Motion redundancy parallel mechanism inverse solution optimal selection method considering multiple targets

Abstract

The invention relates to the technical field of motion redundancy parallel mechanisms, in particular to a motion redundancy parallel mechanism inverse solution optimization method considering multiple targets, which comprises the following steps: establishing kinematics, rigidity and elastodynamics theoretical models of a mechanism, and obtaining a certain number of samples based on a Latin hypercube design experiment method; calculating an optimal position inverse solution for each sample point by applying a particle swarm optimization algorithm, establishing a comprehensive performance evaluation index by extracting a characteristic value and a unit characteristic vector of a correlation coefficient matrix, and constructing a polynomial response surface mapping model between the optimal position inverse solution of the mechanism and the output pose of the moving platform; according to the position inverse solution optimization method, the position inverse solution is optimally selected according to the optimal comprehensive performance of the mechanism, an area with poor comprehensive performance is avoided as much as possible, and the comprehensive performance of the mechanism is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of motion redundant parallel mechanisms, and in particular to a method for optimizing the position inverse solution of a motion redundant parallel mechanism taking multiple objectives into consideration. Background Art

[0002] Compared with serial mechanisms, parallel mechanisms have the advantages of high stiffness, high precision, high load-bearing capacity, and good dynamic response. They have been widely used in the fields of sorting and handling, motion simulation, and parts processing. However, parallel mechanisms also have some shortcomings, such as small working space, many singular configurations, and complex control. After research, scholars at home and abroad found that motion redundancy can be used to improve this problem. The motion redundant parallel mechanism can not only avoid singularity and improve stiffness, but also increase the working space and improve other performance of the mechanism. However, for a given dynamic platform posture, the position inverse solution of the motion redundant parallel mechanism is not unique. The optimization of the position inverse solution of the motion redundant parallel mechanism refers to the optimization of the position inverse solution of the mechanism considering the kinematics, stiffness, dynamics and other performance of the mechanism. It is the basis for the controller design, drive selection and trajectory planning of the motion redundant parallel mechanism, and improves the working performance of the mechanism. Summary of the invention

[0003] In view of the deficiencies in the prior art, an object of the present invention is to provide a method for optimizing the position inverse solution of a kinematic redundant parallel mechanism taking multiple objectives into consideration.

[0004] To achieve the above object, the present invention provides the following technical solution: a method for optimizing the position inverse solution of a kinematic redundant parallel mechanism considering multiple objectives, the steps of which are:

[0005] (1) Based on the closed-loop vector method, the kinematic model of the kinematic redundant parallel mechanism is established to solve the inverse position solution and motion / force transmission performance indicators of the mechanism;

[0006] (2) According to the static stiffness modeling method of the kinematic redundant parallel mechanism, the static stiffness model of the mechanism is established, and the minimum linear displacement stiffness performance index of the mechanism is solved. According to the elastic dynamics modeling method of the kinematic redundant parallel mechanism, the elastic dynamics equation of the mechanism is derived, and the corresponding fundamental frequency index is calculated;

[0007] (3) Based on the Latin hypercube design experiment method, a certain number of samples are obtained, and for each sample point, the particle swarm optimization algorithm is used to calculate the optimal position inverse solution;

[0008] (4) Apply principal component analysis to establish a comprehensive evaluation function for kinematic redundant parallel mechanisms;

[0009] (5) Use polynomial fitting technology to establish a polynomial response surface model between the comprehensive performance evaluation function and the design parameters, and carry out cross-validation and external validation to evaluate the accuracy of the response surface model;

[0010] (6) Based on the established polynomial response surface model, the inverse position solution with the optimal comprehensive performance of the kinematic redundant parallel mechanism is quickly obtained, thereby achieving efficient selection of the inverse position solution.

[0011] In some embodiments, according to steps (1)-(3),

[0012] Based on the kinematic redundant parallel mechanism, the mechanism is assumed to consist of n branches, each of which consists of a series of m connecting rods. Considering the kinematics, stiffness and elastic dynamics performance of the mechanism,

[0013] The multi-objective drive optimization mathematical model of the kinematic redundant parallel mechanism is defined as:

[0014]

[0015] Where LTI is the motion / force transmission performance index; LSI is the minimum linear displacement stiffness performance index; LDI is the fundamental frequency index, and qmin and qmax represent the minimum and maximum values ​​of the driving joint qi, respectively.

[0016] Consider three single performance indicators, assuming that each indicator has n samples, and the sample data is X = (x1, x2, x3), x i =(x 1i , x 2i , ..., x ni ) T , Since the dimensions of the sample data are not uniform, the Z-Score transformation is used to standardize the sample data. The formula is:

[0017]

[0018] In the formula, Mean variance

[0019] In some embodiments, according to step (4),

[0020] Since the motion / force transmission performance index, the minimum linear displacement stiffness performance index and the fundamental frequency index have different degrees of correlation, and the information provided is cross-overlapping, a correlation analysis is performed on these three performance indicators, and the correlation coefficient matrix R is calculated as follows:

[0021]

[0022] Through the equation group (λE-R)X=0, the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R are obtained. The three eigenvalues ​​are arranged in ascending order as λ1≥λ2≥λ3≥0, and the corresponding eigenvectors are (a1, a2, a3), ai=(a 1i , a2i , a 3i ) T , the number of principal components is determined according to the cumulative contribution rate δ of the eigenvalues, and the number of principal components k is determined when the cumulative contribution rate δ ≥ 85%.

[0023]

[0024] The standardized eigenvector can be used as the coefficient in front of each single performance indicator, so the i-th principal component can be expressed as:

[0025]

[0026] The comprehensive performance evaluation index of the kinematic redundant parallel mechanism can be obtained by extracting the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R, and the expression is:

[0027]

[0028] Compared with the prior art, the beneficial effects of the present invention are: comprehensively considering the kinematics, stiffness and elastic dynamics performance of the mechanism, based on the idea of ​​multi-objective optimization, applying the principal component analysis method, and converting the three single performance indicators into a comprehensive performance evaluation indicator through data dimensionality reduction, objectively establishing the comprehensive performance evaluation function of the motion redundant parallel mechanism, and proposing a method for optimizing the position inverse solution of the motion redundant parallel mechanism.

[0029] According to the best comprehensive performance of the mechanism, the inverse solution of the position is optimized and selected to avoid the area with poor comprehensive performance as much as possible to improve the comprehensive performance of the mechanism.

[0030] Details of one or more embodiments of the present application are presented in the following drawings and descriptions to make other features, purposes and advantages of the present application more concise and easy to understand. The present application is fully described and understood through the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 General model (a) and finite element model (b) of kinematic redundant parallel mechanism;

[0032] Figure 2 It is the optimal flow chart of the position inverse solution of the present invention;

[0033] Figure 3 It is a geometric relationship diagram of the 2PUPR-PRPU parallel mechanism of the present invention;

[0034] Figure 4 QQ plot of sample point data and theoretical prediction data;

[0035] Figure 5 The optimal distribution diagram of comprehensive performance indicators of 2PUPR-PRPU parallel mechanism at different heights;

[0036] Figure 6 This is the driving distribution diagram for the 2PUPR-PRPU parallel mechanism with optimal comprehensive performance at different heights. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] The present invention provides a technical solution: a method for optimizing the position inverse solution of a motion redundant parallel mechanism considering multiple objectives. The general model of the motion redundant parallel mechanism is as follows: Figure 1 As shown in (a), without loss of generality, assume that the mechanism consists of n branches, each of which consists of a series of m connecting rods connected in series. The corresponding finite element model is as follows: Figure 1 (b) as shown.

[0039] Taking into account the kinematics, stiffness and elastic dynamics of the mechanism, based on the idea of ​​multi-objective optimization, the principal component analysis method is applied to convert the three single performance indicators into a comprehensive performance evaluation indicator by means of data dimension reduction, and the comprehensive performance evaluation function of the kinematic redundant parallel mechanism is objectively established. The inverse solution optimization method of the kinematic redundant parallel mechanism is proposed. Figure 2 The detailed steps are as follows:

[0040] (1) Based on the closed-loop vector method, the kinematic model of the motion-redundant parallel mechanism is established to solve the inverse position solution and motion / force transmission performance indicators of the mechanism.

[0041] (2) According to the static stiffness modeling method of the kinematic redundant parallel mechanism, the static stiffness model of the mechanism is established, and the minimum linear displacement stiffness performance index of the mechanism is solved. According to the elastic dynamics modeling method of the kinematic redundant parallel mechanism, the elastic dynamics equation of the mechanism is derived, and the corresponding fundamental frequency index is calculated.

[0042] (3) Based on the Latin hypercube design experimental method, a certain number of samples are obtained, and for each sample point, the particle swarm optimization algorithm is used to calculate the optimal position inverse solution. The multi-objective drive optimization mathematical model of the kinematic redundant parallel mechanism can be defined as

[0043]

[0044] Where LTI is the motion / force transmission performance index; LSI is the minimum linear displacement stiffness performance index; LDI is the fundamental frequency index, and qmin and qmax represent the minimum and maximum values ​​of the driving joint qi, respectively.

[0045] Consider three single performance indicators. Assume that each indicator has n samples and the sample data is X = (x1, x2, x3). i =(x 1i , x 2i , ..., x ni ) T Since the dimensions of the sample data are not uniform, the Z-Score transformation is used to standardize the sample data. The formula is:

[0046]

[0047] In the formula, Mean variance

[0048] (4) The principal component analysis method is used to establish a comprehensive evaluation function for the motion redundant parallel mechanism. Since the motion / force transmission performance index, the minimum linear displacement stiffness performance index, and the fundamental frequency index have different degrees of correlation, the information provided may overlap, so the correlation analysis of these three performance indicators is performed and the correlation coefficient matrix R is calculated as follows:

[0049]

[0050] Through the equation system (λE-R)X=0, the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R are obtained. The three eigenvalues ​​are arranged in ascending order as λ1≥λ2≥λ3≥0, and the corresponding eigenvectors are (a1, a2, a3), a i =(a 1i , a 2i , a 3i ) T The number of principal components is determined based on the cumulative contribution rate δ of the eigenvalues. Usually, the cumulative contribution rate δ ≥ 85% is used to determine the number of principal components k.

[0051]

[0052] The standardized eigenvector can be used as the coefficient in front of each single performance indicator, so the i-th principal component can be expressed as

[0053]

[0054] The comprehensive performance evaluation index of the kinematic redundant parallel mechanism can be obtained by extracting the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R, and the expression is:

[0055]

[0056] (5) A polynomial response surface model between the comprehensive performance evaluation function and the design parameters was established using polynomial fitting technology, and cross-validation and external validation were carried out to evaluate the accuracy of the response surface model.

[0057] (6) Based on the established polynomial response surface model, the inverse position solution with the optimal comprehensive performance of the kinematic redundant parallel mechanism is quickly obtained, thereby achieving efficient selection of the inverse position solution.

[0058] Through this technical solution, the 2PUPR-PRPU parallel mechanism is selected for position inverse solution optimization.

[0059] The geometric relationship of the 2PUPR-PRPU parallel mechanism is as follows: Figure 3 As shown. It can be found in the figure that the fixed coordinate system O-xyz is fixed on the fixed platform, the origin O is located at the center point of A1A2, the x-axis is along the OA3 direction, the y-axis is perpendicular to the x-axis, and along the direction of the guide rail driving P pair, and the z-axis is determined by the right-hand rule. The moving coordinate system o-uvw is fixed on the moving platform, the origin o is located at the center point of the moving platform, the u-axis is parallel to the x-axis and collinear with oB3, the v-axis is parallel to the y-axis and along the OB2 direction, and the w-axis is determined by the right-hand rule. The dimensional parameters of the 2PUPR-PRPU parallel mechanism are: OA1=q4, OA2=q5, OA3=q6, oB1=l a1 , oB2=l a1 , oB3=l a2 In the fixed coordinate system O-xyz, A i The coordinates of the points (i=1, 2, 3) are (0, -q4, 0) respectively. T , (0, q5, 0) T and (q6, 0, 0) T .

[0060] According to the degree of freedom analysis of the 2PUPR-PRPU parallel mechanism, it can be known that the moving platform first rotates around the y-axis by an angle of β, and then rotates around the u-axis of the moving platform by an angle of α. The rotation matrix R of the moving coordinate system o-uvw relative to the fixed coordinate system O-xyz is p for

[0061]

[0062] In the formula, R y，β and R u，α Represent the rotation matrices around the y-axis of the fixed coordinate system and the u-axis of the moving coordinate system respectively.

[0063] According to the geometric relationship of the 2PUPR-PRPU parallel mechanism, it can be obtained that the origin o of the moving platform is always limited to the plane y = 0. Therefore, the position vector P of the origin o of the moving platform in the fixed coordinate system O-xyz is m It can be written as

[0064] P m =(ztanβ,0,z) T (8)

[0065] Where z represents the distance between the origin O of the fixed coordinate system and the moving coordinate system o.

[0066] Position vector b i (i=1,2,3) can be written as

[0067]

[0068] Position vector a i (i=1,2,3) can be written as

[0069]

[0070] Apply the rotation matrix R p , position vector a i (i=1,2,3) can be written as

[0071]

[0072] Using the closed-loop vector method, the vector equation of the 2PUPR-PRPU parallel mechanism is obtained as follows:

[0073] q i =P m +a i -b i (i=1,2,3) (12)

[0074] Substituting equations (8)-(11) into equation (12), we can obtain

[0075]

[0076] According to formula (13), when the output posture parameters (α, β and z) of the dynamic platform are known, the driving distances q1 and q4 of branch 1 are related, the driving distances q2 and q5 of branch 2 are related, and the driving distances q3 and q6 of branch 3 are related. Therefore, the driving distances q of the three branches of the 2PUPR-PRPU parallel mechanism are i (i=1, 2, ..., 6) are not unique.

[0077] A high-quality posture workspace is selected as the processing area in the mechanism workspace: the height of the moving platform z∈(400mm, 600mm), and the posture angle is (α, β)∈(-20°, 20°). Based on the Latin hypercube design experimental method, sampling is performed in the interval. In order to ensure the fitting accuracy, this paper selects 2187 sampling points. According to the theoretical calculation formulas of the above kinematic, stiffness and elastic dynamics performance indicators, the particle swarm optimization algorithm is applied to obtain the original data of each indicator at each sampling point as shown in Table 1;

[0078] After standardizing the sample data using the Z-Score method, the standardized data of each performance index are shown in Table 2. The results show that the motion / force transmission performance index LTI t , Minimum linear displacement stiffness performance index LSI t and fundamental frequency index LDI t There is a certain amount of information overlap between them. The correlation coefficient matrix R can not only eliminate the overlapping data information, but also better reflect the correlation between the performance indicators. The correlation coefficient matrix R is shown in Table 3. As can be seen from Table 3, LTI t , LSI t and LDI t Positive correlation, that is, the trend of each indicator is the same. t and LSI t The correlation coefficient is 0.2022, LTI t and LDI t The correlation coefficient is 0.2582, which is small and the correlation is weak. t and LDI t The correlation coefficient is 0.9591, which is large and has a strong correlation. It can be seen that the three indicators have different degrees of correlation with each other. The correlation coefficient matrix reflects the internal connections between the performance indicators, and the principal components are determined based on these internal connections between the indicators.

[0079] Table 1 Original data of performance indicators of 2PUPR-PRPU parallel mechanism

[0080] Sample No. <![CDATA[LTI t ]]> <![CDATA[LSI t ]]> <![CDATA[LDI t ]]> 1 0.3043 1.1624E7 81.8748 ... ... ... ... 2186 0.6044 3.3559E7 125.8891 2187 0.7578 4.7761E67 147.1119

[0081] Table 2 Standardized data of performance indicators of 2PUPR-PRPU parallel mechanism

[0082] Sample No. <![CDATA[LTI t ]]> <![CDATA[LSI t ]]> <![CDATA[LDI t ]]> 1 -1.4799 -0.4188 -0.3401 ... ... ... ... 2186 0.0363 1.9740 1.1004 2187 0.8113 3.5232 1.7950

[0083] Table 3 Correlation coefficient matrix R of performance indicators

[0084] Performance Indicators <![CDATA[LTI t ]]> <![CDATA[LSI t ]]> <![CDATA[LDI t ]]> <![CDATA[LTI t ]]> 1 0.2022 0.2582 <![CDATA[LSI t ]]> 0.2022 1 0.9591 <![CDATA[LDI t ]]> 0.2582 0.9591 1

[0085] The principal components can be determined by analyzing the eigenvalues ​​and unit eigenvectors of the correlation coefficient matrix R. In other words, according to the motion / force transmission performance index LTI t , Minimum linear displacement stiffness performance index LSI t and fundamental frequency index LDI t The number of principal components can be calculated by the cumulative variance contribution rate. Usually, the number of principal components is determined by taking the cumulative contribution rate greater than or equal to 85%. The eigenvalues, eigenvectors and cumulative contribution rates of the correlation coefficient matrix R are shown in Table 4. It can be seen from Table 4 that the cumulative contribution rate of the two principal components is 98.69%, which is far more than 85%. Therefore, it can more comprehensively reflect the motion / force transmission performance index LTI t , Minimum linear displacement stiffness performance index LSI t and fundamental frequency index LDI t All information contained in the first and second principal component expressions of the motion / force transmission performance index LTI t , Minimum linear displacement stiffness performance index LSI t and fundamental frequency index LDI t The coefficients of can be obtained by extracting the values ​​of the corresponding eigenvectors.

[0086] Table 4 Eigenvalues, eigenvectors and cumulative contribution rates of correlation coefficient matrix R

[0087] Eigenvalue Eigenvector Cumulative contribution rate 2.0592 <![CDATA[[0.2940,0.6718,0.6799] T ]]> 68.64％ 0.9016 <![CDATA[[0.9548,-0.2389,-0.1768] T ]]> 98.69％ 0.0392 <![CDATA[[0.0437,0.7011,-0.7117] T ]]> 100％

[0088] The expression of the first principal component is

[0089]

[0090] The expression of the second principal component is

[0091]

[0092] The motion / force transmission performance index LTI of the 2PUPR-PRPU parallel mechanism is analyzed by principal component analysis. t , Minimum linear displacement stiffness performance index LSI t and fundamental frequency index LDI t Converted into a comprehensive performance evaluation index, the expression is:

[0093]

[0094] The particle swarm optimization algorithm is applied to each sampling point to optimize the optimal position inverse solution of the sampling point, and the polynomial fitting technology is used to establish the response surface mapping model between the optimal position inverse solution and the output posture parameters of the dynamic platform. The QQ plot of the sample point data and the theoretical prediction data of the polynomial response surface model obtained by the above method is shown in Figure 2. Figure 4As shown in the figure, it can be found that the data of the two distributions are approximately on a straight line, indicating that the polynomial response surface model has a good fitting effect.

[0095] According to the structure and material parameters of the 2PUPR-PRPU parallel mechanism, the optimal distribution of the comprehensive performance index F of the mechanism at different heights can be obtained by using the above inverse solution optimization method. Figure 5 As shown. When the center point of the moving platform is at a height of z = 400mm, the maximum comprehensive performance index of the mechanism is 12.03. When the center point of the moving platform is at a height of z = 500mm, the maximum comprehensive performance index of the mechanism is 6.917. When the center point of the moving platform is at a height of z = 600mm, the maximum comprehensive performance index of the mechanism is 3.294. It can be found that the comprehensive performance index of the mechanism decreases with the increase of the height z. The main reason is that with the increase of the operating height of the moving platform, the branch rods of the mechanism become longer, and the elastic deformation of the rods increases, which reduces the stiffness and dynamic performance of the mechanism. At any height, the comprehensive performance indicators of the mechanism are symmetrical about the angle α, which is consistent with the structural characteristics of the mechanism. In addition, the minimum values ​​of the comprehensive performance indicators of the 2PUPR-PRPU parallel mechanism occur in the edge area of ​​β = -20°. In order to improve the comprehensive performance of the mechanism, the mechanism should be kept away from this area as much as possible during work. As the β angle increases, the comprehensive performance index F of the mechanism increases, mainly because the PRPU branch is located in the positive direction of the coordinate axis. The larger the β angle, the shorter the driving rod of the PRPU branch, and the better the overall stiffness and dynamic performance of the mechanism. When the posture range is α∈(-20°, 20°), β∈(10°, 20°), the comprehensive performance index F of the 2PUPR-PRPU parallel mechanism is large, and it has good comprehensive performance. Therefore, the mechanism should work within this posture range as much as possible.

[0096] Figure 6 The optimal driving values ​​of the 2PUPR-PRPU parallel mechanism at different heights are given. When the center point of the mechanism's moving platform is at a height of z = 400 mm, its optimal driving displacements q4, q5 and q6 are Figure 6 (a)-(c). It can be found that the driving displacements q4 and q5 increase with the increase of angle β, while the optimal driving displacement q6 decreases with the increase of angle β. When the center point of the mechanism moving platform is at a height of z = 500 mm, its optimal driving displacements q4, q5 and q6 are Figure 6(d)-(f). It can be found that the driving displacements q4 and q5 increase with the increase of angle β. When the posture range is α∈(-20°, 20°), β∈(10°, 20°), the driving displacements q4 and q5 increase with the increase of angle β, and the maximum driving displacement appears in the edge area of ​​β=20°. The driving displacement q6 does not change in the posture space, indicating that the comprehensive performance index F is not sensitive to the driving displacement q6 at this height. When the center point of the moving platform of the 2PUPR-PRPU parallel mechanism is at a height of z=600mm, its optimal driving displacements q4, q5 and q6 are respectively Figure 6 (g)-(i). It can be found that the drive displacements q4 and q5 increase with the increase of angle β. When the posture range is α∈(-20°, 20°), β∈(10°, 20°), the drive displacements q4 and q5 increase with the increase of angle β, and the maximum drive displacement appears in the edge area of ​​β=20°. When the drive displacement q6 takes the maximum value of 600mm, the comprehensive performance index F of the mechanism is the best, indicating that the comprehensive performance of the mechanism cannot be changed by changing the drive displacement q6 at this height.

[0097] Combination Figure 5 and Figure 6 It can be found that the configuration parameters of the mechanism have an important influence on the comprehensive performance distribution of the mechanism, and the optimal driving displacement changes differently at different heights. During the working process of the mechanism, according to the best comprehensive performance of the mechanism, the inverse solution of the position is optimized to avoid the area with poor comprehensive performance as much as possible to improve the comprehensive performance of the mechanism.

[0098] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, 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 attached claims.

[0099] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing the position inverse solution of a kinematic redundant parallel mechanism considering multiple objectives, characterized in that: The steps are: (1) Based on the closed-loop vector method, the kinematic model of the motion-redundant parallel mechanism is established to solve the inverse position solution and motion / force transmission performance indicators of the mechanism; (2) According to the static stiffness modeling method of the kinematic redundant parallel mechanism, the static stiffness model of the mechanism is established, and the minimum linear displacement stiffness performance index of the mechanism is solved. According to the elastic dynamics modeling method of the kinematic redundant parallel mechanism, the elastic dynamics equation of the mechanism is derived, and the corresponding fundamental frequency index is calculated; (3) Based on the Latin hypercube design experiment method, a certain number of samples are obtained, and for each sample point, the particle swarm optimization algorithm is used to calculate the optimal position inverse solution; (4) Apply principal component analysis to establish a comprehensive evaluation function for kinematic redundant parallel mechanisms; (5) Use polynomial fitting technology to establish a polynomial response surface model between the comprehensive performance evaluation function and the design parameters, and carry out cross-validation and external validation to evaluate the accuracy of the response surface model; (6) Based on the established polynomial response surface model, the inverse position solution with the optimal comprehensive performance of the kinematic redundant parallel mechanism is quickly obtained, thereby achieving efficient selection of the inverse position solution.

2. The method for inverse solution optimization of the position of a kinematic redundant parallel mechanism considering multiple objectives according to claim 1, characterized in that: According to steps (1)-(3), Based on the kinematic redundant parallel mechanism, the mechanism is assumed to consist of n branches, each of which consists of a series of m connecting rods. Considering the kinematics, stiffness and elastic dynamics performance of the mechanism, The multi-objective drive optimization mathematical model of the kinematic redundant parallel mechanism is defined as: Where, LTI is the motion / force transmission performance index; LSI is the minimum linear displacement stiffness performance index; LDI is the fundamental frequency index, q min With q max They represent the driving joint q i The minimum and maximum values ​​of . Consider three single performance indicators, assuming that each indicator has n samples, and the sample data is X = (x1, x2, x3), x i =(x 1i ,x 2i ,...,x ni ) T , Since the dimensions of the sample data are not uniform, the Z-Score transformation is used to standardize the sample data. The formula is: In the formula, Mean variance 3. The method for inverse solution optimization of the position of a kinematic redundant parallel mechanism considering multiple objectives according to claim 2, characterized in that: According to step (4), Since the motion / force transmission performance index, the minimum linear displacement stiffness performance index and the fundamental frequency index have different degrees of correlation, and the information provided is cross-overlapping, a correlation analysis is performed on these three performance indicators, and the correlation coefficient matrix R is calculated as follows: Through the equation group (λE-R)X=0, the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R are obtained. The three eigenvalues ​​are arranged in ascending order as λ1≥λ2≥λ3≥0, and the corresponding eigenvectors are (a1, a2, a3), a i =(a 1i ,a 2i ,a 3i ) T , the number of principal components is determined according to the cumulative contribution rate δ of the eigenvalues, and the number of principal components k is determined when the cumulative contribution rate δ ≥ 85%. The standardized eigenvector can be used as the coefficient in front of each single performance indicator, so the i-th principal component can be expressed as: The comprehensive performance evaluation index of the kinematic redundant parallel mechanism can be obtained by extracting the eigenvalues ​​and eigenvectors of the correlation coefficient matrix R, and the expression is:

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