Industrial robot wrist point positioning error compensation method based on spatial similarity

Abstract

The application discloses an industrial robot wrist point positioning error compensation method based on spatial similarity, and particularly relates to the technical field of intelligent manufacturing of aviation high-end equipment. The application locks the movement of the last three axes in the sampling stage, reversely calculates the measured coordinates of the flange center to the wrist point, constructs a spatial error similarity model based on the wrist point, effectively avoids the coupling interference of the attitude errors of the last three axes, greatly improves the estimation accuracy and compensation effect of the absolute positioning error of the robot, reduces the number of sampling points, breaks the conventional idea of directly establishing a six-degree-of-freedom error model at the flange center or TCP, and creatively proposes a spatial sampling method by locking the last three axes and reversely calculating the wrist point coordinates. This processing method perfectly decouples the macro spatial position error determined by the first three axes and the nonlinear attitude error determined by the last three axes, and significantly improves the purity and generalization ability of the error similarity model.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing technology for high-end aerospace equipment, specifically relating to a method for compensating for wrist point positioning errors in industrial robots based on spatial similarity. Background Technology

[0002] Industrial robots, with their significant advantages of low cost, large workspace, and high flexibility, have been widely used in high-precision machining and assembly operations such as automated drilling, milling, and riveting in aerospace products. However, the unique open-chain, multi-link linkage structure of industrial robots is affected by a combination of geometric parameter errors, such as link length, joint offset, and torsion angle errors, as well as non-geometric errors, such as joint clearance, gear friction, and insufficient stiffness. This results in their end-effector absolute positioning accuracy typically only reaching the millimeter level, far from meeting the sub-millimeter standards required in aerospace manufacturing, such as the stringent standard of hole position accuracy within 0.50 mm.

[0003] To improve the absolute positioning accuracy of industrial robots, the industry currently mainly employs two technical approaches: error parameter calibration and error similarity compensation. Traditional kinematic parameter calibration methods require establishing complex system dynamics or kinematic equations containing multiple error sources. This is not only cumbersome and computationally intensive in parameter identification, but also highly dependent on the low-level open access of the robot control system, resulting in extremely high engineering implementation costs. In recent years, compensation methods based on error space similarity theory have gained widespread attention because they treat the robot as a black box, achieving accuracy improvements without modifying the controller's low-level parameters. The core idea of ​​this method is to select several sampling points within the robot's workspace and measure their actual positioning errors. Since the robot's positioning errors exhibit strong similarity and correlation in continuous space, the errors of unknown target points can be estimated using the errors of known sampling points, and feedforward compensation can be implemented.

[0004] However, most existing error compensation methods based on spatial similarity directly use the center point (TCP, usually the flange center or tool tip) of the robot's end effector as the object of error modeling and compensation. This conventional approach has a significant technical drawback: industrial robots are typically six-degree-of-freedom serial mechanisms, where the first three joints mainly determine the macroscopic position of the end effector in space, while the latter three joints (the wrist) mainly determine the spatial attitude of the end effector. When directly measuring the positioning error of the TCP point, this error is the final result of the superposition of the position errors of the first three axes and the attitude errors of the latter three axes through complex nonlinear coupling. When constructing the spatial error mesh, even tiny angular adjustments of the latter three axes will be amplified by the long lever arm and transformed into huge positional jumps at the TCP point. If all six joints are allowed to move simultaneously during the sampling process, the attitude error noise introduced by the latter three axes will severely affect the mapping relationship of the spatial position errors of the first three axes, resulting in poor generalization ability and low estimation accuracy of the established TCP spatial error similarity model, making it difficult to achieve stable and high-precision full-space compensation.

[0005] Therefore, how to isolate the interference of the rear three-axis attitude error on the system's spatial positioning error model, establish a more stable and accurate error similarity feedforward compensation model based on wrist points, and achieve error decoupling and targeted compensation is a key technical problem that urgently needs to be solved in the field of high-precision control of industrial robots for aviation. Summary of the Invention

[0006] The purpose of this invention is to provide a method for compensating for wrist point positioning errors in industrial robots based on spatial similarity, so as to solve the above-mentioned problems.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for compensating for wrist point positioning errors in industrial robots based on spatial similarity, the specific steps of which are as follows: S1, within the effective working space of the industrial robot, generates a preset number of sampling points based on processing requirements; S2, based on the pre-calibrated rigid transformation relationship between the flange center and the wrist point of the industrial robot and the theoretical target pose of the flange center in S1, reversely calculate the corresponding theoretical three-dimensional coordinates of the wrist point. S3, perform robot inverse kinematics calculation on each set of theoretical target poses of flange center generated in S1 to obtain theoretical joint commands containing six joint angle values. S4 performs execution error measurement. By truncating the theoretical joint commands generated by S3, the last three joints of the robot are locked in a fixed initial zero position or a preset fixed pose. Only the angle values ​​of the first three joints in the theoretical joint commands are sent to the robot controller to drive the robot to move to the measurement pose. S5. Use a laser tracker to measure the actual three-dimensional coordinates of the target ball fixed at the center of the flange or the end effector; based on the prior condition that the rear three axes are locked, use the measured actual coordinates of the target ball and the calibrated relative relationship to reverse calculate the actual three-dimensional coordinates of the wrist point of the industrial robot. S6. Calculate the difference between the theoretical three-dimensional coordinates of the wrist point obtained in S2 and the actual three-dimensional coordinates of the wrist point obtained in S5 to obtain the wrist point positioning error. Using the theoretical wrist point coordinates as the independent variable and the wrist point positioning error as the dependent variable, use the variogram function to analyze the spatial correlation of the error and construct an error estimation model based on the spatial similarity of the wrist point. S7, Error Feedforward Compensation: In the actual processing, when a new target instruction is received, the corresponding theoretical wrist point position is calculated, and the position is input into the error estimation model constructed by S6 to predict the wrist point error. The error is then compensated in reverse to the issued joint instruction or target pose, and then sent to the robot to complete the compensation. The specific process of reverse-calculating the actual three-dimensional coordinates of the industrial robot's wrist point is as follows: First, establish the base coordinate system, wrist coordinate system, and flange coordinate system in the SA software. Then, calibrate the coordinates of the target ball in the home pose (0°, 0°, 0°, 0°, 90°, 0°). The target ball position measured by SA The rotation matrix defined by Euler angles The fixed spatial position vector of the wrist point pointing to the target ball As input, calculate the measured position of the wrist point. .

[0008] The specific method for establishing various coordinate systems in SA is as follows: 1. Base coordinate system 1) Move the robot to the initial pose (home pose), that is, the joint angles of the robot are (0°, 0°, 0°, 0°, 90°, 0°), and place the target ball of the laser tracker on the target mount of the end effector; 2) Keeping the other joint axes stationary, slowly rotate the robot's A1 axis while using a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Then, use SA software to fit this series of measurement points into a circle C1 and obtain the center O1. 3) Control the robot to move back to the home pose, keep other joint axes stationary, and slowly rotate the robot's A2 axis. Using the same method as in step 2), use a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Use these measurement points to fit a circle C2 and obtain the center O2. 4) Draw a plane through the center O1, perpendicular to the normal of circle C2, and then project the center O2 onto the plane to obtain the projection point. Then, construct a plane that is perpendicular to the normal of circle C1 and passes through the projection point. By translating plane two downwards along the normal of the plane by a distance d (d=1000mm in this example, determined according to the specific robot model), the plane containing the robot's base coordinate system can be obtained. 5) Place the center O1 and the projection point respectively. Project the points onto the robot's base coordinate system plane to obtain the projection points. and The projection point O1 is taken as the origin of the base coordinate system, the normal of the base coordinate system plane is taken as the z-axis, and the x-axis of the base coordinate system is collinear with the straight line. Based on the obtained origin, x-axis and z-axis, the coordinate system is established. The robot base coordinate system is now established. 2. Wrist coordinate system 1) Move the robot to the initial pose (home pose), that is, the joint angles of the robot are (0°, 0°, 0°, 0°, 90°, 0°), and place the target ball of the laser tracker on the target mount of the end effector; 2) Keeping the other joint axes stationary, slowly rotate the robot's A5 axis while using a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Then, use SA software to fit this series of measurement points into a circle C5 and obtain the center O5. 3) Control the robot to move back to the home pose, keep other joint axes stationary, and slowly rotate the robot's A6 axis. Using the same method as in step 2), use a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Use these measurement points to fit a circle C6 and obtain the center O6. 4) Draw a plane four through the center O5, perpendicular to the normal of circle C6. Project the center O6 onto the plane four to obtain the projection point. , This is the origin of the wrist coordinate system. At the same time, the positive X-axis of the wrist coordinate system is in the same direction as the negative X-axis of the base coordinate system, the positive Z-axis of the wrist coordinate system is in the same direction as the negative Z-axis of the base coordinate system, and the Y-axis of the wrist coordinate system is determined by the right-hand rule. Thus, the wrist coordinate system is established. 3. Flange coordinate system 1) The flange coordinate system is the wrist coordinate system translated along the Z-axis of the wrist coordinate system in the SA. You can get it immediately; By setting the wrist coordinate system as the working coordinate system in SA, the fixed spatial position vector pointing from the wrist point to the target ball is extracted. , Substitute the measured 3D coordinates of the wrist point into the equation:

[0009] In the formula, The measured three-dimensional coordinates of the wrist point. The measured three-dimensional coordinates of the target sphere. Let be a rotation matrix. It is a fixed spatial position vector pointing from the wrist point to the target ball; The process of constructing the error estimation model in S6 is as follows: the measured three-dimensional coordinates of the 200 wrist points calculated in S5 are compared with the theoretical three-dimensional coordinates of the 200 wrist points calculated in S1 to calculate the positioning error of each wrist point. Kriging interpolation and other methods are used to spatially map the positioning error and then linear unbiased optimal estimation is performed to construct the positioning error compensation model. The positioning error compensation model is used to predict the error of the point to be compensated and perform feedforward compensation.

[0010] Preferably, S1 specifically involves planning sampling points within the robot's effective workspace; using Latin hypercube sampling, 200 sets of theoretical target pose data for the flange center are generated within the defined Cartesian workspace boundary. Each set of pose data contains not only spatial location information but also pose information, which can be represented as a vector: ; In the formula, The theoretical pose of the flange center is represented by X, Y, and Z, which represent the theoretical three-dimensional coordinates of the flange center in the world coordinate system; A, B, and C represent the Euler angles of rotation around a fixed axis, characterizing the theoretical pose of the flange coordinate system; these 200 sets of data constitute the benchmark sample library for subsequent error detection and model training.

[0011] Preferably, the wrist point in S2 is the spatial intersection of the fourth, fifth, and sixth joint axes of the industrial robot; the rigid transformation relationship between the flange center and the wrist point is a constant offset determined by the spatial translation vector when the latter three axes are in the locked state. S2 specifically refers to the theoretical target pose of the flange center in S1. The rotation matrix defined by Euler angles The fixed spatial position vector of the wrist point pointing to the center of the flange As input, the fixed spatial position vector pointing from the wrist point to the flange center is extracted using the link offset data from the robot's standard DH parameter table. For a standard six-DOF serial robot, this fixed spatial position vector is the offset along the Z-axis of the flange coordinate system. ,Right now , Substitute the theoretical three-dimensional coordinates of the wrist point into the equation: ; In the formula, The theoretical three-dimensional coordinates of the wrist point. For the theoretical three-dimensional coordinates of the flange center, Let be a rotation matrix. The fixed spatial vector from the wrist point to the center of the flange; In this way, all 200 sets of sampling points are solved separately to establish the corresponding theoretical position set of wrist points.

[0012] Preferably, S3 introduces a constant joint constraint state quantity to force the constraint inverse solution algorithm to find a unique closed solution within the same attitude quadrant; The analytical solution of the inverse kinematics of a six-DOF industrial robot was adopted, and the optimal path was selected by minimizing the current joint space distance. Finally, the rotation vectors of the six driven joints were solved. , denoted as: .

[0013] Preferably, during the sampling motion, it is forcibly overwritten to a fixed constant, so that it remains absolutely stationary throughout the entire sampling process; The control system only transmits the truncated commands for the first three axes. The command is sent to the robot actuator; at this time, the first, second and third axes of the robot drive the entire arm to move to the target space area, while the fourth, fifth and sixth axes follow without any relative rotation. Once the robot reaches a steady state, a securely mounted laser tracker automatically searches for and locks onto a high-precision target ball mounted at the center or end of the robot flange, measuring the target ball's actual three-dimensional coordinates in the world coordinate system. ; Because the rear three axes are locked during the movement, the rigid geometric relationship between the wrist point and the center of the target ball does not undergo any attitude change and remains a constant local vector. ; Based on the actual drop angle of the first three axes Using the robot's forward kinematics, the absolute rotation matrix of the local coordinate system of the wrist point (the end of the three front axes) in the world coordinate system is calculated. ; The specific calculation process is as follows: 1. Input Parameter and Variable Mapping: The input parameters in this derivation process are the angles of the first three independent control commands actually issued by the control system to the robot hardware driver, denoted as vectors. Based on the mapping relationship between link variables and actual joint control angles established in S3, the control angles are converted into link variables in the standard DH parameter model: Link variable one: Physical rotation angle of joint 1 ; Link variable two: Physical rotation angle of joint 2 ; Link variable three: Physical rotation angle of joint 3 ; 2. Construction of the homogeneous transformation matrix between links: Based on the standard DH parameter homogeneous transformation model, the general expression for the homogeneous transformation matrix between adjacent links is... As shown below: ; Known structural constants of industrial robots, including base height. Offset distance upper arm length and the joint variables of the current sampling point Substituting into the above equation, we can construct the homogeneous transformation matrices between adjacent links of the first three axes in turn: Transformation matrix of joint 1 relative to the base coordinate system: ; Transformation matrix of joint 2 relative to the coordinate system of joint 1: ; Transformation matrix of joint 3 relative to the coordinate system of joint 2: ; 3. Extraction of the forward kinematics of the first three axes and the absolute rotation matrix; Based on the theory of series multiplication of rigid body kinematic chains, by sequentially left-multiplying the link transformation matrices of the first three axes, a total homogeneous transformation matrix is ​​constructed from the ends of the first three arms (i.e., the local coordinate system of the wrist point) to the base coordinate system. :

[0014] The total homogeneous transformation matrix It has the following block matrix structure:

[0015] In this partitioned model, the 3x3 orthogonal submatrix at its top left corner is extracted, which outputs the absolute rotation matrix of the ends of the first three axes in the world coordinate system. : ; Subsequently, by subtracting the constant deviation vector after rotational attitude adjustment from the target ball position measured by the laser tracker, the actual three-dimensional coordinates of the wrist point were calculated.

[0016] In the formula, The measured three-dimensional coordinates of the wrist point. The actual measured three-dimensional coordinates of the target ball. This represents the absolute rotation matrix of the ends of the first three axes in the world coordinate system. It is a constant local vector between the wrist point and the center of the target ball in the post-three-axis locked state.

[0017] By iterating through 200 sets of measurement actions, 200 corresponding sets were finally collected. Data; This inversion calculation avoids the nonlinear attitude errors caused by the subsequent three-axis machining and assembly, and obtains the true position data reflecting the macroscopic spatial accuracy of the robot's main structure.

[0018] Preferably, the three-dimensional difference between the theoretical wrist point coordinates and the actual wrist point coordinates in the above 200 sets of data is calculated, which is the measured positioning error of the wrist point: ; In the formula, The actual measurement positioning error at the wrist point, The measured three-dimensional coordinates of the wrist point. The theoretical three-dimensional coordinates of the wrist point; We introduce the function of variation from statistics to quantitatively describe the similarity characteristics of errors in spatial distribution; let h be the positional segmentation of any two wrist points in space, then the experimental function of variation for wrist point errors... The calculation formula is: ; In the formula, and It is the positioning error corresponding to the two sets of joint inputs segmented by h, where N(h) represents the number of pairs of joint inputs that satisfy the segmentation amount h; since the above formula is calculated based on measured data, therefore It is called the experimental variation function; Where N(h) is the number of sample point pairs with segmentation h; by fitting the experimental variogram scatter plot, the theoretical variogram curve is obtained, and then the spatial correlation radius and sill value of the error are determined; After establishing the error correlation evaluation system, the interpolation model is constructed using the optimal linear unbiased estimation theory; For any unknown new target wrist point within the workspace The estimated compensation error is obtained by linearly weighting the sum of the errors of 200 known sampling points: ; Among them, the weight coefficient matrix The result is obtained by solving the system of equations for minimizing the unbiased variance matrix using the Lagrange multiplier method; When the offline programming software issues a new target hole position for machining, the system first calculates the theoretical flange coordinates based on the machining process and end tool properties; Then, using the same calculation method as S2, the theoretical wrist coordinates corresponding to this point are calculated. ; Will The input is fed into the spatial similarity error model that has been built and resides in memory in the S60, and the system quickly outputs the wrist point error estimation vector at that point. ; Because it belongs to a feedforward open-loop control system, the system directly performs inverse superposition correction on the original command pose at the coordinate level. Let the final corrected theoretical wrist point coordinates be... : ; Finally, using the revised By combining the target machining posture of the rear three axes again, a precise inverse kinematics calculation of all six axes is performed. The six joint commands obtained at this time include the offset components of the spatial position error of the front three axes. After the robot executes this command, the actual wrist position it reaches is pulled back to the ideal geometric position required by the process, while the rear three axes can still accurately execute the posture pointing. In the end, the entire robot system achieves an improvement in the absolute spatial positioning accuracy of the end tool center through precise control of the wrist position.

[0019] The technical effects and advantages of this invention are as follows: 1. This invention breaks away from the conventional approach of directly establishing a six-degree-of-freedom error model at the flange center or TCP, and creatively proposes to perform spatial sampling by locking the rear three axes and back-calculating the wrist point coordinates. This processing method perfectly decouples the macroscopic spatial position error determined by the front three axes from the nonlinear attitude error determined by the rear three axes, avoiding the pollution of the model caused by the fine angular error of the rear three axes under the magnification of the long arm, and significantly improving the purity and generalization ability of the error similarity model.

[0020] 2. Reduced Sampling Dimension and Computational Complexity: Traditional methods require exploring error patterns in a six-dimensional space (X, Y, Z, A, B, C), necessitating a massive number of sampling points to ensure model accuracy. This invention reduces the sampling dimension to a simple three-dimensional location space (X, Y, Z), maintaining or improving compensation accuracy while reducing the number of required sampling points, further shortening measurement time and computational load.

[0021] 3. System versatility and non-destructive intervention: The wrist point error compensation method proposed in this invention belongs to feedforward open-loop compensation control. It does not require knowledge of the extremely complex dynamic or kinematic error parameters inside the robot control system, nor does it require cracking and modifying the underlying algorithm of the controller. It only requires intercepting and modifying the issued instructions on the host computer or offline programming terminal. It has strong versatility and can be quickly deployed in industrial robot processing platforms of different models and different loads. Attached Figure Description

[0022] Figure 1 This is an overall flowchart of the industrial robot wrist point positioning error compensation method of the present invention. Figure 2 This is a topological diagram showing the rigid geometric relationship between the flange center, target ball, and wrist point of the industrial robot in the rear three-axis locked state according to the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] This invention provides a method for compensating for wrist point positioning errors in industrial robots based on spatial similarity, as shown in the figure. The specific steps are as follows: S1, within the effective working space of the industrial robot, generates a preset number of sampling points based on processing requirements; S2, based on the pre-calibrated rigid transformation relationship between the flange center and the wrist point of the industrial robot and the theoretical target pose of the flange center in S1, reversely calculate the corresponding theoretical three-dimensional coordinates of the wrist point. S3, perform robot inverse kinematics calculation on each set of theoretical target poses of flange center generated in S1 to obtain theoretical joint commands containing six joint angle values. S4 performs execution error measurement. By truncating the theoretical joint commands generated by S3, the last three joints of the robot are locked in a fixed initial zero position or a preset fixed pose. Only the angle values ​​of the first three joints in the theoretical joint commands are sent to the robot controller to drive the robot to move to the measurement pose. S5. Use a laser tracker to measure the actual three-dimensional coordinates of the target ball fixed at the center of the flange or the end effector; based on the prior condition that the rear three axes are locked, use the measured actual coordinates of the target ball and the calibrated relative relationship to reverse calculate the actual three-dimensional coordinates of the wrist point of the industrial robot. S6. Calculate the difference between the theoretical three-dimensional coordinates of the wrist point obtained in S2 and the actual three-dimensional coordinates of the wrist point obtained in S5 to obtain the wrist point positioning error. Using the theoretical wrist point coordinates as the independent variable and the wrist point positioning error as the dependent variable, use the variogram function to analyze the spatial correlation of the error and construct an error estimation model based on the spatial similarity of the wrist point. S7, Error Feedforward Compensation: In the actual processing, when a new target instruction is received, the corresponding theoretical wrist point position is calculated, and the position is input into the error estimation model constructed by S6 to predict the wrist point error. The error is then compensated in reverse to the issued joint instruction or target pose, and then sent to the robot to complete the compensation. The specific process of reverse-calculating the actual three-dimensional coordinates of the industrial robot's wrist point is as follows: First, establish the base coordinate system, wrist coordinate system, and flange coordinate system in the SA software. Then, calibrate the coordinates of the target ball in the home pose (0°, 0°, 0°, 0°, 90°, 0°). The target ball position measured by SA The rotation matrix defined by Euler angles The fixed spatial position vector of the wrist point pointing to the target ball As input, calculate the measured position of the wrist point. .

[0025] The specific method for establishing various coordinate systems in SA is as follows: 1. Base coordinate system 1) Move the robot to the initial pose (home pose), that is, the joint angles of the robot are (0°, 0°, 0°, 0°, 90°, 0°), and place the target ball of the laser tracker on the target mount of the end effector; 2) Keeping the other joint axes stationary, slowly rotate the robot's A1 axis while using a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Then, use SA software to fit this series of measurement points into a circle C1 and obtain the center O1. 3) Control the robot to move back to the home pose, keep other joint axes stationary, and slowly rotate the robot's A2 axis. Using the same method as in step 2), use a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Use these measurement points to fit a circle C2 and obtain the center O2. 4) Draw a plane through the center O1, perpendicular to the normal of circle C2, and then project the center O2 onto the plane to obtain the projection point. Then, construct a plane that is perpendicular to the normal of circle C1 and passes through the projection point. By translating plane two downwards along the normal of the plane by a distance d (d=1000mm in this example, determined according to the specific robot model), the plane containing the robot's base coordinate system can be obtained. 5) Place the center O1 and the projection point respectively. Project the points onto the robot's base coordinate system plane to obtain the projection points. and The projection point O1 is taken as the origin of the base coordinate system, the normal of the base coordinate system plane is taken as the z-axis, and the x-axis of the base coordinate system is collinear with the straight line. Based on the obtained origin, x-axis and z-axis, the coordinate system is established. The robot base coordinate system is now established.

[0026] 2. Wrist coordinate system 1) Move the robot to the initial pose (home pose), that is, the joint angles of the robot are (0°, 0°, 0°, 0°, 90°, 0°), and place the target ball of the laser tracker on the target mount of the end effector; 2) Keeping the other joint axes stationary, slowly rotate the robot's A5 axis while using a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Then, use SA software to fit this series of measurement points into a circle C5 and obtain the center O5. 3) Control the robot to move back to the home pose, keep other joint axes stationary, and slowly rotate the robot's A6 axis. Using the same method as in step 2), use a laser tracker to measure the coordinates of the target ball's center position during the movement until the light is cut off. Use these measurement points to fit a circle C6 and obtain the center O6. 4) Draw a plane four through the center O5, perpendicular to the normal of circle C6. Project the center O6 onto the plane four to obtain the projection point. , The negative X-axis of the base coordinate system is in the same direction as the base coordinate system, the positive Z-axis of the wrist coordinate system is in the same direction as the negative Z-axis of the base coordinate system, and the Y-axis of the wrist coordinate system is determined by the right-hand rule. At this point, the wrist coordinate system is established. 3. Flange coordinate system The flange coordinate system is essentially a translation of the wrist coordinate system along the Z-axis of the wrist coordinate system within the SA. You can get it immediately; By setting the wrist coordinate system as the working coordinate system in SA, the fixed spatial position vector pointing from the wrist point to the target ball is extracted. , Substitute the measured 3D coordinates of the wrist point into the equation: ;

[0027] In the formula, The measured three-dimensional coordinates of the wrist point. The measured three-dimensional coordinates of the target sphere. Let be a rotation matrix. It is a fixed spatial position vector pointing from the wrist point to the target ball; The process of constructing the error estimation model in S6 is as follows: the measured three-dimensional coordinates of the 200 wrist points calculated in S5 are compared with the theoretical three-dimensional coordinates of the 200 wrist points calculated in S1 to calculate the positioning error of each wrist point. Kriging interpolation and other methods are used to spatially map the positioning error and then linear unbiased optimal estimation is performed to construct the positioning error compensation model. The positioning error compensation model is used to predict the error of the point to be compensated and perform feedforward compensation.

[0028] Preferably, S1 specifically involves planning sampling points within the robot's effective workspace; using Latin hypercube sampling, 200 sets of theoretical target pose data for the flange center are generated within the defined Cartesian workspace boundary. Each set of pose data contains not only spatial location information but also pose information, which can be represented as a vector: ; In the formula, The theoretical pose of the flange center is represented by X, Y, and Z, which represent the theoretical three-dimensional coordinates of the flange center in the world coordinate system; A, B, and C represent the Euler angles of rotation around a fixed axis, characterizing the theoretical pose of the flange coordinate system; these 200 sets of data constitute the benchmark sample library for subsequent error detection and model training.

[0029] Preferably, the wrist point in S2 is the spatial intersection of the fourth, fifth, and sixth joint axes of the industrial robot; the rigid transformation relationship between the flange center and the wrist point is a constant offset determined by the spatial translation vector when the latter three axes are in the locked state. S2 specifically refers to the theoretical target pose of the flange center in S1. The rotation matrix defined by Euler angles The fixed spatial position vector of the wrist point pointing to the center of the flange As input, the fixed spatial position vector pointing from the wrist point to the flange center is extracted using the link offset data from the robot's standard DH parameter table. For a standard six-DOF serial robot, this fixed spatial position vector is the offset along the Z-axis of the flange coordinate system. ,Right now , Substitute the theoretical three-dimensional coordinates of the wrist point into the equation: ; In the formula, The theoretical three-dimensional coordinates of the wrist point. For the theoretical three-dimensional coordinates of the flange center, Let be a rotation matrix. The fixed spatial vector from the wrist point to the center of the flange; In this way, all 200 sets of sampling points are solved separately to establish the corresponding theoretical position set of wrist points.

[0030] Preferably, S3 introduces a constant joint constraint state quantity to force the constraint inverse solution algorithm to find a unique closed solution within the same attitude quadrant; The analytical solution of the inverse kinematics of a six-DOF industrial robot was adopted, and the optimal path was selected by minimizing the current joint space distance. Finally, the rotation vectors of the six driven joints were solved. , denoted as: .

[0031] Preferably, during the sampling motion, it is forcibly overwritten to a fixed constant, so that it remains absolutely stationary throughout the entire sampling process; The control system only transmits the truncated commands for the first three axes. The command is sent to the robot actuator; at this time, the first, second and third axes of the robot drive the entire arm to move to the target space area, while the fourth, fifth and sixth axes follow without any relative rotation. Once the robot reaches a steady state, a securely mounted laser tracker automatically searches for and locks onto a high-precision target ball mounted at the center or end of the robot flange, measuring the target ball's actual three-dimensional coordinates in the world coordinate system. ; Because the rear three axes are locked during the movement, the rigid geometric relationship between the wrist point and the center of the target ball does not undergo any attitude change and remains a constant local vector. ; Based on the actual drop angle of the first three axes Using the robot's forward kinematics, the absolute rotation matrix of the local coordinate system of the wrist point (the end of the three front axes) in the world coordinate system is calculated. ; The specific calculation process is as follows: 1. Input Parameter and Variable Mapping: The input parameters in this derivation process are the angles of the first three independent control commands actually issued by the control system to the robot hardware driver, denoted as vectors. Based on the mapping relationship between link variables and actual joint control angles established in S3, the control angles are converted into link variables in the standard DH parameter model: Link variable one: Physical rotation angle of joint 1 ; Link variable two: Physical rotation angle of joint 2 ; Link variable three: Physical rotation angle of joint 3 ; 2. Construction of the homogeneous transformation matrix between links: Based on the standard DH parameter homogeneous transformation model, the general expression for the homogeneous transformation matrix between adjacent links is... As shown below: ; Known structural constants of industrial robots, including base height. Offset distance upper arm length and the joint variables of the current sampling point Substituting into the above equation, we can construct the homogeneous transformation matrices between adjacent links of the first three axes in turn: Transformation matrix of joint 1 relative to the base coordinate system: ; Transformation matrix of joint 2 relative to the coordinate system of joint 1: ; Transformation matrix of joint 3 relative to the coordinate system of joint 2: ; 3. Extraction of the forward kinematics of the first three axes and the absolute rotation matrix; Based on the theory of series multiplication of rigid body kinematic chains, by sequentially left-multiplying the link transformation matrices of the first three axes, a total homogeneous transformation matrix is ​​constructed from the ends of the first three arms (i.e., the local coordinate system of the wrist point) to the base coordinate system. :

[0032] The total homogeneous transformation matrix It has the following block matrix structure:

[0033] In this partitioned model, the 3x3 orthogonal submatrix at its top left corner is extracted, which outputs the absolute rotation matrix of the ends of the first three axes in the world coordinate system. : ; Subsequently, by subtracting the constant deviation vector after rotational attitude adjustment from the target ball position measured by the laser tracker, the actual three-dimensional coordinates of the wrist point were calculated.

[0034] In the formula, The measured three-dimensional coordinates of the wrist point. The actual measured three-dimensional coordinates of the target ball. This represents the absolute rotation matrix of the ends of the first three axes in the world coordinate system. It is a constant local vector between the wrist point and the center of the target ball in the post-three-axis locked state.

[0035] By iterating through 200 sets of measurement actions, 200 corresponding sets were finally collected. Data; This inversion calculation avoids the nonlinear attitude errors caused by the subsequent three-axis machining and assembly, and obtains the true position data reflecting the macroscopic spatial accuracy of the robot's main structure.

[0036] Preferably, the three-dimensional difference between the theoretical wrist point coordinates and the actual wrist point coordinates in the above 200 sets of data is calculated, which is the measured positioning error of the wrist point: ; In the formula, The actual measurement positioning error at the wrist point, The measured three-dimensional coordinates of the wrist point. The theoretical three-dimensional coordinates of the wrist point; We introduce the function of variation from statistics to quantitatively describe the similarity characteristics of errors in spatial distribution; let h be the positional segmentation of any two wrist points in space, then the experimental function of variation for wrist point errors... The calculation formula is: ; In the formula, and It is the positioning error corresponding to the two sets of joint inputs segmented by h, where N(h) represents the number of pairs of joint inputs that satisfy the segmentation amount h; since the above formula is calculated based on measured data, therefore It is called the experimental variation function; Where N(h) is the number of sample point pairs with segmentation h; by fitting the experimental variogram scatter plot, the theoretical variogram curve is obtained, and then the spatial correlation radius and sill value of the error are determined; After establishing the error correlation evaluation system, the interpolation model is constructed using the optimal linear unbiased estimation theory; For any unknown new target wrist point within the workspace The estimated compensation error is obtained by linearly weighting the sum of the errors of 200 known sampling points: ; Among them, the weight coefficient matrix The result is obtained by solving the system of equations for minimizing the unbiased variance matrix using the Lagrange multiplier method; When the offline programming software issues a new target hole position for machining, the system first calculates the theoretical flange coordinates based on the machining process and end tool properties; Then, using the same calculation method as S2, the theoretical wrist coordinates corresponding to this point are calculated. ; Will The input is fed into the spatial similarity error model that has been built and resides in memory in the S60, and the system quickly outputs the wrist point error estimation vector at that point. ; Because it belongs to a feedforward open-loop control system, the system directly performs inverse superposition correction on the original command pose at the coordinate level. Let the final corrected theoretical wrist point coordinates be... : ; Finally, using the revised By combining the target machining posture of the rear three axes again, a precise inverse kinematics calculation of all six axes is performed. The six joint commands obtained at this time include the cancellation components of the spatial position error of the front three axes. After the robot executes this command, the actual wrist position it reaches is pulled back to the ideal geometric position required by the process, while the rear three axes can still accurately execute the posture pointing. In the end, the entire robot system achieves an improvement in the absolute spatial positioning accuracy of the end tool center through precise control of the wrist position. In the following description, axes A1, A2, A3, A4, A5, and A6 represent the first, second, third, fourth, fifth, and sixth axes, respectively. The detailed implementation process is shown below, specifically including: Step S10: Target point generation and theoretical calculation; To fully cover the working area of ​​the industrial robot and ensure the statistical significance of the error model, sampling points first need to be planned within the robot's effective workspace. Using Latin hypercube sampling, 200 sets of theoretical target pose data for the flange center are generated within the defined Cartesian workspace boundaries.

[0037] Each set of pose data contains not only spatial location information but also pose information, which can be represented as a vector: Where X, Y, and Z represent the theoretical three-dimensional coordinates of the flange center in the world coordinate system; A, B, and C represent the Euler angles of rotation about a fixed axis, characterizing the theoretical orientation of the flange coordinate system. These 200 sets of data constitute the benchmark sample library for subsequent error detection and model training.

[0038] Step S20: Relative pose calibration of flange center and wrist point: For a standard six-DOF serial industrial robot with a ball-shaped wrist joint, the axes of its fourth, fifth, and sixth joints typically intersect at the same point in space, which is defined as the robot's wrist point. The position of the wrist point in space is entirely determined by the motion of the first, second, and third joints, while the rotation of the fourth, fifth, and sixth joints only changes the orientation of the end flange and does not change the absolute position of the wrist point in space.

[0039] When the robot is in its mechanical zero position or any specified locked posture, there is a fixed translation vector offset between the flange center and the wrist point. Let the homogeneous transformation matrix of the flange center coordinate system relative to the wrist point coordinate system be... .

[0040] Based on the robot's standard DH parameter table or actual high-precision pre-calibration data, the fixed spatial vector from the wrist point to the flange center in the tool coordinate system can be extracted. .

[0041] Based on the geometric translation relationship, and using the known theoretical pose of the flange center in S10... Combining the rotation matrix defined by Euler angles The theoretical three-dimensional coordinates of the corresponding wrist point can be calculated by reverse spatial translation. : In this way, all 200 sets of sampling points are solved separately to establish the corresponding theoretical position set of wrist points.

[0042] Step S30: Inverse kinematics calculation and full joint command generation Based on the robot's ideal kinematics model, the theoretical target pose of each flange center generated in S10 is... Perform inverse kinematics solution.

[0043] Considering that the inverse kinematics solution of a six-degree-of-freedom robot usually has multiple closed solutions, such as left arm / right arm, wrist up / down, etc., this embodiment introduces constant joint constraint state variables and forces the constraint inverse kinematics algorithm to find a unique closed solution in the same posture quadrant.

[0044] By solving the inverse kinematics, we can obtain the six theoretical joint angle values ​​that satisfy the theoretical pose of the flange center, denoted as: These joint angles are the theoretical angle commands that each servo motor should rotate to bring the robot flange center to its theoretical pose.

[0045] Step S40, Cut-off Control and Independent Drive of the First Three Axes This step is the core of the error decoupling process in this invention. In the traditional calibration or sampling process, the control system sends all six joint angles obtained by S30 to the robot, resulting in a six-dimensional composite error at the end effector.

[0046] To eliminate interference from errors in the last three axes, this invention intercepts complete joint commands at the communication control layer. This applies regardless of the original inverse solution obtained... Why is this value, when performing sampling motion, forcibly overwritten to a fixed constant, so that it remains absolutely stationary throughout the entire sampling process?

[0047] The control system only transmits the truncated commands for the first three axes. The command is sent to the robot actuator. At this point, the robot's first, second, and third axes drive the entire arm to move to the target space area, while the fourth, fifth, and sixth axes follow without any relative rotation.

[0048] Step S50: Inverse calculation of the measured coordinates of the target ball and the wrist point. Once the robot reaches a steady state, a securely mounted laser tracker automatically searches for and locks onto a high-precision target sphere (SMR) mounted at the center or end of the robot flange, measuring the target sphere's actual three-dimensional coordinates in the world coordinate system. .

[0049] Because the rear three axes are locked during the movement, the rigid geometric relationship between the wrist point and the center of the target ball does not undergo any attitude change and remains a constant local vector. .

[0050] It's important to note that while the local vectors are constant in the wrist coordinate system, the robot's overall posture changes in the world coordinate system due to the rotation of the first three axes. Therefore, the actual downward angles of the first three axes must be used to determine the robot's orientation. The absolute rotation matrix of the forearm ends (i.e., the wrist point local coordinate system) in the world coordinate system is calculated using forward kinematics. .

[0051] Subsequently, by subtracting the constant deviation vector after rotational attitude adjustment from the target ball position measured by the laser tracker, the actual three-dimensional coordinates of the wrist point were calculated.

[0052] By iterating through 200 sets of measurement actions, 200 corresponding sets were finally collected. Data. This inversion calculation avoids the nonlinear attitude errors caused by the subsequent three-axis machining and assembly, and obtains true position data reflecting the macroscopic spatial accuracy of the robot's main structure.

[0053] Step S60: Wrist point error similarity space modeling Calculate the three-dimensional difference between the theoretical wrist point coordinates and the actual wrist point coordinates in the above 200 sets of data; this is the measured positioning error of the wrist point. Since noise from the last three axes has been eliminated, this error vector It exhibits high spatial smoothness. To model this error continuously, a function of variation from statistics is introduced to quantitatively describe the similarity characteristics of the error in its spatial distribution. Let h be the distance between any two wrist points in space, then the experimental function of variation for the wrist point error... The calculation formula is: Where N(h) is the number of sample point pairs with a segmentation amount h. By fitting the experimental variogram scatter plot, the theoretical variogram curve can be obtained, and thus the spatial correlation radius and sill value of the error can be determined.

[0054] After establishing an error correlation evaluation system, an interpolation model is constructed using the optimal linear unbiased estimation theory. For any unknown new target wrist point within the workspace... The estimated compensation error is obtained by linearly weighting the sum of the errors of 200 known sampling points: Among them, the weight coefficient matrix This method is derived by solving the system of equations for minimizing the unbiased variance matrix using the Lagrange multiplier method. Compared to simple inverse distance weighting, this method comprehensively considers the clustering effect and spatial anisotropy among sample points through the correlation covariance matrix, thus ensuring the mathematical optimality of the wrist point error estimation.

[0055] Step S70: Online error feedforward compensation When the offline programming software issues a new target hole position for machining, the system first calculates the theoretical flange coordinates based on the machining process and end tool properties.

[0056] Then, the theoretical wrist coordinates corresponding to this point are calculated using the homologous algorithm in step S20. .

[0057] Will The input is fed into the spatial similarity error model that has been built and resides in memory in the S60, and the system quickly outputs the wrist point error estimation vector at that point. .

[0058] Because it belongs to a feedforward open-loop control system, the system directly performs inverse superposition correction on the original command pose at the coordinate level. Let the final corrected theoretical wrist point coordinates be... : ; Finally, using the revised Then, combining the target machining posture of the rear three axes, a precise inverse kinematics calculation is performed across all six axes. The resulting six joint commands now include components that compensate for the spatial position errors of the front three axes. After the robot executes this command, its actual wrist position is precisely pulled back to the ideal geometric position required by the process, while the rear three axes still accurately execute the orientation. Ultimately, the entire robot system achieves improved absolute spatial positioning accuracy of the end-effector center through precise control of the wrist position.

[0059] Example: After applying this solution to real-world working conditions, it is possible to reduce the number of sampling points within a sampling space of 800mm*1200mm*900mm and improve the absolute spatial positioning accuracy in the subsequent compensation process, as shown in the table below: Table 1: Comparison of Absolute Positioning Error and Number of Sampling Points

[0060] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for compensating for wrist point positioning errors in industrial robots based on spatial similarity, characterized in that: The specific steps are as follows: S1, within the effective working space of the industrial robot, generates a preset number of sampling points based on processing requirements; S2, based on the pre-calibrated rigid transformation relationship between the flange center and the wrist point of the industrial robot and the theoretical target pose of the flange center in S1, reversely calculate the corresponding theoretical three-dimensional coordinates of the wrist point. S3, perform robot inverse kinematics calculation on each set of theoretical target poses of flange center generated in S1 to obtain theoretical joint commands containing six joint angle values. S4 performs execution error measurement. By truncating the theoretical joint commands generated by S3, the last three joints of the robot are locked in a fixed initial zero position or a preset fixed pose. Only the angle values ​​of the first three joints in the theoretical joint commands are sent to the robot controller to drive the robot to move to the measurement pose. S5. Use a laser tracker to measure the actual three-dimensional coordinates of the target ball fixed at the center of the flange or the end effector; based on the prior condition that the rear three axes are locked, use the measured actual coordinates of the target ball and the calibrated relative relationship to reverse calculate the actual three-dimensional coordinates of the wrist point of the industrial robot. S6. Calculate the difference between the theoretical three-dimensional coordinates of the wrist point obtained in S2 and the actual three-dimensional coordinates of the wrist point obtained in S5 to obtain the wrist point positioning error. Using the theoretical wrist point coordinates as the independent variable and the wrist point positioning error as the dependent variable, use the variogram function to analyze the spatial correlation of the error and construct an error estimation model based on the spatial similarity of the wrist point. S7, Error Feedforward Compensation: In the actual processing, when a new target instruction is received, the corresponding theoretical wrist point position is calculated, and the position is input into the error estimation model constructed by S6 to predict the wrist point error. The error is then used to compensate the issued joint instruction or target pose, and then sent to the robot to complete the compensation.

2. The method for compensating for wrist point positioning errors in industrial robots based on spatial similarity according to claim 1, characterized in that: Specifically, S1 involves planning sampling points within the robot's effective workspace; using Latin hypercube sampling, 200 sets of theoretical target pose data for the flange center are generated within the defined Cartesian workspace boundary. Each set of pose data contains not only spatial location information but also pose information, represented in vector form: ； In the formula, The theoretical pose of the flange center is represented by X, Y, and Z, which represent the theoretical three-dimensional coordinates of the flange center in the world coordinate system; A, B, and C represent the Euler angles of rotation about a fixed axis, which characterize the theoretical pose of the flange coordinate system. These 200 sets of data constitute the benchmark sample library for subsequent error detection and model training.

3. The method for compensating for wrist point positioning errors in industrial robots based on spatial similarity according to claim 1, characterized in that: The wrist point in S2 is the spatial intersection of the fourth, fifth, and sixth joint axes of the industrial robot; the rigid transformation relationship between the flange center and the wrist point is a constant offset determined by the spatial translation vector when the latter three axes are in the locked state. S2 specifically refers to the theoretical target pose of the flange center in S1. The rotation matrix defined by Euler angles The fixed spatial position vector of the wrist point pointing to the center of the flange As input, the fixed spatial position vector pointing from the wrist point to the flange center is extracted using the link offset data from the robot's standard DH parameter table. For a standard six-DOF serial robot, this fixed spatial position vector is the offset along the Z-axis of the flange coordinate system. ,Right now , Substitute the theoretical three-dimensional coordinates of the wrist point into the equation: ; In the formula, The theoretical three-dimensional coordinates of the wrist point. For the theoretical three-dimensional coordinates of the flange center, For rotation matrix, The fixed spatial vector from the wrist point to the center of the flange; In this way, all 200 sets of sampling points are solved separately to establish the corresponding theoretical position set of wrist points.

4. The method for compensating for wrist point positioning errors in industrial robots based on spatial similarity according to claim 1, characterized in that: The S3 introduces a constant joint constraint state quantity, and forces the constraint inverse solution algorithm to find a unique closed solution in the same attitude quadrant. The analytical solution of the inverse kinematics of a six-DOF industrial robot was adopted, and the optimal path was selected by minimizing the current joint space distance. Finally, the rotation vectors of the six driven joints were solved. , denoted as: 。 5. The method for compensating for wrist point positioning errors in industrial robots based on spatial similarity according to claim 1, characterized in that: When performing the sampling motion, it is forced to be overwritten with a fixed constant, so that it remains absolutely stationary throughout the entire sampling process; The control system only transmits the truncated commands for the first three axes. The command is sent to the robot driver; at this time, the first, second and third axes of the robot drive the entire arm to move to the target space area, while the fourth, fifth and sixth axes follow without any relative rotation.

6. The method for compensating for wrist point positioning errors in industrial robots based on spatial similarity according to claim 1, characterized in that: Once the robot reaches a steady state, a securely mounted laser tracker automatically searches for and locks onto a high-precision target ball mounted at the center or end of the robot flange, measuring the target ball's actual three-dimensional coordinates in the world coordinate system. ; Because the rear three axes are locked during the movement, the rigid geometric relationship between the wrist point and the center of the target ball does not undergo any attitude change and remains a constant local vector. ; Based on the actual drop angle of the first three axes Using the robot's forward kinematics, the absolute rotation matrix of the local coordinate system of the wrist point (the end of the three front axes) in the world coordinate system is calculated. ; Subsequently, by subtracting the constant deviation vector after rotational attitude adjustment from the target ball position measured by the laser tracker, the actual three-dimensional coordinates of the wrist point were calculated. ; In the formula, The measured three-dimensional coordinates of the wrist point. The actual measured three-dimensional coordinates of the target ball. This represents the absolute rotation matrix of the ends of the first three axes in the world coordinate system. It is a constant local vector between the wrist point and the center of the target ball in the state of triaxial locking; By iterating through 200 sets of measurement actions, 200 corresponding sets were finally collected. Data; This inversion calculation avoids the nonlinear attitude errors caused by the subsequent three-axis machining and assembly, and obtains the true position data reflecting the macroscopic spatial accuracy of the robot's main structure.

7. The method for compensating for wrist point positioning errors in industrial robots based on spatial similarity according to claim 6, characterized in that: Calculate the three-dimensional difference between the theoretical wrist point coordinates and the actual wrist point coordinates in the above 200 sets of data; this is the measured positioning error of the wrist point. ； In the formula, The actual measurement positioning error at the wrist point, The measured three-dimensional coordinates of the wrist point. The theoretical three-dimensional coordinates of the wrist point; We introduce the function of variation from statistics to quantitatively describe the similarity characteristics of errors in spatial distribution; let h be the positional segmentation between any two wrist points in space, then the experimental function of variation for wrist point errors... The calculation formula is: ； In the formula, and It is the positioning error corresponding to the two sets of joint inputs segmented by h, where N(h) represents the number of pairs of joint inputs that satisfy the segmentation amount h; since the above formula is calculated based on measured data, therefore It is called the experimental variation function; Where N(h) is the number of sample point pairs with segmentation h; by fitting the experimental variogram scatter plot, the theoretical variogram curve is obtained, and then the spatial correlation radius and sill value of the error are determined; After establishing an error correlation evaluation system, an interpolation model is constructed using the optimal linear unbiased estimation theory. For any unknown new target wrist point within the workspace The estimated compensation error is obtained by linearly weighting the sum of the errors of 200 known sampling points: ； Among them, the weight coefficient matrix This is obtained by solving the system of equations for minimizing the unbiased variance matrix using the Lagrange multiplier method.

8. The method for compensating for wrist point positioning errors in industrial robots based on spatial similarity according to claim 7, characterized in that: When the offline programming software issues a new target hole position for machining, the system first calculates the theoretical flange coordinates based on the machining process and end tool properties; Then, using the same calculation method as S2, the theoretical wrist coordinates corresponding to this point are calculated. ; Will The input is fed into the spatial similarity error model that has been built and resides in memory in the S60, and the system quickly outputs the wrist point error estimation vector at that point. ; Because it belongs to a feedforward open-loop control system, the system directly performs inverse superposition correction on the original command pose at the coordinate level; let the final corrected theoretical wrist point coordinates be... : ; Finally, using the revised By combining the target machining posture of the rear three axes again, a precise inverse kinematics calculation of all six axes is performed. The six joint commands obtained at this time include the offset components of the spatial position error of the front three axes. After the robot executes this command, the actual wrist position it reaches is pulled back to the ideal geometric position required by the process, while the rear three axes can still accurately execute the posture pointing. In the end, the entire robot system achieves an improvement in the absolute spatial positioning accuracy of the end tool center through precise control of the wrist position.

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