A parallel robot workspace efficient solving method based on seed space segmentation and principal component analysis

Abstract

The application relates to a kind of parallel robot work space efficient solving method based on seed space segmentation and principal component analysis, the method uses Monte Carlo and stratification method as the basis of solving algorithm, through the fusion of both, in addition to the seed space segmentation for boundary space screening and the principal component analysis algorithm for the stratification direction of boundary seed space, the design of overall solving algorithm is realized.The method can segment the larger work space of parallel robot, and the rough boundary of work space is quickly and independently screened out by the ratio of reversible point and non-reversible point in the segmented space, the range of overall solving space is reduced, and the optimal stratification direction of boundary seed space is selected by the principal component analysis method, the number of stratification layers in the direction with large gradient change is increased, the feature loss is reduced, and the solving accuracy of overall work space boundary is improved.

Description

TECHNICAL FIELD

[0001] The application relates to a method for improving the solving efficiency and accuracy of a parallel robot workspace, in particular to a parallel robot workspace efficient solving method based on seed space segmentation and principal component analysis. BACKGROUND

[0002] With the upgrading of traditional industries in China and the entry into a new stage of manufacturing intelligence, robots replacing natural persons to carry out intelligent factory operations have become the mainstream development trend. From the application level, parallel robots have high stiffness, large bearing, high precision, fast speed and compact structure due to the closed-loop structure, can make up for the shortcomings of serial robots, and are widely used in important fields such as orthopedic surgical robots, sorting robots, large airplane multi-degree-of-freedom simulation platforms and parallel machining machine tools. With the continuous development and deepening of the application industry of parallel robots, the performance requirements such as workspace and precision of the parallel robots are further improved. Workspace solving is an important link for analyzing the performance and optimizing the structural parameters of the parallel robot. The finite discrete method is a general solving method for the workspace of the parallel robot, and the solving process is simple and convenient. However, in the workspace solving process, the uniform generation of the solving numerical points and the solving accuracy depend on the number of the solving numerical points; or there is a feature loss problem in the transition area with large gradient change, and the workspace solving accuracy is easily affected by the configuration of the parallel robot, thereby affecting the accuracy of the performance analysis of the parallel robot. Therefore, in order to faster and more accurately analyze the performance and optimize the structural parameters of the parallel robot, it is necessary to study the workspace solving algorithm of the parallel robot.

[0003] The finite discrete method is a general method for solving the workspace of the parallel robot, the point discrete method generates numerical points randomly, fits the workspace boundary, and has high universality, but the numerical points are randomly distributed and not concentrated, which leads to low solving accuracy and waste of calculation; and the interval discrete method adopts the interval block solving method, improves the solving efficiency of the interval block workspace boundary points through interval constraint solving, but in the transition area of the interval block with large gradient change, there is a feature loss, thereby affecting the final workspace solving accuracy. The application utilizes the seed space segmentation to screen the approximate boundary space, reduces the calculation cost to improve the solving efficiency, and determines the cutting direction of the boundary seed space through principal component analysis to reduce the feature loss and improve the final workspace solving accuracy. SUMMARY

[0004] The application mainly aims at the above-mentioned problems, divides the workspace of the parallel robot, excludes invalid internal and external regions through seed space type judgment, obtains the rough workspace boundary to improve the solving efficiency, and determines the cutting direction of the boundary seed space through principal component analysis to reduce the feature loss, thereby improving the accuracy of the final workspace.

[0005] To achieve the above object, the application adopts the following scheme:

[0006] A high-efficiency parallel robot workspace solving method based on seed space segmentation and principal component analysis,

[0007] Specifically includes the following steps:

[0008] Step S1. Obtain an approximate cuboid based on the traditional Monte Carlo method to preliminarily limit the workspace;

[0009] Step S2. Enlarge the preliminarily limited workspace, and determine the number of seed workspaces according to the allowable internal hole diameter inside, to complete seed workspace segmentation;

[0010] Step S3. Calculate the volume coefficient of each seed workspace by uniformly generating points, divide the seed workspace type, and obtain the rough boundary range of the workspace;

[0011] Step S4. Perform principal component analysis on the boundary seed workspace to determine the cutting direction of the boundary seed workspace;

[0012] Step S5. Determine the workspace approximate boundary of a single section layer through grid contraction iteration, and obtain the overall workspace boundary by fitting the approximate boundaries in all boundary seed space layers.

[0013] Further, the step S1 specifically includes:

[0014] According to the robot structure size, obtain the limit motion range of the robot in the spatial coordinate axis direction: (x min , x max ), (y min , y max ) and (z min , z max ), and determine the workspace solving precision w acc and the maximum allowable internal hole diameter d hole . Randomly generate N position points within the above limit motion range, substitute into the parallel robot inverse kinematics model, retain the points with inverse kinematics solution among the position points, respectively obtain the minimum and maximum values of the retained points in the three coordinate directions, as the approximate cuboid range of the robot workspace: (x min1 , x max1 ), (y min1 , y max1 ) and (z min1 , z max1 ).

[0015] Further, the step S2 specifically includes:

[0016] Considering that the traditional Monte Carlo method has low approximation accuracy for the workspace when the number of numerical points is small, one Δ1 is added to the maximum value and one Δ1 is subtracted from the minimum value in the single direction of the three coordinates, where Δ1 = 10*w acc , and the maximum value and the minimum value are respectively rounded up and down, and the update range is (x min2 , x max2 ), (y min2 , y max2 ) and (z min2 , z max2 ). Then, according to the maximum diameter d hole of the internal hole allowed by the workspace and formulas (1)-(4), the number Num hole of seed workspaces can be determined, where ceil is the rounding up of the internal formula.

[0017] x num = ceil[(x max2 -x min2 ) / d hole ] (1)

[0018] y num = ceil[[(y max2 -y min2 ) / d hole ] (2)

[0019] z num = ceil[(z max2 -z min2 ) / d hole ] (3)

[0020] Num hole = x num *y num *z num (4)

[0021] Further, the step S3 specifically comprises:

[0022] Since the more the solving regions are, the lower the solving efficiency is, a relationship model of the workspace boundary and the seed workspace is established to refine the solving regions. Discrete points are uniformly generated in the workspace, and a seed space volume coefficient α is used to evaluate the seed space. The coefficient α represents the ratio of the reachable discrete points in the seed space to the theoretical discrete points.

[0023] The seed space type can be divided by formula (5) through the volume coefficient.

[0024]

[0025] Wherein: Case1 represents the current seed space is at the boundary of the robot workspace, the seed space is the external seed space; Case2 represents the current seed space is at the transition of the robot workspace boundary, the seed space is the boundary seed space; Case3 represents the current seed space is in the interior of the robot workspace, the seed space is the internal seed space.

[0026] With the above basis for the classification of seed space types, N2 numerical points are uniformly generated in each seed workspace, the volume coefficient a of each seed space is calculated, the seed space is divided, the boundary seed workspace is separated, and the rough workspace boundary composed of reversible numerical points in the boundary seed workspace is obtained.

[0027] Further, the step S4 specifically comprises:

[0028] In order to refine the rough workspace boundary and obtain the final workspace, the obtained boundary seed space needs to be further layered and cut. The determination of the cutting direction of the curved surface can be regarded as the characterization of three-dimensional data points through a two-dimensional plane, which is consistent with the characteristics of principal component analysis, so the cutting direction of the boundary seed space can be determined by the principal component analysis method.

[0029] Principal component analysis is a commonly used data dimension reduction algorithm, and its principle and implementation steps are as follows:

[0030] Suppose there are m samples {X 1 , X 2 ,..., X m}, where any sample is n-dimensional data First, the centering operation is performed on all sample data, as shown in formulas (6) and (7):

[0031]

[0032]

[0033] After the sample data is averaged, the covariance matrix C is constructed as shown in formula (8):

[0034]

[0035] Then, the eigenvalues of the covariance matrix C are solved, and the corresponding eigenvectors are solved by the eigenvalues, as follows:

[0036] Cu=λu (9)

[0037] Wherein: λ is the eigenvalue, and u is the eigenvector.

[0038] The specific steps of determining the boundary seed space according to the principal component analysis are as follows:

[0039] Take the boundary seed space starting point as the initial origin, and randomly generate N3 value points as sample data points for principal component analysis with the seed space length as the step size After obtaining the sample, based on the principal component analysis principle described above, the sample data eigenvalues are calculated and sorted, and the dimension with the largest eigenvalue is selected as the cutting direction of the boundary seed space. When the largest dimension is not unique, select according to the order of X, Y and Z.

[0040] Further, the step S5 specifically includes:

[0041] The workspace solving precision w acc As a cutting step, the boundary seed space is layered according to the cutting direction determined in step S4, and then the four corner points of the section are determined to determine the section layer area type: a. All internal points, b. All external points, c. One side is internal point and the other side is external point. The section of type a and b is not operated. The section of type c is gridded, and the type c section is divided into 4 equal parts according to the area type of the section. The type c section is divided into 4 equal parts, and the area type of the divided section is judged. Repeat this process until the minimum grid length generated is less than or equal to the workspace solving precision w acc After completing the iteration, the points inside the workspace in the second last iteration are determined as the approximate boundary. After completing the generation of the approximate boundary of the boundary seed space, the boundary points are fitted to obtain the final refined workspace boundary.

[0042] The method provided by the application can quickly screen out the rough boundary of the parallel robot workspace, reduce the overall solving range, improve the solving efficiency, and determine the boundary seed space layering direction through principal component analysis, increase the number of layers in the direction with large gradient change, and thus improve the solving precision of the overall workspace boundary. Especially in the condition that the workspace range is large and the transition area of the interval block has large gradient change, the rough boundary of the workspace can be quickly and autonomously found, the workspace solving precision of the transition area with large gradient change is improved, and the refined workspace solving is completed. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a schematic diagram of seed space segmentation;

[0044] Figure 2 is a schematic diagram of rough workspace boundary;

[0045] Figure 3 is a schematic diagram of the boundary seed space after sectioning;

[0046] Figure 4 is a schematic diagram of the approximate boundary determined by grid contraction iteration;

[0047] Figure 5 is a structural schematic diagram and a physical diagram of a parallel robot (4PPa-2PaR type) implemented by the present application;

[0048] Figure 6 is a schematic diagram of a work space boundary solved by the present application. DETAILED DESCRIPTION

[0049] The technical solutions of the present application will be further described in detail below in combination with the drawings and specific examples.

[0050] With reference to Figure 1 , the parallel robot work space solving method based on seed space segmentation and principal component analysis of the present application first obtains the approximate work space of the robot according to the limit motion space of the robot, and segments the approximate work space to generate a seed work space according to the solving accuracy. Specifically, an approximate cuboid is first obtained based on the traditional Monte Carlo method to preliminarily limit the work space, the limit motion range of the robot in the spatial coordinate axis direction is obtained according to the structural size of the robot, and the solving accuracy of the work space and the maximum diameter of the internal hole allowed are determined according to the limit motion range. N position points are randomly generated within the above limit motion range, substituted into the inverse kinematics model of the parallel robot, and the points with inverse kinematics solution are retained, and the minimum and maximum values of the retained points in the three coordinate directions are obtained as the approximate cuboid range of the robot work space: (x min1 , x max1 ), (y min1 , y max1 ) and (z min1 , z max1 ); Considering that the traditional Monte Carlo method has low approximation accuracy for the work space when the number of numerical points is small, an Δ1 is added in the maximum and minimum value directions of the three coordinate single directions respectively, and an Δ1 is reduced, taking Δ1 = 10*w acc , and the maximum and minimum values are respectively rounded up and down, and the range is updated as (x min2 , x max2 ), (y min2 , y max2 ) and (z min2 , z max2 ), thereby enlarging the preliminarily limited work space, and then determining the number of seed work spaces Num hole according to the maximum diameter d hole of the internal hole allowed by the work space, wherein ceil is the rounding up of the internal formula value:

[0051] x num = ceil[(x max2 -x min2 ) / d hole] (1)

[0052] y num =ceil[(y max2 -y min2 ) / d hole ] (2)

[0053] z num =ceil[(z max2 -z min2 ) / d hole ] (3)

[0054] Num hole =x num *y num *z num (4),

[0055] complete seed workspace partitioning;

[0056] Since the more the solving regions, the lower the solving efficiency, a relationship model between workspace boundary and seed workspace is established to refine the solving regions, specifically, the volume coefficient a of each seed space is calculated, and the seed workspace type is determined according to the proportion of internal reversible points and non-reversible points,

[0057]

[0058] wherein: Case 1 represents that the current seed space is at the robot workspace boundary, and the seed space is an external seed space; Case 2 represents that the current seed space is at the transition of the robot workspace boundary, and the seed space is a boundary seed space; and Case 3 represents that the current seed space is in the internal of the robot workspace, and the seed space is an internal seed space.

[0059] Then, the reversible points of the boundary seed workspace are integrated to obtain a rough workspace boundary; as shown in Figure 2 .

[0060] After the boundary seed space is found, the principal component analysis is used to determine the cutting direction of the boundary seed space, and the workspace solving precision w acc is taken as the cutting step to cut the boundary seed space, so as to refine the rough workspace boundary and obtain the final workspace; a schematic diagram of cutting is shown in Figure 3 .

[0061] After the dissection is completed, the approximate boundary of each layer is solved, the type of the section is judged according to the four corner points, if all the four corner points are reachable or unreachable, the section is not operated. If one side of the four corner points is reversible and the other side is not reversible, the section grid is divided into four parts, the type of the grid section after the division is judged, and the process is repeated until the edge length of the smallest section grid is less than the solving precision. After the iteration is completed, the reversible point in the second last iteration is taken as the approximate boundary. Figure 4 The dissection iteration of the grid and the generation of the approximate boundary are shown.

[0062] The above method of the application is used for solving the workspace boundary of a parallel robot (4PPa-2PaR type), the structural diagram and the actual diagram of the robot are as shown in Figure 5 , and the solved workspace boundary diagram is as shown in Figure 6 . The method can quickly screen out the rough boundary of the workspace of the parallel robot, and can increase the number of layers in the direction with large gradient change, thereby improving the solving precision.

Claims

1. A method for efficiently solving the workspace of parallel robots based on seed space partitioning and principal component analysis, comprising the following steps: Step S1.Obtaining an approximate cuboid based on the traditional Monte Carlo method to preliminarily define the workspace; Step S2.Enlarging the preliminarily defined workspace and determining the number of seed workspaces according to the internal hole diameter allowed in the interior to complete seed workspace partitioning; Step S3.Calculating the volume coefficient of each seed workspace by uniformly generating points, dividing the seed workspace type, and obtaining the rough boundary range of the workspace; Step S4.Performing principal component analysis on the boundary seed workspace to determine the cutting direction of the boundary seed workspace; Step S5.Determining the workspace approximate boundary of a single section layer through grid contraction iteration and obtaining the overall workspace boundary by fitting the approximate boundaries in all boundary seed space layers; The step S3 specifically comprises: The step S1 specifically comprises: Discrete points are generated evenly within the workspace, and a seed space volume coefficient is used to evaluate the seed space represents the ratio of the reachable discrete points in the seed space to the theoretical discrete points; the seed space type can be classified by the volume coefficient through equation (5):​ ， wherein: represents that the current seed space is outside the robot workspace, and the seed space is an external seed space; represents that the current seed space is at the transition of the robot workspace boundary, and the seed space is a boundary seed space; represents that the current seed space is inside the robot workspace, and the seed space is an internal seed space; With the above basis for seed space type division, uniformly generate a number of numerical points in each seed workspace, calculate the volume coefficient of each seed space , divide the seed space, separate the boundary seed workspace, and thus obtain a rough workspace boundary composed of reversible numerical points in the boundary seed workspace.

2. The parallel robot workspace efficient solving method based on seed space partitioning and principal component analysis of claim 1, wherein, The step S2 specifically comprises: S11, Based on the robot's structural dimensions, obtain the robot's limit range of motion in the spatial coordinate axis directions: ( , ), ( , )as well as( , ); S12, determining workspace solving precision according to extreme motion range and the maximum diameter of the internal hole that can be allowed ; S13, randomly generate N position points within the above-mentioned limit motion range, substitute them into the inverse kinematics model of the parallel robot, retain the points among the position points that have inverse kinematic solutions, and obtain the minimum and maximum values ​​of the retained points in the three coordinate directions, which are used as the approximate cuboid range of the robot's workspace: ( , ), ( , )as well as( , ).

3. The parallel robot workspace efficient solving method based on seed space partitioning and principal component analysis of claim 1, wherein, The step S4 specifically comprises: S21, considering that the traditional Monte Carlo method has low approximation accuracy for the workspace when solving the case of less numerical points, one and one are added to the maximum and minimum value directions of the three coordinates respectively =10* , wherein , , , and , is the solving accuracy of the determined workspace; and the maximum value and the minimum value are respectively rounded up and down, and the updated range is ( , ), , and ( , ). S22, the maximum diameter of the internal hole allowed by the workspace and the number of seed workspaces can be determined by equations (1)-(4) where ceil is the ceiling function that rounds up the value of the internal formula. ， ， ， 。 4. The parallel robot workspace efficient solving method based on seed space partitioning and principal component analysis of claim 1, wherein, The specific steps for determining the boundary seed space according to the principal component analysis are as follows: The step S5 specifically comprises: S41, with the boundary seed space starting point as the initial origin, the seed space length as the step, randomly generate a number of value points as sample data points for principal component analysis ; S42, based on the above principal component analysis principle, the sample data eigenvalues are obtained and sorted, the dimension with the largest eigenvalue is taken as the cutting direction of the boundary seed space, and when the largest dimension is not unique, the selection is performed in the order of .

5. The parallel robot workspace efficient solving method based on seed space partitioning and principal component analysis of claim 1, wherein, S52.Determine the section layer area type by judging the four corner points of the section: a.all internal points, b.all external points, c.one side internal point and one side external point; wherein the sections of types a and b do not perform the step S53; S51, solving workspace accuracy As the sectioning step, the boundary seed space is layered according to the sectioning direction determined in step S4; S54.After completing the generation of the approximate boundaries of all boundary seed space layers, fit the boundary points to obtain the final refined workspace boundary. S53, the profile is meshed, according to the region type in S52, the profile square of type c is divided into 4 equal parts, the region type of the divided square is judged, and the process is repeated until the minimum square edge length generated is less than or equal to the workspace solving precision After completing the iteration, the point judged in the second last iteration inside the workspace is taken as the approximate boundary; ​

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