A System Decomposition-Based Error Modeling and Calibration Method for 3-P(RR-RRR)SR Parallel Mechanisms

Abstract

This invention relates to the field of parallel robot technology, and in particular to a system decomposition-based error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism. The method decomposes the mechanism into three branch subsystems and a moving platform subsystem, establishing closed-loop vector equations for the branches and the moving platform respectively. A first error mapping model is established based on the differential method to map the branch structural parameter errors to the ball joint position errors. A second error mapping model is established to map the ball joint position errors to the moving platform pose errors. The first and second error mapping models are fused to construct an overall error mapping model. Actual pose data is collected using a laser tracker. Structural parameter errors are identified based on the deviation between the actual and theoretical poses. Kinematic model parameters are compensated, and calibration results are verified. This invention aims to significantly improve the accuracy and efficiency of error parameter identification, effectively enhancing the positioning accuracy and operational reliability of parallel robots in precision machining, assembly, and other scenarios.

Description

Technical Field

[0001] This invention relates to the field of parallel robot technology, specifically to a system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism. Background Technology

[0002] The motion and positioning accuracy of parallel robots are crucial performance indicators. Among the main factors affecting the accuracy of parallel robots, nearly 95% of them can have their position and orientation errors reduced through calibration techniques. Currently, the positioning accuracy of parallel robots on the market only reaches the millimeter level. Therefore, it is necessary to improve the motion and positioning accuracy of the robotic arm's end effector through kinematic calibration and error compensation techniques to expand its application areas. In recent years, with the explosive growth of parallel robotic arms in automated production lines and the continuous advancement of the "machine replacement project" in China, the importance of kinematic calibration and error compensation for parallel robots has become increasingly prominent. Error modeling is the foundation of kinematic calibration. For kinematically redundant parallel mechanisms, accurate error modeling and efficient calibration methods are particularly crucial. Currently, the main overall error modeling calibration methods suffer from low computational efficiency and complex identification matrices. Therefore, a new technical solution is needed to improve these technical problems. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to provide a system decomposition-based error modeling and calibration method for 3-P(RR-RRR)SR parallel mechanisms.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a system decomposition-based error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism, the steps of which are as follows: S1. System Decomposition and Sub-model Establishment: The parallel mechanism is cut off at the ball joints of each branch, decomposing it into three branch subsystems and one moving platform subsystem; a first error mapping model is established for each branch subsystem, and a second error mapping model is established for the moving platform subsystem; the first error mapping model represents the mapping relationship between the structural parameter error of each branch and the position error of its corresponding ball joint center, and the second error mapping model represents the mapping relationship between the position error of all ball joint centers and the pose error of the moving platform end; S2. Construction of the overall error model: Substitute the first error mapping model of each branch subsystem established in step S1 into the second error mapping model of the moving platform subsystem to obtain the overall error mapping model of the parallel mechanism. This overall error mapping model represents the mapping relationship between all structural parameter errors and the end pose error of the moving platform. S3. Data Measurement and Acquisition: Control the end of the parallel mechanism to move along a preset trajectory, use a laser tracker to measure and record the actual spatial pose of the end during the movement, and record the joint drive value corresponding to each movement point. S4. Error Parameter Identification and Compensation: Based on the actual spatial pose and joint drive values ​​collected in step S3, the end-effector pose error is calculated; the end-effector pose error is substituted into the overall error mapping model constructed in step S2 to identify the actual structural parameter error of the parallel mechanism; the identified structural parameter error is used to compensate and correct the theoretical kinematic model of the parallel mechanism.

[0005] In some embodiments, step S1, establishing the first error mapping model for each branch subsystem, specifically involves: For each branch, a closed-loop vector equation is established from the fixed platform to the center of the ball joint at the end of the branch; the total differential of the closed-loop vector equation is used to derive the linear mapping relationship between the structural parameter error vector of the branch and the position error vector of its ball joint, which is the first error mapping model.

[0006] In some embodiments, step S1, establishing the second error mapping model of the moving platform subsystem, specifically involves: Establish a closed-loop vector equation from the three ball joint centers to the center of the moving platform; perform total differential on the closed-loop vector equation to derive the linear mapping relationship between the position error vectors of the three ball joint centers and the pose error vector of the moving platform center, which is the second error mapping model.

[0007] In some embodiments, in step S2, the overall error mapping model is constructed in the following manner: The structural parameter error vectors of each branch are used as sub-blocks and combined to form the total structural parameter error vector of the parallel mechanism. The Jacobian matrix of the first error mapping model of each branch is used as a sub-matrix and arranged and combined in the order of the branches to form a mapping matrix from the total structural parameter error to the total error of all ball joint positions. Substituting this mapping matrix into the second error mapping model, we obtain the overall error mapping model from the total structural parameter error vector to the pose error vector of the moving platform end.

[0008] In some embodiments, in step S3, the preset trajectory is a spiral trajectory located within the workspace of the parallel mechanism.

[0009] In some embodiments, a step of constructing a global base coordinate system is included before step S3: Targets are installed on the three sliding joints of the parallel mechanism, and each sliding joint is driven to move along its joint axis. The position of the target is measured using a laser tracker, and the joint axes of the three sliding joints are fitted. An inscribed circle is drawn for the three joint axes. The center of the circle is taken as the origin, the perpendicular direction from the origin to the joint axis of the first branch sliding joint is taken as the X-axis, and the normal direction of the plane containing the three joint axes is taken as the Z-axis. The Y-axis is determined according to the right-hand rule, thereby establishing the global base coordinate system.

[0010] In some embodiments, the actual spatial pose is obtained in step S3 as follows: At least three targets are installed at a specific position at the center of the moving platform. A laser tracker is used to measure the spatial coordinates of each target in the global base coordinate system. The actual position and attitude of the end of the moving platform are calculated through data processing.

[0011] In some embodiments, the end-effector pose error is calculated in step S4 as follows: Substitute the joint drive values ​​recorded in step S3 into the theoretical forward kinematics model of the parallel mechanism to calculate the theoretical spatial pose of the end effector; subtract the actual spatial pose from the theoretical spatial pose to obtain the end effector pose error.

[0012] In some embodiments, step S4, which involves compensating and correcting the theoretical kinematic model using the identified structural parameter errors, specifically includes: The nominal structural parameter values ​​in the theoretical model are added to the identified structural parameter error values ​​to obtain the corrected actual structural parameter values, which are then used to update the kinematic model.

[0013] In some embodiments, a verification step is included after step S4: The parallel mechanism is controlled to move again using the compensated and corrected kinematic model. Steps S3 and S4 are repeated. The accuracy of parameter identification and the effectiveness of compensation are verified by comparing the end pose error before and after the iteration.

[0014] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention utilizes an innovative "subsystem decomposition" method to break down the 3-P(RR-RRR)SR parallel mechanism into a branch subsystem and a moving platform subsystem for system decomposition modeling, overcoming the limitations of traditional overall calibration methods for multi-link mechanisms. This method significantly reduces the computational dimensionality through modular modeling. As the robot's degrees of freedom increase, the computational complexity only increases linearly rather than exponentially as in overall modeling, thus improving the computational efficiency of the calibration process.

[0015] 2. The system decomposition error modeling system of this invention achieves accurate mapping between end-effector errors and joint parameters. It integrates regularized least squares algorithm and system iterative optimization strategy. By introducing adaptive regularization coefficients, it improves the error parameter identification accuracy of the 3-P(RR-RRR)SR parallel mechanism and effectively solves the overfitting problem in high-dimensional parameter identification. After kinematic parameter identification, it ensures that the 3-P(RR-RRRR)SR parallel mechanism can maintain a better high-precision standard during operation.

[0016] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. The embodiments of this application will provide a detailed description and understanding of the application. Attached Figure Description

[0017] Figure 1 A physical diagram of the 3-P[RR-RRR]SR parallel mechanism; Figure 2 A simplified diagram of the closed-loop link of the i-th branch of the 3-P[RR-RRR]SR parallel mechanism; Figure 3 Top view of the initial state of the moving and stationary platforms; Figure 4 Diagram showing the relationship between the 3-P[RR-RRR]SR parallel mechanism subsystem and the overall system; Figure 5 This is the overall flowchart for calibrating the error parameters of the 3-P[RR-RRR]SR parallel mechanism based on a laser tracker in this implementation case. Detailed Implementation

[0018] 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.

[0019] This invention establishes a geometric error model by decomposing the parallel mechanism into a branch subsystem and a moving platform subsystem, resulting in a new algorithm for calibrating error parameters of a 3-P(RR-RRR)SR parallel robot based on a laser tracker. This algorithm aims to significantly improve the accuracy and efficiency of error parameter identification, and effectively enhance the positioning accuracy and operational reliability of parallel robots in precision machining, assembly, and other scenarios.

[0020] This invention employs a high-precision laser tracker to measure the pose error in the workspace of a parallel mechanism caused by various factors such as its own structural errors and measurement errors. This error is then mapped onto a decomposed parallel mechanism error model to obtain its true structural parameters, thereby compensating for the kinematic model. The robot is then controlled based on the new kinematic model, thereby reducing the motion error of the robot's end effector.

[0021] A system decomposition-based error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism includes the following steps: 1) Based on the existing 3-P(RR-RRR)SR parallel robot model, such as Figure 1 As shown, the kinematics of the three sub-chains to the three ball joints are first derived using the closed-loop vector method. Then, the differential method is used to establish error mapping models that map the structural errors of the three sub-chains to the position errors of the three ball joints. Next, closed-loop vector equations are established from the three ball joints to the center of the moving platform, deriving the error mapping models from the position errors of the three ball joints to the position errors of the moving platform center. Finally, the error mapping models of the three sub-chains are added to the established parallel structure error model from the ball joints to the center of the moving platform, thus obtaining the system decomposition error parameter calibration model of the 3-P(RR-RRR)SR parallel mechanism.

[0022] 2) Determine a spiral trajectory within the robot's workspace, with a spiral radius of r and a pitch of h. After verifying the feasibility of the trajectory through a robot simulation model, conduct a calibration experiment.

[0023] 3) Write a motion control program for the robot based on the given robot motion trajectory in the robot control software. Use the written program to drive the robot to perform helical motion. Verify the correctness of the robot's kinematic model by comparing the consistency between the actual motion trajectory and the ideal motion trajectory.

[0024] 4) To build Figure 3 The coordinate system of the 3-P(RR-RRR)SR parallel mechanism consists of three target ball seats placed on three prismatic joints. Each branch P joint is moved along the joint axis of the P joint, and the position of the target ball placed on it is measured with a laser tracker. The three joint axes of the P joints are fitted in the software. The center of the inscribed circle of these three joint axes is the origin of the coordinate system. The perpendicular line from the origin to the joint axis of the first branch P joint is taken as the x-axis, and the upward direction of the normal to the plane containing the three joint axes of the P joints is taken as the z-axis. The y-axis is then determined according to the right-hand rule, thus constructing a global coordinate system.

[0025] 5) To build Figure 3The moving coordinate system of the 3-P(RR-RRR)SR parallel mechanism is used. Three target ball seats are installed at a specific position in the center of the moving platform of the parallel mechanism. The robot is started and the pre-programmed program is executed, so that the end effector moves along the spiral trajectory. The joint drive value corresponding to each movement point of the robot end is read when the robot end moves in the spiral and the motion state of the robot end is monitored in real time. The spatial position of the three target balls at the end of the trajectory under the base coordinate system is recorded by a laser tracker.

[0026] 6) Read the experimental data in MATLAB software, process the data, and obtain the actual spatial pose of the robot's end effector. Then, based on the established robot forward kinematics model, substitute the driving values ​​corresponding to the actual trajectory to calculate the theoretical spatial pose of the robot's end effector in the experiment.

[0027] 7) Based on step 6), in MATLAB, the difference between the actual spatial pose and the theoretical spatial pose is calculated according to the established error mapping model to obtain the end-effector pose error. This error is then substituted into the error mapping model to identify the actual structural parameter error of the robot. Subsequently, the identified structural parameter error is added to the structural parameters in the theoretical model to compensate for the robot's motion error. The corrected model is then substituted into the experiment, and the above steps are repeated to verify the accuracy and effectiveness of the identified parameters.

[0028] In step 2), the set spiral trajectory is based on the z-axis of the base coordinate system. The spiral radius and pitch are determined according to the robot's workspace, thereby realizing the robot's movement in space.

[0029] In step 5), the continuous motion of the robot in space is discretized, that is, it needs to be stationary and stable during the motion so that the laser tracker can measure the position when the robot is stable.

[0030] The error modeling involved in this invention has the following characteristics: This invention addresses the complex structure of the 3-P[RR-RRR]SR parallel mechanism, which contains numerous links within its branches, making traditional kinematic modeling methods cumbersome and computationally intensive. Therefore, traditional error modeling methods are not suitable for this type of mechanism. For parallel mechanisms with complex branches, a "subsystem decomposition" method is employed. This method cuts off the mechanism at the ball joints of each branch, dividing the entire mechanism into three branch subsystems and one moving platform subsystem. Each subsystem is modeled separately, thus obtaining a mapping model from the end-effector pose error to the overall structural error of the parallel mechanism.

[0031] The specific implementation process of the above timely solution is as follows: (1) Derivation of the error mapping model for the three branches: First, the kinematics of the three branches of the parallel mechanism are derived, such as... Figure 2 As shown, the closed-loop vector equations of the branch-loop link are established. The branch-loop link describes the values ​​of each drive joint. , , With the ball joint position vector The mapping relationship between them.

[0032] Depend on Figure 2 The first in The closed-loop link of each branch can be obtained as the following closed-loop vector equation: In the formula, the ball joint position vector , each component , and Representing the center of the ball joint Along the Cartesian coordinate system Projections on each axis. Other link vectors. , and They are represented as follows: To solve for the driving values ​​of each branch drive joint , , Regarding the position vector of the ball joint The parsing expression is defined with the following intermediate variable relationships: In the formula, , and As an intermediate variable, To bypass Shaft rotation Rotation matrix of angle.

[0033] Based on the above closed-loop vector equation, the mapping relationship between the position error of the ball joint in the parallel mechanism and the parameter error of the branch structure is derived using the differential method. The mapping relationship between branches 1, 2, and 3 on the fixed platform and the three ball joints can be obtained by taking the total differential of both sides of the closed-loop vector equation, as shown below: Simplifying the above relationships, we obtain the mapping relationship between the geometric parameter errors of the three subchains and the positional errors of the three ball joints: ① Mapping relationship from branch 1 to ball joint 1: This yields the mapping relationship between the position error of the first ball joint and the structural parameter error of the first sub-chain: In the formula: This represents the positional error of the first ball joint. =[ , , , , ] T For the structural parameter error of the first branch, , = .

[0034] ② The mapping relationship from branch 2 to ball joint 2: This yields the mapping relationship between the position error of the second ball joint and the structural parameter error of the second sub-chain: In the formula: This represents the positional error of the second ball joint. =[ , , , , ] T For the structural parameter error of the second branch, , = .

[0035] ③ Mapping relationship from branch 3 to hinge 3: This yields the mapping relationship between the position error of the third ball joint and the structural parameter error of the third sub-chain: In the formula: For the positional error of the third ball joint, =[ , , , , ] T For the structural parameter error of the first branch, , = .

[0036] (2) Derivation of the error mapping model of the moving platform.

[0037] Depend on Figure 2 The closed-loop link of the moving platform can be obtained as follows: the closed-loop vector equation describes the ball joint position vector of each branch. With dynamic platform generalized variables ( Mapping relationship between ) The mapping relationship between the pose error and the closed-loop structural parameter error from the three hinges to the center of the moving platform is derived using the differential method as follows: Simplifying the above formulas, we obtain the error mapping model from the hinge to the center of the moving platform: The mapping relationship between the hinge-to-moving platform center pose error and the geometric parameter error can be obtained as follows: In the formula: =[ , , , , , , , , ] T The pose error of the moving platform center; =[ , , , , , , , , , , , ] T The structural parameter error between the ball joint and the moving platform; ; ; = .

[0038] (3) Overall error modeling and simulation.

[0039] By adding the error mapping models of the three branches to the error mapping model from the ball joint to the end of the moving platform, the mapping relationship between the pose error of the moving platform end of the 3-P[RR-RRR]SR parallel mechanism and the overall structural parameter error of the mechanism can be obtained: In the formula: express A matrix of 1-3 columns; express A 4-6 column matrix; express A matrix of 7-9 columns; express A 10-12 column matrix; .

[0040] (4) Based on the established overall error model, a tool end error model also needs to be established. Firstly, due to the position of the tool end point The relationship between the pose and the position of the moving platform is: in Represents the rotation matrix of the moving coordinate system relative to the fixed coordinate system; Represents the rotation matrix of the end relative to the X-axis of the fixed coordinate system; This represents the rotation matrix of the end relative to the Y-axis of the fixed coordinate system; The rotation matrix representing the end point relative to the Z-axis of the fixed coordinate system; the tool end point The actual position vector in the fixed coordinate system is Coordinates of the center of the moving platform ; This indicates the theoretical dimensions of the cutting tool.

[0041] Based on the relationship between the position of the end effector platform and the tool, and applying a first-order linear perturbation to both sides, the following is obtained: in For the position error of the moving platform; This refers to the error in the position of the tool tip. This refers to the tool end-effector posture error. This refers to the error term of the tool end point in the moving coordinate system.

[0042] Further analysis reveals: in (This is essentially solving for the angular velocity of the moving platform rotating around its center of mass), based on the mapping relationship between the antisymmetric matrix of the angular velocity and the rotation matrix. The antisymmetric matrix of the angular velocity of the moving platform can be obtained: Furthermore, the angular velocity of the moving platform can be obtained as: so At this point, the parallel terminal error mapping model can be derived, where... Thus, the mapping relationship between structural parameter errors and end-position errors is obtained, as shown below: in The Jacobian matrix represents the mapping between positional error and structural error. express The first three rows of the matrix, express The 7th to 9th rows of the matrix, This indicates the overall structural error of the parallel robot, including tooling error.

[0043] Thus, the mapping relationship between structural parameter errors and tool end-effector pose errors is obtained, as shown below: in =[ , , , , , , , , ,] T , express The first to sixth rows of the matrix, The Jacobian matrix represents the mapping between the tool end pose error and the structural error.

[0044] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0045] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A system decomposition-based error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism, characterized in that: The steps are as follows: S1. System Decomposition and Sub-model Establishment: The parallel mechanism is cut off at the ball joints of each branch, decomposing it into three branch subsystems and one moving platform subsystem; a first error mapping model is established for each branch subsystem, and a second error mapping model is established for the moving platform subsystem; the first error mapping model represents the mapping relationship between the structural parameter error of each branch and the position error of its corresponding ball joint center, and the second error mapping model represents the mapping relationship between the position error of all ball joint centers and the pose error of the moving platform end; S2. Construction of the overall error model: Substitute the first error mapping model of each branch subsystem established in step S1 into the second error mapping model of the moving platform subsystem to obtain the overall error mapping model of the parallel mechanism. This overall error mapping model represents the mapping relationship between all structural parameter errors and the end pose error of the moving platform. S3. Data Measurement and Acquisition: Control the end of the parallel mechanism to move along a preset trajectory, use a laser tracker to measure and record the actual spatial pose of the end during the movement, and record the joint drive value corresponding to each movement point. S4. Error Parameter Identification and Compensation: Based on the actual spatial pose and joint drive values ​​collected in step S3, the end-effector pose error is calculated; the end-effector pose error is substituted into the overall error mapping model constructed in step S2 to identify the actual structural parameter error of the parallel mechanism; the identified structural parameter error is used to compensate and correct the theoretical kinematic model of the parallel mechanism.

2. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: In step S1, the establishment of the first error mapping model for each branch subsystem is specifically as follows: For each branch, a closed-loop vector equation is established from the fixed platform to the center of the ball joint at the end of the branch; the total differential of the closed-loop vector equation is used to derive the linear mapping relationship between the structural parameter error vector of the branch and the position error vector of its ball joint, which is the first error mapping model.

3. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 2, characterized in that: In step S1, the establishment of the second error mapping model for the moving platform subsystem is specifically as follows: Establish a closed-loop vector equation from the three ball joint centers to the center of the moving platform; perform total differential on the closed-loop vector equation to derive the linear mapping relationship between the position error vectors of the three ball joint centers and the pose error vector of the moving platform center, which is the second error mapping model.

4. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: In step S2, the overall error mapping model is constructed in the following way: The structural parameter error vectors of each branch are used as sub-blocks and combined to form the total structural parameter error vector of the parallel mechanism. The Jacobian matrix of the first error mapping model of each branch is used as a sub-matrix and arranged and combined in the order of the branches to form a mapping matrix from the total structural parameter error to the total error of all ball joint positions. Substituting this mapping matrix into the second error mapping model, we obtain the overall error mapping model from the total structural parameter error vector to the pose error vector of the moving platform end.

5. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: In step S3, the preset trajectory is a spiral trajectory located within the workspace of the parallel mechanism.

6. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: Before step S3, the process also includes the step of constructing a global base coordinate system: Targets are installed on the three sliding joints of the parallel mechanism, and each sliding joint is driven to move along its joint axis. The position of the target is measured using a laser tracker, and the joint axes of the three sliding joints are fitted. An inscribed circle is drawn for the three joint axes. The center of the circle is taken as the origin, the perpendicular direction from the origin to the joint axis of the first branch sliding joint is taken as the X-axis, and the normal direction of the plane containing the three joint axes is taken as the Z-axis. The Y-axis is determined according to the right-hand rule, thereby establishing the global base coordinate system.

7. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: In step S3, the actual spatial pose is obtained as follows: At least three targets are installed at a specific position at the center of the moving platform. A laser tracker is used to measure the spatial coordinates of each target in the global base coordinate system. The actual position and attitude of the end of the moving platform are calculated through data processing.

8. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: In step S4, the end-effector pose error is calculated as follows: Substitute the joint drive values ​​recorded in step S3 into the theoretical forward kinematics model of the parallel mechanism to calculate the theoretical spatial pose of the end effector; subtract the actual spatial pose from the theoretical spatial pose to obtain the end effector pose error.

9. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: In step S4, the compensation and correction of the theoretical kinematic model using the identified structural parameter errors specifically involves: The nominal structural parameter values ​​in the theoretical model are added to the identified structural parameter error values ​​to obtain the corrected actual structural parameter values, which are then used to update the kinematic model.

10. The system decomposition error modeling and calibration method for a 3-P(RR-RRR)SR parallel mechanism according to claim 1, characterized in that: Step S4 is followed by a verification step: The parallel mechanism is controlled to move again using the compensated and corrected kinematic model. Steps S3 and S4 are repeated. The accuracy of parameter identification and the effectiveness of compensation are verified by comparing the end pose error before and after the iteration.

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