A robot position error and interval prediction method, device and medium thereof

Abstract

This invention relates to a method for predicting robot position errors and their intervals. The steps include: acquiring the joint angle vectors of an industrial robot during operation and calculating the difference between the theoretical and actual positions to construct a dataset containing the joint angle vectors and position errors; inputting the dataset containing the joint angle vectors and position errors into a neural network-based prediction model; predicting the position error interval by calculating the predicted interval coverage probability and the average predicted interval width, while ensuring the predicted interval coverage probability meets the standard and minimizing the average predicted interval width; generating relative weights for the predicted interval boundaries by defining learnable parameters and using mean squared error loss to regress the predicted values ​​to predict the position error; and outputting the position error value and its interval prediction result from the prediction model. Compared with existing technologies, this invention can not only predict position errors but also predict the error range, improving the applicability and effectiveness of position error prediction.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to a method for predicting the position error and its range of an industrial robot based on a quality-driven neural network. Background Technology

[0002] Industrial robot platforms are widely used in industrial manufacturing fields such as aerospace drilling, spraying, grinding, and welding. Industrial robots typically have high repeatability but low absolute positioning accuracy. With the increasing demand for high-precision positioning in industrial manufacturing, the absolute positioning accuracy of robots can no longer meet practical needs. Geometric parameter errors caused by factors such as machining and assembly errors are the main source of robot absolute position errors. For robot position errors caused by geometric parameter errors, domestic and international research mainly uses parameter identification methods to estimate geometric parameter errors, thereby improving the accuracy of robot kinematic modeling and further enhancing robot positioning accuracy. However, parameter identification methods ignore the influence of non-geometric parameter errors such as load, thermal effects, deformation, joint gear backlash, and disturbances. Researchers have used neural networks and machine learning methods to predict and compensate for non-geometric parameter errors. Although the above methods compensate for robot position errors caused by non-geometric parameter errors, they all currently assume that the robot's position error is a fixed value. In reality, due to the influence of random errors, the robot's position error is a random variable. Currently, there is limited research on predicting the distribution range of random variables. Therefore, predicting the position error and its range of industrial robots is of great significance for improving robot positioning accuracy.

[0003] Existing industrial robot position compensation methods mainly focus on predicting position errors, while paying less attention to the confidence level and possible range of the prediction results. This method may not be able to fully capture dynamic error changes caused by various factors (such as mechanical wear, temperature changes, etc.) when the robot is performing complex tasks. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art in failing to fully capture dynamic error changes, and to provide a method, device and medium for predicting robot position error and its interval.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A method for predicting robot position error and its interval, comprising the following steps:

[0007] Obtain the joint angle vectors of the industrial robot during operation, calculate the difference between the theoretical position and the actual position, and construct a dataset containing joint angle vectors and position errors;

[0008] Input the dataset containing joint angle vectors and position errors into the neural network-based prediction model;

[0009] By calculating the predicted interval coverage probability and the average predicted interval width, the location error interval is predicted while minimizing the average predicted interval width, thus ensuring that the predicted interval coverage probability meets the standard.

[0010] Position error prediction is performed by generating relative weights for the prediction interval boundaries by defining learnable parameters and using mean squared error loss to regress the predicted values.

[0011] The prediction model outputs the location error value and its interval prediction result.

[0012] As a preferred technical solution, the Prediction Interval Coverage Probability (PICP) is expressed as follows:

[0013]

[0014] Where c is the total number of data points within the estimated prediction interval; n is the number of joint angle vector groups;

[0015] The Mean Prediction Interval Width (MPIW) is expressed as follows:

[0016]

[0017] in, These are the upper and lower bounds of the prediction for the i-th sample, respectively.

[0018] As a preferred technical solution, the method employs a probability-based approach to find the neural network parameters that maximize PICP; adjusts the width of the prediction interval by minimizing the loss function; and uses Lagrange multipliers to balance the interval width and coverage to optimize the prediction model.

[0019] As a preferred technical solution, the method minimizes the average prediction interval width under the premise that the prediction interval coverage probability meets the standard, according to the HQ (High-Quality) criterion.

[0020] Points falling outside the interval are not included in the calculation. The expression for the average prediction interval width loss function is as follows:

[0021]

[0022] Where c represents the total number of data points within the estimated prediction interval; Let k represent the upper and lower bounds of the prediction interval, respectively. i This indicates whether sample i is within the estimated prediction interval.

[0023] As a preferred technical solution, the method employs a probability-based approach to find the neural network parameter ω that maximizes the probability of the predicted interval being covered.

[0024]

[0025] Where vector k represents whether each sample is within the estimated prediction interval, and each element k i It is treated as a binary variable, taking the value 1 with a probability of (1-α).

[0026] As a preferred technical solution, when the sample size is large enough, k i The binomial distribution approximates a normal distribution with mean n(1-α) and variance nα(1-α):

[0027]

[0028] The problem of maximizing the likelihood function is solved by minimizing the negative log-likelihood function, where k i The normal distribution simplifies to:

[0029]

[0030] The penalty is applied only when the predicted interval coverage probability is less than (1-α), and the expression for the predicted interval coverage probability loss function is as follows:

[0031]

[0032] As a preferred technical solution, the position error e x (θ i By defining a learnable parameter v, the boundary relative weights of the position error are generated, and the formula for position error prediction is as follows:

[0033]

[0034] Where v∈(0,1), the mean squared error loss is used to regress the predicted value. The expression for the mean squared error loss function for location error prediction is:

[0035]

[0036] As a preferred technical solution, the loss function of the neural network model adjusts the influence of interval width and coverage by introducing the Lagrange multiplier λ, and the expression is:

[0037]

[0038] in, Loss represents the average prediction interval width loss function; PICP Loss represents the probability loss function for predicting interval coverage. MSE This represents the mean squared error loss function for location error prediction.

[0039] As a preferred technical solution, the neural network model includes:

[0040] The input layer accepts multi-dimensional vectors of the joint angles of the industrial robot.

[0041] Hidden layers, including fully connected layers with q hidden units and ReLU activation function;

[0042] The output layer consists of three nodes, which represent the upper and lower bounds of the predicted interval and the relative weights of the predicted boundary with respect to the location error.

[0043] As a preferred technical solution, the method subsamples the training set and performs neural network fitting on each subset to train multiple neural network models and form a diverse model set.

[0044] The prediction results of various neural network models are aggregated to predict the range and specific values ​​of the samples.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] This invention proposes a quality-driven neural network method that can predict not only positional errors but also the possible range of those errors. Furthermore, it makes no prior assumptions about the data distribution within the prediction interval, thereby improving its applicability and the effectiveness of the predictions in various practical application scenarios. This interval prediction method provides an error range, thus improving the robustness and reliability of the compensation to a certain extent. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the method for predicting the position error and its range of an industrial robot based on a quality-driven neural network, according to the present invention.

[0048] Figure 2 This is a schematic diagram illustrating the definitions of the Predicted Interval Coverage Probability (PICP) and the Average Predicted Interval Width (MPIW).

[0049] Figure 3 This is a schematic diagram of the quality-driven neural network construction of this invention. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0051] Example 1

[0052] To address the problem that existing technologies may fail to adequately capture dynamic error changes caused by multiple factors when robots perform complex tasks, this invention proposes a method for predicting the position error and its range using a quality-driven neural network. For example... Figure 1 As shown, joint angle vectors are randomly selected within the workspace of the industrial robot. The theoretical position coordinates are calculated, the end effector is controlled to reach these positions, and the actual position coordinates are recorded. The position error is calculated, and a dataset containing joint angle vectors and position errors is constructed. A target variable (e.g., x-axis position error) and prediction confidence (e.g., 95% or 99%) are set, and a vector is constructed to represent whether a sample is within the prediction interval. The Prediction Interval Coverage Probability (PICP) and Mean Prediction Interval are calculated. The method minimizes the MPIW (Minimum Prediction Interval Width) while ensuring PICP (Plan-Increase Target) meets the requirements, and applies the HQ (High-Quality) criterion. A probability-based approach is used to optimize neural network parameters, adjusting the prediction interval width by minimizing the loss function and balancing the interval width and coverage using Lagrange multipliers. Learnable parameters are defined to generate prediction interval boundaries, and mean squared error (MSE) loss is used for prediction regression. The input layer receives a multi-dimensional vector of joint angles, which is passed through a fully connected layer and a ReLU activation function to the output layer. The output layer has three nodes representing the upper and lower bounds of the prediction interval and boundary weights. A diverse model ensemble is constructed by subsampling the training set and fitting multiple neural network models, aggregating the prediction results of each model to improve accuracy and robustness. The method includes the following steps:

[0053] 1) Construct a sample set D of input joint angle vectors and position errors. Randomly select n sets of joint angle vectors θ = [θ1, θ2, ..., θ] in the workspace of the industrial robot. n ] T , where θ i(i = 1, 2, ..., n) is a p-dimensional vector representing the number of joint angles of the industrial robot. In this embodiment, the number of joint angles of the robot is p = 6. The theoretical position coordinates of the corresponding sampling positions are calculated using the robot's forward kinematics formula. Then, the robot's end effector is controlled by the robot control system to reach the sampling position. The measuring device measures the n sets of end effector positions to obtain the actual position coordinates. The difference between the actual position and the theoretical position is the required end effector position error. Finally, the joint angle vector and the corresponding position error err(θ) = [e(θ1), e(θ2), ..., e(θ3)] are obtained. n )] T This is used to construct a dataset 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, ..., n) represents the error along the three coordinate axes. Since the end position error is a vector composed of position errors along the x, y, and z directions, the prediction method for the confidence intervals along the three directions is the same for each dataset. The subsequent steps, taking the prediction of the confidence interval for the position error along the x-axis in the dataset as an example, will use a new dataset err. x (θ)={θ,e x (θ)}, where θ represents the input joint angle vector matrix, e x (θ) represents the error along the x-axis.

[0054] 2) such as Figure 2 The diagram shows the definitions of variables such as Predicted Interval Coverage Probability (PICP) and Average Predicted Interval Width (MPIW), which are defined as follows:

[0055] 2.1) Given a set of joint angle inputs θ i =[θ1,θ2,...,θ p ] T For sample i, the position error e in the x-axis direction of the predicted target variable is... x (θ i There is a probability that γ∈[0,1] falls within the prediction interval (PI), where PI is defined as... The value of γ is typically set to 0.95 or 0.99 to express confidence in the accuracy of the prediction. This level of confidence is also represented by α, where γ = 1 - α. In this embodiment, α = 0.05 is used to represent a 95% confidence interval, calculated as shown in equation (1):

[0056]

[0057] 2.2) Given n sets of joint angle vectors, construct vector k to represent whether each sample is within the estimated prediction interval, where each element k i ∈{0,1}, defined as expression (2):

[0058]

[0059] The quality of the generated prediction interval is evaluated by measuring the prediction interval coverage probability (PICP), as defined by expression (3):

[0060]

[0061] Wherein, the total number of data points within the estimated prediction interval is defined as c, and is defined as expression (4):

[0062]

[0063] Meanwhile, the average prediction interval width MPIW is defined as expression (5):

[0064]

[0065] According to the HQ (High-Quality) criterion, MPIW should be minimized under the premise that PICP meets the standard, i.e., α≤0.05. To minimize MPIW, formula (5) is incorporated into the loss function, but points falling outside the interval are not calculated. Therefore, the concept of capturing MPIW is proposed, and the loss function of the MPIW part is finally defined as expression (6):

[0066]

[0067] 2.3) For PICP, a probability-based approach is used to find the neural network parameter ω that maximizes it, as shown in formula (7):

[0068]

[0069] Where each element k i Treated as a binary variable, taking the value 1 with a probability of (1-α), these elements can be represented as a Bernoulli random variable k. i ~Bernoulli(1-α), and each k iAll are independent and identically distributed. This assumption holds for a subset of all randomly sampled data points, such as the mini-batch used in stochastic gradient descent (SGD). Based on this, the total number of captured points can be expressed using a binomial distribution, i.e., c ~ Bernoulli(n, 1-α). Further analysis is then performed using the probability mass function (PMF), expressed as in equation (8):

[0070]

[0071] Since the factorial operation in the binomial coefficients is quite complex in actual calculations, by applying the central limit theorem, when the sample size is large enough, the binomial distribution can be approximated as a normal distribution with mean n(1-α) and variance nα(1-α). For a large n (in this example, n = 512), we have:

[0072]

[0073] The problem of maximizing the likelihood function is usually solved by minimizing the negative log-likelihood function, so formula (9) can be simplified to:

[0074]

[0075] Among them, the penalty is only applied when PICP is less than (1-α), so the loss function of PICP is defined as expression (11):

[0076]

[0077] 2.4) For input θ i Position error e x (θ i Instead of generating the error directly through a network, a learnable parameter v is defined to generate the boundary relative weights of the position error. The formula for position error prediction is as follows:

[0078]

[0079] Where v∈(0,1), the mean squared error (MSE) loss is used to regress the predicted value, and the loss function for this part is defined as expression (13):

[0080]

[0081] In summary, to balance the importance of interval width and coverage, a Lagrange multiplier λ is introduced to adjust the degree of influence of these two factors, resulting in a new loss function:

[0082]

[0083] 3) such as Figure 3 As shown, a neural network model is built.

[0084] 3.1) First, the input layer accepts a p-dimensional input vector representing the joint angles of the industrial robot. This vector is then fed into a fully connected hidden layer with q hidden units. In this embodiment, q = 100. The output is obtained by applying the ReLU activation function, which effectively reduces gradient vanishing and accelerates the convergence speed of network training. Next, the output of the hidden layer is passed to the output layer, which contains three nodes representing the upper and lower bounds of the predicted interval for the sample and the relative weights v of the predicted boundary with respect to position error. Then, the loss function of formula (14) is used for backpropagation of the error to update the weights.

[0085] 3.2) Train m models. By subsampling the training set and fitting a neural network to each subset, m models are trained, generating a diverse set of models. This diversity stems from the differences between each subset, which in turn affects the fitted neural network model. Prediction is performed using this model set, and the following steps are used to perform interval prediction and specific value prediction for each sample:

[0086]

[0087]

[0088]

[0089] in, This represents the upper bound of the prediction for the i-th sample in the j-th model. Let represent the mean of the upper bounds of the predictions for the i-th sample from m models. Let be the variance of the m predicted outcomes, and 1.96 be a statistical constant used to calculate the 95% confidence interval, representing the model uncertainty, which will ultimately be used. As the upper bound of the final estimate, similarly, the lower bound of the interval is...

[0090] Similarly, based on steps 1 to 3, the intervals and specific values ​​of the measurement errors along the y-axis and z-axis are calculated, and offline programming is used to compensate for them. This method does not make any prior assumptions about the distribution of the data within the prediction interval, thereby improving its applicability and the effectiveness of the predicted values ​​in various practical application scenarios.

[0091] This invention example uses a quality-driven neural network to predict the position error and its range of an industrial robot, including the following steps: (1) Dataset construction: Randomly select multiple joint angle vectors in the workspace of the industrial robot, calculate the theoretical position coordinates using the forward kinematics formula; control the robot's end effector to reach these positions, and record the actual position coordinates using a high-precision measuring device; calculate the difference between the actual and theoretical positions to obtain the end position error, and construct a dataset containing joint angle vectors and position errors. (2) Prediction interval setting: Set a target variable for each sample, such as the position error in the x-axis direction, and determine the prediction confidence level, such as 95% or 99%, to reflect confidence in the prediction accuracy. (3) Prediction interval quality assessment: Construct a vector to represent whether the sample falls within the estimated prediction interval, calculate the prediction interval coverage probability (PICP) and the average prediction interval width (MPIW), and apply the HQ criterion to minimize MPIW while ensuring that PICP meets the standard. (4) Optimize the prediction model: Use a probability-based method to find the neural network parameters that maximize PICP, and adjust the width of the prediction interval by minimizing the loss function, while using Lagrange multipliers to balance the interval width and coverage. (5) Position Error Generation: Instead of directly predicting the position error through the network, a learnable parameter is defined to represent the boundary weights, and regression is performed using mean squared error (MSE) loss. (6) Neural Network Construction and Training: The input layer receives a multi-dimensional vector of joint angles, which is passed through a fully connected layer with q hidden units and a ReLU activation function to the output layer. The output layer has 3 nodes representing the upper and lower bounds of the prediction interval and the boundary weights, and is trained using a specific loss function. (7) Model Set Construction and Prediction: A diverse model set is constructed by subsampling the training set and fitting multiple neural network models. The prediction results of each model are aggregated to improve the accuracy and robustness of the prediction.

[0092] Example 2

[0093] As a second aspect of the present invention, this application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the robot position error and its interval prediction method as described above. In addition to the processors, memory, and interface described above, any data processing device in the embodiments may also include other hardware depending on the actual function of the data processing device, which will not be elaborated further.

[0094] Example 3

[0095] As a third aspect of the present invention, this application also provides a computer-readable storage medium storing computer instructions thereon, which, when executed by a processor, implement the robot position error and its interval prediction method as described above. The computer-readable storage medium can be an internal storage unit of any data processing device as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium can also be an external storage device, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc., equipped on the device. Furthermore, the computer-readable storage medium can include both internal storage units of any data processing device and external storage devices. The computer-readable storage medium is used to store the computer program and other programs and data required by the data processing device, and can also be used to temporarily store data that has been output or will be output.

[0096] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for predicting robot position error and its interval, characterized in that the steps include... include: Obtain the joint angle vectors of the industrial robot during operation, calculate the difference between the theoretical position and the actual position, and construct a dataset containing joint angle vectors and position errors; Input the dataset containing joint angle vectors and position errors into the neural network-based prediction model; Position error interval prediction is performed by calculating the predicted interval coverage probability and the average predicted interval width, while minimizing the average predicted interval width to ensure the predicted interval coverage probability meets the standard; the predicted interval coverage probability is expressed as: in, This represents the estimated total number of data points within the prediction interval. The number of joint angle vector groups; The average prediction interval width is expressed as: in, , The first The samples are within the upper and lower bounds of the prediction; A probability-based approach is used to find the neural network parameters that maximize PICP; the width of the prediction interval is adjusted by minimizing the loss function; and the prediction model is optimized by balancing the interval width and coverage using Lagrange multipliers. According to the HQ criterion, the average prediction interval width is minimized while ensuring that the prediction interval coverage probability meets the target. Points falling outside the interval are not included in the calculation. The expression for the average prediction interval width loss function is as follows: in, This represents the total number of data points within the estimated prediction interval; , These represent the upper and lower bounds of the prediction interval, respectively. Indicates sample Whether it is within the estimated prediction range; A probability-based approach is used to find neural network parameters that maximize the probability of predicting interval coverage. : Where, vector This indicates whether each sample is within the estimated prediction interval, where each element... Treated as a binary variable, The probability is 1. When the sample size is large enough, The binomial distribution approximates the mean as The variance is Normal distribution: The problem of maximizing the likelihood function is solved by minimizing the negative log-likelihood function. The normal distribution simplifies to: When the predicted interval coverage probability is less than The penalty is applied at certain times, and the expression for the prediction interval coverage probability loss function is as follows: Position error prediction is performed by generating relative weights for the prediction interval boundaries by defining learnable parameters and using mean squared error loss to regress the predicted values; the position error... By defining a learnable parameter The relative weights of the boundary for generating the position error are given, and the formula for position error prediction is as follows: in, The mean squared error loss function is used to regress the predicted values. The expression for the mean squared error loss function for location error prediction is as follows: The loss function of the neural network model is determined by introducing Lagrange multipliers. To adjust the influence of interval width and coverage, the expression is: in, This represents the average prediction interval width loss function; This represents the probability loss function for predicting interval coverage. The mean squared error loss function represents the location error prediction. The prediction model outputs the location error value and its interval prediction result.

2. The robot position error and its interval prediction method according to claim 1, characterized in that, Neural network models include: The input layer accepts multi-dimensional vectors of the joint angles of the industrial robot. Hidden layers, including those with n A fully connected layer with hidden units and a ReLU activation function; The output layer consists of three nodes, which represent the upper and lower bounds of the predicted interval and the relative weights of the predicted boundary with respect to the location error.

3. The robot position error and its interval prediction method according to claim 2, characterized in that, The method trains multiple neural network models by subsampling the training set and fitting each subset with a neural network, thus forming a diverse set of models. The prediction results of various neural network models are aggregated to predict the range and specific values ​​of the samples.

Images