Step-by-step error modeling calibration method for series arm with closed-loop subchain

Abstract

The invention relates to the technical field of robot control, in particular to a step-by-step error modeling calibration method for a series arm with a closed-loop subchain, which comprises the following steps of: establishing a geometric error model of the closed-loop subchain and a series robot tail end error mapping model step by step; according to the novel error parameter calibration algorithm for the series robot with the closed-loop subchain based on the laser tracker, the high-precision laser tracker equipment is adopted, and pose errors existing in a working space caused by various factors such as self-structure errors and measurement errors of a mechanical arm are measured, so that the error parameter calibration algorithm for the series robot with the closed-loop subchain based on the laser tracker is obtained. And the error is mapped to the error model with the closed-loop subchain series arm, so that the real structural parameters of the error are obtained to compensate the kinematic model, and then the robot is controlled according to the new kinematic model, so that the kinematic error of the tail end pose of the robot is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of robot control, and specifically to a step-by-step error modeling and calibration method for a serial arm with a closed-loop sub-chain. Background Art

[0002] Robot machining has the advantages of large working space, strong flexibility, low cost, etc., and is considered a technology with great development prospects in modern manufacturing. However, the inherently low absolute positioning accuracy of serial industrial robots and the low stiffness caused by the serial structure limit the wide application of such devices in industry. The latter usually causes unwanted static and even dynamic deformation errors in robot machining. To increase the system stiffness, many robot manufacturers provide industrial robots with dedicated closed-loop sub-chains for machining applications. Although the stiffness of such industrial robots is improved, the absolute positioning accuracy of industrial robots within the working space is usually several millimeters, which cannot meet the requirements of manufacturing applications. One way to solve this problem is to improve the theoretical kinematic model through kinematic calibration, thereby improving the absolute positioning accuracy of the robot.

[0003] In recent years, under the background of the blowout application of robotic arms in domestic automated production lines and the continuous promotion of the "robot replacement project", the significance of kinematic calibration and error compensation for robots has become increasingly prominent. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the purpose of the present invention is to provide a step-by-step error modeling and calibration method for a serial arm with a closed-loop sub-chain.

[0005] To achieve the above purpose, the present invention provides the following technical solution: A step-by-step error modeling and calibration method for a serial arm with a closed-loop sub-chain, the steps of which are as follows:

[0006] (1) According to the existing serial robot model with a closed-loop sub-chain, operate to form a serial arm model without a closed-loop sub-chain, conduct kinematic derivation on it, and then establish an error calibration model for the serial robot without a sub-chain according to the differential motion equation; then establish closed-loop constraint equations for the two closed-loop sub-chains respectively, and derive an error model between the structural parameter errors of the closed-loop sub-chains and the rotation angle errors of the passive joints on the main chain; finally, add the error models of the two closed-loop sub-chains to the previously established error model of the serial manipulator without a sub-chain, so as to obtain an overall error parameter calibration model for the serial arm with a closed-loop sub-chain;

[0007] (2) Determine a helical trajectory located within the robot's working space, with a radius of r and a pitch of h for the helix, verify the feasibility of the trajectory through the robot simulation model, and then conduct a calibration experiment;

[0008] (3) Set the robot's motion trajectory on the robot control software for the given robot motion trajectory, drive the robot to perform a helical motion, verify that its actual motion trajectory is consistent with the originally planned motion trajectory, and verify the correctness of the model;

[0009] (4) To construct the base coordinate system of the robotic arm, place three target ball seats at specific positions on the base plane of the robotic arm. After measuring the positions of the target balls placed on them with a laser tracker, take the center point of the three points as the origin of the coordinate system, take the measuring point direction in the direction of the robotic arm from the origin as the x-axis, and the upward direction of the normal line of the measuring point plane as the z-axis. Then determine the y-axis according to the right-hand rule to construct the global base coordinate system;

[0010] (5) Install 3 target ball seats at the end of the robot, start the robot and execute the set robot motion trajectory, so that the end effector moves along the helical trajectory, read the joint drive values corresponding to each motion point when the end of the robot is making a helical motion and monitor the motion state of the end of the robot in real time, and use a laser tracker to record the spatial positions of the 3 target balls at the end on the trajectory in the base coordinate system;

[0011] (6) Read the saved experimental data in MATLAB software, process the data to obtain the actual spatial pose of the end of the robot, and then substitute the drive values corresponding to the trajectory into the forward kinematic equation of the robot to calculate the theoretical spatial pose of the end of the robot;

[0012] (7) On the basis of step (6), in MTATLAB, according to the established error mapping model, subtract the actual spatial pose from the theoretical spatial pose to obtain the end pose error, and then substitute it into the error mapping model to identify the actual structural parameter error of the robot. Subsequently, add the identified structural parameter error to the structural parameters in the theoretical model to achieve the compensation of the robot motion error. Substitute the corrected model into the experiment and repeat the above steps to verify the accuracy and effectiveness of the identified parameters.

[0013] In some embodiments, in step (2), the set helical trajectory takes the x-axis direction of the base coordinate system as the axis, and the radius and pitch of the helix are determined according to the working space of the robot, so as to realize the motion of the robot in space.

[0014] In some embodiments, 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.

[0015] In some embodiments, the derivation method of the main motion chain error mapping model is as follows:

[0016] For the operation, a serial arm model without a closed-loop sub-chain is formed, which is the main kinematic chain of this mechanism. It is a three-degree-of-freedom serial manipulator. A fixed Cartesian coordinate system is established in the mechanism.

[0017] By performing forward kinematics derivation on the main kinematic chain, the relationship between the joint drive values and the real-time pose of the center of the end-effector coordinate system in the fixed coordinate system O-XYZ is obtained. The forward kinematics expression is as follows:

[0018]

[0019] In the formula: s(), c(), t() represent the trigonometric functions sin(), cos(), tan() respectively. θ 12 is the abbreviation of θ1 + θ2;

[0020] Based on the differential method, the mapping relationship between the pose error and the structural parameter error of the serial arm is derived. This mapping relationship is obtained by taking the total differential of both sides of the forward kinematics equation, and is specifically expressed as follows:

[0021]

[0022] After organizing the above relationship, the mapping relationship between the end pose error and the kinematic error parameters of the main chain is obtained:

[0023]

[0024] In the formula: δx, δy, δz, δβ, δγ are the end pose errors,

[0025] δh, δL2, δL6, δd1, δd7, δθ0, δθ1, δθ2 are the structural errors of the main chain;

[0026] So far, the mapping relationship between the end pose error of the manipulator and the structural parameter error of the main chain is obtained:

[0027] δpose = J0δr0

[0028] In the formula: δpose = [δx, δy, δz, δβ, δγ] T ,

[0029] δr = [δh, δL2, δL6, δd1, δd7, δθ0, δθ1, δθ2] T .

[0030] In some of the embodiments, the derivation method of the closed-loop sub-chain error mapping model is as follows:

[0031] When there are errors in the rod length and the driving joint variables, the actual passive joint variables are calculated for the closed-loop sub-chain structure, which includes the first closed-loop sub-chain structure and the second closed-loop sub-chain structure.

[0032] First, set the closed-loop constraint equation of the first closed-loop sub-chain as:

[0033]

[0034] Based on the differential method, the mapping relationship between the passive joint variable error of the serial arm and the closed-loop structure parameter error is derived. This mapping relationship can be obtained by taking the total differential of both sides of the closed-loop vector equations E 1x and E 1z as follows:

[0035]

[0036] After organizing the above formulas, the mapping relationship between the error of the first passive joint variable of the main chain and the error of the first closed-loop sub-chain structure is obtained:

[0037]

[0038] In the formula: δθ1 is the error of the first passive joint variable of the main chain, and δL1, δL4, δd3, δd4, δq1 are the errors of the first closed-loop sub-chain structure parameters;

[0039] Then the mapping relationship between the error of the first passive joint variable and the error of the first closed-loop sub-chain structure parameters is obtained:

[0040]

[0041] In the formula: δr1 = [δL1, δL4, δd3, δd4, δq1] T ,

[0042] Similarly, set the closed-loop constraint equation of the second closed-loop sub-chain:

[0043]

[0044] Based on the differential method, the mapping relationship between the passive joint variable error of the serial arm and the closed-loop structure parameter error is derived. This mapping relationship can be obtained by taking the total differential of both sides of the closed-loop vector equations E 2x and E 2z as follows:

[0045]

[0046] After organizing the above formulas into matrix form, the mapping between the error of the second passive joint variable of the main chain and the error of the second closed-loop sub-chain structure is obtained:

[0047]

[0048] Where: δθ2 is the error of the second passive joint variable of the main chain, and δh1, δd5, δβ0, δd6, δL5, δd2, δq2 are the error of the structural parameters of the second closed-loop sub-chain;

[0049] Thus, the mapping relationship between the error of the second passive joint variable and the error of the structural parameters of the second closed-loop sub-chain is obtained:

[0050]

[0051] Where: δr2 = [δh1, δd5, δβ0, δd6, δL5, δd2, δq2] T ,

[0052] So far, the error mapping models of the two closed-loop sub-chains have been obtained.

[0053] In some of these embodiments, the establishment and simulation method of the overall error mapping model of the robotic arm with a closed-loop sub-chain is as follows:

[0054] Applying the mapping relationship between the error of the passive joint variable and the error of the structural parameters of the closed-loop sub-chain to the error mapping model of the main motion chain of the serial arm, the following overall error mapping model can be obtained:

[0055]

[0056] δpose = Jδr

[0057] Where: δr = [δh, δL2, δL6, δd1, δd7, δθ0, δr1, δr2] T 。

[0058] Compared with the prior art, the beneficial effects of the present invention are:

[0059] 1. An error parameter mapping model of a robotic arm with a closed-loop sub-chain proposed by the present invention can effectively perform error parameter modeling of the robotic arm with a closed-loop sub-chain based on a laser tracker and ensure the least squares solution of the error parameters. It not only improves the calibration accuracy of the robot but also enhances its stability and repeatability in continuous or repetitive operations. In addition, by adopting the least squares iterative strategy with a regularization term, the phenomenon of overfitting of the model is further reduced, making the error parameters after robot calibration more accurate and greatly improving the reliability of the model;

[0060] 2. The error parameter modeling of the serial arm with a closed-loop sub-chain in this embodiment is mainly achieved by establishing a comprehensive error parameter mapping model and model, which combine the kinematic error mapping models of the serial manipulator and the closed-loop sub-chain. The accuracy of the identification model is optimized through iterative operations, thereby improving the accuracy of the error parameter identification of the serial arm with a closed-loop sub-chain. After the kinematic parameters are identified, it is ensured that the serial arm with a closed-loop sub-chain can maintain a better high-precision standard during operation.

[0061] Details of one or more embodiments of the present application are set forth in the following drawings and description to make other features, objects, and advantages of the present application more concise and understandable. The present application is described in detail and understood through the embodiments of the present application. Brief Description of the Drawings

[0062] Figure 1 Schematic structural diagram of a robotic arm with a closed-loop sub-chain;

[0063] Figure 2 Schematic diagram of the first closed-loop structure of a robotic arm with a closed-loop sub-chain;

[0064] Figure 3 Schematic diagram of the second closed-loop structure of a robotic arm with a closed-loop sub-chain;

[0065] Figure 4 Overall flow chart of the error parameter calibration of a robotic arm with a closed-loop sub-chain based on a laser tracker in this embodiment. Detailed Embodiments

[0066] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0067] Some existing studies have derived the error model in the closed loop based on a perfect parallelogram mechanism. However, the passive joint variable error only linearly depends on the driving joint variable error, and the structural parameter error in the closed loop is not error-modeled, which does not meet the integrity of the error mapping model. Therefore, it is necessary to establish an error mapping model that includes all the closed-loop structure errors.

[0068] The present invention provides a technical solution: a step-by-step error modeling and calibration method for a series arm with a closed-loop sub-chain. By using a high-precision laser tracker device, the pose error existing in the working space of the robotic arm due to various factors such as its own structural error and measurement error is measured, and this error is mapped into the error model of the series arm with a closed-loop sub-chain, so as to obtain its true structural parameters, thereby compensating the kinematic model. Then, the robot is controlled according to the new kinematic model, so as to reduce the motion error of the end pose of the robot.

[0069] Refer to Figure 4 as shown in the figure, which includes the following steps:

[0070] 1) According to the existing series robot model with a closed-loop sub-chain, the closed-loop sub-chain can be virtually cut first to form a series arm model without a closed-loop sub-chain. Kinematic derivation is carried out on it, and then an error calibration model of the series robot without a sub-chain is established according to the differential motion equation. Then, closed-loop constraint equations are established for the two closed-loop sub-chains respectively, and an error model of the structural parameter error of the closed-loop sub-chain and the rotation angle error of the passive joints on the main chain is derived. Finally, the error models of the two closed-loop sub-chains are added to the previously established error model of the series robotic arm without a sub-chain, so as to obtain the overall error parameter calibration model of the series arm with a closed-loop sub-chain.

[0071] 2) Determine a helical trajectory located within the working space of the robot, with a helical radius of r and a pitch of h. Verify the feasibility of the trajectory through the robot simulation model, and then conduct a calibration experiment.

[0072] 3) Write a motion control program for the given robot motion trajectory on the robot control software, and use the written program to drive the robot to perform helical motion, verify that its actual motion trajectory is consistent with the originally planned motion trajectory, and verify the correctness of the model.

[0073] 4) To construct the base coordinate system of the robotic arm, place three target ball seats at specific positions on the base plane of the robotic arm. After measuring the positions of the target balls placed on them with a laser tracker, take the center point of the three points as the origin of the coordinate system, take the measuring point direction in the direction of the robotic arm from the origin as the x-axis, and the normal upward direction of the measuring point plane as the z-axis. Then, determine the y-axis according to the right-hand rule, so as to construct the global base coordinate system.

[0074] 5) Install 3 target ball seats at the end of the robot, start the robot and execute the already programmed program, so that the end effector moves along the helical trajectory. Read the joint drive values corresponding to each motion point when the end of the robot is making helical motion and monitor the motion state of the end of the robot in real time. Use a laser tracker to record the spatial positions of the 3 target balls at the end at each point on the trajectory in the base coordinate system.

[0075] 6) Read the saved experimental data in MATLAB software, process the data, and obtain the actual spatial pose of the robot end. Then, according to the forward kinematic equation of the robot, substitute the driving values corresponding to the trajectory to calculate the theoretical spatial pose of the robot end.

[0076] 7) On the basis of step 6), in MTATLAB, according to the established error mapping model, subtract the actual spatial pose from the theoretical spatial pose to obtain the end pose error, and then substitute it into the error mapping model to identify the actual structural parameter error of the robot. Subsequently, add the identified structural parameter error to the structural parameters in the theoretical model to compensate for the motion error of the robot. Substitute the corrected model into the experiment and repeat the above steps to verify the accuracy and effectiveness of the identified parameters.

[0077] In step 2), the set helical trajectory takes the x-axis direction of the base coordinate system as the axis, and the radius and pitch of the helix are determined according to the working space of the robot, so as to realize the movement of the robot in space.

[0078] In step 5), discretize the continuous movement of the robot in space, that is, it needs to be stationary and stable during the movement so that the laser tracker can measure the position when the robot is stable.

[0079] The error modeling involved in the present invention has the following characteristics: the rotating joints of the main chain are passive joints, which are different from the structural errors brought by the complex structures in the active joints. It can be considered that the structural errors of the passive joints on the main chain are caused by the structural errors on the closed-loop sub-chain. Therefore, a mapping model from the end pose error to the structural error of the main motion chain can be established first, and then a mapping model from the structural error of the closed-loop sub-chain to the structural error of the main chain joints can be established, so as to obtain a mapping model from the end pose error to the overall structural error of the robot.

[0080] The technical solution of the present invention will be further elaborated below with reference to the accompanying drawings.

[0081] The implementation of the present invention includes the following steps:

[0082] Derivation of the error mapping model of the main motion chain

[0083] Virtually cut the closed-loop sub-chain of the mechanism targeted by the present invention to form a series arm model without the closed-loop sub-chain, which is the main motion chain of this mechanism. It is a three-degree-of-freedom serial manipulator, and a projection diagram reference of a fixed Cartesian coordinate system is established in the mechanism. Figure 1 As shown, where the X-axis is collinear with O1A2, the Z-axis is along the direction of O0O1, the Y-axis satisfies the right-hand rule, and the origin of the end tool coordinate system Ot-XYZ is the midpoint of O3, where the end tool coordinate system has the same direction as the base coordinate system.

[0084]

[0085] By performing forward kinematic derivation on the main kinematic chain, the relationship between the joint drive values and the real-time pose of the center of the end-effector coordinate system in the fixed coordinate system O-XYZ is obtained. The forward kinematic expression is as follows:

[0086] In the formula: s(), c(), t() represent the trigonometric functions sin(), cos(), tan() respectively. θ 12 is the abbreviation of θ1 + θ2.

[0087] Based on the differential method, the mapping relationship between the pose error and the structural parameter error of the serial arm is derived. This mapping relationship can be obtained by taking the total differential of both sides of the forward kinematic equation, and is specifically expressed as follows:

[0088]

[0089] After organizing the above relationship, the mapping relationship between the end-effector pose error and the main chain kinematic error parameters is obtained:

[0090] In the formula: δx, δy, δz, δβ, δγ are the end-effector pose errors,

[0091] δh, δL2, δL6, δd1, δd7, δθ0, δθ1, δθ2 are the structural errors of the main chain.

[0092] So far, the mapping relationship between the end-effector pose error of the robotic arm and the structural parameter error of the main chain is obtained:

[0093] δpose = J0δr0

[0094] In the formula: δpose = [δx, δy, δz, δβ, δγ]T,

[0095] δr = [δh, δL2, δL6, δd1, δd7, δθ0, δθ1, δθ2]T.

[0096] (2) Derivation of the closed-loop sub-chain error mapping model.

[0097] When there are errors in the rod lengths and the driving joint variables, the actual passive joint variables should be calculated for the Figure 2 , Figure 3 shown closed-loop sub-chain structure.

[0098] As Figure 2 shown in the first closed-loop sub-chain structure diagram, first set the closed-loop constraint equation of the first closed-loop sub-chain as:

[0099]

[0100] Based on the differential method, the mapping relationship between the variable errors of the passive joints in the series arm and the structural errors of the closed-loop structure is deduced. This mapping relationship can be obtained by taking the total differential of both sides of the closed-loop vector equations E1x and E1z, and is specifically expressed as follows:

[0101]

[0102] After organizing the above formulas, the mapping relationship between the error of the first passive joint variable in the main chain and the structural error of the first closed-loop sub-chain is obtained:

[0103]

[0104] In the formula: δθ1 is the error of the first passive joint variable in the main chain, and δL1, δL4, δd3, δd4, δq1 are the structural parameter errors of the first closed-loop sub-chain.

[0105] Then the mapping relationship between the error of the first passive joint variable and the structural parameter errors of the first closed-loop sub-chain is obtained:

[0106]

[0107] In the formula: δr1 = [δL1, δL4, δd3, δd4, δq1]T,

[0108] As Figure 3 shown in the structural diagram of the second closed-loop sub-chain, similarly, the closed-loop constraint equations of the second closed-loop sub-chain are listed again:

[0109]

[0110] Based on the differential method, the mapping relationship between the variable errors of the passive joints in the series arm and the structural errors of the closed-loop structure is deduced. This mapping relationship can be obtained by taking the total differential of both sides of the closed-loop vector equations E2x and E2z, and is specifically expressed as follows:

[0111]

[0112] After organizing the above formulas into matrix form, the mapping between the error of the second passive joint variable in the main chain and the structural error of the second closed-loop sub-chain is obtained:

[0113]

[0114] In the formula: δθ2 is the error of the second passive joint variable in the main chain, and δh1, δd5, δβ0, δd6, δL5, δd2, δq2 are the structural parameter errors of the second closed-loop sub-chain.

[0115] Thus, the mapping relationship between the error of the second passive joint variable and the structural parameter errors of the second closed-loop sub-chain is obtained:

[0116]

[0117] where: δr2 = [δh1, δd5, δβ0, δd6, δL5, δd2, δq2]T,

[0118] Thus, the error mapping models of the two closed-loop sub-chains are obtained.

[0119] (3) Establishment and simulation of the overall error mapping model of the robotic arm with closed-loop sub-chains

[0120] Applying the mapping relationship between the passive joint variable errors and the structural parameter errors of the closed-loop sub-chains to the error mapping model of the main motion chain of the serial arm, the overall error mapping model can be obtained as follows:

[0121]

[0122] δpose = Jδr

[0123] where: δr = [δh, δL2, δL6, δd1, δd7, δθ0, δr1, δr2]T.

[0124] The above embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

[0125] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A step - by - step error modeling and calibration method for a series arm with a closed - loop sub - chain, characterized in that: The steps are as follows: (1) Based on the existing serial robot model with a closed-loop sub-chain, operate to form a serial arm model without a closed-loop sub-chain, conduct kinematic derivation on it, and then establish an error calibration model for the serial robot without a sub-chain according to the differential motion equation; then establish closed-loop constraint equations for the two closed-loop sub-chains respectively, and derive an error model for the structural parameter error of the closed-loop sub-chain and the rotation angle error of the passive joints on the main chain; finally, add the error models of the two closed-loop sub-chains to the previously established error model of the serial manipulator without a sub-chain, so as to obtain an overall error parameter calibration model for the serial arm with a closed-loop sub-chain; (2) Determine a helical trajectory located within the robot's workspace, with a helical radius of r and a pitch of h. Verify the feasibility of the trajectory through the robot simulation model, and then conduct a calibration experiment; (3) Set the robot's motion trajectory for the given robot motion trajectory on the robot control software, drive the robot to perform helical motion, verify that its actual motion trajectory is consistent with the originally planned motion trajectory, and verify the correctness of the model; (4) To construct the base coordinate system of the manipulator, place three target ball seats at specific positions on the base plane of the manipulator. After measuring the positions of the target balls placed on them with a laser tracker, take the center point of the three points as the origin of the coordinate system, take the measuring point direction in the direction of the manipulator from the origin as the x-axis, and take the upward normal direction of the measuring point plane as the z-axis. Then determine the y-axis according to the right-hand rule, so as to construct the global base coordinate system; (5) Install 3 target ball seats at the end of the robot, start the robot and execute the robot motion trajectory that has been set, so that the end effector moves along the helical trajectory. Read the joint drive values corresponding to each motion point when the end of the robot is doing helical motion and monitor the motion state of the end of the robot in real time. Use a laser tracker to record the spatial positions of the 3 target balls at the end at each point on the trajectory in the base coordinate system; (6) Read the saved experimental data in the MATLAB software, process the data to obtain the actual spatial pose of the end of the robot, and then substitute the drive values corresponding to the trajectory into the forward kinematic equation of the robot according to the forward kinematic equation of the robot, so as to calculate the theoretical spatial pose of the end of the robot; (7) On the basis of step (6), in MTATLAB, according to the established error mapping model, subtract the actual spatial pose from the theoretical spatial pose to obtain the end pose error, and then substitute it into the error mapping model to identify the actual structural parameter error of the robot. Subsequently, add the identified structural parameter error to the structural parameters in the theoretical model to achieve compensation for the robot motion error. Substitute the corrected model into the experiment, and repeat the above steps to verify the accuracy and effectiveness of the identified parameters.

2. A step-by-step error modeling and calibration method for a series arm with a closed-loop sub-chain according to claim 1, characterized in that: In step (2), the set helical trajectory takes the x-axis direction of the base coordinate system as the axis, and the helical radius and pitch are determined according to the robot's workspace, so as to realize the motion of the robot in space.

3. A step-by-step error modeling and calibration method for a series arm with a closed-loop sub-chain according to claim 1, characterized in that: In step (5), discretize the continuous motion of the robot in space, 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.

4. The step-by-step error modeling and calibration method for a series arm with a closed-loop sub-chain according to claim 1 is characterized in that: The derivation method of the main kinematic chain error mapping model is as follows: For the serial arm model formed by the operation without a closed-loop sub-chain, which is the main kinematic chain of this mechanism. It is a three-degree-of-freedom serial manipulator. A fixed Cartesian coordinate system is established in the mechanism. By performing forward kinematic derivation on the main kinematic chain, the relationship between the joint drive values and the real-time pose of the center of the end-effector coordinate system in the fixed coordinate system O-XYZ is obtained. The forward kinematic expression is as follows: Where: s(), c(), t() represent the trigonometric functions sin(), cos(), and tan() respectively. θ 12 It is the abbreviation of θ1+θ2; Based on the differential method, the mapping relationship between the pose error and the structural parameter error of the serial arm is derived. This mapping relationship is obtained by taking the total differential of both sides of the forward kinematic equation, and is specifically expressed as follows: After organizing the above relationship, the mapping relationship between the end pose error and the kinematic error parameters of the main chain is obtained: In the formula: δx, δy, δz, δβ, δγ are the end pose errors. δh, δL2, δL6, δd1, δd7, δθ0, δθ1, δθ2 are the structural errors of the main chain; Thus, the mapping relationship between the end pose error of the manipulator and the structural parameter error of the main chain is obtained: δpose = J0δr0 where: δpose = [δx, δy, δz, δβ, δγ] T , δr=[δh,δL2,δL6,δd1,δd7,δθ0,δθ1,δθ2] T 。 5. A step-by-step error modeling and calibration method for a series arm with a closed-loop sub-chain according to claim 4, characterized in that: The derivation method of the closed-loop sub-chain error mapping model is as follows: When there are errors in the link lengths and the driving joint variables, the actual passive joint variables are calculated for the closed-loop sub-chain structure, which includes the first closed-loop sub-chain structure and the second closed-loop sub-chain structure. First, set the closed-loop constraint equation of the first closed-loop sub-chain as: Based on the differential method, the mapping relationship between the variable error of the series-arm passive joint and the error of the closed-loop structure parameters is deduced. This mapping relationship can be obtained by taking the total differential of both sides of the closed-loop vector equations E 1x and E 1z as follows: After organizing the above formula, the mapping relationship between the error of the first passive joint variable of the main chain and the structural error of the first closed-loop sub-chain is obtained: In the formula: δθ1 is the error of the first passive joint variable of the main chain, and δL1, δL4, δd3, δd4, δq1 are the structural parameter errors of the first closed-loop sub-chain; Then, the mapping relationship between the error of the first passive joint variable and the structural parameter error of the first closed-loop sub-chain is obtained: where: δr1 = [δL1, δL4, δd3, δd4, δq1] T , Similarly, set the closed-loop constraint equation of the second closed-loop sub-chain: Based on the differential method, the mapping relationship between the variable error of the passive joint in the series arm and the error of the closed-loop structure parameters is derived. This mapping relationship can be obtained by taking the total differential of both sides of the closed-loop vector equations E 2x and E 2z as follows: After organizing the above formula into matrix form, the mapping between the error of the second passive joint variable of the main chain and the structural error of the second closed-loop sub-chain is obtained: In the formula: δθ2 is the error of the second passive joint variable of the main chain, and δh1, δd5, δβ0, δd6, δL5, δd2, δq2 are the structural parameter errors of the second closed-loop sub-chain; Thus, the mapping relationship between the error of the second passive joint variable and the structural parameter error of the second closed-loop sub-chain is obtained: where: δr2 = [δh1, δd5, δβ0, δd6, δL5, δd2, δq2] T , Thus, the error mapping models of the two closed-loop sub-chains are obtained.

6. A step-by-step error modeling and calibration method for a series arm with a closed-loop sub-chain according to claim 5, characterized in that: The establishment and simulation method of the overall error mapping model of the manipulator with a closed-loop sub-chain is as follows: Applying the mapping relationship between the passive joint variable error and the structural parameter error of the closed-loop sub-chain to the main kinematic chain error mapping model of the serial arm, the overall error mapping model can be obtained as follows: δpose = Jδr where: δr = [δh, δL2, δL6, δd1, δd7, δθ0, δr1, δr2] T .

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