Pb为定值；P b is the coordinate of the first circular target point P under the robot base coordinate {B}, and P b is a fixed value;

Figure GDA0003077444840000141
和
Figure GDA0003077444840000142
分别为Pc和Pb转换的转置矩阵；
Figure GDA0003077444840000141
and
Figure GDA0003077444840000142
are the transposed matrices of P c and P b transformations, respectively;

(B2)由于在步骤(S102)中，机器人末端6姿态保持不变，机器人末端6 依次运动到多个位置，选取两个位置，在双目视觉系统坐标系{C}下得到第一圆形靶点P的测量值

Figure GDA0003077444840000143
和
Figure GDA0003077444840000144
分别代入公式(a1)，可以建立以下方程：(B2) Since the posture of the robot end 6 remains unchanged in step (S102), the robot end 6 moves to multiple positions in turn, selects two positions, and obtains the first circle in the binocular vision system coordinate system {C} Measured value of target point P
Figure GDA0003077444840000143
and
Figure GDA0003077444840000144
Substituting into formula (a1) respectively, the following equations can be established:

Figure GDA0003077444840000145
Figure GDA0003077444840000145

两式相减可得：Subtract the two formulas to get:

Figure GDA0003077444840000146
Figure GDA0003077444840000146

因为R为正交矩阵，上式可变为：Because R is an orthogonal matrix, the above formula can be changed to:

Figure GDA00030774448400001411
Figure GDA00030774448400001411

依次进行四次测量第一圆形靶点P在双目视觉系统坐标系{C}下不同的位置参数，得到第一圆形靶点P的测量值

Figure GDA0003077444840000147
和
Figure GDA0003077444840000148
并代公式(a2)中，可得：Measure the different position parameters of the first circular target point P in the binocular vision system coordinate system {C} four times in turn, and obtain the measured value of the first circular target point P
Figure GDA0003077444840000147
and
Figure GDA0003077444840000148
Substituting into formula (a2), we can get:

Figure GDA0003077444840000149
Figure GDA0003077444840000149

即RcA＝b；That is, R c A = b;

可得出，

Figure GDA00030774448400001410
It can be concluded that,
Figure GDA00030774448400001410

b＝RT[T1-T2 T2-T3 T3-T4]；b=RT [ T 1 -T 2 T 2 -T 3 T 3 -T 4 ];

利用矩阵奇异值分解求解可得RC。R C can be obtained by solving the matrix singular value decomposition.

(B3)由于在步骤(S103)中，第一圆形靶点(P)在双目视觉系统坐标系 {C}下的坐标值随着机器人做变位姿运动变化而变化，选取两个移动位置，得到第一圆形靶点P的测量值

Figure GDA0003077444840000151
和
Figure GDA0003077444840000152
建立以下方程：(B3) Since in step (S103), the coordinate value of the first circular target point (P) in the binocular vision system coordinate system {C} changes with the change of the robot's pose-changing motion, select two moving position to obtain the measured value of the first circular target point P
Figure GDA0003077444840000151
and
Figure GDA0003077444840000152
Build the following equations:

Figure GDA0003077444840000153
Figure GDA0003077444840000153

两式相减，可得：Subtracting the two equations, we get:

Figure GDA0003077444840000154
Figure GDA0003077444840000154

Figure GDA0003077444840000155
的值可以由双目视觉系统测得，将上述已经求得的RC代入式中，求得TC，标定出手眼关系
Figure GDA0003077444840000156
Figure GDA0003077444840000155
The value of can be measured by the binocular vision system. Substitute the obtained RC into the formula to obtain TC, and calibrate the hand - eye relationship.
Figure GDA0003077444840000156

在本实施例中，作业工具5末端的TCP标定的流程包括：In this embodiment, the TCP calibration process at the end of the working tool 5 includes:

将平面镜3放置在工作平台上，将第二圆形靶点Pa粘贴于机器人末端6的作业工具5末端处，控制机器人1将第二圆形靶点Pa设置于平面镜3上方，保持机器人末端6垂直于平面镜3。Place the plane mirror 3 on the working platform, paste the second circular target point Pa on the end of the working tool 5 of the robot end 6, control the robot 1 to set the second circular target point Pa above the plane mirror 3, keep the robot The end 6 is perpendicular to the plane mirror 3 .

在本实施例中，TCP标定逻辑运算模块的逻辑运算包括：In this embodiment, the logic operation of the TCP calibration logic operation module includes:

作业工具5末端上的第二圆形靶点Pa在平面镜3里的点为投影点P'a，通过双目视觉系统测得投影点P'a在双目视觉系统坐标系{C}中的值，通过

Figure GDA0003077444840000157
可求得投影点P'a在机器人末端坐标系{E}的值(x',y',z')；然后根据平面镜3的镜面对称计算出第二圆形靶点Pa在机器人末端坐标系{E}下的值，完成TCP的标定。The point of the second circular target point P a on the end of the working tool 5 in the plane mirror 3 is the projection point P' a , and the projection point P' a measured by the binocular vision system is in the binocular vision system coordinate system {C} value, through
Figure GDA0003077444840000157
The value (x', y', z') of the projection point P' a in the coordinate system {E} of the robot end can be obtained; then the coordinates of the second circular target point P a at the end of the robot are calculated according to the mirror symmetry of the plane mirror 3 Set the value under {E} to complete the TCP calibration.

在本实施例中，在TCP标定逻辑运算模块的逻辑运算的过程中，然后根据所述平面镜3的镜面对称计算出第二圆形靶点Pa在机器人末端坐标系{E}下的值，具体步骤包括：In this embodiment, in the process of the logical operation of the TCP calibration logic operation module, the value of the second circular target point Pa in the robot end coordinate system {E} is then calculated according to the mirror plane symmetry of the plane mirror 3, Specific steps include:

假设第二圆形靶点Pa在机器人末端坐标系{E}的值为(x,y,z)；由垂直关系可得x＝x'，y＝y'；在工作平台上选取对称点Pm，先求得对称点Pm在机器人末端坐标系{E}下的Z轴坐标值zm，根据对称性可得z＝z'-2×(z'-zm)，最后求得第二圆形靶点Pa在机器人末端坐标系{E}下的值，完成TCP的标定。在某些实施例中，对称点Pm设置在第一圆形靶点P处，对称点Pm即为第一圆形靶点P,在其他实施例中，对称点Pm也可以是在工作平台上第一圆形靶点P之外的点。Assume that the value of the second circular target point P a in the coordinate system {E} of the robot end is (x, y, z); from the vertical relationship, x=x', y=y'; select a symmetrical point on the working platform P m , first obtain the Z-axis coordinate value z m of the symmetrical point P m in the robot end coordinate system {E}, according to the symmetry, z=z'-2×(z'-z m ) can be obtained, and finally obtain The value of the second circular target point Pa in the robot end coordinate system {E} completes the calibration of the TCP. In some embodiments, the symmetric point P m is set at the first circular target point P, and the symmetric point P m is the first circular target point P. In other embodiments, the symmetric point P m can also be at Points other than the first circular target point P on the working platform.

本发明的基于垂直反射的机器人TCP标定方法及系统，是一种以手眼关系为基础，基于垂直反射的TCP标定方法及系统。通过求得机器人末端坐标系{E} 和摄像机坐标系{C}之间的坐标转换关系

Figure GDA0003077444840000161
实现TCP的快速准确标定。如图1 所示，设机器人基坐标系为{B}，机器人末端坐标系为{E}，双目视觉系统坐标系为{C}，摄像机视觉范围内水平平台上固定第一圆形靶点P，其在坐标系{C} 下的坐标为Pc，在基坐标系{B}下的坐标为Pb，且Pb为定值。
Figure GDA0003077444840000162
为机器人末端坐标系{E}和基坐标系{B}之间的转换关系；
Figure GDA0003077444840000163
为双目视觉系统坐标系{C}和机器人末端坐标系{E}之间的转换关系，即手眼关系。控制机器人携带摄像机对点P进行多次变化测量，利用固定点约束，即可确定出
Figure GDA0003077444840000164
将平面镜放置于平台之上，并将圆形靶点粘贴于作业工具5末端，然后控制机器人作线性运动至镜面上方 (保持机器人末端6垂直于镜面)，由双目视觉系统可测得投影点Pa'在双目视觉系统坐标系{C}的值，由
Figure GDA0003077444840000165
可求得点Pa'在机器人末端坐标系{E}的值(x',y',z')。根据对称性关系可计算出Pa在机器人末端坐标系{E}下的值，完成TCP标定。The vertical reflection-based robot TCP calibration method and system of the present invention is a vertical reflection-based TCP calibration method and system based on the hand-eye relationship. By obtaining the coordinate transformation relationship between the robot end coordinate system {E} and the camera coordinate system {C}
Figure GDA0003077444840000161
Realize fast and accurate calibration of TCP. As shown in Figure 1, the robot base coordinate system is {B}, the robot end coordinate system is {E}, the binocular vision system coordinate system is {C}, and the first circular target is fixed on the horizontal platform within the visual range of the camera. P, its coordinate under the coordinate system {C} is P c , the coordinate under the base coordinate system {B} is P b , and P b is a fixed value.
Figure GDA0003077444840000162
is the transformation relationship between the robot end coordinate system {E} and the base coordinate system {B};
Figure GDA0003077444840000163
is the conversion relationship between the binocular vision system coordinate system {C} and the robot end coordinate system {E}, that is, the hand-eye relationship. Control the robot to carry the camera to measure the point P multiple times, and use the fixed point constraint to determine the
Figure GDA0003077444840000164
Place the plane mirror on the platform, paste the circular target on the end of the working tool 5, and then control the robot to move linearly above the mirror surface (keep the robot end 6 perpendicular to the mirror surface), and the projection point can be measured by the binocular vision system The value of P a ' in the binocular vision system coordinate system {C}, given by
Figure GDA0003077444840000165
The value (x', y', z') of the point P a ' in the coordinate system {E} of the robot end can be obtained. According to the symmetry relationship, the value of Pa in the robot end coordinate system {E} can be calculated to complete the TCP calibration.

本发明的基于垂直反射的机器人TCP标定方法及系统，无需额外的辅助标定设备，仅需要一面镜子，成本低廉，操作方便；仅需要控制机器人做四次运动即可完成TCP标定，实现了快速精确标定,可满足实际工业生产中机器人末端工具参数的标定需求；本方法区别于接触式标定方法，无碰撞风险，安全系数高。The robot TCP calibration method and system based on vertical reflection of the present invention does not require additional auxiliary calibration equipment, only needs a mirror, has low cost, and is convenient to operate; it only needs to control the robot to perform four movements to complete the TCP calibration, and realizes fast and accurate. Calibration can meet the calibration requirements of robot end tool parameters in actual industrial production; this method is different from the contact calibration method, has no collision risk, and has a high safety factor.

以上详细描述了本发明的较佳具体实施例。应当理解，本领域的普通技术人员无需创造性劳动就可以根据本发明的构思作出诸多修改和变化。因此，凡本技术领域中技术人员依本发明的构思在现有技术的基础上通过逻辑分析、推理或者有限的实验可以得到的技术方案，皆应在由权利要求书所确定的保护范围内。The preferred embodiments of the present invention have been described above in detail. It should be understood that those skilled in the art can make many modifications and changes according to the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art through logical analysis, reasoning or limited experiments on the basis of the prior art according to the concept of the present invention shall fall within the protection scope determined by the claims.

Claims (6)

1.一种基于垂直反射的机器人TCP标定系统，其特征是：包括机器人(1)、平面镜(3)和双目视觉系统，所述双目视觉系统包括两台摄像机(2)，两台所述摄像机(2)分别设置在所述机器人末端(6)两侧，所述平面镜(3)设置在所述双目视觉系统的摄像范围内，还包括逻辑运算模块和数据采集模块，所述数据采集模块设置在所述逻辑运算模块和双目视觉系统之间，所述数据采集模块用于采集双目视觉系统测量的测量值，所述数据采集模块将采集到的数据传送给所述逻辑运算模块，所述逻辑运算模块包括人眼关系逻辑运算模块和TCP标定逻辑运算模块，所述人眼关系逻辑运算模块通过机器人运动学和空间坐标变换来确定双目视觉系统坐标系{C}相对于机器人末端坐标系{E}的变换矩阵
Figure FDA0003077444830000011
为机器人手眼关系；所述TCP标定逻辑运算模块通过求得的机器人手眼关系
Figure FDA0003077444830000012
来完成作业工具(5)末端TCP的标定；确定所述机器人手眼关系
Figure FDA0003077444830000013
流程如下：1. a robot TCP calibration system based on vertical reflection, is characterized in that: comprise robot (1), plane mirror (3) and binocular vision system, and described binocular vision system comprises two cameras (2), two The cameras (2) are respectively arranged on both sides of the robot end (6), the plane mirrors (3) are arranged in the camera range of the binocular vision system, and also include a logic operation module and a data acquisition module, the data The acquisition module is arranged between the logic operation module and the binocular vision system, the data acquisition module is used to collect the measurement values measured by the binocular vision system, and the data acquisition module transmits the collected data to the logic operation Module, the logic operation module includes a human-eye relationship logic operation module and a TCP calibration logic operation module, and the human-eye relationship logic operation module determines that the binocular vision system coordinate system {C} is relative to the coordinate system of the binocular vision system through robot kinematics and spatial coordinate transformation. Transformation matrix of robot end coordinate system {E}
Figure FDA0003077444830000011
is the robot hand-eye relationship; the robot hand-eye relationship obtained by the TCP calibration logic operation module
Figure FDA0003077444830000012
to complete the calibration of the TCP at the end of the work tool (5); determine the hand-eye relationship of the robot
Figure FDA0003077444830000013
The process is as follows: (S101)建立机器人手眼关系为
Figure FDA0003077444830000014
其中，RC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的旋转矩阵且为定值；TC为机器人末端坐标系{E}和双目视觉系统坐标系{C}转换的平移向量且为定值；(S101) The robot hand-eye relationship is established as
Figure FDA0003077444830000014
Among them, RC is the rotation matrix of the transformation between the robot end coordinate system {E} and the binocular vision system coordinate system { C } and is a fixed value; T C is the robot end coordinate system {E} and the binocular vision system coordinate system {C } Converted translation vector and is a fixed value; (S102)在工作平台上设置第一圆形靶点(P)，第一圆形靶点为固定点，所述机器人末端(6)姿态保持不变，所述机器人(1)做线性运动，所述机器人末端(6)依次运动到多个位置并对所述第一圆形靶点(P)进行测量；(S102) a first circular target point (P) is set on the working platform, the first circular target point is a fixed point, the posture of the robot end (6) remains unchanged, and the robot (1) performs linear motion, The robot end (6) moves to multiple positions in sequence and measures the first circular target point (P); (S103)依次控制所述机器人(1)做变位姿运动到多个位置并在双目视觉系统坐标系{C}下对所述第一圆形靶点P进行测量；(S103) sequentially controlling the robot (1) to move to a plurality of positions with variable poses and measure the first circular target point P under the binocular vision system coordinate system {C}; (S104)将步骤(S102)和步骤(S103)对所述第一圆形靶点(P)的测量值通过机器人运动学和空间坐标变换的关系计算得出RC和TC，即标定出机器人手眼关系
Figure FDA0003077444830000021
(S104) Calculate the measured values of the first circular target point (P) in steps (S102) and (S103) through the relationship between robot kinematics and spatial coordinate transformation to obtain R C and T C , that is, to calibrate Robot hand-eye relationship
Figure FDA0003077444830000021
 2.如权利要求1所述的基于垂直反射的机器人TCP标定系统，其特征是：两台所述摄像机(2)通过连接支架(4)固定在作业工具(5)上，两台所述摄像机(2)分别固定设置在所述连接支架(4)的两端。2. The robot TCP calibration system based on vertical reflection as claimed in claim 1, wherein the two cameras (2) are fixed on the working tool (5) through the connecting bracket (4), and the two cameras are fixed on the working tool (5). (2) are respectively fixed on both ends of the connecting bracket (4). 3.如权利要求1所述的基于垂直反射的机器人TCP标定系统，其特征是：所述人眼关系逻辑运算模块中的机器人运动学和空间坐标变换逻辑运算包括：3. the robot TCP calibration system based on vertical reflection as claimed in claim 1, is characterized in that: the robot kinematics in described human eye relation logic operation module and space coordinate transformation logic operation comprise: (B1)建立机器人末端坐标系{E}相对于机器人基坐标{B}的变换矩阵
Figure FDA0003077444830000022
其中，R为机器人基坐标{B}和机器人末端坐标系{E}转换的旋转矩阵，由于所述机器人(1)做线性运动过程中，机器人末端(6)姿态是保持不变的，即R不变，R为定值；T为机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量；(B1) Establish the transformation matrix of the robot end coordinate system {E} relative to the robot base coordinate {B}
Figure FDA0003077444830000022
Among them, R is the rotation matrix of the transformation between the robot base coordinate {B} and the robot end coordinate system {E}. Since the robot (1) performs linear motion, the robot end (6) posture remains unchanged, that is, R unchanged, R is a fixed value; T is the translation vector converted from the robot base coordinate {B} and the robot end coordinate system {E}; 由坐标转换公式可得：It can be obtained from the coordinate conversion formula:
Figure FDA0003077444830000023
Figure FDA0003077444830000023
 展开得到：Expand to get:
Figure FDA0003077444830000024
Figure FDA0003077444830000024
 Pc的坐标值可由双目视觉系统测量得到；The coordinate value of P c can be measured by the binocular vision system; 其中，Pc为所述第一圆形靶点P在双目视觉系统坐标系{C}下的坐标；Wherein, P c is the coordinate of the first circular target point P in the binocular vision system coordinate system {C}; Pb为所述第一圆形靶点P在机器人基坐标{B}下的坐标，Pb为定值；P b is the coordinate of the first circular target point P under the robot base coordinate {B}, and P b is a fixed value;
Figure FDA0003077444830000031
和
Figure FDA0003077444830000032
分别为Pc和Pb转换的转置矩阵；
Figure FDA0003077444830000031
and
Figure FDA0003077444830000032
are the transposed matrices of P c and P b transformations, respectively; (B2)由于在步骤(S102)中，所述机器人末端(6)姿态保持不变，所述机器人末端(6)依次运动到多个位置，选取两个位置，在双目视觉系统坐标系{C}下得到第一圆形靶点(P)的测量值
Figure FDA0003077444830000033
和
Figure FDA0003077444830000034
分别代入公式(a1)，可以建立以下方程：(B2) Since in step (S102), the posture of the robot end (6) remains unchanged, the robot end (6) moves to a plurality of positions in sequence, selects two positions, and is in the binocular vision system coordinate system { C} to obtain the measured value of the first circular target point (P)
Figure FDA0003077444830000033
and
Figure FDA0003077444830000034
Substituting into formula (a1) respectively, the following equations can be established:
Figure FDA0003077444830000035
Figure FDA0003077444830000035
 两式相减可得：Subtract the two formulas to get:
Figure FDA0003077444830000036
Figure FDA0003077444830000036
 因为R为正交矩阵，上式可变为：Because R is an orthogonal matrix, the above formula can be changed to:
Figure FDA0003077444830000037
Figure FDA0003077444830000037
 依次进行四次测量所述第一圆形靶点(P)在双目视觉系统坐标系{C}下不同的位置参数，得到第一圆形靶点(P)的测量值
Figure FDA0003077444830000038
和
Figure FDA0003077444830000039
并代公式(a2)中，可得：Measure the different position parameters of the first circular target point (P) in the binocular vision system coordinate system {C} four times in turn to obtain the measured value of the first circular target point (P).
Figure FDA0003077444830000038
and
Figure FDA0003077444830000039
Substituting into formula (a2), we can get:
Figure FDA00030774448300000310
Figure FDA00030774448300000310
 即RcA＝b；That is, R c A = b; 可得出，
Figure FDA00030774448300000311
It can be concluded that,
Figure FDA00030774448300000311
 b＝RT[T1-T2 T2-T3 T3-T4]；b=RT [ T 1 -T 2 T 2 -T 3 T 3 -T 4 ]; 利用矩阵奇异值分解求解可得RC；R C can be obtained by solving the matrix singular value decomposition; 其中，
Figure FDA00030774448300000312
和
Figure FDA00030774448300000313
分别为第一圆形靶点(P)在双目视觉系统坐标系{C}下的坐标；
Figure FDA00030774448300000314
和
Figure FDA00030774448300000315
分别为
Figure FDA00030774448300000316
和
Figure FDA00030774448300000317
的转置矩阵；in,
Figure FDA00030774448300000312
and
Figure FDA00030774448300000313
are the coordinates of the first circular target point (P) in the binocular vision system coordinate system {C};
Figure FDA00030774448300000314
and
Figure FDA00030774448300000315
respectively
Figure FDA00030774448300000316
and
Figure FDA00030774448300000317
The transposed matrix of ; T1、T2、T3和T4分别为所述机器人(1)运动时不同位置下机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量；T 1 , T 2 , T 3 and T 4 are respectively translation vectors converted from the robot base coordinate {B} and the robot end coordinate system {E} at different positions when the robot (1) moves; (B3)由于在步骤(S103)中，所述第一圆形靶点(P)在双目视觉系统坐标系{C}下的坐标值随着机器人做变位姿运动变化而变化，选取两个移动位置，得到第一圆形靶点(P)的测量值
Figure FDA0003077444830000041
和
Figure FDA0003077444830000042
建立以下方程：(B3) Since in step (S103), the coordinate value of the first circular target point (P) in the binocular vision system coordinate system {C} changes with the change of the robot's pose-changing motion, select two Move the position to get the measured value of the first circular target point (P)
Figure FDA0003077444830000041
and
Figure FDA0003077444830000042
Build the following equations:
Figure FDA0003077444830000043
Figure FDA0003077444830000043
 两式相减，可得：Subtracting the two equations, we get:
Figure FDA0003077444830000044
Figure FDA0003077444830000044
Figure FDA0003077444830000045
的值可以由双目视觉系统测得，将上述已经求得的RC代入式中，求得TC，标定出手眼关系
Figure FDA0003077444830000046
Figure FDA0003077444830000045
The value of can be measured by the binocular vision system. Substitute the obtained RC into the formula to obtain TC, and calibrate the hand - eye relationship.
Figure FDA0003077444830000046
 其中，R11和R22分别为所述机器人变位姿运动时不同位置下机器人基坐标{B}和机器人末端坐标系{E}转换的旋转矩阵；Wherein, R 11 and R 22 are respectively the rotation matrices converted from the robot base coordinate {B} and the robot end coordinate system {E} at different positions when the robot moves in a variable pose; T11和T22分别为所述机器人变位姿运动时不同位置下机器人基坐标{B}和机器人末端坐标系{E}转换的平移向量； T11 and T22 are respectively the translation vectors converted from the robot base coordinate {B} and the robot end coordinate system {E} under different positions when the robot moves in a variable pose;
Figure FDA0003077444830000047
和
Figure FDA0003077444830000048
分别为第一圆形靶点(P)在双目视觉系统坐标系{C}下的坐标；
Figure FDA0003077444830000049
和
Figure FDA00030774448300000410
分别为
Figure FDA00030774448300000411
和
Figure FDA00030774448300000412
的转置矩阵。
Figure FDA0003077444830000047
and
Figure FDA0003077444830000048
are the coordinates of the first circular target point (P) in the binocular vision system coordinate system {C};
Figure FDA0003077444830000049
and
Figure FDA00030774448300000410
respectively
Figure FDA00030774448300000411
and
Figure FDA00030774448300000412
The transposed matrix of . 4.如权利要求1所述的基于垂直反射的机器人TCP标定系统，其特征是：作业工具(5)末端的TCP标定的流程包括：4. the robot TCP calibration system based on vertical reflection as claimed in claim 1, is characterized in that: the flow process of the TCP calibration of the end of working tool (5) comprises: 将平面镜(3)放置在工作平台上，将第二圆形靶点(Pa)粘贴于所述机器人末端(6)的作业工具(5)末端处，控制所述机器人(1)将所述第二圆形靶点(Pa)设置于所述平面镜(3)上方，保持机器人末端(6)垂直于所述平面镜(3)。The plane mirror (3) is placed on the working platform, the second circular target point (P a ) is pasted at the end of the working tool (5) of the robot end (6), and the robot (1) is controlled to place the The second circular target point (P a ) is arranged above the plane mirror (3), keeping the robot end (6) perpendicular to the plane mirror (3). 5.如权利要求4所述的基于垂直反射的机器人TCP标定系统，其特征是：5. the robot TCP calibration system based on vertical reflection as claimed in claim 4 is characterized in that: 所述TCP标定逻辑运算模块的逻辑运算包括：The logic operation of the TCP calibration logic operation module includes: 所述作业工具(5)末端上的第二圆形靶点(Pa)在所述平面镜(3)里的点为投影点(P'a)，通过双目视觉系统测得投影点(P'a)在双目视觉系统坐标系{C}中的值，通过
Figure FDA0003077444830000051
可求得投影点(P'a)在机器人末端坐标系{E}的值(x',y',z')；假设第二圆形靶点(Pa)在机器人末端坐标系{E}的值为(x,y,z)；由垂直关系可得x＝x'，y＝y'；在所述工作平台上选取对称点(Pm)，先求得对称点(Pm)在机器人末端坐标系{E}下的Z轴坐标值zm，根据对称性可得z＝z'-2×(z'-zm)，最后求得第二圆形靶点(Pa)在机器人末端坐标系{E}下的值，完成TCP的标定。The point of the second circular target point (P a ) on the end of the working tool (5) in the plane mirror (3) is the projection point (P' a ), and the projection point (P' a ) is measured by the binocular vision system ' a ) The value in the binocular vision system coordinate system {C}, via
Figure FDA0003077444830000051
The value (x', y', z') of the projection point (P' a ) in the robot end coordinate system {E} can be obtained; it is assumed that the second circular target point (P a ) is in the robot end coordinate system {E} The value of is (x, y, z); x=x', y=y' can be obtained from the vertical relationship; select the symmetrical point (P m ) on the working platform, first obtain the symmetrical point (P m ) at The Z-axis coordinate value z m in the robot end coordinate system {E}, according to the symmetry, z=z'-2×(z'-z m ) can be obtained, and finally the second circular target point (P a ) is obtained at The value in the coordinate system {E} of the robot end to complete the calibration of the TCP. 6.如权利要求1至5任一所述的基于垂直反射的机器人TCP标定系统，其特征是：还包括控制装置，所述机器人(1)、所述逻辑运算模块、所述数据采集模块和所述双目视觉系统均与所述控制装置连接。6. The robot TCP calibration system based on vertical reflection according to any one of claims 1 to 5, characterized in that: further comprising a control device, the robot (1), the logic operation module, the data acquisition module and The binocular vision systems are all connected with the control device.
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