Industrial robot position error and interval prediction method and electronic equipment

Abstract

The invention relates to an industrial robot position error and interval prediction method and electronic equipment. The method comprises the following steps: constructing a data set containing a joint angle vector and a position error; projecting a joint angle vector to a high-dimensional space by using kernel principal component analysis, and performing feature dimension raising; the features after feature dimension raising and the corresponding position errors serve as input and labels of a Bayesian neural network respectively, and the Bayesian neural network is trained; and performing feature dimension raising on the test set data according to the same method, inputting the test set data into the trained Bayesian neural network, and outputting prediction of a position error and a confidence interval thereof. Compared with the prior art, the method has the advantages that the position error and the interval of the robot are predicted, the predicted value is more accurate, the applicability is good and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of robot positioning, and in particular to a method for predicting position errors and intervals of industrial robots. Background Art

[0002] High positioning accuracy operation is one of the important functions of industrial robot platforms in the field of precision manufacturing and processing. Usually, the absolute positioning accuracy of industrial robots is low and cannot meet the needs of high-precision operation. Improving the absolute positioning accuracy of industrial robots is an important way to achieve high-precision operation.

[0003] The reason for the low precision of industrial robots is that the actual kinematic model of the robot is inconsistent with the theoretical kinematic model. The influencing factors include: processing and assembly errors of industrial robot parts, gear backlash, load, ambient temperature changes, external disturbances, etc. To solve this problem, domestic scholars have proposed an industrial robot kinematic parameter error identification method. The geometric parameter errors of industrial robots are identified through optimization algorithms to improve the kinematic modeling accuracy of robots, thereby achieving compensation for absolute positioning accuracy. This method cannot compensate for errors caused by non-geometric parameter errors such as temperature changes and external interference. Later, scholars proposed to use a neural network method to compensate for non-geometric parameter errors. Scholars also proposed to use a spatial interpolation method to compensate for the absolute positioning accuracy of industrial robots. The above methods mainly realize the prediction of the absolute positioning error of industrial robots, while there is little research on the interval prediction of absolute positioning errors.

[0004] How to implement a prediction method for the position error and its range of an industrial robot has become a technical problem that needs to be solved. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting the position error and range of an industrial robot in order to overcome the defects of the prior art.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] According to one aspect of the present invention, a method for predicting position error and its interval of an industrial robot is provided, characterized in that the method comprises the following steps:

[0008] Step S1, constructing a data set including joint angle vectors and position errors;

[0009] Step S2, using kernel principal component analysis to project the joint angle vector of step S1 into a high-dimensional space to perform feature dimensionality upgrade;

[0010] Step S3, using the feature after dimension upgrade and the corresponding position error as the input and label of the Bayesian neural network respectively, and training the Bayesian neural network;

[0011] Step S4, perform feature dimension upgrading on the test set data according to the method in step S2 and input the data into the trained Bayesian neural network to output the prediction of the position error and its confidence interval.

[0012] Preferably, in step S1, the process of constructing a data set including joint angle vectors and position errors comprises: randomly selecting 2n groups of joint angle vectors in the working area of ​​the industrial robot; vector θ=[θ 1 ,θ 2 ,...,θ 2n ] T , where θ i is a p-dimensional vector, where p represents the number of joint angles of the industrial robot;

[0013] Calculate the theoretical position coordinates of the corresponding sampling points, move the robot end to the sampling point position, use the measuring equipment to measure n groups of end positions, and obtain the actual position coordinates. The difference between the actual position and the theoretical position is the required end position error e(θ i ), so we get the joint angle vector and the corresponding position error err(θ), and then construct the data set D, that is

[0014] err(θ)=[e(θ 1 ),e(θ 2 ),...,e(θ 2n )] T ,

[0015] Among them, 2n is the number of joint angle vectors.

[0016] More preferably, the position error includes a vector composed of errors in the directions of three coordinate axes x, y and z, and the deviation prediction method for each set of data sets in these three directions is the same.

[0017] Preferably, the step S4 includes performing feature dimension upgrading on the joint angle vectors of the x-axis, y-axis and z-axis respectively, inputting the features into a trained Bayesian neural network, and predicting the confidence intervals of the position errors along the x-axis, y-axis and z-axis respectively.

[0018] Preferably, in step S2, the eigenvectors corresponding to the first k largest eigenvalues ​​are taken, that is, the features after projection are:

[0019] x n×k =K center V n×k

[0020] Where k is the number of principal components, Vn×k is the matrix V n×n The matrix of eigenvectors corresponding to the first k largest eigenvalues, V n×n is a matrix obtained by arranging the eigenvectors of the normalized kernel matrix from large to small according to their eigenvalues.

[0021] Preferably, the Bayesian neural network comprises two hidden layers with multiple units.

[0022] Preferably, the Bayesian neural network introduces probability distribution and variational inference methods.

[0023] The loss function of the Bayesian neural network is:

[0024]

[0025] Among them, w (i) represents the i-th sample collected from the variational distribution; q(w (i) |θ) is a variational distribution, and the posterior probability distribution p(D|w (i) ) approximation; p(w (i) ) is w (i) The prior probability density of .

[0026] Preferably, the training process of the Bayesian neural network includes: performing error back propagation according to the loss of the Bayesian neural network, and using a gradient descent optimization method to learn the parameters of the variational distribution, and training the Bayesian neural network until a specified number of training steps is reached or the loss converges to a predetermined value, and the training is completed.

[0027] More preferably, k is 10, 20 or 30.

[0028] According to another aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the method described above is implemented when the processor executes the program.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1) The present invention improves the dimensionality of the joint angles of industrial robots through kernel principal component analysis to deal with nonlinear relationships and provide more feature information. At the same time, a Bayesian neural network is introduced for error regression, which can not only predict the position error but also give a confidence interval, thereby improving the applicability, accuracy and effectiveness of the predicted value in a variety of practical application scenarios.

[0031] 2) The present invention introduces probability distribution and variational inference into the Bayesian neural network, which is suitable for situations with less data volume, simplifies the complexity of the network, and can well solve the problem of replacing complex models of kinematic position errors of industrial robots. It has the advantages of high universality and good versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic flow chart of a method for predicting the position error and interval of an industrial robot in the present invention;

[0033] Figure 2 Schematic diagram of the structure of the Bayesian neural network in the present invention;

[0034] Figure 3 This is a schematic diagram of the results of predicting the position error and its interval using the trained Bayesian neural network in the present invention. DETAILED DESCRIPTION

[0035] 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 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 should fall within the scope of protection of the present invention.

[0036] The present invention proposes a method for predicting the position error and its interval of an industrial robot based on kernel principal component analysis and Bayesian neural network, which can predict the absolute positioning error interval of the industrial robot. The method improves the dimension of the joint angle of the industrial robot through kernel principal component analysis to handle nonlinear relationships and provide more feature information, and introduces Bayesian neural network for error regression. It can not only predict the position error, but also give a confidence interval, thereby improving its applicability in a variety of practical application scenarios and the effectiveness of the predicted value. The method can well solve the problem of replacing the complex model of the kinematic position error model of the industrial robot, and has the advantages of high universality and good versatility.

[0037] This embodiment relates to a method for predicting the position error and interval of an industrial robot. Figure 1 , including the following steps:

[0038] 1) Randomly select joint angle vectors in the workspace of the industrial robot, calculate the theoretical position coordinates, control the end effector to reach these positions, record the actual position coordinates, calculate the position error, and construct a data set containing joint angle vectors and position errors.

[0039] Create a joint angle input vector and position error data set D. Randomly select 2n groups of joint angle vectors in the working area of ​​the industrial robot. Vector θ = [θ 1 ,θ 2 ,...,θ 2n ] T , where θ i is a p-dimensional vector, indicating the number of joint angles of the industrial robot. The object studied in this embodiment is p=6. The theoretical position coordinates of the corresponding sampling points are calculated by the robot forward kinematics formula, and then the robot end is moved to the sampling point position by the robot control system. The n groups of end positions are measured using a measuring device to obtain the actual position coordinates. The difference between the actual position and the theoretical position is the required end position error; finally, the joint angle vector and the corresponding position error err(θ)=[e(θ 1 ),e(θ 2 ),...,e(θ 2n )] T , thus constructing the data set D. In the position error err(θ), err(θ i )=[e x (θ i ),e y (θ i ),e z (θ i )] T (i=1,2,…,2n) represents the error in the three coordinate axes. Since the end position error is a vector composed of position errors along the x, y, and z directions, the deviation prediction method for each data set in these three directions is the same. In the subsequent steps, the prediction of the confidence interval of the position error along the x-axis in the data set is taken as an example. The new data set err x (θ)={θ,e x (θ)}, where θ represents the joint angle vector matrix, e x (θ) represents the error along the x-axis.

[0040] 2) If Figure 2 , KPCA is used to upgrade the feature dimension of the joint angle vector to handle nonlinear relationships and provide more feature information, thereby improving the accuracy of the regression task. The specific steps are as follows: select the kernel function and calculate the kernel matrix, center the kernel matrix, perform feature decomposition to obtain eigenvalues ​​and eigenvectors, select the eigenvectors corresponding to the first k largest eigenvalues, and project the original data onto these eigenvectors to obtain new features.

[0041] Kernel Principal Component Analysis (KPCA) is used to map joint angles to high-dimensional space to handle nonlinear relationships and improve model fitting capabilities. At the same time, high-dimensional space provides more feature information and can more accurately capture subtle differences in data, thereby improving the accuracy of regression tasks. In addition, high-dimensional mapping increases feature combination methods and enriches data expression capabilities.

[0042] Kernel principal component analysis: Project the joint angle vector to a high-dimensional space. You can select different kernel functions (polynomial kernel, exponential kernel, Gaussian kernel, etc.) and retain different feature dimensions to construct different inputs and find the best combination. This includes the following steps:

[0043] 2.1) Randomly select n groups of joint angles and corresponding position errors from the position error err(θ) to form a training set, and the remaining n groups to form a test set. Assume that the position error err(θ) is x n×p , indicating that there are n groups of joint angles, each group of joint angles is p-dimensional, and the covariance matrix C is listed. The calculation formula is as follows:

[0044]

[0045] Where n represents the number of samples, X is the representation of the joint angle in the high-dimensional feature space, and x i is the joint angle, φ(x i ) represents the mapping function that maps data to a high-dimensional space, but the specific form is unknown. Therefore, the kernel technique is used to directly calculate the inner product in the low-dimensional space without explicitly defining the mapping to solve the above problem.

[0046] 2.2) The kernel matrix K is defined as expression (2):

[0047]

[0048] Among them, κ(x i ,x j ) is the kernel function, and the kernel matrix K is normalized and defined as expression (3):

[0049] K center =K-1 n×n K-K1 n×n +1 n×n K1 n×n (3)

[0050] Among them, 1 n×n represents an n-order matrix with 1 / n elements. Assuming that the eigenvalue of the kernel matrix is ​​u and the eigenvector is λ, it is defined as expression (4):

[0051] XX T u=λu (4)

[0052] 2.3) Multiply both sides of formula (4) by X T , defined as expression (5):

[0053] X T X(X T u)=λ(X T u) (5)

[0054] It can be concluded that X T u is X T The eigenvector of X is converted into the unit eigenvector, that is, the projection direction v in the high-dimensional space, which is defined as expression (6):

[0055]

[0056] 2.4) Due to X T It is still unknown, but we can directly find the projection l of any vector φ(x′) on it, which is defined as expression (7):

[0057]

[0058] Formulas (1)-(7) use kernel functions to project features into high-dimensional space, and the projection direction is the normalized kernel matrix K center The eigenvalues ​​of the eigenvectors correspond to the eigenvalues. The larger the eigenvalues, the larger the variance. Therefore, the normalized kernel matrix K center The eigenvectors are arranged from large to small according to their eigenvalues ​​to obtain the matrix V n×n .

[0059] 2.5) In practical applications, the number of eigenvectors selected will directly affect the accuracy of the prediction model, because the model may be interfered by noise and redundant data. The present invention selects the eigenvectors corresponding to the first k (k = 10, 20, 30) largest eigenvalues, that is, the projected features are:

[0060] x n×k =K center V n×k (8)

[0061] Where k is the number of principal components, V n×k is the matrix V n×n Take the matrix of eigenvectors corresponding to the first k largest eigenvalues.

[0062] 3) If Figure 2 As shown in Figure 1, a Bayesian neural network is constructed for error prediction. The features after feature dimensionality upgrade are used as input, and the corresponding position error is used as the label. The Bayesian neural network contains two hidden layers with 100 units.

[0063] The dimension of the joint angle of the industrial robot is increased from p dimension to k dimension, which provides more feature information and can more accurately capture the subtle differences in the data. Finally, the features after the dimension increase are used for error regression. Compared with the artificial neural network that only provides point prediction, the present invention introduces the Bayesian neural network for error prediction. By introducing probability distribution and Bayesian inference, the Bayesian neural network provides better uncertainty quantification and can simultaneously predict the position error and interval of the industrial robot. In addition, it performs well in alleviating the overfitting problem and is particularly suitable for situations with less data. The specific definition is as follows:

[0064] 3.1) Assume that the prior probability distribution of the Bayesian neural network weight w is w~p(w), given n sets of joint angle vectors θ=[θ 1 ,θ 2 ,...,θ n ] T (denoted as X) and its corresponding position error err x (θ)=[e x (θ 1 ),e x (θ 2 ),...,e x (θ n )] T (denoted as Y), we can get the following Bayesian formula, defined as expression (9):

[0065]

[0066] Among them, p(Y|X,w) is the probability that the neural network outputs Y given the parameter w and input X, and P(Y|X) is a constant determined by the training set.

[0067] 3.2) In the Bayesian neural network, the network is relatively complex and has many parameters, which makes the denominator in formula (9) difficult to integrate. Therefore, the variational inference method is introduced to use a simple distribution q(w|θ) to approximate the posterior probability distribution p(w|D), where θ is the parameter of the approximate distribution q, and Kullback–Leibler (KL) is used to measure the distance between them, which is defined as expression (10):

[0068]

[0069] When the KL divergence is 0, it means that the two distributions are completely consistent, so the problem is transformed into an optimization problem to solve the minimum value of the KL divergence, which is defined as expression (11):

[0070]

[0071] 3.3) The loss function of formula (11) is also called the evidence lower bound (ELBO). Markov Chain Monte Carlo (MCMC) is usually used to approximate formula (11) to obtain the loss function, which is defined as expression (12):

[0072]

[0073] Among them, w (i) represents the i-th sample collected from the variational distribution; q(w (i) |θ) is a variational distribution, and the posterior probability distribution p(D|w (i) ) approximation; p(w (i) ) is w (i) The prior probability density of .

[0074] 4) Error back propagation: Train the constructed Bayesian neural network to obtain a trained Bayesian neural network.

[0075] The error is back-propagated according to the loss, and the gradient descent optimization method is used to learn the parameters of the variational distribution. It is remembered that each weight in the Bayesian neural network can be approximated by a Gaussian distribution, and the parameters of the Gaussian distribution are μ and σ. The specific process is as follows:

[0076]

[0077] ω i ←μ+softplus(σ)·∈ i (14)

[0078]

[0079] Then calculate the gradient:

[0080]

[0081] Parameter update:

[0082]

[0083] in, represents Gaussian distribution, μ is the mean, σ is the variance, softplus(σ)=log(1+e σ ), It is a gradient operator. When the specified number of training steps is reached or the loss converges to a predetermined value, the training is completed.

[0084] 5) Reconstruct the centralized kernel matrix of the test set, apply the same kernel function and dimension increase to the test set, and send it into the trained Bayesian neural network to predict the position error and its interval.

[0085] After completing the training of the Bayesian neural network, the model is evaluated on the test set. First, the centralized kernel matrix K of the test set needs to be reconstructed test ; Then, it is combined with the normalized kernel matrix K of the training set center The eigenvectors are arranged from large to small according to their eigenvalues ​​to form a matrix V n×n However, in practical applications, the number of eigenvectors selected will directly affect the accuracy of the prediction model, because the model may be interfered by noise and redundant data. Therefore, the present invention selects the eigenvectors corresponding to the first k (k = 10, 20, 30) largest eigenvalues ​​for projection, that is, V n×k , calculate the data of the test set after dimensionality increase; finally, input these data into the trained Bayesian neural network to obtain the position error and its confidence interval. Figure 3 , the prediction error represented by the blue line in the figure is very close to the measurement error represented by the red point, indicating that the prediction value is very accurate. Secondly, the 95% confidence interval represented by the yellow area can effectively cover most of the prediction points, and the interval range is small, showing the stability and reliability of the prediction results. Therefore, whether from the results of position error or confidence interval, this method performs well in terms of accuracy.

[0086] 6) According to step 1) to step 5), the interval and specific value of the measurement error along the y-axis and z-axis are calculated respectively, and they are compensated by offline programming. This method improves the dimension of the joint angle of the industrial robot through kernel principal component analysis to deal with nonlinear relationships and provide more feature information. At the same time, the Bayesian neural network is introduced for error regression, which can not only predict the position error, but also give the confidence interval, thereby improving its applicability and the effectiveness of the predicted value in a variety of practical application scenarios.

[0087] Example 2

[0088] The electronic device of the present invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in a read-only memory (ROM) or loaded from a storage unit into a random access memory (RAM). In the RAM, various programs and data required for device operation can also be stored. The CPU, ROM and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0089] Multiple components in the device are connected to the I / O interface, including: input units, such as keyboards, mice, etc.; output units, such as various types of displays, speakers, etc.; storage units, such as disks, optical disks, etc.; and communication units, such as network cards, modems, wireless communication transceivers, etc. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunication networks.

[0090] The processing unit performs the various methods and processes described above, such as methods 1) to 6). For example, in some embodiments, methods 1) to 6) can be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program can be loaded and / or installed on the device via a ROM and / or a communication unit. When the computer program is loaded into the RAM and executed by the CPU, one or more steps of methods 1) to 6) described above can be performed. Alternatively, in other embodiments, the CPU can be configured to perform methods 1) to 6) by any other appropriate means (for example, by means of firmware).

[0091] The functions described above herein may be performed at least in part by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that may be used include: field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), complex programmable logic devices (CPLDs), and the like.

[0092] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code can be executed entirely on the machine, partially on the machine, partially on the machine as a stand-alone software package and partially on a remote machine, or entirely on a remote machine or server.

[0093] In the context of the present invention, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0094] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for predicting the position error and its interval of an industrial robot, characterized in that: The method comprises the following steps: Step S1, constructing a data set including joint angle vectors and position errors; Step S2, using kernel principal component analysis to project the joint angle vector of step S1 into a high-dimensional space to perform feature dimensionality upgrade; Step S3, using the feature after dimension upgrade and the corresponding position error as the input and label of the Bayesian neural network respectively, and training the Bayesian neural network; Step S4, perform feature dimension upgrading on the test set data according to the method in step S2 and input it into the trained Bayesian neural network, and output the prediction of the position error and its confidence interval.

2. The method for predicting the position error and its interval of an industrial robot according to claim 1, characterized in that: In step S1, the process of constructing a data set including joint angle vectors and position errors includes: randomly selecting 2n groups of joint angle vectors θ=[θ1, θ2, ..., θ 2n ] T , where θ i is a p-dimensional vector, where p represents the number of joint angles of the industrial robot; Calculate the theoretical position coordinates of the corresponding sampling points, move the robot end to the sampling point position, use the measuring equipment to measure n groups of end positions, and obtain the actual position coordinates. The difference between the actual position and the theoretical position is the required end position error e(θ i ), so we get the joint angle vector and the corresponding position error err(θ), and then construct the data set D, that is err(θ)=[e(θ1),e(θ2),...,e(θ 2n )] T , Among them, 2n is the number of joint angle vectors.

3. The method for predicting the position error and interval of an industrial robot according to claim 2, characterized in that: The position error includes a vector composed of errors in the directions of three coordinate axes x, y and z, and the deviation prediction method for each set of data sets in these three directions is the same.

4. The method for predicting the position error and its interval of an industrial robot according to claim 1, characterized in that: The step S4 includes performing feature dimension upgrading on the joint angle vectors of the x-axis, y-axis and z-axis respectively, inputting the features into the trained Bayesian neural network, and predicting the confidence intervals of the position errors along the x-axis, y-axis and z-axis respectively.

5. The method for predicting the position error and its interval of an industrial robot according to claim 1, characterized in that: In step S2, the eigenvectors corresponding to the first k largest eigenvalues ​​are taken, that is, the projected features are: x n×k =K center V n×k Where k is the number of principal components, V n×k is the matrix V n×n The matrix of eigenvectors corresponding to the first k largest eigenvalues, V n×n is a matrix obtained by arranging the eigenvectors of the normalized kernel matrix from large to small according to their eigenvalues.

6. The method for predicting the position error and interval of an industrial robot according to claim 1, characterized in that: The Bayesian neural network includes two hidden layers with multiple units.

7. The method for predicting the position error and interval of an industrial robot according to claim 1, characterized in that: The probability distribution and variational inference method are introduced into the Bayesian neural network, and the loss function of the Bayesian neural network is: Among them, w (i) represents the i-th sample collected from the variational distribution; q(w (i) |θ) is a variational distribution, and the posterior probability distribution p(D|w (i) ) approximation; p(w (i) ) is w (i) The prior probability density of .

8. The method for predicting the position error and interval of an industrial robot according to claim 1, characterized in that: The training process of the Bayesian neural network includes: performing error back propagation according to the loss of the Bayesian neural network, and using a gradient descent optimization method to learn the parameters of the variational distribution, and training the Bayesian neural network until a specified number of training steps is reached or the loss converges to a predetermined value, and the training is completed.

9. The method for predicting the position error and interval of an industrial robot according to claim 5, characterized in that: The k is 10, 20 or 30.

10. An electronic device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the program, the method according to any one of claims 1 to 9 is implemented.

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