Six-axis industrial robot kinematics calibration method based on sub-space identification

Abstract

The invention discloses a six-axis industrial robot kinematics calibration method based on sub-space identification, and belongs to the field of robot kinematics calibration. The robot is controlled to carry out three-axis linkage and six-axis linkage and move according to the planned four S-shaped paths and one planar circular path, and the error of the robot at the end effector is obtained through measurement of a QC20-W ball rod instrument. And a sub-space identification method is provided to identify and obtain a robot kinematics error parameter, and the error is compensated to a robot kinematics model, so that kinematics calibration of the six-axis industrial robot is realized. And after calibration, the precision is better than that of a whole six-axis linkage compensation method, and a new method is provided for kinematics calibration of the six-axis industrial robot.

Description

Technical Field

[0001] The invention relates to the field of robot kinematics calibration, and in particular to a six-axis industrial robot kinematics calibration method based on space identification. Technical Background

[0002] Industrial robots have been widely used in many fields such as automobiles, electronics, video, chemicals, logistics, etc. due to their advantages of high repeatability, good reliability and good applicability. With the expansion and deepening of robot applications, industrial robots have begun to enter some high-precision manufacturing fields, such as aircraft manufacturing, laser cutting, flexible grinding, etc. These fields have put forward new technical requirements for robots such as high precision and high efficiency. Industrial robots generally have a high repeatability positioning accuracy, which can generally reach ±0.1mm. Some robots such as ABB-IRB120 and KUKA-ARC5 have a repeatability positioning accuracy of ±0.01mm, but the absolute positioning accuracy is still not high. However, the positioning accuracy when executing the work program depends on the absolute positioning accuracy of the robot. As the application field of industrial robots continues to develop towards high precision, higher requirements are put forward for their absolute positioning accuracy. Therefore, robot precision compensation technology has become particularly important.

[0003] The core of robot precision compensation technology is robot error calibration. In recent years, a lot of research has been done on robot error calibration. After in-depth research by researchers at home and abroad, relatively remarkable results have been achieved in robot kinematic calibration. However, in the field of sub-space identification methods, there is a lack of explanation on how to divide the robot workspace and the problem of complicated experimental process. Moreover, the robot error measurement method mostly uses laser trackers as measuring instruments. These measuring instruments are usually expensive, cumbersome to operate, require high operators, and the installation of measuring equipment is complicated. The ballbar can quickly, conveniently and economically measure and evaluate the robot accuracy, but the designed paths are generally circular paths on the horizontal plane of the experimental platform. Therefore, it is very important to invent a six-axis industrial robot calibration method with simpler operation and better calibration effect. Summary of the invention

[0004] The purpose of the present invention is to propose a kinematic calibration method for a six-axis industrial robot based on space identification. The robot is controlled to perform three-axis linkage and six-axis linkage and move according to the planned four "S"-shaped paths and one planar circular path, and the error of the robot at the end effector is measured by the QC20-W ballbar. The space identification method is proposed to identify the robot kinematic error parameters, and the error is compensated to the robot kinematic model, and finally the kinematic calibration of the robot is completed. The specific method steps are as follows:

[0005] Step 1: Establish a suitable six-axis industrial robot link coordinate system, establish the robot's kinematic model based on the DH model, and establish a differential error model that can reflect the robot's end positioning error.

[0006] Step 2: Install the mobile tool cup and fixed tool cup of the QC20-W ballbar on the robot end and the robot experimental platform respectively through the magnetic base. The ballbar body is mounted on the tool cup through magnetism, and the ballbar is used to detect the robot accuracy.

[0007] Step 3: Based on the measured change in the length of the ballbar, the robot's error in each direction of X, Y, and Z can be obtained. A robot sub-space identification method is proposed to identify the robot's kinematic error parameters, which are substituted into the original DH model to obtain a DH model that is closer to reality.

[0008] Step 4: The kinematic error parameters of the robot are obtained through ballbar measurement experiments, and the Newton-Raphson compensation method is used to compensate the robot errors. The joint angles corresponding to the points on the motion trajectory are recalculated based on the compensated kinematic model to complete the robot compensation work.

[0009] Step 5: Use MATLAB to recalculate the trajectory points after compensation using the Newton-Raphson compensation method, then use RobotStudio to replan the robot's compensated path and import it into the robot's teach pendant. Then follow the above steps to install the ballbar and perform a compensation experiment on the compensated DH model.

[0010] In step 1, according to the ABB IRB120 robot structure model, the connecting rod coordinate system is established, the robot kinematic model is established according to the DH model, and the differential error model that can reflect the robot end positioning error is established, including the following steps:

[0011] Step 1.1: First, establish the robot kinematic model under ideal conditions based on the DH model. The robot has four DH parameters, including the joint angle θ i , connecting rod offset d i , connecting rod length a i 、Joint torsion angle α i Therefore, the transformation from coordinate system {i-1} to coordinate system {i} can be regarded as two translation transformations and two rotation transformations:

[0012] i-1 T i =R(θ i )T(d i )T(a i )R(α i )

[0013] Rewrite the above formula into matrix form:

[0014]

[0015] Since the axes of the second and third axes of the ABB IRB120 robot are parallel, the β parameter of the joint axis 2 needs to be introduced during the modeling process to solve the problem of parameter singularity. i Parameters are used to replace the parameter error d i , similarly, the transformation from coordinate system {i-1} to coordinate system {i} is:

[0016] i-1 T i =R(θ i )T(a i )R(α i )R(β i )

[0017] Rewrite the above formula into matrix form:

[0018]

[0019] Where s represents sin and c represents cos. By multiplying these transformation matrices, we can get the transformation matrix from the base coordinate system to the robot end coordinate system:

[0020]

[0021] Step 1.2: Due to the inevitable installation and manufacturing errors of the joint links, there are slight errors between the actual and theoretical geometric parameters of each joint link of the industrial robot. The accumulation of slight errors in the parameters of each link causes deviations in the posture of the robot end effector. The slight posture change between two adjacent links is represented by Δθ i , Δd i , Δa i , Δα i , Δβ i The actual relationship between two adjacent joints can be described by slight changes in these five kinematic parameters:

[0022]

[0023] In the formula, is the nominal matrix between two adjacent coordinate systems, d i-1 T i is the differential change caused by the kinematic parameter error. Since the error is very small, the kinematic equation can be fully differentiated to approximate the error equation, that is, the robot end position error is:

[0024]

[0025] Substitute parameter values ​​into the matrix (q i Represents θ i d i 、a i , α i , β2) can obtain the partial derivatives of the matrix transformation formula for each kinematic parameter, and then from the formula Obtain 0 The partial derivative of T6 with respect to the kinematic parameters gives the expression of the position error Δp:

[0026]

[0027] Where Δp represents the position error vector of the robot end in the X, Y, and Z directions. They correspond to the first three rows of the last column in the partial derivative matrix. J represents the Jacobian matrix that describes the influence of the joint parameter errors on the robot end position. Δu = [Δθ i Δd i Δa i Δα i Δβ i ] represents the error vector composed of the deviation of each joint parameter. So far, a differential error model that can reflect the positioning error of the robot end has been established, which can be used to identify the errors of the robot's kinematic parameters.

[0028] In step 2, the error of the six-axis industrial robot is measured by the QC20-W ballbar, including the following steps:

[0029] Step 2.1. First, find the appropriate installation position of the tool cup of the fixed end of the ballbar on the experimental platform, determine the coordinates of the trajectory center in the robot base coordinate system as (329.5, -151.92, 201.15), and use the software RobotStudio and MATLAB to complete the experimental path planning of the robot, which is divided into six-axis linkage and front three-axis linkage. When the front three-axis linkage is used, it is required that only the front three axes rotate for trajectory planning, and the rear three axes are locked. The robot motion path is based on the fixed end center as the sphere center and the four radii of the circle center. The three-axis linkage also has five paths. The spatial "S"-shaped path is more in line with the actual working conditions of industrial robots, and can obtain more measurement data to improve recognition accuracy. Each path has a value point every 3°, and a path consists of 120 measurement points. Import the programmed robot path into the teach pendant.

[0030] Step 2.2, the ballbar measurement system mainly consists of 4 parts, namely the mobile tool cup, the fixed tool cup, the ballbar body, and the ballbar detection software. Install the mobile tool cup at the end of the robot, control the robot's end effector (TCP) to move to the center of the fixed end, install the ballbar's fixed tool cup according to the TCP position at this point, then control the robot to move to the path starting position to install the ballbar body, and then connect the ballbar measurement software via Bluetooth, and you are ready.

[0031] Step 2.3: Control the robot TCP to move along the planned path and record the ballbar measurement data Δl at each measurement point i After completing the experimental measurement trajectory of the robot's six-axis linkage, the trajectory measurement of the three-axis linkage industrial robot is carried out in the same way. After completing all measurement work, stop the robot, disassemble the ballbar, and turn off the robot host.

[0032] In step 3, since the errors of the first three joints have a greater impact on the positioning accuracy of the end, the specific robot error parameter identification space can be divided into two subspaces, including the steps:

[0033] Step 3.1, subspace S1 is composed of joints 1, 2, and 3, and subspace S2 is composed of joints 4, 5, and 6. According to the sensitivity analysis of the robot joint length parameter error, the error accumulates at the end of the joint. Therefore, when only the first three axes are controlled, the joint length parameter error of the 4th to 6th axes will also affect the end positioning error, so it is necessary to set Δd i , Δa i (i=4~6) are put into the recognition space S1.

[0034] Step 3.2: Divide the error identification and compensation scheme into the following two types:

[0035] Solution A: All six axes of the robot participate in error identification and compensation (participating identification parameters Δθ i , Δd i , Δa i , Δα i , Δβ2, i=1-6);

[0036] Solution B: Spatial identification compensation (S1: Δθ i , Δd i , Δa i , Δα i , Δβ2, i = 1 to 3 and Δd i , Δa i , i = 4 to 6; S2: Δθ i , Δα i , i=4~6).

[0037] Step 3.3, the identification formula of scheme A is: Δp A =J A Δu A , where Δp A is the robot end positioning error caused by six-axis linkage, Δu A is Δθ i , Δd i , Δa i , Δα i , Δβ2, i=1~6.

[0038] The identification formula of scheme B is: Δp B1 =J B1 Δu B1 , where Δp B1 is the robot end positioning error caused by the front three-axis linkage, Δu B1 is Δθ i , Δd i , Δa i , Δα i , Δβ2, i = 1 to 3 and Δd i , Δa i , i = 4 to 6; Δp B2 =J B2 Δu B2 , where Δp B2 It is the difference between the robot end positioning error caused by the six-axis linkage and the robot end positioning error caused by the first three-axis linkage, that is, Δp B2 =Δp A -Δp B1 , Δu B2 is Δθ i , Δα i , i=4~6.

[0039] Step 3.4: Use these two identification methods to identify various error parameters respectively, and substitute them into the original DH model to obtain a DH model that is closer to the actual kinematic parameters.

[0040] In step 4, the kinematic error parameters of the robot are obtained by ballbar measurement experiment, but due to manufacturer restrictions, the DH parameters inside the robot cannot be directly changed. Therefore, the present invention adopts the Newton-Raphson compensation method, the principle of which is to use the compensated kinematic model to directly compensate the joint angle.

[0041] In step 5, the joint angles corresponding to the points on the motion trajectory are recalculated according to the kinematic model compensated by the Newton-Raphson compensation method, and the trajectory points compensated by the Newton-Raphson compensation method are recalculated again by MATLAB. Then, the compensated path of the robot is replanned by RobotStudio and imported into the robot's teach pendant. The ballbar is installed to perform compensation experiments on the compensated DH model. The specific experimental steps are the same as those before compensation. Repeat the above steps to process the ballbar data before and after compensation.

[0042] The present invention uses the DH modeling method to model the kinematics of a six-axis industrial robot and proposes a method for space identification and compensation. The "S" path measurement experiment of the ballbar effectively obtains the robot end positioning errors of the front three-axis linkage and all six-axis linkage, and establishes a geometric error model for the six-axis industrial robot based on the differential kinematics principle. The kinematic parameter errors of the six-axis industrial robot are calibrated by two identification and compensation methods, and the calibration results are compared and analyzed. After calibration by the proposed method, the robot end positioning accuracy is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of the ABB IRB120 robot structure.

[0044] Figure 2 This is a schematic diagram of the robot's link coordinate system.

[0045] Figure 3 It is a trajectory planning diagram in an embodiment of the method of the present invention.

[0046] Figure 4 This is an "S" type experimental detection path diagram in the embodiment of the method of the present invention.

[0047] Figure 5 Schematic diagram of ballbar installation in an embodiment of the method of the present invention.

[0048] Figure 6 1 is a flow chart of error compensation in an embodiment of the method of the present invention.

[0049] Figure 7 This is a comparison diagram of the calibration effects of four “S”-shaped paths in an embodiment of the method of the present invention.

[0050] Figure 8 It is a comparison diagram of the plane circle path calibration effect in the embodiment of the method of the present invention. DETAILED DESCRIPTION

[0051] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0052] Attached Figure 1The figure shows the schematic diagram of the structure of the ABB IRB120 robot. Taking the six-axis industrial robot as an example, the method of the present invention is described.

[0053] In step 1, according to the robot structure model, the connecting rod coordinate system is established as follows: Figure 2 As shown, a robot kinematic model is established based on the DH model, and a differential error model that can reflect the robot end positioning error is established, including the following steps:

[0054] Step 1.1: First, establish the robot kinematic model under ideal conditions based on the DH model. The robot has four DH parameters, including the joint angle θ i , connecting rod offset d i , connecting rod length a i 、Joint torsion angle α i Therefore, the transformation from coordinate system {i-1} to coordinate system {i} can be regarded as two translation transformations and two rotation transformations:

[0055] i-1 T i =R(θ i )T(d i )T(a i )R(α i )

[0056] Rewrite the above formula into matrix form:

[0057]

[0058] Since the axes of the second and third axes of the ABB IRB120 robot are parallel, the β parameter of the joint axis 2 needs to be introduced during the modeling process to solve the problem of parameter singularity. i Parameters are used to replace the parameter error d i , similarly, the transformation from coordinate system {i-1} to coordinate system {i} is:

[0059] i-1 T i =R(θ i )T(a i )R(α i )R(β i )

[0060] Rewrite the above formula into matrix form:

[0061]

[0062] Where s represents sin and c represents cos. By multiplying these transformation matrices, we can get the transformation matrix from the base coordinate system to the robot end coordinate system:

[0063]

[0064] Step 1.2: Due to the inevitable installation and manufacturing errors of the joint links, there are slight errors between the actual and theoretical geometric parameters of each joint link of the industrial robot. The accumulation of slight errors in the parameters of each link causes deviations in the posture of the robot end effector. The slight posture change between two adjacent links is represented by Δθ i , Δd i , Δa i , Δα i , Δβ i The actual relationship between two adjacent joints can be described by slight changes in these five kinematic parameters:

[0065]

[0066] In the formula, is the nominal matrix between two adjacent coordinate systems, d i-1 T i is the differential change caused by the kinematic parameter error. Since the error is very small, the kinematic equation can be fully differentiated to approximate the error equation, that is, the robot end position error is:

[0067]

[0068] Substitute parameter values ​​into the matrix (q i Represents θ i d i 、a i , α i , β2) can obtain the partial derivatives of the matrix transformation formula for each kinematic parameter, and then from the formula Obtain 0 The partial derivative of T6 with respect to the kinematic parameters gives the expression of the position error Δp:

[0069]

[0070] Where Δp represents the position error vector of the robot end in the X, Y, and Z directions. They correspond to the first three rows of the last column in the partial derivative matrix. J represents the Jacobian matrix that describes the influence of the joint parameter errors on the robot end position. Δu = [Δθ i Δd i Δa i Δα i Δβ i] represents the error vector composed of the deviation of each joint parameter. So far, a differential error model that can reflect the positioning error of the robot end has been established, which can be used to identify the errors of the robot's kinematic parameters.

[0071] In step 2, the error of the six-axis industrial robot is measured by the QC20-W ballbar, including the following steps:

[0072] Step 2.1. First, find a suitable installation position for the tool cup at the fixed end of the ballbar on the experimental platform, determine the coordinates of the trajectory center in the robot base coordinate system as (329.5, -151.92, 201.15), and use the software RobotStudio and MATLAB to complete the experimental path planning of the ABB IRB120 robot as follows: Figure 3 As shown, there are two types: six-axis linkage and front three-axis linkage. When the front three-axis linkage is used, only the front three axes are required to rotate for trajectory planning, and the rear three axes are locked. The robot motion path is based on the fixed end center as the sphere center and the four radii as the circle center. The four "S"-shaped paths and the flat circular path with a radius of 100 mm are the same five paths for the three-axis linkage. Figure 4 As shown in the figure, this path is more in line with the actual working conditions of industrial robots, and can obtain more measurement data to improve recognition accuracy. Each path has a value point every 3°, and a path consists of 120 measurement points. Import the programmed robot path into the teach pendant.

[0073] Step 2.2, the ballbar measurement system mainly consists of 4 parts, namely the mobile tool cup, fixed tool cup, ballbar body, and ballbar detection software. Install the mobile tool cup at the end of the robot, control the robot's end effector (TCP) to move to the center of the fixed end, install the fixed end tool cup of the ballbar according to the TCP position at this point, and then control the robot to move to the path starting position to install the ballbar body. The ballbar installation diagram is shown in the figure below. Figure 5 As shown, then connect the ballbar measurement software via Bluetooth and you are ready to go.

[0074] Step 2.3: Control the robot TCP to move along the planned path and record the ballbar measurement data Δl at each measurement point i After completing the experimental measurement trajectory of the robot's six-axis linkage, the trajectory measurement of the three-axis linkage industrial robot is carried out in the same way. After completing all measurement work, stop the robot, disassemble the ballbar, and turn off the robot host.

[0075] In step 3, since the errors of the first three joints have a greater impact on the positioning accuracy of the end, the specific robot error parameter identification space can be divided into two subspaces, including the steps:

[0076] Step 3.1, subspace S1 is composed of joints 1, 2, and 3, and subspace S2 is composed of joints 4, 5, and 6. According to the sensitivity analysis of the robot joint length parameter error, the error accumulates at the end of the joint. Therefore, when only the first three axes are controlled, the joint length parameter error of the 4th to 6th axes will also affect the end positioning error, so it is necessary to set Δd i , Δa i (i=4~6) are put into the recognition space S1.

[0077] Step 3.2: Divide the error identification and compensation scheme into the following two types:

[0078] Solution A: All six axes of the robot participate in error identification and compensation (participating identification parameters Δθ i , Δd i , Δa i , Δα i , Δβ2, i=1-6);

[0079] Solution B: Spatial identification compensation (S1: Δθ i , Δd i , Δa i , Δα i , Δβ2, i = 1 to 3 and Δd i , Δa i , i = 4 to 6; S2: Δθ i , Δα i , i=4~6).

[0080] Step 3.3, the identification formula of scheme A is: Δp A =J A Δu A , where Δp A is the robot end positioning error caused by six-axis linkage, Δu A is Δθ i , Δd i , Δa i , Δα i , Δβ2, i=1~6.

[0081] The identification formula of scheme B is: Δp B1 =J B1 Δu B1 , where Δp B1 is the robot end positioning error caused by the front three-axis linkage, Δu B1 is Δθ i , Δd i , Δa i , Δα i , Δβ2, i = 1 to 3 and Δd i , Δa i , i = 4 to 6; ΔpB2 =J B2 Δu B2 , where Δp B2 It is the difference between the robot end positioning error caused by the six-axis linkage and the robot end positioning error caused by the first three-axis linkage, that is, Δp B2 =Δp A -Δp B1 , Δu B2 is Δθ i , Δα i , i=4~6.

[0082] Step 3.4: Use these two identification methods to identify various error parameters respectively, and substitute them into the original DH model to obtain a DH model that is closer to the actual kinematic parameters.

[0083] In step 4, the kinematic error parameters of the robot are obtained by ballbar measurement experiment, but due to manufacturer restrictions, the DH parameters inside the robot cannot be directly changed. Therefore, the present invention adopts the Newton-Raphson compensation method, the principle of which is to use the compensated kinematic model to directly compensate the joint angle. The flow chart of this method is as follows: Figure 6 shown.

[0084] In step 5, the joint angles corresponding to the points on the motion trajectory are recalculated according to the kinematic model compensated by the Newton-Raphson compensation method, and the trajectory points compensated by the Newton-Raphson compensation method are recalculated again by MATLAB. Then, the compensated path of the robot is replanned by RobotStudio and imported into the robot's teach pendant. The ballbar is installed to perform compensation experiments on the compensated DH model. The specific experimental steps are the same as those before compensation. Repeat the above steps to process the ballbar data before and after compensation.

[0085] The results of the robot calibration experiment are shown in Figure 7 and Figure 8 As shown, Figure 7 (a) to (d) show the comparison of the effects after two identification and compensation methods. The average positioning error of the "S" path before robot compensation is 0.16943mm, and the average error after six-axis identification and compensation is 0.06784mm, which is reduced by 59.96%; the average error after space identification and compensation is 0.04154mm, which is reduced by 75.48%; Figure 8 The figure shows the comparison of the robot's performance on a planar circular path after two identification and compensation methods. Figure 8 It can also be seen that the robot's compensation effect on plane roundness error is better after the space identification compensation method, and the calibration results are shown in Table 1.

[0086] Table 1 Comparison of position errors before and after plane circle compensation (unit: mm)

[0087] Table 1 shows that the roundness error is reduced from 0.6347mm to 0.2805mm and 0.2143mm after six-axis calibration and space calibration, respectively. The average positioning error is reduced from 0.1646mm to 0.0683mm and 0.0360mm, respectively. The standard deviation is reduced from 0.1849mm to 0.0718mm and 0.0452mm, respectively. This shows that the space calibration method has not only better calibration effect than the six-axis calibration method, but also better stability of the compensation value.

[0088] The present invention is a kinematic calibration method for a six-axis industrial robot based on space identification. The accompanying drawings are only a preferred example, and the above embodiments are only for describing the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be covered within the protection scope of the present invention.

Claims

1. A kinematic calibration method for a six-axis industrial robot based on space identification, characterized in that: The steps include: Step 1: Establish a suitable six-axis industrial robot link coordinate system, establish the robot's kinematic model based on the DH model, and establish a differential error model that can reflect the robot's end positioning error. Step 2: Install the mobile tool cup and fixed tool cup of the QC20-W ballbar on the robot end and the robot experimental platform respectively through the magnetic base. The ballbar body is mounted on the tool cup through magnetism, and the ballbar is used to detect the robot accuracy. Step 3: Based on the measured change in ballbar length, the error of the robot in each of the X, Y, and Z directions can be obtained. A robot sub-space identification method is proposed to identify the robot kinematic error parameters, which are substituted into the original DH model to obtain a DH model that is closer to reality. Step 4: The kinematic error parameters of the robot are obtained through ballbar measurement experiments, and the Newton-Raphson compensation method is used to compensate the robot errors. The joint angles corresponding to the points on the motion trajectory are recalculated based on the compensated kinematic model to complete the robot compensation work. Step 5: Recalculate the trajectory points after compensation by the Newton-Raphson compensation method through MATLAB, then use RobotStudio to replan the compensation path and import it into the robot teaching pendant, and then install the ballbar according to the above steps to perform compensation experiments on the compensated DH model.

2. The kinematic calibration method for a six-axis industrial robot based on space identification according to claim 1 is characterized in that: In the step 1, a connecting rod coordinate system is established according to the ABB IRB120 robot structure model, a robot kinematic model is established according to the DH model, and a differential error model that can reflect the positioning error of the robot end is established, including the steps of: Step 1.1: First, establish the robot kinematic model under ideal conditions based on the DH model. The robot has four DH parameters, including the joint angle θ i , connecting rod offset d i , connecting rod length a i 、Joint torsion angle α i Therefore, the transformation from coordinate system {i-1} to coordinate system {i} can be regarded as two translations and two rotations: i-1 T i =R(θ i )T(d i )T(a i )R(α i ) Rewrite the above formula into matrix form: Since the axes of the second and third axes of the ABB IRB120 robot are parallel, the β parameter of the joint axis 2 needs to be introduced to rotate around the Y axis during the modeling process to solve the problem of parameter singularity. i Parameters are used to replace the parameter error d i , similarly, the transformation from coordinate system {i-1} to coordinate system {i} is: i-1 T i =R(θ i )T(a i )R(a i )R(β i ) Rewrite the above formula into matrix form: Where s represents sin and c represents cos. By multiplying these transformation matrices, we can get the transformation matrix from the base coordinate system to the robot end coordinate system: <h2 style=";text-align:left;direction:ltr"> 0 <h2 style=";text-align:left;direction:ltr"> T6=<h2 style=";text-align:left;direction:ltr"> 0 <h2 style=";text-align:left;direction:ltr"> T1<h2 style=";text-align:left;direction:ltr"> 1 <h2 style=";text-align:left;direction:ltr"> T2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> T3<h2 style=";text-align:left;direction:ltr"> 3 <h2 style=";text-align:left;direction:ltr"> T4<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> T5<h2 style=";text-align:left;direction:ltr"> 5 <h2 style=";text-align:left;direction:ltr"> T6 Step 1.2: Due to the inevitable installation and manufacturing errors of the joint links, there are slight errors between the actual and theoretical geometric parameters of each joint link of the industrial robot. The accumulation of slight errors in the parameters of each link causes deviations in the posture of the robot end effector. The slight posture change between two adjacent links is represented by Δθ i , Δd i , Δa i , Δα i , Δβ i The actual relationship between two adjacent joints can be described by slight changes in these five kinematic parameters: i-1 T i c = i-1 T i +d i-1 T i In the formula, i-1 T i c is the nominal matrix between two adjacent coordinate systems, d i-1 T i is the differential change caused by the kinematic parameter error. Since the error is very small, the kinematic equation can be fully differentiated to approximate the error equation, that is, the robot end position error is: Substitute parameter values ​​into the matrix (q i Represents θ i d i 、a i , α i , β2) can obtain the partial derivatives of the matrix transformation formula for each kinematic parameter, and then from the formula Obtain 0 The partial derivative of T6 with respect to the kinematic parameters gives the expression of the position error Δp: Where Δp represents the position error vector of the robot end in the X, Y, and Z directions. They correspond to the first three rows of the last column in the partial derivative matrix. J represents the Jacobian matrix that describes the influence of the joint parameter errors on the robot end position. Δu = [Δθ i Δd i Δa i Δα i Δβ i ] represents the error vector composed of the deviation of each joint parameter. So far, a differential error model that can reflect the positioning error of the robot end has been established, which can be used to identify the errors of the robot's kinematic parameters.

3. The kinematic calibration method for a six-axis industrial robot based on space identification according to claim 1 is characterized in that: In step 2, the error of the six-axis industrial robot is measured by using a QC20-W ballbar, including the steps of: Step 2.

1. First, find a suitable installation position for the tool cup of the fixed end of the ballbar on the experimental platform, determine the coordinates of the trajectory center in the robot base coordinate system as (329.5, -151.92, 201.15), and use the software RobotStudio and MATLAB to complete the experimental path planning of the robot, which is divided into six-axis linkage and front three-axis linkage. When the front three-axis linkage is used, it is required that only the front three axes rotate for trajectory planning, and the rear three axes are locked. The robot motion path is based on the fixed end center as the sphere center and the four radii of the circle center. The three-axis linkage also has five paths. The spatial "S" path is more in line with the actual working conditions of industrial robots, and can obtain more measurement data to improve recognition accuracy. Each path has a value point every 3°, and a path consists of 120 measurement points. Import the programmed robot path into the teach pendant. Step 2.2, the ballbar measurement system mainly consists of 4 parts, namely the mobile tool cup, the fixed tool cup, the ballbar body, and the ballbar detection software. Install the mobile tool cup at the end of the robot, control the robot's end effector (TCP) to move to the center of the fixed end, install the ballbar's fixed tool cup according to the TCP position at this point, then control the robot to move to the path starting position to install the ballbar body, and then connect the ballbar measurement software via Bluetooth, and you are ready. Step 2.3: Control the robot TCP to move along the planned path and record the ballbar measurement data Δl at each measurement point i After completing the experimental measurement trajectory of the robot's six-axis linkage, the trajectory measurement of the three-axis linkage industrial robot is carried out in the same way. After completing all measurement work, stop the robot, disassemble the ballbar, and turn off the robot host.

4. The kinematic calibration method for a six-axis industrial robot based on space identification according to claim 1 is characterized in that: In step 3, since the errors of the first three joints have a greater impact on the positioning accuracy of the end, the specific robot error parameter identification space can be divided into two subspaces, including the steps of: Step 3.1, subspace S1 is composed of joints 1, 2, and 3, and subspace S2 is composed of joints 4, 5, and 6. According to the sensitivity analysis of the robot joint length parameter error, the error accumulates at the end of the joint. Therefore, when only the first three axes are controlled, the joint length parameter error of the 4th to 6th axes will also affect the end positioning error, so it is necessary to set Δd i , Δa i (i=4~6) are put into the recognition space S1. Step 3.2: Divide the error identification and compensation scheme into the following two types: Solution A: All six axes of the robot participate in error identification and compensation (participating identification parameters Δθ i , Δd i , Δa i , Δα i , Δβ2, i=1-6); Solution B: Spatial Identification Compensation (S1: Δθ i , Δd i , Δa i , Δα i , Δβ2, i = 1 to 3 and Δd i , Δa i , i = 4 to 6; S2: Δθ i , Δα i , i = 4 to 6). Step 3.3, the identification formula of scheme A is: Δp A =J A Δu A , where Δp A is the robot end positioning error caused by six-axis linkage, Δu A is Δθ i , Δd i , Δa i , Δα i , Δβ2, i=1~6. The identification formula of scheme B is: Δp B1 =J B1 Δu B1 , where Δp B1 is the robot end positioning error caused by the front three-axis linkage, Δu B1 is Δθ i , Δd i , Δa i , Δα i , Δβ2, i = 1 to 3 and Δd i , Δa i , i = 4 to 6; Δp B2 =J B2 Δu B2 , where Δp B2 It is the difference between the robot end positioning error caused by the six-axis linkage and the robot end positioning error caused by the first three-axis linkage, that is, Δp B2 =Δp A -Δp B1 , Δu B2 is Δθ i , Δα i , i=4~6. Step 3.4: Use these two identification methods to identify various error parameters respectively, and substitute them into the original DH model to obtain a DH model that is closer to the actual kinematic parameters.

5. The kinematic calibration method for a six-axis industrial robot based on space identification according to claim 1 is characterized in that: In step 4, the kinematic error parameters of the robot are obtained by ballbar measurement experiment, but due to manufacturer restrictions, the DH parameters inside the robot cannot be directly changed. Therefore, the present invention adopts the Newton-Raphson compensation method, the principle of which is to use the compensated kinematic model to directly compensate the joint angle.

6. The kinematic calibration method for a six-axis industrial robot based on space identification according to claim 1 is characterized in that: In step 5, the joint angles corresponding to the points on the motion trajectory are recalculated according to the kinematic model compensated by the Newton-Raphson compensation method, and the trajectory points compensated by the Newton-Raphson compensation method are recalculated again by MATLAB. Then, the compensation path is replanned using RobotStudio, and the robot teaching pendant is imported to install the ballbar to perform a compensation experiment on the compensated DH model. The specific experimental steps are the same as the experimental steps before compensation. The above steps are repeated to process the ballbar data before and after compensation.

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