Six-dimensional force / torque sensor calibration data enhancement method and system

Abstract

The application discloses a kind of six-dimensional force / torque sensor calibration data enhancement methods, first using weight hammer type loading method is carried out calibration experiment to six-dimensional force / torque sensor, the output data of sensor is acquired in real time, the data vector of the output data of each loading point sensor and actual loading force value constitutes training data and test data;Again, according to the local linear error of each loading point, adaptive interpolation is carried out, and data is expanded;Finally, training data and the expanded data obtained by interpolation are merged, input into six-dimensional force / torque decoupling model for weighted training, the model parameters are fixed, and the final decoupling model is obtained, the test data is used to test the decoupling effect of the model, so as to realize data enhancement.The method of the present application enhances the spatial density and feature expression ability of the training data set without increasing the complexity of the experiment, improves the generalization ability of the nonlinear decoupling model under unknown loading conditions, and improves the measurement accuracy and stability of the six-dimensional force / torque sensor.

Description

Technical Field

[0001] This invention belongs to the technical field of six-dimensional force / torque sensor data calibration, and mainly relates to a method and system for enhancing six-dimensional force / torque sensor calibration data. Background Technology

[0002] Six-dimensional force / torque sensors, as high-precision force measurement devices, can simultaneously sense force components in three directions and torque components in three directions in space. They are widely used in various fields such as robot end-effector force control, intelligent manufacturing, aerospace assembly, biomedical equipment, and virtual reality interaction. With the development of related technologies, the requirements for the accuracy, robustness, and decoupling capability of six-dimensional force / torque sensors are constantly increasing. Currently, one of the key issues restricting the improvement of the accuracy of six-dimensional force / torque sensors is inter-dimensional coupling error, which is the phenomenon that when the sensor is loaded in one direction, non-zero output signals appear in other directions. To solve the coupling error problem, researchers generally use decoupling algorithms to reconstruct the sensor signals.

[0003] Existing decoupling methods mainly fall into two categories: hardware decoupling implemented through structural design and software decoupling driven by experimental data. Among these, software decoupling methods are widely used due to their flexibility, low cost, and ease of deployment. Representative decoupling algorithms include least squares, support vector regression, backpropagation neural networks, and extreme learning machines. These algorithms rely on high-quality calibration datasets to establish the mapping relationship from sensor voltage output to actual force / torque input.

[0004] The current mainstream calibration method uses a weight-based loading method, where standard weights are applied to the sensor in different directions via pulley and rope systems to achieve gradual loading, and then the sensor output is collected. Although this method has high accuracy, it is limited by the discreteness of the weight and the complexity of manual loading, resulting in sparse calibration data. This makes it difficult to meet the data density and diversity requirements of nonlinear decoupling algorithms, and it is prone to overfitting. Summary of the Invention

[0005] This invention addresses the problems of limited and sparsely distributed calibration data acquired during traditional six-dimensional force / torque sensor calibration processes, which can easily lead to overfitting in decoupling models. It provides a data augmentation method for six-dimensional force / torque sensor calibration. First, a weight-based loading method is used to calibrate the six-dimensional force / torque sensor, acquiring the sensor's output data in real time. The data vector composed of the sensor's output data and the actual loaded force value at each loading point constitutes the training and test data. Next, adaptive interpolation is performed based on the local linearity error at each loading point to expand the data. Finally, the training data and the interpolated expanded data are merged and input into the six-dimensional force / torque decoupling model for weighted training. The model parameters are fixed to obtain the optimal decoupling model. Validation data is used to verify the model's decoupling effect, thus achieving data augmentation. This invention enhances the spatial density and feature representation capability of the training dataset without increasing experimental complexity, improves the generalization ability of the nonlinear decoupling model under unknown loading conditions, and enhances the measurement accuracy and stability of the six-dimensional force / torque sensor.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is: a method for augmenting calibration data of a six-dimensional force / torque sensor, comprising the following steps:

[0007] S1. Data Acquisition: A calibration experiment was conducted on the six-dimensional force / torque sensor using a weight-based loading method, and the sensor's output data was acquired in real time. The calibration experiment was divided into a high-density calibration experimental group and a low-density calibration experimental group according to the step size. In the high-density calibration experimental group, the data vector composed of the sensor's output data and the actual loaded force value at each loading point constituted the training data. In the low-density calibration experimental group, the data vector composed of the sensor's output data and the actual loaded force value at each loading point constituted the test data.

[0008] S2. Error-based adaptive interpolation: The training data obtained in step S1 is subjected to error-based adaptive interpolation. Linear fitting is performed on the training data obtained in step S1 to obtain the linear prediction output of each loading point in the training data. Linear error analysis is performed on the training data based on the linear prediction output to obtain the error bin number of each loading point. Finally, cubic spline interpolation is performed based on the error bin number to obtain the augmented data.

[0009] S3. Training and Evaluation: The training data obtained in step S1 and the augmented data obtained after interpolation in step S2 are merged and input into the six-dimensional force / torque decoupling model for weighted training. The model parameters are fixed to obtain the optimal decoupling model. The test data is input into the optimal decoupling model, and the difference between the model output and the actual applied force value is compared to obtain the measurement accuracy of the sensor, thereby confirming the achievement of data augmentation.

[0010] As an improvement of the present invention, the calibration step size of the high-density calibration experimental group is no more than one-tenth of the range, the calibration step size of the low-density calibration experimental group is no less than one-eighth of the range, and the calibration step size of the low-density calibration experimental group is greater than that of the high-density calibration experimental group; both experimental groups use the full-process calibration method for loading and unloading the weights; the output data of the sensor is a six-dimensional voltage analog quantity, and the actual loading force value is the actual six-dimensional loading force / torque value during the calibration process in each direction.

[0011] As an improvement of the present invention, the weight loading process of the calibration test is specifically as follows: at the positive loading end of the calibration platform, the weight is gradually increased from zero to the upper limit of the sensor range, and then gradually decreased to zero; at the negative loading end of the calibration platform, the weight is gradually increased to the lower limit of the sensor range, and then gradually decreased to zero.

[0012] As another improvement of the present invention, the linear error analysis in step S2 specifically includes the following steps:

[0013] S21: Calculate the linear fitting error at each loading point, where the error at the i-th loading point is e. i :

[0014]

[0015] Among them, y i Let be the output vector at the i-th loading point, representing the actual loading force value. The linear prediction output for the i-th loading point;

[0016] S22: Set of linear errors at the loading point Sort the data in ascending order to obtain the sorted linear error sequence. Where N is the total number of loading points in the training data;

[0017] S23: Define the percentile function P -1 (q):

[0018] P -1 (q) = E[qN]

[0019] Where q is the percentile probability between 0 and 1, [·] represents the floor operation, and E[qN] represents the [qN]th number in the linear error sequence E;

[0020] S24: Perform percentile segmentation on the linear error sequence E obtained in step S22 to obtain n error bins. The number of bins n can be adjusted according to the actual situation. Then, the error interval range corresponding to the j-th bin is:

[0021]

[0022] Among them B j-1 B j These represent the lower and upper bounds of the error for the j-th box, respectively.

[0023] S25: Each loading point is assigned to the corresponding box according to the magnitude of its own linear error, and the corresponding error box number is obtained.

[0024] As another improvement of the present invention, the cubic spline interpolation in step S2 specifically includes the following steps:

[0025] S26: Design an adaptive interpolation density based on the error bin number of each calibration data point, and define the interpolation density factor M. i Specifically:

[0026]

[0027] Where α is the interpolation factor, b j To record the box number of data point i;

[0028] S27: Determine the interpolation range at each loading point as half the distance between the current point and its neighboring points, and reduce the interpolation range by half at the endpoints. For the i-th loading point, define the interpolation range using the input vector of the loading point:

[0029]

[0030] Where x i This represents the input vector of the i-th loading point in the training data, i.e., the sensor output data;

[0031] S28: Construct a cubic spline function S(x) from the input vector to the output vector on the training data. The function is a cubic polynomial in each interpolation interval, and satisfies the following conditions: the function value is continuous at the interpolation nodes, the function value is consistent with the actual output, and the first and second derivatives are continuous at each node, satisfying natural boundary conditions at the boundaries; specifically:

[0032] S(x i )=y i ,S(x i+1 )=y i+1

[0033]

[0034] S″(x1)=S″(x N ) = 0

[0035] in and Let these represent the first left and first right derivatives of the cubic spline function at the i-th loading point. and Let S″(x1) and S″(x2) represent the second left and second right derivatives of the cubic spline function at the i-th loading point. N () represents the second derivative values ​​of the cubic spline function at the first and last loading points;

[0036] S29: At each loading point, based on the interpolation range and interpolation factor M i Insert new points uniformly. For the i-th loading point, interpolate M... i -1 new points, where the input vector x of the k-th new point is... interp (k) and output vector y interp (k) is:

[0037]

[0038] y interp (k)=S(x interp (k))

[0039] Where S(x) interp (k) represents the cubic spline function obtained in step S28 in x. interp The value at (k) is used to obtain all the new points that form the expanded data.

[0040] As another improvement of the present invention, the dataset D used for weighted training of the six-dimensional force / torque decoupling model in step S3 is specifically as follows:

[0041]

[0042] Where N total x represents the total number of data points. i y i and w i Let w be the input vector, output vector, and weights of the i-th data point. real For training data weights, w aug ∈(0,1) represents the weights of the augmented data.

[0043] As another improvement of the present invention, the six-dimensional force / torque decoupling model in step S3, when inputting a decoupling model based on the support vector machine method, is subjected to weighted training by adjusting the optimization objective function:

[0044]

[0045] Where w and b are model parameters, ξ,ξ * Let C be a slack variable and C be a penalty coefficient.

[0046] When inputting a decoupled model based on the backpropagation neural network method, weighted training is achieved by modifying the loss function. The loss function Loss is defined using the weighted mean squared error:

[0047]

[0048] in This is the predicted output vector of the current model;

[0049] When the input is a decoupled model based on the extreme learning machine method, a weighting operation is introduced in the output layer weight parameter solution step to construct the weight matrix W. d Randomly initialize the input weight matrix W in Given a bias b, calculate the hidden layer output matrix H, and finally use weighted least squares to calculate the output layer weights W. out :

[0050] W d =diag(w1,w2,…,w N )

[0051] H=φ(XW in +b)

[0052] W out =(H T W d H) -1 H T W d Y

[0053] Where φ(·) represents the hidden layer activation function, diag(w1,w2,…,w N ) represents a diagonal matrix consisting of the weights of the 1st to Nth data points, X is the input matrix of the training dataset, and Y is the reference output matrix of the training dataset.

[0054] To achieve the above objectives, the present invention also adopts the following technical solution: a six-dimensional force / torque sensor calibration data enhancement system, comprising a computer program, wherein the computer program, when executed by a processor, implements the steps of any of the methods described above.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] (1) The method of the present invention performs adaptive interpolation based on the linear error of the original data, which can dynamically adjust the interpolation density according to the local nonlinear characteristics, thereby optimizing the spatial distribution of the data and significantly improving the richness and effectiveness of the training dataset.

[0057] (2) The number of bins in the error analysis process and the interpolation multiple in the adaptive interpolation process of the present invention can be adjusted according to the specific error degree of the data, which has high flexibility and can adapt to different task requirements.

[0058] (3) The method of the present invention adopts a weighted training mechanism to ensure that the training process is dominated by real data, while making full use of interpolated data to enrich the model training, effectively ensuring the stability of practical applications.

[0059] (4) The method of the present invention is applicable to the mainstream six-dimensional force / torque sensor software decoupling algorithm, which can improve the overfitting problem of nonlinear decoupling model and enhance the robustness of the model to unknown data.

[0060] (5) The method of the present invention can significantly expand the training dataset through data augmentation without adding extra complexity and cost to the calibration experiment. It is easy to implement and has good practical promotion value and broad application prospects. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the sensor calibration process in step S1 of the method of the present invention;

[0062] Figure 2 This is a schematic diagram of the full-process calibration method used in step S1 of the method of the present invention;

[0063] Figure 3 This is a schematic diagram of the error-based adaptive interpolation algorithm in step S2 of the method of the present invention;

[0064] Figure 4 This is a schematic diagram of the training and evaluation process in step S3 of the method of the present invention. Detailed Implementation

[0065] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0066] Example 1

[0067] A method for augmenting calibration data of a six-dimensional force / torque sensor, specifically including the following steps:

[0068] Step S1, Data Acquisition: The six-dimensional force / torque sensor is calibrated using a weight-based loading method, and the sensor's output data is acquired in real time.

[0069] like Figure 1The diagram shows the sensor calibration process. A weight-based loading method was used to calibrate a six-dimensional force / torque sensor. The calibration was performed independently along the X, Y, and Z axes in a Cartesian coordinate system, with the sensor's output data recorded in real time. The process includes the following steps:

[0070] S11: A calibration platform is built using the weight-and-hammer loading method, and a six-dimensional force / torque sensor is installed.

[0071] S12: Conduct calibration experiments, including a high-density calibration experimental group and a low-density calibration experimental group. Specifically, the high-density calibration experimental group uses the full-process calibration method to load and unload weights with a small calibration step size, and repeats the process multiple times. Specifically, the low-density calibration experimental group uses the full-process calibration method to load and unload weights with a larger calibration step size, which is at least greater than the calibration step size of the high-density calibration experimental group, and repeats the process multiple times. The calibration step size is the mass of the weight loaded / unloaded in a single operation in the full-process calibration method.

[0072] S13: The experimental data collected in step S12 are classified and organized. The experimental data from the high-density calibration experimental group constitutes the training data, which is used to feed into the error-based adaptive interpolation stage for further processing. The experimental data from the low-density calibration experimental group constitutes the test data, which is used to test the error in the training and evaluation stages.

[0073] The whole-process calibration method is as follows: Figure 2 As shown, the specific process is as follows: First, at the positive loading end of the calibration platform, the load weight is gradually increased from zero to the upper limit of the sensor's range, and then gradually decreased to zero. Then, at the negative loading end of the calibration platform, the load weight is gradually increased to the lower limit of the sensor's range, and then gradually decreased to zero. During this process, the sensor output data is collected in real time.

[0074] The training and validation data mentioned above are both composed of multiple loading points. Each loading point is a data vector consisting of the sensor's data output and the actual loading force value. The sensor's data output is a six-dimensional analog voltage quantity; the actual loading force value is the six-dimensional force / torque value actually applied during the calibration process in each direction.

[0075] Step S2, Error-based adaptive interpolation: Perform error-based adaptive interpolation on the training data obtained in step S1.

[0076] Figure 3 This is a schematic diagram of an error-based adaptive interpolation algorithm, which includes three parts: linear fitting, linear error analysis, and cubic spline interpolation.

[0077] First, a linear fit is performed. The sensor data outputs from each loading point in the training data are used as the input sample matrix X, and the actual loading force values ​​are used as the output sample matrix Y. N is the number of loading points, x i y i Let W be the input vector and output vector at the i-th loading point, respectively. Solve for the coefficient matrix W using the linear least squares method:

[0078] W = (X T X) -1 X T Y

[0079]

[0080] Next, linear error analysis is performed, including the following steps:

[0081] S1: Calculate the linear fitting error at each loading point, where the error at the i-th loading point is e. i :

[0082]

[0083] S2: Set of linear errors at the loading point Sort the data in ascending order to obtain the sorted linear error sequence.

[0084] S3: Define the percentile function P -1 (q), where q is the percentile probability between 0 and 1, and [·] represents the floor operation.

[0085] P -1 (q) = E[qN]

[0086] S4: Divide the linear error sequence E into percentiles to obtain n error bins. Then, the error interval range corresponding to the j-th bin is:

[0087]

[0088] Among them B j-1 B j These represent the lower and upper bounds of the error for the j-th box, respectively.

[0089] S5: Each loading point is assigned to the corresponding box according to the magnitude of its own linear error, and the corresponding error box number is obtained.

[0090] Finally, cubic spline interpolation is performed, including the following steps:

[0091] S1: Design an adaptive interpolation density based on the error bin number of each calibration data point, with an interpolation factor of α, and denote the bin number of data point i as b. j Define the interpolation density factor Mi :

[0092]

[0093] S2: Determine the interpolation range at each loading point as half the distance between the current point and its neighboring points, and reduce the interpolation range by half at the endpoints. For the i-th loading point, define the interpolation range using the input vector of the loading point:

[0094]

[0095] S3: Construct a cubic spline function S(x) from the input vector to the output vector on the training data. This function is a cubic polynomial within each interpolation interval, satisfying the following conditions: continuous function values ​​at interpolation nodes, consistent with the actual output, continuous first and second derivatives at each node, and natural boundary conditions at the boundaries. Specifically:

[0096] S(x i )=y i ,S(x i+1 )=y i+1

[0097]

[0098] S″(x1)=S″(x N ) = 0

[0099] in and Let these represent the first left and first right derivatives of the cubic spline function at the i-th loading point. and Let S' represent the second left derivative and the second right derivative of the cubic spline function at the i-th loading point, and let S''(x1) and S''(xN) represent the values ​​of the second derivative of the cubic spline function at the first loading point and the last loading point, respectively.

[0100] S4: At each loading point, based on the interpolation range and interpolation factor M i Insert new points uniformly. For the i-th loading point, interpolate M... i -1 new points, where the input vector x of the k-th new point is... interp (k) and output vector y interp (k) is:

[0101]

[0102] y interp (k)=S(x interp (k))

[0103] Where S(x) interp(k) represents the cubic spline function obtained in step S28 in x. interp The value at (k) is used to obtain all the new points that form the expanded data.

[0104] Step S3, Training and Evaluation: (e.g.) Figure 4 As a schematic diagram of the training and evaluation process, the training data and the interpolated augmented data are first merged and fed into a specific six-dimensional force / torque decoupling model for weighted training. The model parameters are fixed, and then the test data is used to verify the decoupling effect of the model.

[0105] In weighted training of the model, different training weights are assigned to the training data and the augmented data, where the training data weight w real =1, the weight of the augmented data is w aug ∈(0,1) and can be adjusted as needed to construct the complete training dataset D:

[0106]

[0107] Where N total x represents the total number of data points. i y i and w i These are the input vector, output vector, and weights for the i-th data point, respectively.

[0108] For different types of nonlinear decoupling algorithms, corresponding weighted training methods are constructed:

[0109] For decoupled models based on the support vector machine method, weighted training is performed by adjusting the optimization objective function:

[0110]

[0111] Where w and b are model parameters, ξ,ξ * Let C be a slack variable and C be a penalty coefficient.

[0112] For decoupled models based on backpropagation neural networks, weighted training is achieved by modifying the loss function. The loss function Loss is defined using weighted mean square error:

[0113]

[0114] in This is the predicted output vector of the current model.

[0115] For decoupled models based on the extreme learning machine method, a weighting operation is introduced in the output layer weight parameter solution step. First, the weight matrix W is constructed. d Then, the input weight matrix W is randomly initialized. inGiven a bias b, calculate the hidden layer output matrix H, and finally use weighted least squares to calculate the output layer weights W. out :

[0116] W d =diag(w1,w2,…,w N )

[0117] H=φ(XW in +b)

[0118] W out =(H T W d H) -1 H T W d Y

[0119] Where φ(·) represents the hidden layer activation function, diag(w1,w2,…,w N ) represents a diagonal matrix consisting of the weights of the 1st to Nth data points, X is the input matrix of the training dataset, and Y is the reference output matrix of the training dataset.

[0120] The model parameters are solved using gradient descent or the Moore-Penrose generalized inverse to obtain the final decoupled model.

[0121] Finally, the decoupled model is run on the test data, and the difference between the model output and the actual applied force value is compared under indicators such as root mean square error and interdimensional coupling error to obtain the measurement accuracy of the sensor and complete the data augmentation.

[0122] Test case

[0123] This test case selected three mainstream six-dimensional force decoupling algorithms for comparative experiments: support vector regression, backpropagation neural network, and extreme learning machine. The calibration experiments included two high-density calibration groups and eight low-density calibration groups. The step size of the weight loading / unloading process in the high-density calibration groups was half that of the low-density calibration groups, resulting in two sets of test data and eight sets of training data. Data augmentation was performed on the training data to obtain expanded data. The expanded data and training data were used for model training, while the test data were used to compare the decoupling performance of the models. Test metrics included root mean square error in each direction and inter-dimensional coupling error.

[0124] (1) Root mean square error (MSE) is defined as:

[0125]

[0126] Among them, y ij and and represent the true value and the predicted output of the decoupling algorithm at the i-th test point in the j-th direction, respectively.

[0127] The experimental results are shown in Table 1. "Before Augmentation" indicates model training using the original eight sets of training data, and "After Augmentation" indicates weighted training using the original eight sets of training data and the augmented data.

[0128] Table 1

[0129]

[0130] As shown in Table 1, after data augmentation, the root mean square error of each decoupling model was significantly reduced. Among them, the backpropagation neural network method improved by 62.6%-82.9% in the three-dimensional force direction and by 10.7%-38.5% in the torque direction; the support vector regression method improved by more than 86% in the Mx and My directions, significantly alleviating the overfitting problem, and also reduced by 20%-47% in the force and Mz directions; the extreme learning machine method achieved an error reduction of more than 64.0% in all directions, with an average improvement of about 80.8%.

[0131] (2) Interdimensional coupling error: This reflects the decoupling accuracy of the algorithm in each measurement direction, and is defined as:

[0132]

[0133] The test results are shown in Table 2:

[0134] Table 2

[0135]

[0136]

[0137] As shown in Table 2, after data augmentation, the interdimensional coupling errors of each decoupled model were significantly reduced, with the backpropagation neural network method showing the greatest improvement of 84%. The support vector regression method also significantly reduced severe overfitting in the torque Mx and My directions after data augmentation, with a maximum improvement exceeding 86%. The extreme learning machine method also showed significant improvement, with overall accuracy across all directions increasing by more than 64.1%, and a maximum improvement exceeding 80%.

[0138] In summary, the method of this invention improves the generalization ability of the nonlinear decoupling model under unknown loading conditions and enhances the measurement accuracy and stability of the six-dimensional force / torque sensor.

[0139] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for augmenting calibration data of a six-dimensional force / torque sensor, characterized in that, Includes the following steps: S1. Data Acquisition: A calibration experiment was conducted on the six-dimensional force / torque sensor using a weight-based loading method, and the sensor's output data was acquired in real time. The calibration experiment was divided into a high-density calibration experimental group and a low-density calibration experimental group according to the step size. In the high-density calibration experimental group, the data vector composed of the sensor's output data and the actual loaded force value at each loading point constituted the training data. In the low-density calibration experimental group, the data vector composed of the sensor's output data and the actual loaded force value at each loading point constituted the test data. S2. Error-based adaptive interpolation: Linear fitting is performed on the training data obtained in step S1 to obtain the linear prediction output of each loading point in the training data. Linear error analysis is performed on the training data based on the linear prediction output to obtain the error bin number of each loading point. Finally, cubic spline interpolation is performed based on the error bin number to obtain the augmented data. S3. Training and Evaluation: The training data obtained in step S1 and the augmented data obtained after interpolation in step S2 are merged and input into the six-dimensional force / torque decoupling model for weighted training. The model parameters are fixed to obtain the optimal decoupling model. The test data is input into the optimal decoupling model, and the difference between the model output and the actual applied force value is compared to obtain the measurement accuracy of the sensor, thereby confirming the achievement of data augmentation.

2. The method for augmenting calibration data of a six-dimensional force / torque sensor as described in claim 1, characterized in that: The calibration step size of the high-density calibration experimental group is no more than one-tenth of the range, and the calibration step size of the low-density calibration experimental group is no less than one-eighth of the range, with the calibration step size of the low-density calibration experimental group being greater than that of the high-density calibration experimental group; both experimental groups use the full-process calibration method for loading and unloading the weights; the output data of the sensor is a six-dimensional voltage analog quantity, and the actual loading force value is the actual six-dimensional loading force / torque value during the calibration process in each direction.

3. The method for augmenting calibration data of a six-dimensional force / torque sensor as described in claim 2, characterized in that: The specific loading process of the calibration test is as follows: at the positive loading end of the calibration platform, the weight is gradually increased from zero to the upper limit of the sensor range, and then gradually decreased to zero; at the negative loading end of the calibration platform, the weight is gradually increased to the lower limit of the sensor range, and then gradually decreased to zero.

4. The method for augmenting calibration data of a six-dimensional force / torque sensor as described in claim 1, characterized in that: The linear error analysis in step S2 specifically includes the following steps: S21: Calculate the linear fitting error at each loading point, the first... Linearity error at each loading point for: ； in, For the first The output vector at each loading point is the actual loaded force value. For the first Linear prediction output for each loading point; S22: Set of linear errors at the loading point Sort in ascending order to obtain the sorted linear error sequence. ;in This represents the total number of loading points in the training data. S23: Define the percentile function : ； Where q is the percentile probability between 0 and 1, and [·] represents the floor function. Represents a linear error sequence The first in Number; S24: The linear error sequence obtained in step S22 Perform percentile segmentation to obtain n error bins, the number of bins is... The error range corresponding to the j-th box can be adjusted according to the actual situation. ； in These represent the lower and upper bounds of the error for the j-th box, respectively. S25: Each loading point is assigned to the corresponding box according to the magnitude of its own linear error, and the corresponding error box number is obtained.

5. The method for augmenting calibration data of a six-dimensional force / torque sensor as described in claim 4, characterized in that: The cubic spline interpolation in step S2 specifically includes the following steps: S26: Design an adaptive interpolation density based on the error bin number of each calibration data point, and define the interpolation density factor. Specifically: ； in, The interpolation factor. To record data points The box number; S27: Determine the interpolation range at each loading point as half the distance between the current point and its neighboring points, and reduce the interpolation range by half at the endpoints. There are 1 loading point, and the interpolation range is defined using the input vector of each loading point: ； ； ； in Indicates the first in the training data The input vector of each loading point, i.e., the sensor output data; S28: Construct a cubic spline function from the input vector to the output vector on the training data. The function is a cubic polynomial within each interpolation interval, satisfying the following conditions: the function value is continuous at the interpolation nodes and the function value is consistent with the actual output. Furthermore, the first and second derivatives are continuous at each node, and the boundary conditions are satisfied. Specifically: ； ； ； in and This indicates that the cubic spline function is at the th... The first left derivative and the first right derivative at each loading point and This indicates that the cubic spline function is at the th... Second left derivative and second right derivative at each loading point and This represents the second derivative values ​​of the cubic spline function at the first and last loading points; S29: At each loading point, based on the interpolation range and interpolation factor... Insert new points evenly, for the first... Each loading point will be used for interpolation. The first new point, of which the The input vector of the new point and output vector for: ； ； in The cubic spline function obtained in step S28 is in The value at the given point is used to obtain all the new points that form the expanded data.

6. The method for augmenting calibration data of a six-dimensional force / torque sensor as described in claim 1, characterized in that: The dataset used in step S3 for weighted training of the six-dimensional force / torque decoupling model Specifically: ； in The total number of data points. , and The first The input vector, output vector, and weights for each data point. For training data weights, To increase the weight of the data.

7. The method for augmenting calibration data of a six-dimensional force / torque sensor as described in claim 6, characterized in that: The six-dimensional force / torque decoupling model in step S3, when inputting a decoupling model based on the support vector machine method, undergoes weighted training by adjusting the optimization objective function: ； in and For model parameters, As slack variables, This is the penalty coefficient; When inputting a decoupled model based on the backpropagation neural network method, weighted training is achieved by modifying the loss function, which is defined using weighted mean square error. : ； in This is the predicted output vector of the current model; When the input is a decoupled model based on the extreme learning machine method, a weighting operation is introduced in the output layer weight parameter solution step to construct a weight matrix. Randomly initialize the input weight matrix and bias Calculate the hidden layer output matrix Finally, the weighted least squares method is used to calculate the output layer weights. : ； ； ； in Represents the hidden layer activation function. Indicates from the 1st to the 1st A diagonal matrix formed by the weights of the data points. The input matrix for the training dataset, This is the reference output matrix for the training dataset.

8. A six-dimensional force / torque sensor calibration data augmentation system, comprising a computer program, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-7 above.

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