Discrete optimization method and system for spatial measurement points of industrial robot precision compensation

Abstract

The present invention provides a method and system for discrete optimization of spatial measurement points of industrial robot precision compensation, which relates to the field of manipulators. The method comprises: establishing a kinematic model and an error model of the industrial robot; obtaining a linear relationship between a terminal positioning error and a kinematic parameter error of the industrial robot based on the kinematic model and the error model of the industrial robot; randomly generating a plurality of sampling points in the working space of the industrial robot; generating a plurality of sampling point combinations based on the plurality of sampling points, wherein the number of sampling points included in any two sampling point combinations is different; for each sampling point combination, calculating an observability index of the sampling point combination based on the linear relationship between the terminal positioning error and the kinematic parameter error of the industrial robot; determining an optimal sampling point combination based on the observability index of each sampling point combination, which has the advantage of determining a suitable number and position of sampling points to find a balance point between sampling efficiency and final compensation accuracy.

Description

Technical Field

[0001] The present invention relates to the field of manipulators, and in particular to a discrete optimization method and system for space measurement points of industrial robot precision compensation. Background Art

[0002] Industrial robots, also known as manipulators, have the advantages of high repeatability, good reliability, and strong applicability. They are gradually being used in high-precision manufacturing fields such as aircraft manufacturing, laser cutting, and flexible grinding. With the expansion of the application scenarios of industrial robots, repeatability and absolute accuracy are becoming more and more important, especially with the popularization of offline programming, absolute accuracy has become more important. The improvement of absolute accuracy mainly depends on precision compensation technology. Industrial robots are highly nonlinear and coupled multi-input and multi-output systems with complex and diverse error sources. It is a very challenging task to build an error model that accurately describes the actual structure of the robot. Due to the incompleteness of the robot error model, the uncertainty of measurement, and the repeatability error of the robot, the residuals of the error model estimation will inevitably be caused during the compensation process. Therefore, the selection of sampling points has an important impact on the subsequent compensation model.

[0003] Regardless of the robot accuracy compensation method used, the collection of robot positioning errors is an essential step. The data obtained through sampling directly reflects the original state of the robot positioning error and provides basic data for positioning error estimation and identification. Therefore, sampling is a key link in accuracy compensation technology. The number and position of sampling points will directly affect the fitting accuracy of the robot error model. If the sampling points are too few or unevenly distributed, the error model may be inaccurate, thus affecting the compensation effect. At the same time, increasing the number of sampling points does not necessarily improve the accuracy infinitely, because the measurement process itself may be time-consuming and resource-constrained.

[0004] Therefore, it is necessary to provide a discrete optimization method and system for the spatial measurement points of industrial robot precision compensation to determine the appropriate number and position of sampling points in order to find a balance between sampling efficiency and final compensation accuracy. Summary of the invention

[0005] The present invention provides a discrete optimization method for precision compensation space measurement points of an industrial robot, comprising: establishing a kinematic model and an error model of the industrial robot; obtaining a linear relationship between a terminal positioning error and a kinematic parameter error of the industrial robot based on the kinematic model and the error model of the industrial robot; randomly generating a plurality of sampling points in a working space of the industrial robot; generating a plurality of sampling point combinations based on the plurality of sampling points, wherein the number of sampling points included in any two sampling point combinations is different; for each of the sampling point combinations, calculating an observability index of the sampling point combination based on the linear relationship between the terminal positioning error and the kinematic parameter error of the industrial robot; and determining an optimal sampling point combination based on the observability index of each of the sampling point combinations.

[0006] Furthermore, the establishment of the kinematic model and error model of the industrial robot includes: determining a connecting rod coordinate system based on conformal geometry algebra corresponding to the industrial robot; determining the kinematic parameters of the industrial robot; establishing the kinematic model based on the connecting rod coordinate system and kinematic parameters based on conformal geometry algebra; introducing error parameters on the basis of the kinematic model to construct the error model.

[0007] Furthermore, based on the kinematic model and error model of the industrial robot, a linear relationship between the end positioning error and the kinematic parameter error of the industrial robot is obtained, including: obtaining the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot through Taylor expansion of a multivariate function.

[0008] Furthermore, randomly generating a plurality of sampling points in the working space of the industrial robot includes: determining the working space of the industrial robot based on the joint angle ranges of a plurality of joints of the industrial robot; and randomly generating a plurality of sampling points in the working space of the industrial robot.

[0009] Furthermore, based on the linear relationship between the terminal positioning error and the kinematic parameter error of the industrial robot, the observability index of the sampling point combination is calculated, including: determining the Jacobian matrix corresponding to the sampling point combination based on the sampling point combination and the linear relationship between the terminal positioning error and the kinematic parameter error of the industrial robot; performing singular value decomposition on the Jacobian matrix corresponding to the sampling point combination to obtain the singular value matrix corresponding to the sampling point combination; and calculating the observability index of the sampling point combination based on the singular value matrix corresponding to the sampling point combination.

[0010] Furthermore, the observability index of the sampling point combination is calculated based on the following formula: ,in, is the observability index of the sampling point combination, is the singular value of the first column of the singular value matrix corresponding to the sampling point combination, is the singular value of the second column of the singular value matrix corresponding to the sampling point combination, is the first singular value matrix corresponding to the sampling point combination The singular values ​​of the columns, is the number of sampling points included in the sampling point combination, is the number of kinematic parameters involved in identification.

[0011] Further, based on the observability index of each of the sampling point combinations, determining the optimal sampling point combination includes: determining the optimal number of sampling points based on the observability index of each of the sampling point combinations; and determining the optimal sampling point combination based on the optimal number of sampling points.

[0012] Further, based on the optimal number of sampling points, determining the optimal sampling point combination includes: using a differential evolution algorithm to determine the optimal sampling point combination based on the multiple sampling points and the optimal number of sampling points.

[0013] Furthermore, a differential evolution algorithm is used to determine the optimal sampling point combination based on the multiple sampling points and the optimal number of sampling points, including: S11, encoding each of the sampling points; S12, encoding each of the sampling points to generate an initial population; S13, calculating the individual observability index of the population; S14, based on the individual observability index of the population, judging whether a preset condition is met, if so, determining the optimal sampling point combination, if not, executing S15; S15, performing crossover and mutation operations, adopting a rounding method to generate new individuals, performing individual selection based on the individual observability index of the new individual and the individuals of the population, updating the population, and executing S14.

[0014] The present invention provides an industrial robot precision compensation space measurement point discrete optimization system, which is used to execute the above-mentioned industrial robot precision compensation space measurement point discrete optimization method, and includes: a model building module, which is used to build a kinematic model and an error model of the industrial robot; an error analysis module, which is used to obtain the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot based on the kinematic model and the error model of the industrial robot; a sampling point generation module, which is used to randomly generate a plurality of sampling points in the working space of the industrial robot; a combination generation module, which is used to generate a plurality of sampling point combinations based on the plurality of sampling points, wherein the number of sampling points included in any two sampling point combinations is different; a combination analysis module, which is used to calculate the observability index of each sampling point combination based on the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot; and a combination optimization module, which is used to determine the optimal sampling point combination based on the observability index of each sampling point combination.

[0015] Compared with the prior art, the discrete optimization method for spatial measurement points of industrial robot precision compensation provided by the present invention has at least the following beneficial effects:

[0016] By establishing the kinematic model and error model of the industrial robot and obtaining the linear relationship between the end positioning error and the kinematic parameter error based on these models, the error source and size during the robot movement process can be accurately analyzed. By randomly generating multiple sampling points in the workspace and generating multiple sampling point combinations based on these sampling points, the observability index of each combination is calculated, and finally the optimal sampling point combination is determined. This process can ensure that the selected sampling point combination is highly sensitive to the robot error, thereby more accurately reflecting the error characteristics of the robot and improving the calibration accuracy. The existing calibration method requires a large number of sampling points to ensure the calibration accuracy, but this will greatly increase the calibration time. This method reduces the number of unnecessary sampling points by optimizing the sampling point combination, thereby shortening the calibration time. The shortening of the calibration time means that the manpower, material and time costs required in the calibration process will be reduced accordingly. In addition, due to the improvement of calibration accuracy, the subsequent adjustment and maintenance costs caused by inaccurate calibration can also be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] This specification will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:

[0018] Figure 1 It is a flowchart of a discrete optimization method for space measurement points of industrial robot precision compensation according to some embodiments of this specification;

[0019] Figure 2 is a schematic diagram of the structure of an industrial robot according to some embodiments of this specification;

[0020] Figure 3 is a schematic diagram of a connecting rod coordinate system based on conformal geometric algebra according to some embodiments of the present specification;

[0021] Figure 4 is a schematic diagram of the results of the random point selection calculation of the first batch shown in some embodiments of this specification;

[0022] Figure 5 is a schematic diagram of the results of random point selection calculation of the second batch shown in some embodiments of this specification;

[0023] Figure 6 is a schematic diagram of the results of random point selection calculation of the third batch shown in some embodiments of this specification;

[0024] Figure 7 is a schematic diagram of the results of random point selection calculation of the fourth batch shown in some embodiments of this specification;

[0025] Figure 8 It is a schematic diagram of a process of determining an optimal sampling point combination using a differential evolution algorithm according to some embodiments of this specification;

[0026] Fig. 9 It is a schematic diagram of the discrete optimization process of the differential evolution algorithm shown in some embodiments of this specification;

[0027] Fig.10 According to some embodiments of this specification x Schematic diagram of the axis compensation effect;

[0028] Fig.11 According to some embodiments of this specification y Schematic diagram of the axis compensation effect;

[0029] Fig.12 According to some embodiments of this specification z Schematic diagram of the axis compensation effect;

[0030] Fig.13 It is a module schematic diagram of a discrete optimization system for space measurement points for industrial robot precision compensation according to some embodiments of this specification. DETAILED DESCRIPTION

[0031] In order to more clearly illustrate the technical solutions of the embodiments of this specification, the following is a brief introduction to the drawings required for the description of the embodiments. Obviously, the drawings described below are only some examples or embodiments of this specification. For ordinary technicians in this field, this specification can also be applied to other similar scenarios based on these drawings without creative work. Unless it is obvious from the language environment or otherwise explained, the same reference numerals in the figures represent the same structure or operation.

[0032] Figure 1 is a flow chart of a discrete optimization method for space measurement points of industrial robot precision compensation according to some embodiments of this specification, such as Figure 1 As shown, the discrete optimization method of spatial measurement points for industrial robot precision compensation may include the following steps.

[0033] Step 110, establishing a kinematic model and an error model of the industrial robot.

[0034] Specifically include:

[0035] Determine the link coordinate system based on conformal geometry algebra corresponding to the industrial robot;

[0036] Determine the kinematic parameters of industrial robots;

[0037] The kinematic model is established based on the link coordinate system and kinematic parameters of conformal geometric algebra;

[0038] Error parameters are introduced on the basis of the kinematic model to construct the error model.

[0039] Specifically, according to the geometric structure of the industrial robot, a coordinate system can be established at each joint angle in sequence. As an example, Figure 2 is a schematic diagram of the structure of an industrial robot according to some embodiments of this specification, such as Figure 2 As shown, the industrial robot can include 6 joint angles, and the coordinate system is established at each joint angle in turn. A , coordinate system B , coordinate system C , coordinate system D and coordinate system E , coordinate system A is the base coordinate system, the joint angle , Located in coordinate system B , joint rotation Located in the coordinate system C , joint rotation , Located in the coordinate system D , joint rotation Located in coordinate system E, coordinate system A and coordinate system B Between The distance in the direction is , coordinate system B and coordinate system C Between The distance in the direction is , coordinate system C and coordinate system D Between Distance of direction ,exist The distance in the direction is ; Coordinate system D and coordinate system E Between The distance in the direction is The link coordinate system corresponding to the industrial robot based on conformal geometric algebra is as follows: Figure 3 shown.

[0040] The kinematic parameters of an industrial robot may include the length of each link and the rotation angle of each joint.

[0041] Still Figure 2 Taking the industrial robot shown in the figure as an example, the conformal geometric model of the industrial robot involves a total of 5 connecting rod lengths ( , , , , ) and 6 joint rotations ( , , , , , ), a total of 11 parameters. The connecting rod parameters are shown in Table 1.

[0042]

[0043] The moving axis, moving operator, rotation axis and rotation operator are determined according to the connecting rod coordinate system, and the kinematic model of the industrial robot is constructed to obtain the spatial position of the end of the industrial robot relative to the base coordinate system under theoretical conditions.

[0044] Still Figure 2 Taking the industrial robot shown in FIG. 1 as an example, the reference axes and corresponding kinematic parameters of the movement operator and rotation operator of the industrial robot are shown in Table 2.

[0045]

[0046] Coordinate system As a starting point for modeling, this method can , , The modeling is prioritized as a rotation in a two-dimensional plane, making the modeling process more intuitive. Considering it last can reduce the amount of calculation. The axes and their coordinate system origin are expressed as:

[0047] ,

[0048] in, , , Coordinate system The axes of the three coordinate axes, For the coordinate system The origin of . In conformal geometric algebra , , is the standard basis vector, indicating , , Direction, Indicates the origin.

[0049] According to the principles of conformal geometric algebra, the mobile operator , and its corresponding conjugate operator , the formula is as follows:

[0050] ,

[0051] In the formula, is the three-dimensional translation vector, is a point at infinity in space, , , , is the length parameter in , , Projection on the axis.

[0052] Move Operator , and its corresponding conjugate operator , the formula is as follows:

[0053] ,

[0054] in, represents the axis of rotation, For mobile operators The corresponding joint rotation angle.

[0055] According to equations (2) and (3), all rotation operators and translation operators can be obtained. The end coordinate system of the industrial robot Relative to the base coordinate system Motion Operator Its corresponding conjugate operator , the formula is as follows:

[0056] ,

[0057] Coordinate system E Relative to the coordinate system The pose of can be expressed as follows:

[0058] ,

[0059] The specific calculation results of the above formula are as follows:

[0060] ,

[0061] in, , , Coordinate system Axis In the coordinate system Three Axes , , The projection size on , , Coordinate system Axis In the coordinate system Three Axes , , The projection size on , , For the coordinate system Axis In the coordinate system The three axes , , The projection size on , , For the coordinate system origin Relative to the coordinate system origin Spatial location. , , , , , , are three-vector primitives, representing a directed volume in three-dimensional space. is the basis vector , , The geometric product of is the basis vector , , The geometry of is the basis vector , , The geometric product of is the basis vector , , The geometric product of is the basis vector , , The geometric product of is the basis vector , , The geometric product of is the basis vector , , The geometric product of . , , Both are infinity coefficients, used to describe the scale of geometric objects and the direction or position at infinity. , , , , , , , , , , , , , , , , are three-vector coefficients, which quantize the size of the three-vector primitives.

[0062] The terminal theoretical pose matrix is ​​sorted out by formula (6) , the results are as follows:

[0063] ,

[0064] Then the theoretical position of the end of the industrial robot is obtained as :

[0065] ,

[0066] in, The theoretical position of the end of the industrial robot in the coordinate system of The coordinate values ​​of the axis, The theoretical position of the end of the industrial robot in the coordinate system of The coordinate values ​​of the axis, The theoretical position of the end of the industrial robot in the coordinate system of The coordinate values ​​of the axis.

[0067] The error parameters may include an error parameter corresponding to the length of each link and an error parameter corresponding to each joint angle.

[0068] Still Figure 2 As an example, the industrial robot shown in the figure has a connecting rod length of , , , : The corresponding error parameter is , , , , ; Joint rotation , , , , : The corresponding error parameter is , , , , , .

[0069] Construct a kinematic error model to obtain the actual position of the end of the industrial robot relative to the base coordinate system in actual situations:

[0070] ,

[0071] in, is the spatial position of the actual end position of the industrial robot relative to the base coordinate system, The actual position of the end of the industrial robot in the coordinate system of The coordinate values ​​of the axis, The actual position of the end of the industrial robot in the coordinate system of The coordinate values ​​of the axis, The actual position of the end of the industrial robot in the coordinate system of The coordinate values ​​of the axis.

[0072] Step 120 , based on the kinematic model and error model of the industrial robot, obtain the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot.

[0073] Specifically include:

[0074] By performing Taylor expansion of multivariate functions and ignoring high-order terms, the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot is obtained, as follows:

[0075] ,

[0076] in, is the Jacobian matrix, is the theoretical kinematic parameter vector of the industrial robot, is the actual kinematic parameter vector of the industrial robot containing error parameters.

[0077] Still Figure 2 Take the industrial robot shown in the figure as an example. The Jacobian matrix of this industrial robot is , theoretical kinematic parameter vector and the actual kinematic parameter vector They are:

[0078] ,

[0079] ,

[0080] ,

[0081] , then formula (10) can be written as:

[0082] ,

[0083] Step 130 : randomly generate a plurality of sampling points in the working space of the industrial robot.

[0084] Specifically include:

[0085] Determine the working space of the industrial robot based on the joint rotation angle ranges of multiple joints of the industrial robot;

[0086] Multiple sampling points are randomly generated in the workspace of the industrial robot.

[0087] Still Figure 2 Taking the industrial robot shown in Figure 2 as an example, 200 sampling points are selected in the workspace of the industrial robot. The corresponding joint angles of these 200 sampling points are all within the range shown in Table 3. Since only the end position of the industrial robot is considered, the end position is not affected by The impact of Keep zero position and do not consider it.

[0088]

[0089] Step 140: Generate multiple sampling point combinations based on the multiple sampling points.

[0090] The number of sampling points included in any two sampling point combinations is different. For example, the number of sampling points in the combination increases from 4 to 200, and multiple sampling point combinations are obtained.

[0091] Step 150 , for each sampling point combination, based on the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot, calculate the observability index of the sampling point combination.

[0092] Specifically include:

[0093] Based on the linear relationship between the sampling point combination and the end positioning error and kinematic parameter error of the industrial robot, the Jacobian matrix corresponding to the sampling point combination is determined;

[0094] Perform singular value decomposition on the Jacobian matrix corresponding to the sampling point combination to obtain the singular value matrix corresponding to the sampling point combination;

[0095] Based on the singular value matrix corresponding to the sampling point combination, the observability index of the sampling point combination is calculated.

[0096] Specifically, for each sampling point combination, according to formula (14), we can get:

[0097] ,

[0098] in, is the number of sampling points included in the sampling point combination, is the end positioning error vector of the industrial robot corresponding to the sampling point combination, The sampling point combination corresponds to The Jacobian matrix of is the number of kinematic parameters involved in identification, is the error parameter vector.

[0099] right Performing singular decomposition, we get:

[0100] ,

[0101] in, is the left singular vector corresponding to the sampling point combination, which is a A matrix whose column vector is the matrix The eigenvector of is the right singular vector corresponding to the sampling point combination, which is a A matrix whose column vector is the matrix The eigenvector of is the error parameter vector; is the singular value matrix corresponding to the sampling point combination, which is a A non-negative real diagonal matrix, when When , its form is as follows:

[0102] ,

[0103] Among them, non-negative real numbers is a matrix The singular values ​​of ,if , which means that the errors of various parameters of the industrial robot can be observed.

[0104] Preferably, the observability index of the sampling point combination is calculated based on the following formula:

[0105] ,

[0106] in, is the observability index of the sampling point combination, is the singular value of the first column of the singular value matrix corresponding to the sampling point combination, is the singular value of the second column of the singular value matrix corresponding to the sampling point combination, is the first singular value matrix corresponding to the sampling point combination The singular values ​​of the columns, is the number of sampling points included in the sampling point combination, is the number of kinematic parameters involved in identification.

[0107] Step 160: Determine the optimal sampling point combination based on the observability index of each sampling point combination.

[0108] Specifically include:

[0109] Based on the observability index of each sampling point combination, the optimal number of sampling points is determined;

[0110] Based on the optimal number of sampling points, the optimal sampling point combination is determined.

[0111] Still Figure 2 Taking the industrial robot shown in the figure as an example, the number of sampling points in the combination increases from 4 to 200, and the observability index corresponding to each combination is calculated in turn. In order to avoid the uncertainty fluctuation of the calculation results caused by random selection of points affecting the judgment of the number of samplings, four batches of random selection of points are calculated. The change of the observability index with the number of sampling points is shown in the figure. Figure 4-Figure 7 As shown, from Figure 4-Figure 7 It can be seen that the curve first rises rapidly, then gradually flattens out. After the number of sampling point combination elements is greater than 100, the curve basically tends to be stable. Repeat this operation for four batches of random point combinations, and take the minimum number of sampling points as the optimal number of sampling points for subsequent sampling point position optimization. The minimum number of sampling points for the four batches is shown in Table 4.

[0112]

[0113] According to the results in Table 4, 20 is taken as the optimal number of sampling points.

[0114] The average value of the observability index of the second half of the sampling point combinations can be calculated, and the sampling point combinations whose observability index is greater than 99% of the average value can be found in the first half of the sampling point combinations, and the number of sampling points in the combination with the minimum number of sampling points can be determined as the optimal number of sampling points.

[0115] Preferably, a differential evolution algorithm is used to determine the optimal sampling point combination based on multiple sampling points and the optimal number of sampling points, specifically including:

[0116] S11, encoding each sampling point;

[0117] S12, encoding each sampling point to generate an initial population;

[0118] S13, calculating the individual observability index of the population;

[0119] S14, based on the individual observability index of the population, determine whether the preset conditions are met, if so, determine the optimal sampling point combination, if not, execute S15, wherein the preset conditions may be that the number of iterations reaches 1000 times or the optimal value of the population observability index reaches 5.5;

[0120] S15, perform crossover and mutation operations, adopt the rounding method to generate new individuals, perform individual selection based on the individual observability index of the new individuals and the individuals in the population, update the population, and execute S14.

[0121] The differential evolution algorithm is an efficient global optimization algorithm. It draws on the evolutionary mechanism of nature and optimizes continuous functions by simulating the inheritance and mutation process of biological populations. The core of the algorithm lies in its unique mutation and crossover mechanisms, which enable the differential evolution algorithm to achieve efficient search in the entire continuous solution space. In each generation, the algorithm randomly selects individuals from the population, calculates the difference vector between them, and multiplies them by the scaling factor to generate mutant individuals. Subsequently, these mutant individuals are cross-operated with the original individuals to generate new candidate solutions. This crossover process helps to maintain the diversity of the population and prevents the algorithm from converging to the local optimal solution too early. By comparing the fitness of the newly generated candidate solutions with the solutions in the current population, the differential evolution algorithm selects better solutions to enter the next generation of population, thereby gradually guiding the population to evolve towards the global optimal solution. According to the encoding of all points, the initial population of the differential evolution algorithm is generated. In the process of crossover and mutation, the rounding method is adopted to ensure that the generated new population can match the sampling point encoding. The observability index is used as the fitness function, and multiple sampling point combinations are generated according to the optimal number of sampling points for discrete optimization. The number of sampling points included in the sampling point combination is the optimal number of sampling points, and a group of sampling point combinations with a better observability index is found as the optimal sampling point combination. The iterative process is as follows Fig. 9 shown.

[0122] Still Figure 2 Taking the industrial robot shown in FIG. 1 as an example, the optimal sampling point combination corresponding to the joint angle of the industrial robot is shown in Table 5.

[0123]

[0124] The effect of this method is verified by experiments below.

[0125] The least square method is used as the error parameter identification algorithm, and the above optimal sampling points are applied to Figure 2 The industrial robot shown (hereinafter referred to as "experimental industrial robot") is subjected to parameter identification and compensation simulation to verify the accuracy of this method.

[0126] The least squares method is a mathematical optimization technique that finds the best function match for data by minimizing the sum of squares of errors. 20 sampling points are used for error parameter identification. According to formula (15), the linear relationship between the end positioning error and the kinematic parameter error of the experimental industrial robot corresponding to these 20 points is obtained. The formula is as follows:

[0127] ,

[0128] in, is a A column vector containing 20 sampling points in , , Errors in three directions. yes The matrix of is the error parameter to be solved.

[0129] Introducing the residual vector , which measures the model prediction The actual observed value The difference between . The residual vector The definition is as follows:

[0130] ,

[0131] Minimize the residual vector The sum of squares , the formula is as follows:

[0132] ,

[0133] in, .

[0134] Up about Differentiate and we get:

[0135] ,

[0136] make ,but:

[0137] ,

[0138] The least square closed solution of the error parameter is obtained as follows:

[0139] ,

[0140] Taking the experimental industrial robot as the object, simulation verification is carried out, and certain parameter errors are introduced into the conformal geometric algebraic error model of the industrial robot, as shown in Table 6.

[0141]

[0142] To simulate the end position due to other non-model errors and measurement uncertainties, a , Gaussian distribution (its distribution area is ), is the geometric error to ensure that the geometric error of each point accounts for more than 80% of the total error.

[0143] The error parameters are identified for the 20 points optimized by the measurement points and the 20 random points. The 20 sampling points optimized by the measurement points are the points in Table 4, the joint angles of the 10 random sampling points are shown in Table 7, the joint angles of the 20 random sampling points are shown in Table 8, and the joint angles of the 30 random sampling points are shown in Table 9.

[0144]

[0145]

[0146]

[0147] Through these points, the error parameters are identified and compensation is performed. , , Comparison of compensation effects in three directions Figure 10-12 The RMS errors between the theoretical points before and after compensation are shown in Table 10.

[0148]

[0149] From the comparison results, the combination of 20 sampling points selected by discrete optimization algorithm performs best in compensation effect. Compared with the compensation effect of randomly selecting 10 sampling points, The axis error was reduced by 84.19%, The axis error was reduced by 86.01%. The axis error is reduced by 87.94%; compared with the compensation effect of randomly selecting 20 sampling points, The axis error was reduced by 62.63%, The axis error was reduced by 57.13%, The axis error is reduced by 38.51%; compared with the compensation effect of randomly selecting 30 sampling points, The axis error was reduced by 6.96%, The axis error was reduced by 7.95%, The axis error was reduced by 3.12%. The compensation effect of the optimized 20 sampling point combination was significantly improved compared with the random 20 sampling point combination, and was close to the compensation effect of the random 30 sampling point combination. This result fully proves the effectiveness and advancement of this method.

[0150] Fig.13 is a schematic diagram of a module of a discrete optimization system for space measurement points of industrial robot precision compensation according to some embodiments of this specification, such as Figure 8 As shown, the industrial robot precision compensation spatial measurement point discrete optimization system can include a model building module, an error analysis module, a sampling point generation module, a combination generation module, a combination analysis module and a combination optimization module.

[0151] The model building module can be used to build the kinematic model and error model of the industrial robot.

[0152] The error analysis module can be used to obtain the linear relationship between the end positioning error and kinematic parameter error of the industrial robot based on the kinematic model and error model of the industrial robot.

[0153] The sampling point generation module can be used to randomly generate multiple sampling points in the working space of the industrial robot.

[0154] The combination generating module may be used to generate a plurality of sampling point combinations based on a plurality of sampling points, wherein the number of sampling points included in any two sampling point combinations is different.

[0155] The combination analysis module can be used to calculate the observability index of each sampling point combination based on the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot.

[0156] The combination optimization module can be used to determine the optimal sampling point combination based on the observability index of each sampling point combination.

[0157] The industrial robot precision compensation spatial measurement point discrete optimization system can be used to execute the industrial robot precision compensation spatial measurement point discrete optimization method. For more descriptions of the industrial robot precision compensation spatial measurement point discrete optimization system, please refer to the relevant descriptions of the industrial robot precision compensation spatial measurement point discrete optimization method, which will not be repeated here.

[0158] Finally, it should be understood that the embodiments described in this specification are only used to illustrate the principles of the embodiments of this specification. Other variations may also fall within the scope of this specification. Therefore, as an example and not a limitation, alternative configurations of the embodiments of this specification may be considered consistent with the teachings of this specification. Accordingly, the embodiments of this specification are not limited to the embodiments explicitly introduced and described in this specification.

Claims

1. A discrete optimization method for spatial measurement points of industrial robot precision compensation, characterized in that: include: Establish kinematic model and error model of industrial robots; Based on the kinematic model and error model of the industrial robot, a linear relationship between the end positioning error and the kinematic parameter error of the industrial robot is obtained; randomly generating a plurality of sampling points in a workspace of the industrial robot; Based on the multiple sampling points, generate multiple sampling point combinations, wherein the number of sampling points included in any two sampling point combinations is different; For each of the sampling point combinations, the observability index of the sampling point combination is calculated based on the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot, and the observability index of the sampling point combination is calculated based on the following formula: ， in, is the observability index of the sampling point combination, is the singular value of the first column of the singular value matrix corresponding to the sampling point combination, is the singular value of the second column of the singular value matrix corresponding to the sampling point combination, is the first singular value matrix corresponding to the sampling point combination w The singular values ​​of the column, is the number of sampling points included in the sampling point combination, is the number of kinematic parameters involved in identification; Based on the observability index of each of the sampling point combinations, determining the optimal sampling point combination specifically includes: using a differential evolution algorithm based on the multiple sampling points and the optimal number of sampling points to determine the optimal sampling point combination.

2. The method for discrete optimization of spatial measurement points for industrial robot precision compensation according to claim 1 is characterized in that: The kinematic model and error model of the industrial robot are established, including: Determine a link coordinate system based on conformal geometric algebra corresponding to the industrial robot; Determining kinematic parameters of the industrial robot; Establishing the kinematic model based on the connecting rod coordinate system and kinematic parameters of conformal geometric algebra; Error parameters are introduced on the basis of the kinematic model to construct the error model.

3. The method for discrete optimization of spatial measurement points for industrial robot precision compensation according to claim 1 is characterized in that: Based on the kinematic model and error model of the industrial robot, a linear relationship between the end positioning error and the kinematic parameter error of the industrial robot is obtained, including: The linear relationship between the end positioning error and the kinematic parameter error of the industrial robot is obtained through Taylor expansion of a multivariate function.

4. The method for discrete optimization of spatial measurement points for industrial robot precision compensation according to claim 1, characterized in that: A plurality of sampling points are randomly generated in the working space of the industrial robot, including: Determining a working space of the industrial robot based on joint rotation angle ranges of a plurality of joints of the industrial robot; A plurality of sampling points are randomly generated in the working space of the industrial robot.

5. The method for discrete optimization of spatial measurement points for industrial robot precision compensation according to any one of claims 1 to 4, characterized in that: Based on the linear relationship between the end positioning error and the kinematic parameter error of the industrial robot, the observability index of the sampling point combination is calculated, including: Determine the Jacobian matrix corresponding to the sampling point combination based on the linear relationship between the sampling point combination and the end positioning error and kinematic parameter error of the industrial robot; Performing singular value decomposition on the Jacobian matrix corresponding to the sampling point combination to obtain a singular value matrix corresponding to the sampling point combination; Based on the singular value matrix corresponding to the sampling point combination, the observability index of the sampling point combination is calculated.

6. The method for discrete optimization of spatial measurement points for industrial robot precision compensation according to any one of claims 1 to 4, characterized in that: Based on the observability index of each sampling point combination, determining the optimal sampling point combination includes: Determining the optimal number of sampling points based on the observability index of each of the sampling point combinations; Based on the optimal number of sampling points, the optimal sampling point combination is determined.

7. The method for discrete optimization of spatial measurement points for industrial robot precision compensation according to claim 1, characterized in that: Determining the optimal sampling point combination based on the multiple sampling points and the optimal number of sampling points using a differential evolution algorithm includes: S11, encoding each of the sampling points; S12, encoding each of the sampling points to generate an initial population; S13, calculating the individual observability index of the population; S14, based on the individual observability index of the population, determine whether the preset conditions are met, if so, determine the optimal sampling point combination, if not, execute S15; S15, perform crossover and mutation operations, adopt the rounding method to generate new individuals, perform individual selection based on the individual observability index of the new individuals and the individuals of the population, update the population, and execute S14.

8. Industrial robot precision compensation spatial measurement point discrete optimization system, characterized by: The method for discrete optimization of spatial measurement points for precision compensation of an industrial robot according to any one of claims 1 to 7 comprises: Model building module, used to build the kinematic model and error model of the industrial robot; An error analysis module, used to obtain a linear relationship between an end positioning error and a kinematic parameter error of the industrial robot based on a kinematic model and an error model of the industrial robot; A sampling point generation module, used to randomly generate a plurality of sampling points in the working space of the industrial robot; A combination generating module, used for generating a plurality of sampling point combinations based on the plurality of sampling points, wherein the number of sampling points included in any two sampling point combinations is different; A combination analysis module, configured to calculate, for each of the sampling point combinations, an observability index of the sampling point combination based on a linear relationship between an end positioning error and a kinematic parameter error of the industrial robot; The combination optimization module is used to determine the optimal sampling point combination based on the observability index of each sampling point combination.

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