An error prediction method for variable-load industrial robots based on active learning and semi-supervised transfer learning

Abstract

The application discloses a variable load industrial robot error prediction method based on active learning and semi-supervised transfer learning, and relates to the technical field of robots. The method comprises the following steps: taking the joint angle of an industrial robot as input, taking the point prediction result and the prediction interval of the end position error as output, building a shared feature extraction network, constructing a point prediction branch and an interval prediction branch, and forming a member model; training multiple member models independently and integrating them based on a source load working condition data set to obtain a source domain pre-training model; taking the parameters of the source domain pre-training model as initialization parameters, performing two-stage semi-supervised transfer fine-tuning on labeled samples and unlabeled samples obtained based on active learning to obtain a target domain prediction model; and inputting the joint angle of the industrial robot into the target domain prediction model under a target load working condition, obtaining the point prediction result and the prediction interval of the end position error through member model fusion, and realizing robot error prediction and uncertainty quantification under a variable load working condition.

Description

Technical Field

[0001] This application relates to the field of robotics technology, and in particular to an error prediction method for variable-load industrial robots based on active learning and semi-supervised transfer learning. Background Technology

[0002] With the rapid development of industrial automation towards higher precision and flexibility, industrial robots have become key equipment in fields such as automobile manufacturing, electronic assembly, and precision machining. These robots need to frequently grasp workpieces of different masses and with different center-of-gravity distributions, making dynamic changes in load conditions a common occurrence. Changes in load directly lead to a series of chain reactions, such as adjustments in the robot's joint drive torque, increased elastic deformation of links, and changes in transmission clearance characteristics. This, in turn, causes a drift in the distribution of end-effector position errors. This phenomenon has become a bottleneck restricting industrial robots from achieving higher precision operations, placing stringent requirements on the adaptability and reliability of error prediction technologies.

[0003] Currently, various technical solutions have been developed in the field of industrial robot error prediction. The mainstream methods include model-based analytical methods and data-based machine learning methods, such as deriving error calculation formulas and fitting and predicting errors. However, these methods all suffer from problems such as insufficient datasets and one-sided consideration of dimensions, ultimately leading to inaccurate error prediction results.

[0004] Therefore, there is an urgent need for a method to accurately predict the errors of industrial robots under variable loads. Summary of the Invention

[0005] This application provides a variable load industrial robot error prediction method based on active learning and semi-supervised transfer learning, which can achieve accurate error prediction.

[0006] To achieve the above objectives, this application adopts the following technical solution: Firstly, this application provides a method for error prediction of variable-load industrial robots based on active learning and semi-supervised transfer learning, including: Using the joint angles of an industrial robot as input and the point prediction results and prediction intervals of the end-effector position error as output, a shared feature extraction network is built, constructing point prediction branches and interval prediction branches to form member models. Multiple member models are independently trained on the source load condition dataset under the source load condition, and the trained member models are integrated to obtain the source domain pre-trained model. Using the parameters of the source domain pre-trained model as initial parameters, a two-stage semi-supervised transfer fine-tuning is performed based on labeled samples and unlabeled samples obtained through active learning to obtain the target domain prediction model. Acquire real-time joint angle data of the target industrial robot under target load conditions; Based on the target domain prediction model, the real-time joint angle data is calculated to obtain the point prediction result and interval half-width of the end position error. Based on the point prediction results and interval half-width of the end position error, the error prediction results of the target industrial robot under the target load condition are determined.

[0007] In some possible implementations, based on a target domain prediction model, real-time joint angle data is calculated to obtain point prediction results and interval half-widths of the end-effector position error, including: Based on each member model, the real-time joint angle data is calculated to obtain the mean prediction error and prediction interval corresponding to that member model; The mean of the prediction error for each member model is calculated to obtain the point prediction result; Based on the prediction intervals and point prediction results corresponding to each member model, the interval half-width is obtained.

[0008] In some possible implementations, the interval half-width is obtained based on the prediction interval and point prediction results corresponding to each member model, including: For each member model, based on the point prediction results and the upper and lower bounds of the prediction interval corresponding to that member model, the half-width of the interval corresponding to that member model is obtained; against y The direction is determined by taking the largest interval half-width in each member model as the direction of the fused model. y Directional interval half-width; against x direction and z In terms of direction, the average half-width of the corresponding interval in each member model is calculated, and the average value is determined as the fused horizontal half-width and vertical half-width, respectively.

[0009] In some possible implementations, the error prediction result of the target industrial robot under the target load condition is determined based on the point prediction result of the end-effector position error and the interval half-width, including: Using the point prediction result as the center, the interval half-width is superimposed to determine the final error prediction interval; where the lower bound of the error prediction interval is the point prediction result minus the interval half-width, and the upper bound of the error prediction interval is the point prediction result plus the interval half-width. Based on the point prediction results and the error prediction interval, the error prediction results of the target industrial robot under the target load condition are determined; wherein, the error prediction interval has a predetermined confidence level.

[0010] In some possible implementations, multiple member models are trained independently on the source load condition dataset under the source load condition, including: Each member model is trained independently based on a subset randomly selected from the source load condition dataset. For each member model, the point prediction branch is optimized using the heteroscedasticity negative log-likelihood loss function to obtain the mean and variance of the prediction error, and the interval prediction branch is optimized using the quantile regression loss function to obtain the upper and lower bounds of the prediction interval.

[0011] In some possible implementations, the parameters of the pre-trained model in the source domain are used as initialization parameters, and a two-stage semi-supervised transfer fine-tuning is performed based on labeled and unlabeled samples obtained through active learning, including: Collect unlabeled samples under the target load conditions to form an unlabeled dataset; Based on the source domain pre-trained model, each unlabeled sample in the unlabeled dataset is predicted. The interval half-width of the unlabeled sample is calculated as an uncertainty measure. The spatial diversity measure of the unlabeled sample is calculated using the minimax strategy. The uncertainty measure and the spatial diversity measure are weighted and fused together to screen candidate samples. The sample that is farthest from the labeled sample set is selected for labeling to obtain the labeled sample. In the first stage of transfer fine-tuning, the shared feature extraction network of the source domain pre-trained model is frozen, and supervised learning is performed on the point prediction branch and the interval prediction branch using only labeled samples, so that the model can be adapted to the label distribution of the target load condition. In the second stage of transfer fine-tuning, the shared feature extraction network is unfrozen, and semi-supervised fine-tuning is performed using labeled and unlabeled samples. The training objective function is composed of a weighted combination of the supervised loss of labeled samples and the consistency regularization loss of unlabeled samples, resulting in the target domain prediction model.

[0012] Secondly, this application provides an error prediction device for variable-load industrial robots based on active learning and semi-supervised transfer learning, comprising: A module is built to construct a shared feature extraction network, using the joint angles of an industrial robot as input and the point prediction results and prediction intervals of the end-effector position error as outputs. This network constructs point prediction branches and interval prediction branches to form member models. Multiple member models are independently trained on the source load condition dataset under the source load condition, and the trained member models are integrated to obtain the source domain pre-trained model. Using the parameters of the source domain pre-trained model as initialization parameters, a two-stage semi-supervised transfer fine-tuning is performed based on labeled and unlabeled samples obtained through active learning to obtain the target domain prediction model. The acquisition module is used to acquire real-time joint angle data of the target industrial robot under the target load condition. The calculation module is used to calculate the real-time joint angle data based on the target domain prediction model to obtain the point prediction result and interval half-width of the end position error. The prediction module is used to determine the error prediction result of the target industrial robot under the target load condition based on the point prediction result and interval half-width of the end position error.

[0013] Thirdly, this application provides a computing device, including a memory and a processor; The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of the first aspects.

[0014] Fourthly, this application provides a computer-readable storage medium for storing a computer program for performing the method as described in any one of the first aspects.

[0015] Fifthly, this application provides a computer program product comprising one or more computer instructions, wherein when the computer instructions are executed by a computer, the computer performs the method as described in any one of the first aspects.

[0016] As can be seen from the above technical solution, this application has at least the following beneficial effects: In this application, by acquiring real-time joint angle data of the target industrial robot under target load conditions, the strong correlation between input features and actual working scenarios is ensured, effectively avoiding prediction inaccuracies caused by cross-load data confusion. This lays a solid data foundation for subsequent high-precision error prediction. Furthermore, real-time acquisition of joint angle data can accurately capture the dynamic changes in the robot's motion state, perfectly adapting to the needs of frequent load switching and real-time adjustment of motion posture in industrial scenarios. This allows the error prediction results to dynamically respond to changes in working conditions, providing strong support for real-time error compensation decisions. Finally, real-time joint angle data can comprehensively reflect the key influencing factors of the robot's end effector position, avoiding the computational complexity introduced by redundant features, and achieving a balance between model input effectiveness and computational efficiency.

[0017] This paper proposes an error prediction method for variable load industrial robots based on active learning and semi-supervised transfer learning. The specific process involves calculating the point prediction result and interval half-width of the end-effector position error based on real-time joint angle data using a pre-trained target domain prediction model. The target domain prediction model is pre-trained on a source load dataset and then fine-tuned under the target load using labeled and unlabeled samples through a two-stage semi-supervised transfer learning process. It consists of at least two independent member models, each including a feature extraction network, a point prediction branch, and an interval prediction branch. The target domain prediction model is constructed through a transfer learning approach combining source domain pre-training and two-stage semi-supervised fine-tuning in the target domain, breaking through the limitations of traditional single-load prediction methods. The model's generalization limitations are eliminated, eliminating the need for retraining for new loads and reducing model adaptation costs and downtime. The integrated structure enhances prediction robustness; the model consists of at least two independent member models, and by fusing the differentiated outputs of multiple sub-models, it effectively reduces the prediction bias and overfitting risk of a single model, improving the stability and reliability of prediction results under varying load scenarios. The dual-branch design provides dual protection against both accuracy and uncertainty; the feature extraction network of each sub-model shares high-order features, the point prediction branch outputs the optimal error estimate, and the interval prediction branch simultaneously quantifies uncertainty, addressing the pain point of traditional error prediction lacking risk assessment and providing complete data support for highly reliable decision-making. Differentiated fusion adapts to directional characteristics, targeting… y High sensitivity in direction (vertical direction) adopts a conservative strategy. x / z The direction adopts an averaging strategy, which ensures sufficient coverage of uncertainties in sensitive directions while making the prediction intervals in other directions more compact, thus balancing the safety and practicality of the prediction. Based on the point prediction results and interval half-width of the end position error, the error prediction results of the target industrial robot under the target load condition are determined. The final error prediction results include both the point prediction results (most likely error value) and the error prediction interval (uncertainty range), thus achieving accurate error prediction and facilitating direct application to the robot control system.

[0018] It should be understood that the descriptions of technical features, technical solutions, beneficial effects, or similar language in this application do not imply that all features and advantages can be achieved in any single embodiment. Rather, it is understood that the description of a feature or beneficial effect means that a specific technical feature, technical solution, or beneficial effect is included in at least one embodiment. Therefore, the descriptions of technical features, technical solutions, or beneficial effects in this specification do not necessarily refer to the same embodiment. Furthermore, the technical features, technical solutions, and beneficial effects described in this embodiment can be combined in any suitable manner. Those skilled in the art will understand that embodiments can be implemented without one or more specific technical features, technical solutions, or beneficial effects of a particular embodiment. In other embodiments, additional technical features and beneficial effects may be identified in specific embodiments that do not embody all embodiments. Attached Figure Description

[0019] Figure 1 An application environment diagram for a variable load industrial robot error prediction method based on active learning and semi-supervised transfer learning, provided for embodiments of this application; Figure 2 A flowchart illustrating a variable-load industrial robot error prediction method based on active learning and semi-supervised transfer learning, provided for an embodiment of this application; Figure 3 A structural diagram of a variable load industrial robot error prediction device based on active learning and semi-supervised transfer learning provided in this application embodiment; Figure 4 This is a schematic diagram of a computing device provided in an embodiment of this application. Detailed Implementation

[0020] The terms "first," "second," and "third," etc., used in this application specification and accompanying drawings are used to distinguish different objects, not to limit a specific order.

[0021] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0022] In view of this, embodiments of this application provide an error prediction method for variable-load industrial robots based on active learning and semi-supervised transfer learning. To make the technical solution of this application clearer and easier to understand, the application scenarios of the technical solution of this application are described below with reference to the accompanying drawings. Figure 1 As shown in the figure, this figure is a schematic diagram of a process provided in an embodiment of this application.

[0023] In this process diagram, terminal 102 acquires real-time joint angle data of the target industrial robot under the target load condition and transmits it to server 104 through a communication network. Then, server 104 performs calculations and predictions based on the real-time joint angle data, and finally obtains the error prediction result of the target industrial robot under the target load condition, and transmits the error prediction result to terminal 102 through a communication network.

[0024] The system acquires operational data from the DC charging pile, such as current and temperature data. For example, current data can be obtained by acquiring the three-phase input current through an input-side current acquisition device (such as a Hall sensor) and the output current through an output-side current acquisition device. Temperature data is obtained by acquiring the temperature of each power transistor through a temperature acquisition device (such as a PT100) installed on the power switching transistor (such as an IGBT). The server 103 can analyze and calculate the data acquired by the sensor 104 to obtain risk monitoring results. Furthermore, the server 103 can transmit the risk monitoring results to the terminal 102 for technical and maintenance personnel to view.

[0025] To make the technical solution of this application clearer and easier to understand, the following describes a variable-load industrial robot error prediction method based on active learning and semi-supervised transfer learning, using the above application scenarios as an example. Figure 2 As shown, this figure is a flowchart of a variable-load industrial robot error prediction method based on active learning and semi-supervised transfer learning provided in an embodiment of this application. The variable-load industrial robot error prediction method includes: S201. Using the joint angles of the industrial robot as input and the point prediction results and prediction intervals of the end-effector position error as output, a shared feature extraction network is built, and point prediction branches and interval prediction branches are constructed to form member models. Multiple member models are independently trained on the source load condition dataset under the source load condition, and the trained member models are integrated to obtain the source domain pre-trained model. Using the parameters of the source domain pre-trained model as initialization parameters, a two-stage semi-supervised transfer fine-tuning is performed based on labeled samples and unlabeled samples obtained by active learning to obtain the target domain prediction model.

[0026] Among them, the joint angles of an industrial robot are the real-time rotation angles of each movable joint of the industrial robot. They are generally 6-dimensional data (6-axis robot), which are model input features that directly reflect the current motion posture of the robot and are an important factor affecting the end effector error.

[0027] End-effector position error is the three-dimensional deviation between the actual position reached by the robot's end effector and the theoretical target position. x / y / zDirection is a crucial element that the model needs to predict, determining the accuracy of the operation.

[0028] Point prediction results provide a single, optimal estimate of the end-position error, representing the most likely magnitude of the error, and are used for direct error compensation.

[0029] The prediction interval is the range of upper and lower bounds of error given with the point prediction as the center and at a specified confidence level (such as 95%). It is used to quantify the uncertainty of the prediction and reflect the reliability of the result.

[0030] The shared feature extraction network is used to uniformly encode the input joint angle data, providing common high-order features for subsequent error prediction and uncertainty quantification, thus improving model training efficiency and feature reuse capability. The point prediction branch outputs the optimal estimate of the industrial robot's end-effector positioning error based on the shared features, achieving accurate error prediction. The interval prediction branch directly learns the upper and lower bounds of the error interval at a specified confidence level based on the shared features, completing the quantitative representation of prediction uncertainty. The member model, composed of the shared feature extraction network, the point prediction branch, and the interval prediction branch, forms the basic model unit for error prediction and uncertainty quantification.

[0031] The source load condition is a baseline load scenario (such as a 35kg load) with sufficient accumulated labeled data. It is the basic scenario for pre-training the target domain prediction model. The error patterns contained in its data provide reusable knowledge for model transfer across loads.

[0032] The point prediction branch is one of the task branches of the member model. It adopts a multilayer perceptron (MLP) structure, with high-order features from the feature extraction network as input and the target industrial robot end effector as output. x , y , z The mean prediction error (main output) and log-variance (used to characterize noise uncertainty) in the three directions are optimized and trained using the heteroscedasticity negative log-likelihood loss function.

[0033] The interval prediction branch is the second task branch of the member model. It adopts a quantile regression design without distribution assumptions. The input is a high-order feature, which directly learns and outputs a prediction interval with a 95% confidence level. The coverage and compactness of the prediction interval are balanced by combining quantile loss and interval width penalty term.

[0034] Member models are the building blocks of the target domain prediction model. Each sub-model is an independently trained complete model, consisting of three main parts: a feature extraction network, a point prediction branch, and an interval prediction branch. The differentiated outputs of multiple sub-models are fused to improve prediction robustness.

[0035] The source load condition dataset is a dataset collected and labeled based on source load conditions (e.g., 35kg load). It includes robot joint angle features and end-effector positioning error labels, used for initial training of member models. The source domain pre-trained model is an ensemble model obtained by fusing the outputs of multiple member models trained independently on the source load condition dataset. It possesses stable error prediction and interval quantization capabilities under source load conditions. Labeled samples are manually labeled samples selected through active learning under target load conditions, used for supervised fine-tuning of the target domain model. Unlabeled samples are samples collected under target load conditions but not labeled, used for semi-supervised fine-tuning and distribution learning of the target domain model. The target domain prediction model is an ensemble model obtained after two stages of semi-supervised transfer fine-tuning in the source domain and the target domain. It can adapt to the target load condition and output high-precision error prediction results and reliable uncertainty quantization intervals, including the six joint angle input features of the industrial robot and their corresponding end-effectors. x , y , z 3D localization error labels are used for pre-training of the target domain prediction model.

[0036] Independent training refers to training each member model using a different subset of training data, so that the training processes of each member model remain independent of each other.

[0037] Model ensemble refers to combining the prediction results of multiple member models and obtaining the final prediction output through methods such as mean fusion or maximum fusion.

[0038] The source domain pre-trained model refers to the initial prediction model obtained after training and integration on the source load condition dataset.

[0039] Initialization parameters refer to using the network weights already learned in the source domain pre-trained model as the starting point for subsequent training.

[0040] Active learning refers to a strategy that selects the most valuable samples for manual labeling by evaluating the information value of unlabeled samples.

[0041] Annotated samples refer to sample data that has been calibrated manually or by measuring equipment and contains actual error values.

[0042] Unlabeled samples refer to sample data that only contains joint angle data and does not contain corresponding error labels.

[0043] Two-stage semi-supervised fine-tuning transfer is a training strategy for adapting the target domain prediction model to the target load conditions. It consists of two stages: the first stage freezes the feature extraction network and fine-tunes the prediction branch using only a small amount of labeled data from the target domain; the second stage unfreezes the entire network and combines the supervised loss of labeled data with the consistency regularization loss of unlabeled data to achieve deep model adaptation, taking into account both source domain knowledge preservation and target domain feature learning.

[0044] For example, multiple member models need to be constructed. Each member model receives input joint angle data by building a shared feature extraction network, and derives two independent branch structures from the high-dimensional features output by this network. The point prediction branch is responsible for outputting the predicted error value, and the interval prediction branch is responsible for outputting the upper and lower bounds of the error prediction interval, thus forming a complete member model with the ability to simultaneously output point prediction and interval prediction. On the source load condition dataset, a pre-set number of member models are trained independently. Each member model randomly selects a portion of data from the source load condition dataset as its own training subset. The training data of each member model is different, and the training process does not interfere with each other, so that different member models learn differentiated feature representations. After all member models have been trained, the point prediction results of each member model are averaged and fused, and the interval prediction results of each member model are fused according to preset rules to obtain the integrated source domain pre-trained model. Subsequently, using the pre-trained network weights from the source domain pre-trained model as initial parameters, an active learning strategy is employed to select the most informative samples from the unlabeled samples of the target load condition for labeling, resulting in a small number of labeled samples while retaining the remaining unlabeled samples. In the first stage of transfer fine-tuning, the parameters of the shared feature extraction network in the source domain pre-trained model are kept unchanged, and only the labeled samples are used for supervised learning of the point prediction branch and the interval prediction branch, enabling the model to quickly learn the error distribution characteristics under the target load condition. In the second stage of transfer fine-tuning, the parameters of the shared feature extraction network are unfrozen, and the complete model is semi-supervised trained using both labeled and unlabeled samples. During training, labeled samples provide supervision signals, while unlabeled samples are constrained by consistency regularization to enhance the model's overall adaptability to the target data distribution. Ultimately, a target domain prediction model capable of simultaneously outputting high-precision point predictions and reliable interval predictions under the target load condition is obtained.

[0045] To verify the prediction performance of the proposed method under both source and target load conditions, the accuracy of point prediction and the quality of interval prediction were quantitatively evaluated. For point prediction, Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) were used as evaluation metrics. For interval prediction, Prediction Interval Coverage Probability (PICP) and Conditional Mean Prediction Interval Width (cMPIW) were used as evaluation metrics. The experimental results are as follows: Table 1 Source Domain Point Prediction Indicators

[0046] As shown in Table 1, under the source load condition dataset, the model point prediction can achieve low mean absolute error and root mean square error, and has stable error numerical prediction capability.

[0047] Table 2 Source Domain Interval Prediction Indicators

[0048] The source domain interval prediction results show that the PICP in the x, y, and z directions are close to the preset confidence level, the cMPIW matches the error characteristics of each direction, and the interval coverage and compactness are balanced.

[0049] Table 3 Target Domain Point Prediction Indicators

[0050] Under the target load condition, after active learning and two-stage semi-supervised transfer fine-tuning, the model's point prediction accuracy decreased slightly but remained at a high level, proving that cross-load transfer learning effectively preserved the prediction capability.

[0051] Table 4 Target Domain Inter-Domain Prediction Indicators

[0052] The target domain interval prediction results show that PICP in all directions still meets the confidence requirements. y The direction remains within a wide range due to the uncertainty caused by the coupling of multiple physical fields, consistent with the differentiated fusion strategy mentioned above, and achieves reliable error prediction and uncertainty quantification under variable load conditions.

[0053] S202. Obtain real-time joint angle data of the target industrial robot under the target load condition.

[0054] Among them, the target industrial robot refers to the specific industrial robot equipment that needs to be predicted for end-positioning error, such as the HSR-JR650 industrial robot, which is the application object of the error prediction method. Its structure includes six movable joints, and the positional accuracy of the end effector directly affects the quality of the operation.

[0055] The target load condition refers to the actual load scenario of the target industrial robot's current operation, that is, the mass and centroid distribution of the workpiece grasped or carried by the robot's end effector, such as a 50kg load condition. Changes in load will cause changes in the robot's joint driving torque, link elastic deformation and other characteristics, which will in turn cause the end effector positioning error distribution to drift. This is a scenario variable that needs to be adapted in error prediction.

[0056] Real-time joint angle data refers to the set of real-time rotation angle values ​​of the six joints (the main components of the robot to achieve spatial movement) when the target industrial robot is working under the target load condition. It is the input feature of the error prediction model. This data directly reflects the robot's motion posture and has a strong correlation with the end-effector positioning error. The corresponding error prediction result can be obtained by mapping through the model.

[0057] For example, when the target industrial robot is performing actual tasks, such as high-precision assembly or precision welding, i.e., when the target industrial robot is under target load conditions (such as gripping a 50kg workpiece), it is necessary to collect data in real time. This can be achieved by using joint angle sensors (such as encoders) on the robot itself to collect the rotation angles of the six joints in real time. The raw data output by the sensors needs to undergo preliminary preprocessing, such as noise reduction and format standardization, to ensure data accuracy and consistency. It should be noted that the collected real-time joint angle data will be analyzed and calculated by a pre-trained target domain prediction model to obtain the end effector. x (horizontal direction), y (Vertical direction) z The prediction results and uncertainty range of positioning error points in the three directions (vertical direction) ultimately provide a basis for error compensation for the robot control system, thereby improving the accuracy of operation.

[0058] S203. Based on the target domain prediction model, calculate the real-time joint angle data to obtain the point prediction result and interval half-width of the end position error.

[0059] Among them, the point prediction result is one of the main outputs of the target domain prediction model. It is the mean calculation result of the prediction error mean of all member models, reflecting the most likely value of the end-positioning error of the target industrial robot, and providing a basis for error compensation.

[0060] The interval half-width is the radius of the prediction interval, which is half the difference between the upper and lower bounds of the prediction interval. It is used to quantify the uncertainty of the prediction results. The interval half-width of a single member model is calculated from its upper and lower bounds of the prediction interval and the point prediction results. The final half-width needs to be determined according to... x (horizontal direction), y (Vertical direction) z (Vertical) characteristic differentiation fusion.

[0061] One possible approach is to calculate the mean prediction error and prediction interval corresponding to each member model based on real-time joint angle data; calculate the mean of the prediction errors corresponding to each member model to obtain the point prediction result; and obtain the interval half-width based on the prediction interval and point prediction result corresponding to each member model.

[0062] Optionally, for each member model, based on the point prediction results and the upper and lower bounds of the prediction interval corresponding to that member model, the half-width of the interval corresponding to that member model is obtained; for y The direction is determined by taking the largest interval half-width in each member model as the direction of the fused model. y Directional interval half-width; targeting x direction and z In terms of direction, the average half-width of the corresponding interval in each member model is calculated, and the average value is determined as the fused horizontal half-width and vertical half-width, respectively.

[0063] The mean prediction error is the best estimate of the end-point positioning error under the target working condition by a single member model. It is the output of the point prediction branch and reflects the most likely size of the error as believed by the sub-model.

[0064] The prediction interval is the range of error uncertainty output by a single member model, including the upper bound (the maximum possible error) and the lower bound (the minimum possible error), corresponding to a 95% confidence level (i.e., the true error has a 95% probability of falling within this interval), and is the carrier of uncertainty quantification.

[0065] y The direction is within the horizontal plane where the industrial robot base is located and the horizontal direction ( x The direction perpendicular to the direction is a sensitive direction for multi-physics coupling. The error is caused by the combined effect of time-varying factors such as flexibility, gap and thermal deformation, resulting in greater uncertainty.

[0066] x The direction is the first horizontal direction within the horizontal plane where the industrial robot base is located (usually the main motion direction of the robot), and the error is mainly dominated by geometric and gravity terms.

[0067] z The direction is perpendicular to the horizontal plane where the robot's base is located (and) x, y (All directions are perpendicular), and the error characteristics are similar to those in the horizontal direction.

[0068] The merged interval half-width is the result of directionally differentiating the interval half-widths of all member models: y The direction is taken as the maximum value of the half width of each sub-model interval (a conservative strategy to ensure sufficient coverage of uncertainty); the horizontal and vertical directions are taken as the arithmetic mean of the half width of each sub-model interval (to balance coverage and compactness and improve practicality).

[0069] For example, for each member model in the target domain prediction model, input propagation is performed, and the preprocessed real-time joint angle data is fed into the feature extraction network of the sub-model. Then, the feature extraction network completes feature encoding, transforming the 6-dimensional joint angle data into higher-order features, and outputs them synchronously to the point prediction branch and the interval prediction branch. Subsequently, point prediction calculation is started. Based on the received higher-order features, the point prediction branch outputs the mean of the prediction error (reflecting the most likely error value) and the logarithmic variance (characterizing noise uncertainty) corresponding to the sub-model. Finally, the interval prediction branch performs interval prediction calculation. Based on the higher-order features and using the quantile regression method, the prediction interval (including the upper and lower bounds, corresponding to a 95% confidence level) corresponding to the sub-model is directly obtained.

[0070] Furthermore, to improve prediction stability, data collection can be performed first, summarizing the average prediction error outputs of all member models in the target domain prediction model. Each member model corresponds to a set of... x (horizontal direction), y (Vertical direction) z The mean error in the three directions (vertical direction) is calculated; then the mean is calculated for... x , y , z In each of the three directions, the arithmetic mean of the error output by all member models in that direction is calculated to obtain the point prediction result for each direction. This result is the optimal estimate of the positioning error of the industrial robot end effector in the corresponding direction under the target load condition.

[0071] The calculation and fusion of interval half-width adopts a direction-differentiated processing method, mainly for adaptation. x (horizontal direction), y (Vertical direction) z The error characteristics in the three directions (vertical direction) are specifically divided into two steps: single-model interval half-width calculation and multi-model interval half-width fusion. The first step is single-model interval half-width calculation. For each member model, based on the upper and lower bounds of its output prediction interval, the half-width of the sub-model is calculated using the formula "interval half-width = (upper bound - lower bound) / 2". x , y , zThe second step is the fusion of the interval half-widths corresponding to the three directions; the second step is the fusion of the interval half-widths of the multiple sub-models, which is specifically for... y In the longitudinal direction, a conservative strategy is adopted, selecting the maximum value from the half-width of the y-direction interval of all member models as the fused value. y The directional interval half-width ensures sufficient coverage of uncertainties in the multiphysics coupling-sensitive direction to support highly reliable decision-making; for the lateral direction ( x Direction) and vertical direction ( z (Direction), using an averaging strategy, respectively for all member models x and z The arithmetic mean of the half-widths of the directional intervals is used to obtain the fused half-widths of the horizontal and vertical intervals. This ensures the coverage of the prediction intervals while making the intervals more compact, thus improving their practicality in real-world applications.

[0072] Ultimately, we will obtain two results: one is the point prediction result, that is... x (horizontal direction), y (Vertical direction) z The results provide two key parameters: first, the optimal error estimates in the three vertical directions; and second, the fused interval half-width, which represents the uncertainty quantification index for each of the three directions. These two results work together to provide crucial data support for constructing the final error prediction interval and enabling highly reliable error compensation decisions for industrial robots under target load conditions.

[0073] S204. Based on the point prediction results and interval half-width of the end position error, determine the error prediction results of the target industrial robot under the target load condition.

[0074] One possible approach is to determine the final error prediction interval by superimposing an interval half-width on the point prediction result as the center; wherein the lower bound of the error prediction interval is the point prediction result minus the interval half-width, and the upper bound of the error prediction interval is the point prediction result plus the interval half-width; based on the point prediction result and the error prediction interval, the error prediction result of the target industrial robot under the target load condition is determined; wherein the error prediction interval has a predetermined confidence level.

[0075] Among them, the error prediction result is the final output product of error prediction for variable load industrial robots. It is a comprehensive result that includes both the optimal error estimate and the uncertainty range. It not only clarifies the most likely size of the end-positioning error, but also quantifies the reliability of the prediction, providing a complete basis for error compensation decisions.

[0076] Error prediction interval is a carrier of uncertainty. It is a numerical range including an upper and lower bound, corresponding to a predetermined confidence level (such as 95%). It indicates that there is a certain probability that the actual end-point positioning error falls within this interval, and is used to quantify the uncertainty caused by model prediction and measurement noise.

[0077] The lower bound of the error prediction interval is the minimum boundary of the error prediction interval. The calculation formula is "point prediction result - fused interval half width", which is the minimum estimate of the actual error.

[0078] The upper bound of the error prediction interval is the maximum value boundary of the error prediction interval. The calculation formula is "point prediction result + fused interval half width", which is the maximum estimated value of the actual error.

[0079] The predetermined confidence level is a standard for the reliability of a pre-set error prediction interval (such as 95%). It represents the probability that the true error will be included in the prediction interval in a large number of repeated prediction scenarios. It is one of the main indicators for measuring the quality of interval prediction.

[0080] For example, the process of determining the error prediction interval can be as follows: taking the previously fused point prediction result as the center, that point prediction result is... x (horizontal direction), y (Vertical direction) z The optimal error estimates for each of the three vertical directions are then superimposed with the half-width of the fused interval for each direction to construct the final error prediction interval for each direction. The specific calculation method is as follows: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] x , y , z For each direction, the lower bound of the interval is obtained by subtracting the half-width of the fused interval for that direction from the predicted point results for that direction; this represents the minimum error prediction interval for that direction. The upper bound of the interval is obtained by adding the half-width of the fused interval for that direction to the predicted point results for that direction; this represents the maximum error prediction interval for that direction. For example, if... x The direction point prediction result is 0.04mm, and the half-width of the fused interval is 0.01mm. x The direction error prediction range is [0.03mm, 0.05mm].

[0081] Will x (horizontal direction), y (Vertical direction) z The "point prediction results" and corresponding "error prediction intervals" for each of the three vertical directions are combined to form an independent comprehensive error prediction result for each direction. The final output is the prediction result for all three directions. The point prediction result serves as an estimate of the error, clearly defining the most likely magnitude of the positioning error in the corresponding direction of the industrial robot's end effector under the target load condition. The error prediction interval (including upper and lower bounds) quantifies the range of uncertainty in the prediction, and this interval meets a predetermined confidence level of 95%, meaning that the actual end-effector positioning error has a 95% probability of falling within this interval. These two elements complement each other, together forming a final error prediction result that combines accuracy and reliability, providing a complete basis for subsequent error compensation decisions.

[0082] The error prediction results directly support the error compensation decision of industrial robots: the robot control system can make basic error corrections based on the point prediction results, and adjust the compensation strategy with reference to the width of the error prediction interval; if the interval is narrow (small uncertainty), it can be accurately compensated according to the point prediction results; if the interval is wide (large uncertainty), a safety margin can be reserved within the interval to ensure that the compensation operation is carried out within the preset risk threshold, and ultimately improve the operational reliability under variable load conditions.

[0083] Based on the above, the variable load industrial robot error prediction method based on active learning and semi-supervised transfer learning ensures a strong correlation between input features and the actual working scenario by acquiring real-time joint angle data of the target industrial robot under the target load condition. This effectively avoids prediction inaccuracies caused by cross-load data confusion, laying a solid data foundation for subsequent high-precision error prediction. Furthermore, real-time acquisition of joint angle data can accurately capture the dynamic changes in the robot's motion state, effectively adapting to the needs of frequent load switching and real-time adjustment of motion posture in industrial scenarios. This allows the error prediction results to dynamically respond to changes in working conditions, providing strong support for real-time error compensation decisions. Finally, real-time joint angle data can comprehensively reflect the key influencing factors of the robot's end effector position, avoiding the computational complexity introduced by redundant features, and achieving a balance between model input effectiveness and computational efficiency.

[0084] Based on a pre-trained target domain prediction model, real-time joint angle data is used to calculate the point prediction result and interval half-width of the end-effector position error. The target domain prediction model is pre-trained on a source load dataset and then transferred under the target load using labeled and unlabeled samples through a two-stage semi-supervised fine-tuning process. It consists of at least two independent member models, each including a feature extraction network, a point prediction branch, and an interval prediction branch. This transfer learning approach, combining source domain pre-training and two-stage semi-supervised fine-tuning in the target domain, overcomes the generalization limitations of traditional single-load models and eliminates the need for retraining for new loads. This reduces model adaptation costs and downtime; the integrated structure enhances prediction robustness, as the model consists of at least two independent member models. By fusing the differentiated outputs of multiple sub-models, it effectively reduces the prediction bias and overfitting risk of a single model, improving the stability and reliability of prediction results under varying load scenarios; the dual-branch design provides dual protection for accuracy and uncertainty, with each sub-model's feature extraction network sharing high-order features. The point prediction branch outputs the optimal error estimate, while the interval prediction branch simultaneously quantifies uncertainty, addressing the pain point of traditional error prediction lacking risk assessment and providing complete data support for highly reliable decision-making; differentiated fusion adapts to directional characteristics, targeting... y High sensitivity in direction (vertical direction) adopts a conservative strategy. x / z The direction adopts an averaging strategy, which ensures sufficient coverage of uncertainties in sensitive directions while making the prediction intervals in other directions more compact, thus balancing the safety and practicality of the prediction. Based on the point prediction results and interval half-width of the end position error, the error prediction results of the target industrial robot under the target load condition are determined. The final error prediction results include both the point prediction results (most likely error value) and the error prediction interval (uncertainty range), thus achieving accurate error prediction and facilitating direct application to the robot control system.

[0085] Based on the above embodiments, this embodiment provides a detailed explanation of the training process of the target domain prediction model, specifically: Unlabeled samples under the target load condition are collected to form an unlabeled dataset. Based on the source domain pre-trained model, predictions are made for each unlabeled sample in the dataset. The interval half-width of the unlabeled sample is calculated as an uncertainty measure, and a minimax strategy is used to calculate the spatial diversity measure. The uncertainty measure and spatial diversity measure are weighted and fused to filter candidate samples. The sample furthest from the labeled sample set is selected for labeling, resulting in labeled samples. In the first stage of transfer fine-tuning, the shared feature extraction network of the source domain pre-trained model is frozen, and supervised learning is performed on the point prediction branch and interval prediction branch using only labeled samples, adapting the model to the label distribution of the target load condition. In the second stage of transfer fine-tuning, the shared feature extraction network is unfrozen, and semi-supervised fine-tuning is performed using labeled and unlabeled samples. The training objective function is a weighted combination of the supervised loss of labeled samples and the consistency regularization loss of unlabeled samples, resulting in the target domain prediction model.

[0086] Among them, unlabeled samples refer to sample data that only contain joint angle data of industrial robots and do not contain corresponding end-positioning error labels.

[0087] A source domain pre-trained model refers to an initial prediction model obtained after training and integration on a source load condition dataset. It has the ability to output both point prediction results and prediction intervals simultaneously.

[0088] Interval half-width refers to half the length of the prediction interval and is used to quantify the degree of uncertainty in the prediction results.

[0089] Uncertainty measure is a quantitative indicator that assesses the reliability of a model’s prediction for a sample by calculating the half-width of the interval for an unlabeled sample.

[0090] The minimax strategy is a spatial diversity sampling method that calculates the minimum distance between each candidate sample and the selected sample, and selects the sample that maximizes the minimum distance, thereby ensuring that the distribution of the selected samples in the feature space is as dispersed as possible.

[0091] Spatial diversity measures are used to quantify the degree of difference in the distribution of unlabeled samples and labeled sample sets in the feature space.

[0092] Weighted fusion refers to the process of combining uncertainty measures and spatial diversity measures according to a certain weight ratio to form a comprehensive score.

[0093] Candidate samples refer to the subset of samples with higher scores selected from the unlabeled dataset based on the weighted fusion comprehensive score.

[0094] The labeled sample set refers to the set of samples for which error labels have been completed, and is used in the supervised learning phase.

[0095] Annotated samples refer to sample data that has been calibrated manually or by measuring equipment and contains actual error values.

[0096] Shared feature extraction networks are neural network backbone structures used by multiple prediction tasks to extract high-dimensional feature vectors from joint-angle data.

[0097] The point prediction branch refers to the output module built on top of the shared feature extraction network, which is used to predict the specific numerical value of the error.

[0098] The interval prediction branch is another output module built on top of the shared feature extraction network, used to predict the range within which the error may fall.

[0099] Supervised learning refers to the process of training a model using labeled samples and optimizing the model parameters by minimizing the loss function between the predicted and the true values.

[0100] Semi-supervised fine-tuning refers to training a model using both labeled and unlabeled samples simultaneously. The unlabeled samples are used to enhance the model's adaptability to the target data distribution through consistency regularization constraints.

[0101] Consistency regularization loss refers to the loss function term generated by applying consistency constraints to the prediction results of the same unlabeled sample before and after applying perturbation.

[0102] It should be noted that the labeled dataset is data obtained after standardization; for example, the standardization process can be as follows: A labeled dataset is constructed by collecting the input feature vectors and corresponding error labels of an industrial robot during its operation. The input feature vectors are denoted as follows: It consists of the six joints of the robot and outputs as the end-effector positioning error vector. , respectively corresponding x , y , zLocalization errors in three directions. To eliminate differences in feature dimensions across different dimensions and improve network training stability, Z-score standardization is applied to the input features.

[0103] First, calculate the input feature vector. In every dimension j mean with standard deviation Assume the total number of samples is... , No. i The first sample j The joint angle values ​​in each direction are The calculation formula is as follows:

[0104]

[0105] in, This represents a small constant used to prevent the denominator from being zero.

[0106] The dimension-by-dimensional standardization result for any sample is:

[0107] in, Indicates the standardized first i The first sample j The joint angle values ​​in each direction. After this processing, each dimension of the input data follows a standard distribution with a mean of 0 and a variance of 1, thus obtaining a standardized dataset.

[0108] For example, the point prediction model can be trained using a multilayer perceptron (MLP) architecture to account for the mean and random uncertainty of the prediction error. The input is the joint angle, and the output is the mean of the prediction error. And an auxiliary log-variance Considering the differences in noise variance among different samples, the loss function of the point prediction model is the heteroscedastic negative log-likelihood loss, while simultaneously optimizing mean prediction and variance estimation:

[0109] in, This is the name identifier for the loss function, representing the heteroscedastic negative log-likelihood loss value; B Batch size; D For output dimensions; For the first i The sample at the th d The true error of each output dimension For the model to the first i The sample at the th d The predicted mean of each output dimension, For the model to the first i The sample at the th d The variance of prediction noise in each output dimension For the first i The sample at the th d The logarithmic term of the predicted variance for the direction is used for numerical stability and participates in the calculation of negative log-likelihood. The residuals are weighted by the variance. The greater the noise, the smaller the penalty to the residuals, which prevents the model from overfitting in areas with large data fluctuations and improves robustness.

[0110] Use softplus to ensure output It is positive and smooth, avoiding gradient jitter and eliminating Risk of degradation approaching zero; simultaneously, L2 regularization is used to suppress degradation. Unrestricted growth or violent fluctuations. L2 regularization formula:

[0111] in, Identifier for the regularization loss term; is the regularization coefficient.

[0112] The total loss function L of the point prediction model is:

[0113] In point prediction training, the negative log-likelihood loss of heteroscedasticity on the validation set is used as a monitoring metric to avoid overfitting the model in noisy regions. The reproducibility and stable convergence of the training results are achieved by saving the optimal weights on the validation set.

[0114] Interval prediction models can be trained using direct interval estimation without requiring the assumption that the error follows a normal distribution; the upper and lower bounds of the prediction interval can be learned directly. Interval prediction learns the lower quantiles. and upper quantile Two quantiles approximately form a prediction interval with a 95% confidence level. The quality of the interval and parameter selection are evaluated using the prediction interval coverage probability (PICP) and the conditional mean prediction interval width (cMPIW) on the validation set. The quantile loss function can be expressed as:

[0115] in, This is the name of the loss function, representing the quantile loss value, used to measure the deviation between the predicted quantile and the true value; The actual value; The predicted quantile boundaries; The target quantile is used. The prediction interval width is adjusted based on the quantile. During training, the loss function is adjusted to ensure interval coverage.

[0116] To avoid quantile crossovers that could invalidate the prediction interval, the lower quantile is directly output, and an unconstrained raw offset value is predicted. This offset is then converted to a strictly positive offset using the Softplus activation function. .in, This refers to the unconstrained original offset output by the model. It is a small positive number to ensure it is strictly greater than zero. The specific expression is:

[0117] in, For the first i The sample, the first d Lower bound of prediction for each output dimension For the first i The sample, the first d The upper bound of the prediction for each output dimension.

[0118] Combinatorial quantile loss:

[0119] in, This serves as a name identifier for the combined quantile loss value, used to comprehensively measure the overall loss across the upper and lower bounds of the prediction interval; The lower quantile, It represents the upper quantile.

[0120] Width penalty aims to balance coverage and compactness of the prediction interval. In uncertainty quantification, the ideal prediction interval should simultaneously satisfy high coverage and low width. Simply using quantile loss may lead to overly loose intervals, as the model tends to widen the interval to increase coverage, thus sacrificing practicality. Width penalty alleviates this problem by explicitly penalizing overly wide intervals, encouraging the model to learn more compact intervals while maintaining coverage.

[0121]

[0122] in, This is an identifier for the loss function name, representing the width penalty loss value of the prediction interval; For the first i The sample at the th d The width of the prediction interval for the dimension; For the first d The penalty weight of the dimension is used to weigh the trade-off between high coverage and narrow intervals.

[0123] The total loss for the prediction interval can be expressed as:

[0124] in, This is the name identifier for the total loss function, representing the final optimization objective of the interval prediction branch.

[0125] Each member model is trained on a slightly different subset of data (80% of the data), and each member model sees slightly different training data, which causes them to learn slightly different parameters.

[0126] train m Each member model in the target domain prediction model undergoes random initialization of its neural network parameters, further increasing the ensemble diversity of the target domain prediction model. Each member model provides a prediction mean and upper and lower bounds for the interval prediction, and the training of each member model is completely independent.

[0127] The center position of the final interval is determined by point prediction fusion:

[0128] in, For the integrated point prediction results (final point prediction center); M The total number of member models; For the first m The model for the first i The sample at the th d Mean prediction error for each dimension.

[0129] Interval prediction fusion first transforms the interval into a width concept.

[0130]

[0131] in, Representing the m The model in the first i The sample at the th d The half-width of the prediction interval for the dimension. for m The model for the first i The sample at the th d Upper bound of the prediction interval on the dimensional output for m The model for the first i The sample at the th d The lower bound of the prediction interval on the dimensional output.

[0132] Then according to x , y , zPerformance in three directions, targeting x , z Directional errors are mainly dominated by geometric and gravitational terms, and the patterns are obvious; while y The direction, as a sensitive direction of multi-physics coupling, exhibits high nonlinearity and uncertainty due to the combined effects of time-varying factors such as flexibility, gaps, and thermal deformation. Two different fusion logics are employed to address this issue. y The direction adopts a conservative strategy; to ensure coverage, as long as any model believes... y The uncertainty in direction is significant, and the target domain prediction model adopts this greatest uncertainty. This explicitly utilizes the divergence between models: if some models are broad and some are narrow, the broadest one is chosen to ensure safety. x and z The directional performance is good, so an averaging strategy is used to obtain a smoother estimate.

[0133]

[0134]

[0135]

[0136] in, For the integrated first i One sample in y The half-width of the fusion interval in the direction, and For the integrated first i One sample in x and z The fusion interval half-width of the direction.

[0137] Ultimately, with a new center Using this as a baseline, and adding the fused interval half-width, the final prediction interval is constructed:

[0138] in, For the integrated first i The sample at the th d The lower bound of the prediction interval for the dimension. For the integrated first i The sample at the th d The upper bound of the prediction interval for the dimension.

[0139] The Predicted Interval Coverage Probability (PICP) can be defined as:

[0140] in, N The total number of samples; i For sample index; This is an indicative function. If the condition within the parentheses is true, i.e., the true value is within the interval, the function value is 1. If the condition is false, i.e., the true value is outside the interval, the function value is 0.

[0141] Conditional average prediction interval width (cMPIW) is used to measure the compactness of the interval.

[0142]

[0143] Wherein, cMPIW is the conditional average prediction interval width, which is the average interval width of the effectively covered samples.

[0144] The second stage aims to achieve effective model adaptation to new load conditions using a small number of labeled samples through active transfer learning and two-stage semi-supervised transfer fine-tuning. This stage mainly includes two steps: (1) Active sampling based on uncertainty and diversity: unlabeled samples are evaluated, and a hybrid batch selection strategy is adopted to comprehensively consider the uncertainty and spatial diversity of the samples. In each round, the most informative samples are selected from the top-k candidate samples with the highest scores for manual labeling; (2) Two-stage semi-supervised transfer fine-tuning: in the first stage, the backbone network is frozen and only the prediction head is fine-tuned to quickly align with the target domain label distribution. In the second stage, the entire model is unfrozen and a consistency regularization loss for unlabeled data is introduced. While suppressing catastrophic forgetting, the distribution information of unlabeled data is fully explored to achieve deep adaptation of the model between labeled samples and unlabeled samples.

[0145] (1) Active sampling based on uncertainty and diversity Using a target domain prediction model pre-trained on the source load condition dataset in an unlabeled dataset The uncertainty of the predicted samples is calculated, and a hybrid batch selection strategy is adopted to balance uncertainty and diversity.

[0146] The calculation process of uncertainty metric: Using a pre-trained target domain prediction model on an unlabeled dataset based on the source load condition dataset. The average half-width of the interval for each sample is calculated as a measure of uncertainty. Specifically, the half-width of the interval is calculated for each target domain prediction model. Then, the half-widths of the models are averaged to obtain the comprehensive half-width. The L2 norm of the comprehensive half-width is taken to obtain a scalar value as the uncertainty score for that sample, which can be expressed as follows:

[0147] in, For the sample x Uncertainty score (final output scalar); For the first m Each member model for samples x The upper bound of the error prediction interval; For the first m Each member model for samples x The lower bound of the error prediction interval.

[0148] The calculation process of diversity measure: Initialization. To prevent getting trapped in local optima from the beginning, the K-Means++ initialization strategy is used to ensure that the initial seeds are as spatially dispersed as possible. Specifically, it can be expressed as:

[0149] in, For the sample x The probability of being selected as a cluster center; For the sample x The shortest Euclidean distance between the cluster and the existing cluster centers.

[0150] Using a max-min strategy, calculate the value of each sample in the remaining pool. Up to the currently selected sample set Find the Euclidean distance and take the minimum value:

[0151] in, Unlabeled samples To the selected sample set The minimum Euclidean distance; The candidate sample (a sample in the unlabeled sample pool) is the sample to be selected from the unlabeled sample pool. For the selected sample set The samples in; For the first i The selected sample set after round selection.

[0152] To eliminate the influence of dimensions, distance and the uncertainty of pre-calculation Mapped to the interval [0,1] using Min-Max normalization.

[0153]

[0154]

[0155] in, The normalized distance value (output result); For the first i The original diversity distance of the unlabeled samples; For all unlabeled samples participating in normalization, the original distance The minimum value; For all unlabeled samples participating in normalization, the original distance The maximum value; It is a tiny positive number, also known as a smoothing term, and is optional. This can maintain numerical stability, thereby avoiding calculation errors or numerical overflow caused by dividing by zero or numbers close to zero; The uncertainty is the result of normalization; For the first i The original uncertainty score of each unlabeled sample; For all unlabeled samples participating in normalization, the original uncertainty score The minimum value; For all unlabeled samples participating in normalization, the original uncertainty score The maximum value.

[0156] The calculation process of dynamic weighted sample selection: The dynamic hybrid scoring function proposes an adaptive trade-off mechanism. The idea is that in the early stages of sampling, labeled samples are sparse, and the model's understanding of the feature space is insufficient. At this time, higher weights should be assigned to diversity to quickly cover the global distribution. As the sampling process progresses, the feature space is largely covered, and higher weights should be assigned to uncertainty to finely adjust the decision boundary. Therefore, a dynamic weight is defined. :

[0157] in, For the first t Samples in round iteration x Dynamic mixed scoring (output scalar); t Indicates the iteration round; x These are unlabeled samples; For the first t Dynamic weights for each iteration; Unlabeled samples x The normalized uncertainty score; Unlabeled samples x Normalized diversity distance; This refers to the unlabeled sample in the unlabeled sample (target load condition), specifically the real-time joint angle data (6-dimensional features) of this sample.

[0158] The weights have been updated to:

[0159] in, This represents the total number of iterations. These are the initial weights.

[0160] In practical applications, directly selecting the sample with the highest mixed score may introduce noise. Therefore, selecting the top-k samples first can reduce the noise impact of individual scores. In each step of the actual selection, the top-k samples are selected first. top-k candidate sample set To further ensure the representativeness of the sampled data and avoid getting trapped in areas of dense local features, in the candidate sample set... Internally, the final sample selection is based on the spatial diversity criterion. Mid-distance currently marked set The farthest sample .

[0161]

[0162] in, These are the final selected samples to be labeled; For candidate set The first in i One unlabeled sample; This is the top-k candidate sample set (sample set) for the mixed score, where k is a hyperparameter. For example, k=20 means selecting the top 20 samples with the mixed score. For candidate set Any unlabeled sample in, and The meanings are consistent, and the symbols are used to simplify the representation. For the first i The labeled sample set after rounds of screening.

[0163] This process is repeated until the target number of samples is reached.

[0164] The two-stage semi-supervised transfer fine-tuning process is divided into two stages, which can be specifically represented as follows: In the first stage, the backbone network of the pre-trained model has already learned transferable features from the source load condition dataset. Direct end-to-end fine-tuning (training and updating all parameters simultaneously) can easily destroy these converged high-level representations. For example, if the data coverage of labeled and unlabeled samples is insufficient, the neural network will overwrite the original representation of physical relationships, leading to a decrease in the neural network's prediction performance. The prediction head parameters are most sensitive to the data distribution of labeled and unlabeled samples. Therefore, a frozen shared backbone network is adopted, and only labeled data is used for supervised learning of the point prediction head and interval prediction head, respectively. The loss function used in the training of the source load condition dataset is adopted during the training process. and This allows the model to quickly adapt to the data distribution of labeled and unlabeled samples while retaining knowledge of the source load condition dataset.

[0165] In the second stage, all parameters are unfrozen, and semi-supervised fine-tuning is performed using a lower learning rate. The training objective function is composed of a weighted combination of supervised loss and unlabeled consistency regularization loss.

[0166] in, For unlabeled loss weights, The supervised loss for the target domain labeled data is completely consistent with the training on the source load condition dataset in the first stage. This represents the consistency loss of unlabeled data.

[0167] Define a perturbation mechanism for unlabeled datasets. any sample in Add Gaussian noise:

[0168] in, This is the sample after perturbation. To and Dimensionally consistent Gaussian noise, For noise intensity, =0.01, It is a six-dimensional identity matrix.

[0169] Specifically, the unlabeled loss of the point prediction model is defined as:

[0170] in, The unlabeled loss for the point prediction branch; The expectation operator is used on unlabeled sample sets. All samples Calculate the average of the expressions within the parentheses; These are the original, unlabeled samples; This is a subset of unlabeled samples (focusing on joint angle data). For the original unlabeled samples The sample obtained after applying a small perturbation; For point prediction branches on the original unlabeled samples The mean of the prediction error; For point prediction branch pairs of perturbed samples The mean of the prediction error; For point prediction branches on the original unlabeled samples The noise variance of the predicted data; For point prediction branch pairs of perturbed samples The noise variance of the predicted data; This is the L1 norm (Manhattan distance) operator, which calculates the sum of the absolute differences between the two vectors (or scalars) within the parentheses.

[0171] The unlabeled loss of the interval prediction branch is defined as:

[0172] in, The unlabeled loss for the interval prediction branch; For interval prediction branching of the original unlabeled samples The lower bound of the prediction interval; For interval prediction branch pairs of perturbed samples The lower bound of the prediction interval; For interval prediction branching of the original unlabeled samples The upper bound of the prediction interval; For interval prediction branch pairs of perturbed samples The upper bound of the prediction interval.

[0173] The two branches calculate the total loss separately and perform gradient updates independently. To prevent overfitting due to insufficient labeled samples, the negative log-likelihood loss of the validation set heteroscedasticity is used as the monitoring metric for the point prediction branch, and the total loss of the validation set quantiles is used as the monitoring metric for the interval prediction branch. This consistency regularization design eliminates the need for pseudo-labels, avoiding the risk of noise label propagation. Simultaneously, it applies smoothing constraints to the prediction mean, variance, and upper and lower quantiles, effectively improving the model's robustness to unlabeled regions in both labeled and unlabeled samples and enhancing the quality of uncertainty quantification.

[0174] After the semi-supervised training employs a two-stage strategy, the final target domain prediction model is obtained. The point prediction and interval prediction branches of each member model (ensemble member) have been fully optimized based on labeled and unlabeled samples, and the weights with optimal validation performance are selected through an early stopping mechanism. At this point, the training process ends. Subsequent forward inference is performed on an independent test set to calculate the ensemble point predictions and ensemble prediction intervals, and the accuracy of point predictions and the quality of prediction intervals are evaluated.

[0175] In this embodiment, multiple member models are independently trained based on random subsets of the source load condition dataset. This improves the robustness of the model ensemble to reduce the risk of overfitting and adapts to the data distribution of industrial scenarios to enhance the generalization foundation. To improve ensemble robustness, non-overlapping subsets are extracted from the source load condition dataset using methods such as bootstrapping to provide differentiated training data for each member model. This intentionally strengthens the diversity among sub-models; for example, some sub-models focus on learning sample features with low joint angles and low errors, while others focus on sample patterns with high joint angles and high errors. Subsequent multi-sub-model output fusion strategies, such as averaging point prediction results and merging intervals by direction, effectively offset the prediction bias of a single model and prevent overfitting of local data features under the source load condition. Compared to traditional single-model training methods, this strategy reduces prediction error fluctuations in variable load scenarios, especially adapting to the dynamic characteristics of industrial robot joint angle data as the load changes. In terms of enhancing generalization, the source load case dataset (e.g., 35kg) covers the complete correspondence between the six joint angles of the industrial robot and the three-dimensional error of the end effector. The training mode based on random subsets ensures that each member model accurately learns the mapping law of "joint angle-error" under the source load. For example, for every 10° increase in the angle of joint 1, x The average increase in orientation error was 0.012 mm, which laid a solid foundation of general features for subsequent cross-load transfer and effectively avoided the problem that the model could only adapt to a specific posture and could not be transferred to other motion scenarios of the target load due to the single training data.

[0176] By employing dual loss functions to optimize the point prediction and interval prediction branches respectively, the predictive advantages of each branch can be fully utilized, thereby improving the overall prediction accuracy, reliability, and scene adaptability of the model. For the point prediction branch, the heteroscedasticity negative log-likelihood loss function exhibits unique advantages in its ability to accurately quantify dynamic uncertainty, perfectly adapting to the characteristics of industrial robot errors that vary with load and posture. The variance of industrial robot errors is not a fixed value; for example, the variance caused by joint elastic deformation under a 50kg load is 1.8 times that under a 35kg load. This loss function can simultaneously optimize both the mean and variance of the prediction error. By using variance-weighted residuals (i.e., the greater the noise, the smaller the penalty to the residual), it effectively avoids overfitting in regions with large data fluctuations, such as high loads and extreme joint angles. This makes the mean prediction error closer to the true value and ensures that the prediction variance accurately reflects the model's grasp of the current input. For example, when the variance > 0.0002, it directly indicates high error uncertainty under that posture, requiring close attention in subsequent interval half-width fusion. Compared to the traditional MSE loss that assumes a fixed error variance, this function can reduce the mean absolute error (MAE) of the point prediction results, especially in industrial scenarios with frequent load changes, improving the stability of prediction accuracy. For the interval prediction branch, the advantages of the quantile regression loss function are concentrated in the balance between interval reliability assurance and coverage / compactness: Industrial robot errors are affected by various factors such as joint clearance and thermal deformation, resulting in a complex and non-standard normal distribution. The quantile regression loss function does not require a pre-defined error distribution and can directly learn the upper and lower bounds of the interval at a specified confidence level (e.g., 95%), ensuring that the actual error has a 95% probability of falling within the prediction interval. This successfully solves the pain point of insufficient coverage (often below 85%) in industrial scenarios for traditional interval prediction based on the normal distribution assumption. Furthermore, by combining the quantile loss with an interval width penalty term, this function can avoid excessively wide intervals while ensuring interval coverage. For example, it can... x The directional interval half-width is controlled within 0.01-0.03mm. Compared with the traditional interval prediction method, the conditional average prediction interval width (cMPIW) is reduced by 25%-30%, providing a more accurate reference for the uncertainty range of industrial robot error compensation and further improving the actual effect of error compensation.

[0177] The above text combined Figures 1 to 2 This application provides a detailed description of the error prediction method for variable load industrial robots based on active learning and semi-supervised transfer learning. The apparatus and equipment provided in this application will be described below with reference to the accompanying drawings.

[0178] This application also provides an error prediction device for variable-load industrial robots based on active learning and semi-supervised transfer learning, such as... Figure 3As shown in the figure, this is a schematic diagram of a variable-load industrial robot error prediction device based on active learning and semi-supervised transfer learning provided in an embodiment of this application. The device includes: Module 301 is used to build a shared feature extraction network, construct point prediction branches and interval prediction branches to form member models; multiple member models are independently trained on the source load condition dataset under the source load condition, and the trained member models are integrated to obtain the source domain pre-trained model; using the parameters of the source domain pre-trained model as initialization parameters, a two-stage semi-supervised transfer fine-tuning is performed based on labeled samples and unlabeled samples obtained by active learning to obtain the target domain prediction model; The acquisition module 302 is used to acquire real-time joint angle data of the target industrial robot under the target load condition; The calculation module 303 is used to calculate the real-time joint angle data based on the target domain prediction model to obtain the point prediction result and interval half-width of the end position error. The prediction module 304 is used to determine the error prediction result of the target industrial robot under the target load condition based on the point prediction result and the interval half-width of the end position error.

[0179] In some possible implementations, the computing module 303 is specifically used for: Based on each member model, the real-time joint angle data is calculated to obtain the mean prediction error and prediction interval corresponding to that member model; The mean of the prediction error for each member model is calculated to obtain the point prediction result; Based on the prediction intervals and point prediction results corresponding to each member model, the interval half-width is obtained.

[0180] In some possible implementations, the computing module 303 is specifically used for: For each member model, based on the point prediction results and the upper and lower bounds of the prediction interval corresponding to that member model, the half-width of the interval corresponding to that member model is obtained; against y In terms of direction, the largest interval half-width in each member model is determined as the fused y-direction interval half-width; against x direction and z In terms of direction, the average half-width of the corresponding interval in each member model is calculated, and the average value is determined as the fused horizontal half-width and vertical half-width, respectively.

[0181] In some possible implementations, the prediction module 304 is specifically used for: Each member model is trained independently based on a subset randomly selected from the source load condition dataset. For each member model, the point prediction branch is optimized using the heteroscedasticity negative log-likelihood loss function to obtain the mean and variance of the prediction error, and the interval prediction branch is optimized using the quantile regression loss function to obtain the upper and lower bounds of the prediction interval.

[0182] In some possible implementations, module 301 is specifically used for: The first training module is used to train each member model independently based on a subset randomly selected from the source load condition dataset. For each member model, the heteroscedastic negative log-likelihood loss function is used to optimize the point prediction branch to obtain the mean and variance of the prediction error, and the quantile regression loss function is used to optimize the interval prediction branch to obtain the upper and lower bounds of the prediction interval.

[0183] In some possible implementations, module 301 is specifically used for: Collect unlabeled samples under the target load conditions to form an unlabeled dataset; Based on the source domain pre-trained model, predictions are made for each unlabeled sample in the unlabeled dataset. The interval half-width of the unlabeled sample is calculated as an uncertainty measure, and the spatial diversity measure of the unlabeled sample is calculated using a minimax strategy. The uncertainty measure and the spatial diversity measure are weighted and fused to filter candidate samples. The sample farthest from the labeled sample set is selected for labeling to obtain labeled samples. In the first stage of transfer fine-tuning, the shared feature extraction network of the source domain pre-trained model is frozen, and supervised learning is performed on the point prediction branch and the interval prediction branch using only the labeled samples to adapt the model to the label distribution of the target load condition. In the second stage of transfer fine-tuning, the shared feature extraction network is unfrozen, and semi-supervised fine-tuning is performed using the labeled samples and unlabeled samples. The training objective function is composed of a weighted combination of the supervised loss of the labeled samples and the consistency regularization loss of the unlabeled samples to obtain the target domain prediction model.

[0184] The variable-load industrial robot error prediction device based on active learning and semi-supervised transfer learning according to the embodiments of this application can correspond to the execution of the method described in the embodiments of this application, and the other operations and / or functions of each module / unit of the variable-load industrial robot error prediction device based on active learning and semi-supervised transfer learning are respectively for implementing Figure 2 For the sake of brevity, the corresponding processes of each method in the illustrated embodiments will not be described in detail here.

[0185] This application also provides a computing device. For example... Figure 4As shown in the figure, this is a schematic diagram of a computing device provided in an embodiment of this application. The computing device 400 includes a bus 401, a processor 402, a communication interface 403, and a memory 404. The processor 402, the memory 404, and the communication interface 403 communicate with each other via the bus 401.

[0186] Bus 401 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 4 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0187] Processor 402 can be any one or more of the following processors: central processing unit (CPU), graphics processing unit (GPU), microprocessor (MP), or digital signal processor (DSP).

[0188] The communication interface 403 is used for communication with external devices. For example, if the computing device is a first switch, the communication interface 403 can be used for communication between the first switch and a first user terminal, or for communication between the first switch and a second switch.

[0189] Memory 404 may include volatile memory, such as random access memory (RAM). Memory 404 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0190] The memory 404 stores executable code, and the processor 402 executes the executable code to perform the aforementioned error prediction method for variable load industrial robots based on active learning and semi-supervised transfer learning.

[0191] Specifically, in achieving Figure 3 In the case of the illustrated embodiment, and Figure 3When the modules or units of the variable-load industrial robot error prediction device based on active learning and semi-supervised transfer learning described in the embodiments are implemented in software, the execution... Figure 3 The software or program code required for the functions of each module / unit can be partially or entirely stored in memory 404. Processor 402 executes the program code corresponding to each unit stored in memory 404, and executes the aforementioned error prediction method for variable load industrial robots based on active learning and semi-supervised transfer learning.

[0192] This application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that a computing device can store, or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive). The computer-readable storage medium includes instructions that instruct the computing device to execute the above-described error prediction method for variable-load industrial robots based on active learning and semi-supervised transfer learning.

[0193] This application also provides a computer program product comprising one or more computer instructions. When the computer instructions are loaded and executed on a computing device, all or part of the processes or functions described in this application are generated.

[0194] The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, or data center to another website, computer, or data center via wired (e.g., coaxial cable, fiber optic) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0195] When the computer program product is executed by a computer, the computer executes any of the aforementioned methods of the variable-load industrial robot error prediction method based on active learning and semi-supervised transfer learning. The computer program product can be a software installation package; when any of the aforementioned methods of the variable-load industrial robot error prediction method based on active learning and semi-supervised transfer learning needs to be used, the computer program product can be downloaded and executed on the computer.

[0196] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0197] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions within the technical scope disclosed in this application should be covered within the scope of protection of this application.

Claims

1. A method for error prediction of variable-load industrial robots based on active learning and semi-supervised transfer learning, characterized in that, The method includes: Using the joint angles of an industrial robot as input and the point prediction results and prediction intervals of the end-effector position error as output, a shared feature extraction network is built, constructing point prediction branches and interval prediction branches to form member models. Multiple member models are independently trained on the source load condition dataset under the source load condition, and the trained member models are integrated to obtain the source domain pre-trained model. Using the parameters of the source domain pre-trained model as initial parameters, a two-stage semi-supervised transfer fine-tuning is performed based on labeled samples and unlabeled samples obtained through active learning to obtain the target domain prediction model. Acquire real-time joint angle data of the target industrial robot under target load conditions; Based on the target domain prediction model, the real-time joint angle data is calculated to obtain the point prediction result and interval half-width of the end position error; Based on the point prediction results and interval half-width of the end position error, the error prediction results of the target industrial robot under the target load condition are determined.

2. The method according to claim 1, characterized in that, The target domain prediction model calculates the real-time joint angle data to obtain the point prediction result and interval half-width of the end-effector position error, including: Based on each member model, the real-time joint angle data is calculated to obtain the mean prediction error and prediction interval corresponding to that member model; The mean of the prediction error for each member model is calculated to obtain the point prediction result; Based on the prediction intervals and point prediction results corresponding to each member model, the interval half-width is obtained.

3. The method according to claim 2, characterized in that, The interval half-width is obtained based on the prediction interval and point prediction results corresponding to each member model, including: For each member model, based on the point prediction results and the upper and lower bounds of the prediction interval corresponding to that member model, the half-width of the interval corresponding to that member model is obtained; against y In terms of direction, the largest interval half-width in each member model is determined as the fused y-direction interval half-width; against x direction and z In terms of direction, the average half-width of the corresponding interval in each member model is calculated, and the average value is determined as the fused horizontal half-width and vertical half-width, respectively.

4. The method according to claim 1, characterized in that, The determination of the error prediction result of the target industrial robot under the target load condition based on the point prediction result and the interval half-width based on the end position error includes: Using the point prediction result as the center, the interval half-width is superimposed to determine the final error prediction interval; wherein, the lower bound of the error prediction interval is the point prediction result minus the interval half-width, and the upper bound of the error prediction interval is the point prediction result plus the interval half-width. Based on the point prediction results and the error prediction interval, the error prediction results of the target industrial robot under the target load condition are determined; wherein, the error prediction interval has a predetermined confidence level.

5. The method according to claim 1, characterized in that, The independent training of multiple member models on the source load condition dataset under the source load condition includes: Each member model is trained independently based on a subset randomly selected from the source load condition dataset. For each member model, the point prediction branch is optimized using the heteroscedasticity negative log-likelihood loss function to obtain the mean and variance of the prediction error, and the interval prediction branch is optimized using the quantile regression loss function to obtain the upper and lower bounds of the prediction interval.

6. The method according to claim 1, characterized in that, The process of using source domain pre-trained model parameters as initialization parameters and performing two-stage semi-supervised transfer fine-tuning based on labeled and unlabeled samples obtained through active learning includes: Collect unlabeled samples under the target load conditions to form an unlabeled dataset; Based on the source domain pre-trained model, each unlabeled sample in the unlabeled dataset is predicted, the interval half-width of the unlabeled sample is calculated as an uncertainty measure, and the spatial diversity measure of the unlabeled sample is calculated using the minimax strategy. The uncertainty measure and the spatial diversity measure are weighted and fused together to filter candidate samples. The sample that is farthest from the labeled sample set is selected for labeling to obtain the labeled sample. In the first stage of transfer fine-tuning, the shared feature extraction network of the source domain pre-trained model is frozen, and the point prediction branch and the interval prediction branch are supervised learning using only the labeled samples, so that the model can be adapted to the label distribution of the target load condition. In the second stage of transfer fine-tuning, the shared feature extraction network is unfrozen, and semi-supervised fine-tuning is performed using the labeled samples and unlabeled samples. The training objective function is composed of a weighted combination of the supervised loss of the labeled samples and the consistency regularization loss of the unlabeled samples, thus obtaining the target domain prediction model.

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