Parallel robot error model verification method and device based on parameter identification

Abstract

The application discloses a parallel robot error model verification method and device based on parameter identification, and the method comprises the following steps: verifying the established parallel robot parameter identification model, and obtaining the parallel robot parameter identification model that passes the verification; performing parameter identification experiments by using the parallel robot parameter identification model that passes the verification, acquiring actual structure parameter errors, correcting the ideal kinematic model of the parallel robot, and thus constructing the actual kinematic model of the parallel robot; based on the result of the parameter identification, establishing the actual error model of the parallel robot, and performing error analysis; subsequently, mapping the influence of the structure parameter errors on the end position point to the joint input quantity, and driving the robot by using the joint input quantity to perform the actual error model verification experiment of the parallel robot based on the parameter identification. The application provides a parallel robot actual error model verification method which is high in operability, simple in principle and low in cost.

Description

Technical Field

[0001] This invention relates to a method and apparatus for verifying the error model of a parallel robot based on parameter identification, belonging to the field of robot calibration technology. Background Technology

[0002] Because robots can replace human labor in harsh environments such as high temperatures and toxic or hazardous conditions, they play a crucial role in major industries such as automotive, metallurgy, electronics, logistics, and petrochemicals. However, structural parameter errors are unavoidable during robot processing and assembly, leading to reduced operational accuracy. Therefore, structural parameter calibration and error compensation are necessary. Both calibration and error compensation rely on error models for theoretical guidance; thus, verifying the correctness of error models is of great significance and can promote the application of robots in high-precision fields.

[0003] Currently, due to the difficulty or inability to measure the errors in robot structural parameters, error analysis models are built in simulation environments, making it impossible to verify the rationality of the error models. Therefore, it is necessary to design error model verification methods to verify the error models of robots. Summary of the Invention

[0004] To address the problem of the inability to verify the rationality of error models for parallel robots, this invention provides a method and apparatus for verifying error models for parallel robots based on parameter identification. This invention has good versatility and can be used for verifying error models for parallel robots, promoting the application of parallel robots in high-precision fields.

[0005] The technical solution of this invention is:

[0006] According to a first aspect of the present invention, a method for verifying the error model of a parallel robot based on parameter identification is provided, comprising the following steps: Step 1, verifying the established parameter identification model of the parallel robot to obtain a verified parameter identification model of the parallel robot; Step 2, conducting parameter identification experiments using the verified parameter identification model of the parallel robot to obtain actual structural parameter errors to correct the ideal kinematic model of the parallel robot, thereby constructing an actual kinematic model of the parallel robot; Step 3, based on the results of parameter identification, establishing an actual error model of the parallel robot and performing error analysis, then mapping the influence of structural parameter errors on the end-effector position to the joint input quantity, and using it to drive the robot to conduct a verification experiment of the actual error model of the parallel robot based on parameter identification.

[0007] Step 1 is described in detail below:

[0008] Step 1.1: Establish the kinematic coordinate system of the parallel robot and establish the ideal kinematic model of the parallel robot f(p,q,s)=0; where p represents the ideal end position of the robot, corresponding to the coordinates of the geometric center of the motion platform in space, q is the ideal joint input, and s is the ideal structural parameter of the parallel robot.

[0009] Step 1.2: Establish the ideal error model of the parallel robot f(p+dp,q,s+ds)=0, where dp represents the end position error of the parallel robot caused by the ideal structural parameter error ds, and ds represents the ideal structural parameter error caused by the processing and assembly of the parallel robot, including the link length error, the circumscribed circle radius error of the motion platform, and the circumscribed circle radius error of the static platform.

[0010] Step 1.3: Preset a set of ideal structural parameter error values ​​ds, and arbitrarily select a set of ideal end positions p in the workspace of the parallel robot. Solve for the corresponding ideal joint input q by using the established ideal kinematic model of the parallel robot f(p,q,s)=0. The ideal joint input q is used to obtain the simulated actual end position p+dp of the parallel robot by using the ideal error model of the parallel robot f(p+dp,q,s+ds)=0.

[0011] Step 1.4: Establish a parameter identification model for the parallel robot: f(p+dp,q^(Δs),s+Δs)=0; where Δs represents the structural parameter error optimization variable, q^(Δs) represents the joint input containing the structural parameter error optimization variable Δs, and s+Δs represents the structural parameter containing the structural parameter error optimization variable Δs.

[0012] Step 1.5: The simulated actual end position p+dp of the parallel robot is obtained by the parallel robot parameter identification model f(p+dp,q^(Δs),s+Δs)=0, which contains the joint input q^(Δs) containing the structural parameter error optimization variable Δs.

[0013] Step 1.6: Establish the fitness function of the parallel robot parameter identification model;

[0014] Step 1.7: Use an optimization algorithm to find the minimum value of the fitness function of the parallel robot parameter identification model, and obtain the optimal structural parameter error optimization variable Δs* for the parallel robot;

[0015] Step 1.8: Subtract the optimal structural parameter error optimization variable Δs* obtained in Step 1.7 from the set of ideal structural parameter errors ds preset in Step 1.3, and determine whether the difference is a higher-order infinitesimal. If it is, it means that the parameter identification result is correct and the ideal structural parameter error ds that causes the robot end position error dp has been found. Otherwise, after adjusting the parameters of the optimization algorithm in Step 1.7, re-identify the parameters until the parameter identification result is correct. This completes the construction and verification of the parallel robot parameter identification model and obtains the verified parallel robot parameter identification model f(p+dp,q^(Δs*),s+Δs*)=0.

[0016] The structural parameters include the link length, the radius of the circumscribed circle of the moving platform, and the radius of the circumscribed circle of the stationary platform.

[0017] The fitness function of the parallel robot parameter identification model is: f min (Δs)=sqrt(∑(q^(Δs)-q) 2 ); where f min (Δs) represents sqrt(∑(q^(Δs)-q) 2 The set of structural parameter optimization variables Δs values ​​when the minimum value is obtained.

[0018] Step 2 is described in detail below:

[0019] Step 2.1: Randomly select a set of ideal end positions p in the workspace of the parallel robot. Solve for the corresponding ideal joint input q by establishing the ideal kinematic model f(p,q,s)=0 of the parallel robot. Drive the parallel robot with the ideal joint input q and use a laser tracker to obtain the measured end position p'.

[0020] Step 2.2: Input the measured end position p' as p+dp into the verified parallel robot parameter identification model to obtain the actual structural parameter error Δs' of the parallel robot.

[0021] Step 2.3: Correct the ideal kinematic model f(p,q,s)=0 of the parallel robot using the actual structural parameter error Δs' of the parallel robot, and obtain the actual kinematic model F(p,q*,s-Δs')=0 of the parallel robot; where s-Δs' represents the actual structural parameters of the parallel robot, p represents the ideal end position of the parallel robot, and q* represents the joint input amount corresponding to the ideal end position p of the parallel robot under actual processing and assembly conditions.

[0022] Step 3 is described in detail below:

[0023] Step 3.1: Based on the actual kinematic model of the parallel robot, establish the actual error model of the parallel robot F(p+datap,q*,s-Δs'+datas)=0, where s-Δs' represents the actual structural parameters of the parallel robot, datas represents the pre-set structural parameter error terms in the error analysis of the actual error model of the parallel robot, and datap represents the end position error caused by the pre-set structural parameter error terms datas in the error analysis of the actual error model of the parallel robot.

[0024] Step 3.2: Randomly assign a set of ideal end position points p 1 For error analysis and verification, the corresponding actual joint input q is solved using the actual kinematic model of the parallel robot F(p,q*,s-Δs'=0. 1 Preset the values ​​of error terms (datas) for different combinations of structural parameters, and then use the actual joint input quantity (q). 1 Substituting the error into the actual error model of the parallel robot and performing error analysis, we obtain the end-effector error position p caused by the structural parameter error term datas. 1 +datap;

[0025] Step 3.3: Using the actual kinematic model of the parallel robot F(p,q*,s-Δs')=0, adjust the structural parameter error term datas to the ideal end position point p. 1 The influence is mapped onto the joint input of the parallel robot, and the equivalent joint input q” is obtained by solving the solution.

[0026] Step 3.4: Drive the parallel robot with the equivalent joint input q” and use a laser tracker to obtain the measured end position p” containing the structural parameter error term datas;

[0027] Step 3.5: Compare the measured end position p” containing the structural parameter error term datas with the end error position p” caused by the structural parameter error term datas. 1 The difference between +datap and Δp is obtained. Δp represents the deviation between the analysis results of the actual error model of the parallel robot and the experimental verification results. If the value of Δp is less than the accuracy index of the parallel robot, it indicates that the design of the actual error model of the parallel robot is reasonable.

[0028] The parallel robots include, but are not limited to, 2TPR&2TPS parallel robots, 3-RRS parallel robots, 3URS-PPPS parallel robots, and 3-PUU parallel robots.

[0029] According to a second aspect of the present invention, a parallel robot error model verification device based on parameter identification is provided, comprising: an acquisition module for verifying an established parallel robot parameter identification model to obtain a verified parallel robot parameter identification model; a construction module for conducting parameter identification experiments using the verified parallel robot parameter identification model to obtain actual structural parameter errors to correct the ideal kinematic model of the parallel robot, thereby constructing an actual kinematic model of the parallel robot; and a verification module for establishing an actual error model of the parallel robot based on the results of parameter identification, performing error analysis, and then mapping the influence of structural parameter errors on the end-effector position point to the joint input quantity, using it to drive the robot to conduct a verification experiment of the actual error model of the parallel robot based on parameter identification.

[0030] According to a third aspect of the present invention, a terminal device is provided, including a memory, a processor, and a program stored in the memory and executable by the processor, wherein the processor executes the program to implement the parallel robot error model verification method based on parameter identification as described in any one of the preceding claims.

[0031] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium comprising a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the parallel robot error model verification method based on parameter identification as described above.

[0032] The beneficial effects of this invention are: this invention provides a method for verifying the actual error model of a parallel robot that is highly operable, simple in principle, and low in cost. Moreover, this method has good versatility and can be applied to the error model verification of various parallel robots, thus promoting the application of parallel robots in high-precision fields. Attached Figure Description

[0033] Figure 1 This is the overall flowchart of the present invention;

[0034] Figure 2 This is a schematic diagram of the parameter identification model of the present invention;

[0035] Figure 3 This is a flowchart of the actual structural parameter error identification process of the present invention;

[0036] Figure 4 This is a flowchart of the actual error model verification process of the present invention;

[0037] Figure 5 This is a diagram of the physical object and simplified mathematical model of the PUU parallel robot of Embodiment 3 of the present invention;

[0038] Figure 6This is a simulation of the end-effector pose error diagram in an embodiment of the present invention;

[0039] Figure 7 This is an evolutionary graph of the average fitness curve of an embodiment of the present invention;

[0040] Figure 8 These are end-effector pose error diagrams under five different scenarios analyzed by the actual error model in this embodiment of the invention.

[0041] Figure 9 This is a deviation diagram between the end-effector pose and the error model verification experiment results in the actual error model analysis of the embodiments of the present invention;

[0042] Figure 10 This is an assembly diagram of the PUU parallel robot of Embodiment 3 of the present invention;

[0043] Figure 11 This is a top view of the PUU parallel robot assembly of Embodiment 3 of the present invention;

[0044] Figure 12 This is a structural diagram of the static platform module of the PUU parallel robot according to Embodiment 3 of the present invention;

[0045] Figure 13 This is a structural diagram of the PUU branch module of the PUU parallel robot according to Embodiment 3 of the present invention;

[0046] Figure 14 This is a structural diagram of the PUU parallel robot motion platform module of Embodiment 3 of the present invention;

[0047] Figure 5 In the diagram: coordinate system o-xyz is a static coordinate system, coordinate system p-x1y1z1 is a moving coordinate system, A oi (i = 1, 2, 3, the same below) are the connection points of the connecting rod and the slider, C i It is A oi The projection onto the xoy plane, connected to C i The circle is the circumcircle R of the static platform, B. pi For the connection point of the linkage hinged moving platform, connect B pi The circle r is the circumcircle of the moving platform. The installation angle of the i-th branch is evenly distributed. L i h is the length of the connecting rod. i These are the input values ​​for each joint.

[0048] The labels in the diagram are as follows: 1-Static platform, 2-PUU support chain, 3-Connecting rod, 4-Moving platform, 5-Fixed base plate, 6-Fixed seat, 7-Fixed corner piece, 8-Column, 9-Servo motor, 10-Servo motor bracket, 11-Coupling, 12-Lead screw, 13-Lead screw bearing seat I, 14-Guide rail, 15-Guide rail slider, 16-Slider, 17-Angular contact ball bearing I, 18-Short shaft I, 19-Type I joint, 20-Hinge pin I, 21-Y-type joint I, 22-Lead screw bearing seat II, 23-Moving platform, 24-Angular contact ball bearing II, 25-Short shaft II, 26-Type I joint, 27-Hinge pin II, 28-Y-type joint. Detailed Implementation

[0049] The invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of the invention is not limited to the description.

[0050] Example 1: As Figure 1-4 As shown, a method for verifying the error model of a parallel robot based on parameter identification includes the following steps: Step 1: Verify the established parameter identification model of the parallel robot to obtain a verified parameter identification model; Step 2: Conduct parameter identification experiments using the verified parameter identification model of the parallel robot to obtain actual structural parameter errors to correct the ideal kinematic model of the parallel robot, thereby constructing the actual kinematic model of the parallel robot; Step 3: Based on the results of parameter identification, establish the actual error model of the parallel robot and perform error analysis. Then, map the influence of structural parameter errors on the end-effector position to the joint input, and use it to drive the robot to conduct a verification experiment of the actual error model of the parallel robot based on parameter identification.

[0051] Furthermore, Step 1 is specifically as follows:

[0052] Step 1.1: Establish the kinematic coordinate system of the parallel robot and establish the ideal kinematic model of the parallel robot f(p,q,s)=0; where p represents the ideal end position of the robot, corresponding to the coordinates of the geometric center of the motion platform in space, q is the ideal joint input, and s is the ideal structural parameter of the parallel robot.

[0053] Step 1.2: Establish the ideal error model of the parallel robot f(p+dp,q,s+ds)=0, where dp represents the end position error of the parallel robot caused by the ideal structural parameter error ds, and ds represents the ideal structural parameter error caused by the processing and assembly of the parallel robot, including the link length error, the circumscribed circle radius error of the motion platform, and the circumscribed circle radius error of the static platform.

[0054] Step 1.3: Preset a set of ideal structural parameter error values ​​ds, and arbitrarily select a set of ideal end positions p in the workspace of the parallel robot. Solve for the corresponding ideal joint input q by using the established ideal kinematic model of the parallel robot f(p,q,s)=0. The ideal joint input q is used to obtain the simulated actual end position p+dp of the parallel robot by using the ideal error model of the parallel robot f(p+dp,q,s+ds)=0.

[0055] Step 1.4: Establish a parameter identification model for the parallel robot: f(p+dp,q^(Δs),s+Δs)=0; where Δs represents the structural parameter error optimization variable, q^(Δs) represents the joint input containing the structural parameter error optimization variable Δs, and s+Δs represents the structural parameter containing the structural parameter error optimization variable Δs.

[0056] Step 1.5: The simulated actual end position p+dp of the parallel robot is obtained by the parallel robot parameter identification model f(p+dp,q^(Δs),s+Δs)=0, which contains the joint input q^(Δs) containing the structural parameter error optimization variable Δs.

[0057] Step 1.6: Establish the fitness function of the parallel robot parameter identification model;

[0058] Step 1.7: Use an optimization algorithm to find the minimum value of the fitness function of the parallel robot parameter identification model, and obtain the optimal structural parameter error optimization variable Δs* for the parallel robot;

[0059] Step 1.8: Subtract the optimal structural parameter error optimization variable Δs* obtained in Step 1.7 from the set of ideal structural parameter errors ds preset in Step 1.3, and determine whether the difference is a higher-order infinitesimal. If it is, it means that the parameter identification result is correct and the ideal structural parameter error ds that causes the robot end position error dp has been found. Otherwise, after adjusting the parameters of the optimization algorithm in Step 1.7, re-identify the parameters until the parameter identification result is correct. This completes the construction and verification of the parallel robot parameter identification model and obtains the verified parallel robot parameter identification model f(p+dp,q^(Δs*),s+Δs*)=0.

[0060] Furthermore, the structural parameters include the link length, the circumscribed circle radius of the moving platform, and the circumscribed circle radius of the stationary platform.

[0061] Furthermore, the fitness function of the parallel robot parameter identification model is: f min (Δs)=sqrt(∑(q^(Δs)-q) 2 ); where f min(Δs) represents sqrt(∑(q^(Δs)-q) 2 The set of structural parameter optimization variables Δs values ​​when the minimum value is obtained.

[0062] Furthermore, Step 2 is specifically as follows:

[0063] Step 2.1: Randomly select a set of ideal end positions p in the workspace of the parallel robot. Solve for the corresponding ideal joint input q by establishing the ideal kinematic model f(p,q,s)=0 of the parallel robot. Drive the parallel robot with the ideal joint input q and use a laser tracker to obtain the measured end position p'.

[0064] Step 2.2: Input the measured end position p' as p+dp into the verified parallel robot parameter identification model to obtain the actual structural parameter error Δs' of the parallel robot.

[0065] Step 2.3: Correct the ideal kinematic model f(p,q,s)=0 of the parallel robot using the actual structural parameter error Δs' of the parallel robot, and obtain the actual kinematic model F(p,q*,s-Δs')=0 of the parallel robot; where s-Δs' represents the actual structural parameters of the parallel robot, p represents the ideal end position of the parallel robot, and q* represents the joint input amount corresponding to the ideal end position p of the parallel robot under actual processing and assembly conditions.

[0066] Furthermore, Step 3 is detailed as follows:

[0067] Step 3.1: Based on the actual kinematic model of the parallel robot, establish the actual error model of the parallel robot F(p+datap,q*,s-Δs'+datas)=0, where s-Δs' represents the actual structural parameters of the parallel robot, datas represents the pre-set structural parameter error terms in the error analysis of the actual error model of the parallel robot, and datap represents the end position error caused by the pre-set structural parameter error terms datas in the error analysis of the actual error model of the parallel robot.

[0068] Step 3.2: Randomly assign a set of ideal end position points p 1 For error analysis and verification, the corresponding actual joint input q is solved using the actual kinematic model of the parallel robot F(p,q*,s-Δs'=0. 1 Preset the values ​​of error terms (datas) for different combinations of structural parameters, and then use the actual joint input quantity (q). 1 Substituting the error into the actual error model of the parallel robot and performing error analysis, we obtain the end-effector error position p caused by the structural parameter error term datas. 1 +datap;

[0069] Step 3.3: Using the actual kinematic model of the parallel robot F(p,q*,s-Δs')=0, adjust the structural parameter error term datas to the ideal end position point p. 1 The influence is mapped onto the joint input of the parallel robot, and the equivalent joint input q” is obtained by solving the solution.

[0070] Step 3.4: Drive the parallel robot with the equivalent joint input q” and use a laser tracker to obtain the measured end position p” containing the structural parameter error term datas;

[0071] Step 3.5: Compare the measured end position p” containing the structural parameter error term datas with the end error position p” caused by the structural parameter error term datas. 1 The difference between +datap and Δp is obtained. Δp represents the deviation between the analysis results of the actual error model of the parallel robot and the experimental verification results. If the value of Δp is less than the accuracy index of the parallel robot, it indicates that the design of the actual error model of the parallel robot is reasonable.

[0072] Furthermore, the parallel robots include, but are not limited to, 2TPR&2TPS parallel robots, 3-RRS parallel robots, 3URS-PPPS parallel robots, and 3-PUU parallel robots.

[0073] Example 2: A parallel robot error model verification device based on parameter identification, comprising: an acquisition module for verifying the established parallel robot parameter identification model to obtain a verified parallel robot parameter identification model; a construction module for conducting parameter identification experiments using the verified parallel robot parameter identification model to obtain actual structural parameter errors to correct the ideal kinematic model of the parallel robot, thereby constructing an actual kinematic model of the parallel robot; and a verification module for establishing an actual error model of the parallel robot based on the results of parameter identification, performing error analysis, and then mapping the influence of structural parameter errors on the end-effector position to the joint input quantity, using it to drive the robot to conduct a verification experiment of the actual error model of the parallel robot based on parameter identification.

[0074] Example 3: The following describes an optional specific implementation of the present invention using a 3-PUU parallel robot as an example. The implementation process is as follows:

[0075] Step 1.1: Establish the kinematic coordinate system of the 3-PUU parallel robot and establish the ideal kinematic model of the 3-PUU parallel robot f(p,q,s)=0; where p represents the ideal end-effector position of the robot, corresponding to the coordinates of the geometric center of the motion platform 23 in space, q is the ideal joint input (corresponding to the distance the guide slider 15 slides on the guide rail 14), and s is the ideal structural parameter of the 3-PUU parallel robot, including the length of the link 3, the radius of the circumcircle of the motion platform 23, and the radius of the circumcircle of the stationary platform 1; the circumcircle of the motion platform is centered on the center of the motion platform and has a radius equal to the vertical distance from the center of the motion platform to the rotation center of the minor axis II 25, and the circumcircle of the stationary platform is centered on the center of the fixed base plate 5 and has a radius equal to the vertical distance from the center of the fixed base plate 5 to the rotation center of the minor axis I 18; the motion platform is a centrally symmetric structure; specifically described as:

[0076] Establish as Figure 5 The simplified mathematical model of the 3-PUU parallel robot is shown, in which a kinematic coordinate system is established. The ideal end-effector position of the 3-PUU parallel robot is p = p(X,Y,Z), and the ideal structural parameters of the 3-PUU parallel robot are s = s(r,R,L1,L2,L3), where r = 100mm, R = 200mm, L1 = 350mm, L2 = 350mm, and L3 = 350mm. The ideal joint input of the 3-PUU parallel robot is q = q(h1,h2,h3). The circumcircle of the motion platform and the circumcircle of the stationary platform are shown in the figure. Figure 11 As shown. According to Figure 5 The kinematic coordinate system established in the figure will link hinge point A. oi B pi In the static coordinate system o-xyz:

[0077]

[0078] Where: i = 1, 2, 3; represents the i-th branch of the 3-PUU parallel robot.

[0079] Hinge point A on the same branch oi and B pi The distance between them is limited to a fixed value L by the linkage. i Therefore, it is possible to establish Substituting the hinge point coordinates, we obtain the kinematic model of the 3-PUU parallel robot:

[0080]

[0081] Solve for h from the above equation i The relationship with p(X,Y,Z) is the inverse kinematics model. The inverse kinematics model of the 3-PUU parallel robot is:

[0082]

[0083] Abbreviated as: h i =f i (X,Y,Z,r,R,L i )

[0084] p(X,Y,Z) and h can be solved from the inverse kinematics model. i The relationship is the forward kinematics model of the 3-PUU parallel robot, which is given here as an implicit equation:

[0085]

[0086] Step 1.2: Establish the ideal error model for the 3-PUU parallel robot: f(p+dp,q,s+ds)=0, where dp represents the end-effector position error caused by the ideal structural parameter error ds, and ds represents the ideal structural parameter error caused by the machining and assembly of the 3-PUU parallel robot, including link length error, circumscribed circle radius error of the motion platform, and circumscribed circle radius error of the stationary platform; specifically described as:

[0087] For the 3-PUU parallel robot, the ideal structural parameter errors ds include the radius error dr of the circumscribed circle of the motion platform, the radius error dR of the circumscribed circle of the stationary platform, the link length error dL1 of branch 1, the link length error dL2 of branch 2, and the link length error dL3 of branch 3. Furthermore, since r and R are coupled in the kinematic equations, i.e., r and R always appear simultaneously in the form of (rR) or (Rr), (dr-dR) is considered equivalent to the structural parameter errors of dr and dR. Adding the corresponding ideal structural parameter errors ds to the positions of the ideal structural parameters s in the ideal kinematic model established in Step 1.1 yields the ideal error model for the three branches of the 3-PUU parallel robot:

[0088]

[0089] Step 1.3: Preset a set of ideal structural parameter error values ​​ds, and arbitrarily select a set of ideal end-effector positions p within the workspace of the 3-PUU parallel robot. Solve for the corresponding ideal joint input q using the ideal kinematic model f(p,q,s)=0 established in Step 1.1. The ideal joint input q is then used to obtain the simulated actual end-effector position p+dp of the 3-PUU parallel robot through the ideal error model f(p+dp,q,s+ds)=0. Specifically:

[0090] Within the workspace of the 3-PUU parallel robot, 30 ideal end positions p are randomly selected, and the corresponding slider input h is solved using the ideal kinematics analytical expression. iBecause the difference between the radius error dr of the moving platform and the radius error dR of the stationary platform in the 3-PUU parallel robot is a constant, the structural parameter errors ds in the ideal error model f(p+dp,q,s+ds)=0 are set as follows: dr=-1.000mm, dR=2.500mm, dL1=3.400mm, dL2=-2.800mm, dL3=2.200mm, (dr-dR)=-3.500mm, h i The simulated actual end-effector position p+dp of the 3-PUU parallel robot was calculated using an ideal error model. Some calculation results are shown in Table 1 (unit: mm). The simulated actual end-effector position error dp of the 3-PUU parallel robot is shown in... Figure 6 As shown.

[0091] Table 1

[0092]

[0093] Step 1.4: Establish a parameter identification model for the 3-PUU parallel robot: f(p+dp,q^(Δs),s+Δs)=0; where Δs represents the structural parameter error optimization variable, q^(Δs) represents the joint input containing the structural parameter error optimization variable Δs, and s+Δs represents the structural parameter containing the structural parameter error optimization variable Δs; specifically described as:

[0094] The end-effector position error of the 3-PUU parallel robot is caused by the ideal structural parameter errors ds(dr, dR, dL1, dL2, dL3, (dr-dR)). The corresponding structural parameter error optimization variables Δs(Δr, ΔR, ΔL1, ΔL2, ΔL3, (Δr-ΔR)) are selected as the structural parameter error optimization variables for the 3-PUU parallel robot parameter identification model. By adjusting the value of the structural parameter error optimization variable Δs, the end-effector position error dp can be made to continuously approach 0. Therefore, the parameter identification model for the 3-PUU parallel robot is established as follows:

[0095]

[0096] Step 1.5: The simulated actual end-effector position p+dp of the 3-PUU parallel robot is used by the 3-PUU parallel robot parameter identification model f(p+dp,q^(Δs),s+Δs)=0 to obtain the joint input q^(Δs) containing the structural parameter error optimization variable Δs; specifically described as:

[0097] Substituting the simulated actual end-effector position p+dp of the 3-PUU parallel robot in Table 1 into the parameter identification model of the 3-PUU parallel robot established in Step 1.4, the corresponding slider input q^(Δs) containing the structural parameter error optimization variable Δs is shown in Table 2:

[0098] Table 2

[0099]

[0100] Step 1.6: The fitness function for establishing the parameter identification model of the 3-PUU parallel robot is as follows:

[0101]

[0102] In the formula, q^(Δs) is the slider input containing the structural parameter error optimization variable Δs, i.e., in Table 2. q is the ideal joint output, i.e., h in Table 1. i .

[0103] Step 1.7: The particle swarm optimization algorithm is used to find the minimum value of the fitness function of the parameter identification model, thereby obtaining the optimal structural parameter error optimization variable Δs* for the 3-PUU parallel robot; specifically described as follows:

[0104] A parameter identification model of a 3-PUU parallel robot was built using MATLAB software. A particle swarm optimization algorithm was written to find the minimum value of the fitness function. After continuous parameter tuning, the optimal optimization variables Δs* were finally obtained as follows: Δr = -1.499mm, ΔR = 2.051mm, ΔL1 = 3.400mm, ΔL2 = -2.800mm, ΔL3 = 2.200mm, (Δr - ΔR) = -3.500mm, and the optimal fitness value was f = 2.922 × 10⁻¹⁰. -10 The fitness evolution curve is as follows Figure 7 As shown.

[0105] It should be noted that, after continuous parameter tuning of the particle swarm optimization algorithm, the particle swarm optimization algorithm parameters in the parameter identification model of the 3-PUU parallel robot in this invention are as follows: the number of particles is set to 300, the number of iterations is set to 200, the feasible solution dimension d = 5, the individual learning factor c1 = 1.5, the swarm learning factor c2 = 1.2, and the inertia weight w = 0.8.

[0106] Step 1.8: Subtract the optimal structural parameter error optimization variable Δs* obtained in Step 1.7 from the set of ideal structural parameter errors ds preset in Step 1.3, and determine whether the difference infinitely approaches 0. If so, it means that the parameter identification result is correct and the ideal structural parameter error ds that causes the robot end-effector position error dp has been found. Otherwise, execute Step 1.7 to adjust the parameters of the particle swarm optimization algorithm and re-perform parameter identification until the parameter identification result is correct. At this point, the construction and verification of the 3-PUU parallel robot parameter identification model are completed, and the verified 3-PUU parallel robot parameter identification model f(p+dp,q^(Δs*),s+Δs*)=0 is obtained; specifically described as:

[0107] In this embodiment, the preset ideal structural parameter errors ds in Step 1.2 are as follows: dr = -1.000mm, dR = 2.500mm, dL1 = 3.400mm, dL2 = -2.800mm, dL3 = 2.200mm, and (dr - dR) = -3.500mm; the optimal structural parameter error values ​​Δs identified in Step 1.7 are as follows: Δr = -1.499mm, ΔR = 2.051mm, ΔL1 = 3.400mm, ΔL2 = -2.800mm, ΔL3 = 2.200mm, and (Δr - ΔR) = -3.500mm. Because of the coupling relationship between structural parameters r and R, the identified Δr and ΔR are not close to the preset values ​​dr and dR. However, the decoupled parameters (Δr-ΔR) and (dr-dR) are completely equal. All other identified parameters are equal to the set values, indicating that the parameter identification results are correct. Thus, the parameter identification model is completed. (According to experiments, through step 1.8, the 3-PUU parallel robot can obtain a verified parameter identification model through the above method.)

[0108] Step 2.1: Randomly select a set of ideal end-effector positions p within the workspace of the 3-PUU parallel robot, and execute Step 1.3 to obtain the ideal joint input q. Use the ideal joint input q to drive the 3-PUU parallel robot and use a laser tracker to obtain the measured end-effector position p'; specifically described as:

[0109] Thirty ideal end-effector positions p are randomly selected within the workspace of the 3-PUU parallel robot, and the corresponding ideal slider input h is solved using the ideal kinematic model. i Input quantity h using an ideal slider i The robot is driven to run, and a laser tracker is used to record the robot's measured end position p', ideal end position p, and ideal slider input h. i Table 3 shows some data of the measured end position p' recorded by the laser tracker.

[0110] Table 3

[0111]

[0112] Step 2.2: Input the measured end position p' as p+dp into the verified 3-PUU parallel robot parameter identification model to obtain the actual structural parameter error Δs' of the 3-PUU parallel robot; specifically, input the measured end position p' collected by the laser tracker in Step 2.1 as d+dp into the verified 3-PUU parallel robot parameter identification model in Step 1.8. The identified actual structural parameter errors Δs' of the 3-PUU parallel robot are as follows: Δr'=-0.9642, ΔR'=-1.6738, ΔL′1=4.8827, ΔL′2=5.6415, ΔL′3=2.8058, (Δr'-ΔR')=0.7096;

[0113] Step 2.3: Correct the ideal kinematic model f(p,q,s)=0 of the 3-PUU parallel robot using the actual structural parameter error Δs', to obtain the actual kinematic model F(p,q*,s-Δs'=0; where s-Δs' represents the actual structural parameters of the 3-PUU parallel robot, p represents the ideal end-effector position of the 3-PUU parallel robot, and q* represents the joint input corresponding to the ideal end-effector position p under actual processing and assembly conditions; specifically described as:

[0114] Based on the ideal structural parameters s of the 3-PUU parallel robot, subtract the actual structural parameter error Δs' obtained from the parameter identification experiment to obtain the actual structural parameters s-Δs' of the 3-PUU parallel robot. Substituting this into the ideal kinematic model, we obtain the actual kinematic model of the 3-PUU parallel robot:

[0115]

[0116] in,

[0117] Step 3.1: Based on the actual kinematic model of the 3-PUU parallel robot, establish the actual error model of the 3-PUU parallel robot F(p+datap,q*,s-Δs'+datas)=0, where s-Δs' represents the actual structural parameters of the 3-PUU parallel robot, datas represents the pre-set structural parameter error terms in the error analysis of the actual error model of the 3-PUU parallel robot, and datap represents the end-effector position error caused by the pre-set structural parameter error terms datas in the error analysis of the actual error model of the 3-PUU parallel robot; specifically described as:

[0118] To verify the rationality of the error model, based on the actual kinematic model of the 3-PUU parallel robot, a structural parameter error term, datas, is superimposed on the actual structural parameter s-Δs' of the 3-PUU parallel robot, thereby establishing the actual error model F(p+datap,q) of the 3-PUU parallel robot. * ,s-Δs'+datas)=0 as follows:

[0119]

[0120] Step 3.2: Randomly assign a set of ideal end position points p 1 For error analysis and verification, the actual joint input q is solved using the actual kinematic model F(p,q*,s-Δs'=0 of the 3-PUU parallel robot. 1 Preset the values ​​of error terms (datas) for different combinations of structural parameters, and then use the actual joint input quantity (q). 1 Substituting the data into the actual error model of the 3-PUU parallel robot for error analysis, we obtain the end-effector error position p caused by the structural parameter error term datas. 1 +datap; Specifically described as:

[0121] Ten ideal end-effector positions p are randomly selected in the motion space of the 3-PUU parallel robot. 1 Used for error analysis and verification, 10 ideal end position points p 1 Substituting into the kinematic model F(p,q*,s-Δs')=0, the corresponding actual joint input q can be solved. 1 10 ideal end position points p 1 (X 1 ,Y 1 Z 1 and corresponding joint input quantities As shown in Table 4, the values ​​of the error term `datas` in the actual error model were then set for five cases: `datar=1mm`, `dataR=0mm`, `dataL1=0mm`, `dataL2=0mm`, `dataL3=0mm` (only `r` has an error); `datar=0mm`, `dataR=1mm`, `dataL1=0mm`, `dataL2=0mm`, `dataL3=0mm` (only `R` has an error); `datar=0mm`, `dataR=0mm`, `dataL1=1mm`, `dataL2=0mm`, `dataL3=0mm` (only `L1` has an error); `datar=0mm`, `dataR=0mm`, `dataL1=0mm`, `dataL2=1mm`, `dataL3=0mm` (only `L2` has an error); `datar=0mm`, `dataR=0mm`, `dataL1=0mm`, `dataL2=0mm`, `dataL3=1mm` (only `L3` has an error). The actual joint input values ​​were then used to set the values ​​of the error term `datas` in the actual error model. Substituting these values ​​into the actual error model of the 3-PUU parallel robot, we obtain the influence of the structural parameter error term on the robot's end-effector position error (i.e., datap) under five different conditions, as follows: Figure 8 As shown (due to the coupling relationship between structural parameters r and R, their influence on the robot end-effector position error is opposite; therefore, for the first and second cases, only the analysis results for the first case datar=1mm, dataR=0mm, dataL1=0mm, dataL2=0mm, and dataL3=0mm are given).

[0122] Table 4

[0123]

[0124] Step 3.3: Using the actual kinematic model of the 3-PUU parallel robot, F(p,q*,s-Δs')=0, adjust the structural parameter error term datas to the ideal end position point p. 1 The influence is mapped onto the joint input of the 3-PUU parallel robot, and the equivalent joint input q” is obtained; that is, the end effector position p of the parallel robot containing structural parameter error terms is calculated. 1 +datap used the actual kinematic model F(p,q*,s-Δs')=0 of the 3-PUU parallel robot to solve for the equivalent joint input q”; the mapped equivalent joint input q” is shown in Table 5.

[0125] Table 5

[0126]

[0127] Step 3.4: Drive the 3-PUU parallel robot with the equivalent joint input q”, and use a laser tracker to obtain the measured end position p” containing the structural parameter error terms datas;

[0128] Step 3.5: Compare the measured end position p” containing the structural parameter error term datas with the end error position p” caused by the structural parameter error term datas. 1 The difference between +datap and Δp is obtained. Δp represents the deviation between the analysis results of the actual error model of the 3-PUU parallel robot and the experimental verification results. If the value of Δp is less than the accuracy index of the 3-PUU parallel robot, it indicates the rationality and correctness of the actual error model of the 3-PUU parallel robot; otherwise, the verification of the actual error model of the 3-PUU parallel robot fails. Thus, the verification of the actual error model of the parallel robot based on parameter identification is completed. Specifically, it involves comparing the measured end position p” collected by the laser tracker in Step 3.4 with the end error position p” of the 3-PUU parallel robot including structural parameter error terms. 1 The difference between +datap and Δp is obtained, such as... Figure 9 As shown. By Figure 9 It can be seen that the deviation between the analysis results of the actual error model of the 3-PUU parallel robot created by the applicant and the experimental results of the error model verification are both within 0.500mm, which meets the 1mm accuracy index of industrial robots. Therefore, the results of the error model verification experiment can prove the correctness and rationality of the actual error model of the 3-PUU parallel robot.

[0129] like Figure 10-14 As shown, the 3-PUU parallel robot includes a static platform 1, a PUU branch chain 2, a link 3, and a moving platform 4; wherein the static platform 1 is used to install and fix the PUU branch chain 2, the moving platform 4 is used to output the end pose of the parallel robot, the PUU branch chain 2 is used to respond to motion control parameters to drive the moving platform 4, and the link 3 is used to connect the PUU branch chain 2 and the moving platform 4.

[0130] Furthermore, the static platform 1 includes a fixed base plate 5, a fixed seat 6, and a fixed corner piece 7; wherein the fixed seat 6 is fixed to the fixed base plate 5 by means of hexagonal screws and fastening nuts, and the fixed corner piece 7, which is installed on the fixed seat 6 by means of T-screws and fastening nuts, is used to fix the column 8 in the PUU branch chain 2.

[0131] Further, the PUU branch chain 2 includes a column 8, a servo motor 9, a servo motor bracket 10, a coupling 11, a lead screw 12, a lead screw support seat I13, a guide rail 14, a guide rail slider 15, a slider 16, an angular contact ball bearing I17, a short shaft I18, an I-type connector I19, a hinge pin I20, a Y-type connector I21, and a lead screw support seat II22; wherein the column 8 is fixed to the fixing seat 6 by the fixing angle piece 7 with T-screws and fastening nuts, the servo motor bracket 10 is fixed to the column 8 by T-screws and fastening nuts, the servo motor 9 is mounted on the servo motor bracket 10 by hexagonal screws and fastening nuts, and the coupling 11 mounted on the output shaft of the servo motor 9 is used to connect the servo motor 9 and the lead screw 12; the lead screw support seat I13 and the lead screw support seat II22 are fixed to the column 9 by T-screws and fastening nuts, and are used to support the two ends of the lead screw 12; the guide rail 14 is connected to the lead screw 12. The slider 16 is fixed to the column 8 by hexagonal screws and fastening nuts. The slider 16 is fixed to the guide rail slider 15 by hexagonal screws. The angular contact ball bearing I17 is installed in the bearing seat of the slider 16 with an transition fit to support the short shaft I18. The I-type connector I19 is connected to both ends of the short shaft I18 by its internal thread. The Y-type connector I21 is connected to the I-type connector I19 by the hinge pin I20. The servo motor 9 serves as the power input of the 3-PUU parallel robot. The servo motor 9 drives the coupling 11 and transmits the power to the lead screw 12. The lead screw 12 drives the slider 16 to move, thereby causing the guide rail slider 15 to slide within the lead of the guide rail 14. The lead screw 12 and the guide rail slider 15 form the P pair of the 3-PUU parallel robot. The angular contact ball bearing I17, the short shaft I18, the I-type connector I19, the hinge pin I20 and the Y-type connector I21 form the U pair of the 3-PUU parallel robot.

[0132] Furthermore, the connecting rod 3 includes a steel pipe with internal threads at both ends and a length of 350mm, used to connect the Y-type connector I21 in the PUU branch chain 2 and the Y-type connector II28 in the moving platform 4.

[0133] Furthermore, the moving platform 4 includes a motion platform 23, an angular contact ball bearing II24, a short shaft II25, an I-type connector II26, a hinge pin II27, and a Y-type connector II28. The angular contact ball bearing II24 is installed in the bearing seat of the motion platform 23 with an transition fit to support the short shaft II25. The I-type connector II26 is threaded to both ends of the short shaft II25, and the Y-type connector II28 is connected to the I-type connector II26 through the hinge pin II27. The angular contact ball bearing II24, the short shaft II25, the I-type connector II26, the hinge pin II27, and the Y-type connector II28 constitute the U-type of the 3-PUU parallel robot.

[0134] Example 4: A terminal device includes a memory, a processor, and a program stored in the memory and executable by the processor. When the processor executes the program, it implements the parallel robot error model verification method based on parameter identification described above.

[0135] Example 5: A computer-readable storage medium comprising a stored program, wherein, when the program is executed, it controls the device where the computer-readable storage medium is located to execute the parallel robot error model verification method based on parameter identification described above.

[0136] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0137] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0138] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for verifying the error model of a parallel robot based on parameter identification, characterized in that, Includes the following steps: Step 1: Verify the established parallel robot parameter identification model to obtain the verified parallel robot parameter identification model f(p+dp,q). ^ (Δs*),s+Δs*)=0; where p represents the ideal end position of the robot, dp represents the end position error of the parallel robot caused by the error of the ideal structural parameters, q represents the ideal joint input, s is the ideal structural parameter of the parallel robot, and Δs* represents the optimal structural parameter error optimization variable of the parallel robot. Step 2: Use the verified parallel robot parameter identification model to conduct parameter identification experiments, obtain the actual structural parameter errors to correct the ideal kinematic model of the parallel robot, and thus construct the actual kinematic model of the parallel robot. Step 3: Based on the results of parameter identification, establish the actual error model of the parallel robot and perform error analysis. Then, map the influence of structural parameter error on the end position point to the joint input quantity and use it to drive the robot to conduct a verification experiment of the actual error model of the parallel robot based on parameter identification. Step 2 is described in detail below: Step 2.1: Randomly select a set of ideal end positions p in the workspace of the parallel robot. Solve for the corresponding ideal joint input q by establishing the ideal kinematic model f(p,q,s)=0 of the parallel robot. Drive the parallel robot with the ideal joint input q and use a laser tracker to obtain the measured end position p'. Step 2.2: Input the measured end position p' as p+dp into the verified parallel robot parameter identification model to obtain the actual structural parameter error Δs' of the parallel robot; Step 2.3: Correct the ideal kinematic model f(p,q,s)=0 of the parallel robot using the actual structural parameter error Δs' of the parallel robot, and obtain the actual kinematic model F(p,q*,s-Δs')=0 of the parallel robot; where s-Δs' represents the actual structural parameters of the parallel robot, p represents the ideal end position of the parallel robot, and q* represents the joint input amount corresponding to the ideal end position p of the parallel robot under actual processing and assembly conditions; Step 3 includes: Step 3.1: Based on the actual kinematic model of the parallel robot, establish the actual error model of the parallel robot F(p+datap,q*,s-Δs'+datas)=0, where s-Δs' represents the actual structural parameters of the parallel robot, datas represents the pre-set structural parameter error terms in the error analysis of the actual error model of the parallel robot, and datap represents the end position error caused by the pre-set structural parameter error terms datas in the error analysis of the actual error model of the parallel robot.

2. The method for verifying the error model of a parallel robot based on parameter identification according to claim 1, characterized in that, Step 1 is described in detail below: Step 1.1: Establish the kinematic coordinate system of the parallel robot and establish the ideal kinematic model of the parallel robot f(p,q,s)=0; where p represents the ideal end position of the robot, corresponding to the coordinates of the geometric center of the motion platform in space, q is the ideal joint input, and s is the ideal structural parameter of the parallel robot. Step 1.2: Establish the ideal error model of the parallel robot f(p+dp,q,s+ds)=0, where dp represents the end position error of the parallel robot caused by the ideal structural parameter error ds, and ds represents the ideal structural parameter error caused by the processing and assembly of the parallel robot, including the link length error, the circumscribed circle radius error of the motion platform, and the circumscribed circle radius error of the static platform. Step 1.3: Preset a set of ideal structural parameter error values ​​ds, and arbitrarily select a set of ideal end positions p in the workspace of the parallel robot. Solve for the corresponding ideal joint input q by establishing the ideal kinematic model of the parallel robot f(p,q,s)=0. The ideal joint input q is used to obtain the simulated actual end position p+dp of the parallel robot by the ideal error model of the parallel robot f(p+dp,q,s+ds)=0. Step 1.4: Establish the parallel robot parameter identification model f(p+dp,q) ^ (Δs), s+Δs)=0; where Δs represents the structural parameter error optimization variable, q ^ (Δs) represents the joint input containing the structural parameter error optimization variable Δs, and s+Δs represents the structural parameter containing the structural parameter error optimization variable Δs; Step 1.5: The simulated actual end-effector position p+dp of the parallel robot is identified by the parallel robot parameter identification model f(p+dp,q). ^ (Δs), s+Δs)=0, yielding the joint input q containing the structural parameter error optimization variable Δs. ^ (Δs); Step 1.6: Establish the fitness function of the parallel robot parameter identification model; Step 1.7: Use an optimization algorithm to find the minimum value of the fitness function of the parallel robot parameter identification model, and obtain the optimal structural parameter error optimization variable Δs* for the parallel robot; Step 1.8: Subtract the optimal structural parameter error optimization variable Δs* obtained in Step 1.7 from the set of ideal structural parameter errors ds preset in Step 1.3, and determine whether the difference is a higher-order infinitesimal. If it is, it means that the parameter identification result is correct and the ideal structural parameter error ds that causes the robot end position error dp has been found. Otherwise, execute Step 1.7 to adjust the parameters of the optimization algorithm and re-identify the parameters until the parameter identification result is correct. This completes the construction and verification of the parallel robot parameter identification model.

3. The method for verifying the error model of a parallel robot based on parameter identification according to claim 2, characterized in that, The structural parameters include the link length, the radius of the circumscribed circle of the moving platform, and the radius of the circumscribed circle of the stationary platform.

4. The method for verifying the error model of a parallel robot based on parameter identification according to claim 2, characterized in that, The fitness function of the parallel robot parameter identification model is: f min (Δs)=sqrt(∑(q ^ (Δs)-q) 2 ); where f min (Δs) represents sqrt(∑(q ^ (Δs)-q) 2 The set of structural parameter optimization variables Δs values ​​when the minimum value is obtained.

5. The method for verifying the error model of a parallel robot based on parameter identification according to claim 1, characterized in that, Step 3 also includes: Step 3.2: Randomly assign a set of ideal end position points p 1 For error analysis and verification, the corresponding actual joint input q is solved using the actual kinematic model of the parallel robot, F(p,q*,s-Δs')=0. 1 Preset the values ​​of error terms (datas) for different combinations of structural parameters, and then use the actual joint input quantity (q). 1 Substituting the data into the actual error model of the parallel robot for error analysis, we obtain the end-effector error position p caused by the structural parameter error term datas. 1 +datap; Step 3.3: Using the actual kinematic model of the parallel robot F(p,q*,s-Δs')=0, adjust the structural parameter error term datas to the ideal end position point p. 1 The influence is mapped onto the joint input of the parallel robot, and the equivalent joint input q'' is solved; Step 3.4: Drive the parallel robot with the equivalent joint input q'' and use a laser tracker to obtain the measured end position p'' containing the structural parameter error terms datas; Step 3.5: Compare the measured end position p'' containing the structural parameter error term datas with the end error position p caused by the structural parameter error term datas. 1 The difference between +datap and Δp is obtained. Δp represents the deviation between the analysis results of the actual error model of the parallel robot and the experimental verification results. If the value of Δp is less than the accuracy index of the parallel robot, it indicates that the design of the actual error model of the parallel robot is reasonable.

6. The method for verifying the error model of a parallel robot based on parameter identification according to claim 1, characterized in that, The parallel robots include 2TPR&2TPS parallel robots, 3-RRS parallel robots, 3URS-PPPS parallel robots, and 3-PUU parallel robots.

7. A parallel robot error model verification device based on parameter identification for performing the method of claim 1, characterized in that, include: The module is used to verify the established parallel robot parameter identification model and obtain the verified parallel robot parameter identification model. The module is used to conduct parameter identification experiments using the validated parallel robot parameter identification model, obtain the actual structural parameter errors to correct the ideal kinematic model of the parallel robot, and thus construct the actual kinematic model of the parallel robot. The verification module is used to establish the actual error model of the parallel robot based on the results of parameter identification, and to perform error analysis. Then, the influence of structural parameter errors on the end position point is mapped to the joint input quantity, which is used to drive the robot to carry out the verification experiment of the actual error model of the parallel robot based on parameter identification.

8. A terminal device, characterized in that: It includes a memory, a processor, and a program stored in the memory and executable by the processor, wherein the processor executes the program to implement the parallel robot error model verification method based on parameter identification as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device containing the computer-readable storage medium to perform the parallel robot error model verification method based on parameter identification as described in any one of claims 1-6.

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