Multi-dimensional force decoupling method for nonlinear coupling error modeling

Abstract

The invention discloses a multi-dimensional force decoupling method for nonlinear coupling error modeling, and belongs to the field of intelligent sensor signal processing. Aiming at the problems of large inter-dimensional coupling nonlinear error, asymmetry in positive and negative directions, poor repeatability and the like of a multi-dimensional force sensor, a three-step method of'precision screening-segmented variable-order fitting-positive and negative matrix 'is provided. The method comprises the following steps of: firstly, preferably selecting a calibration matrix by taking the minimum linearity, hysteresis and repeatability error mode length as a criterion; a coupling curve is fitted through 1-k-order polynomials in a segmented mode, the maximum decision coefficient is adjusted to determine the optimal order and coefficient, an endpoint method linear coefficient is adopted for a main channel, and a positive and negative correction matrix is constructed; during decoupling, corresponding row elements are dynamically selected according to output voltage symbols to form a decoupling matrix, and coupling errors are deducted in real time. The method can meet the high-precision force control requirements of robots, aerospace and the like, is small in calculation amount, and is easy to realize in an embedded manner.

Description

Technical Field

[0001] This invention belongs to the field of intelligent sensor signal processing technology, specifically relating to a multidimensional force decoupling method for nonlinear coupling error modeling. Background Technology

[0002] A multi-axis force / torque sensor is a precision measuring device capable of simultaneously measuring forces and torques acting on an object in multiple directions within three-dimensional space. Its core value lies in converting complex spatial mechanical information into processable electrical signals, providing crucial force sensing capabilities for fields such as robotics and precision manufacturing.

[0003] Multidimensional force sensors, represented by six-dimensional force / torque sensors, are now widely used in aerospace, medical electronics, robotics, and robotic arms, playing a crucial role in scientific research, production, and daily life. In the field of humanoid robots, robot joints, as force control nodes for limb movement execution, often require the deployment of more than 32 sensors per robot to achieve accurate movement trajectories and environmental adaptability. In the aerospace field, robotic arms can provide real-time feedback of contact force / torque for applications such as on-orbit servicing and extravehicular operations, ensuring the safety of space operations and the reliability of missions. In the field of precision manufacturing, such as 3C electronic assembly and aero-engine blade grinding, providing micro-Newton level force control accuracy has become a key process for ensuring product quality.

[0004] Despite their promising application prospects, six-dimensional force sensors also face numerous challenges in their development, such as: crosstalk (inter-dimensional coupling effect), which is essentially mechanical crosstalk between different dimensions of the sensor, leading to abnormal outputs in other dimensions when loaded in one direction; the precision of strain beam manufacturing processes, as strain, as the underlying physical change in force sensors, significantly affects the data accuracy due to the deviation between its actual and theoretical values; and strain gauge placement deviation, as the strain gauge is a key component that senses strain and converts it into a detectable electrical signal, and its precise installation position also affects the sensor's output. Common solutions to reduce the errors of six-dimensional force sensors include: 1) optimizing the deformation structure to reduce inter-dimensional coupling effects; 2) optimizing the sensor housing structure to more effectively transfer the load to the strain gauge; and 3) optimizing the decoupling algorithm to correct the sensor output based on calibration data.

[0005] Over the years, the innovative application of various methods has gradually improved the measurement accuracy of six-dimensional force sensors. However, with the promotion and application of six-dimensional force products, new application scenarios have also placed higher demands on their measurement accuracy. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a multidimensional force decoupling method for nonlinear coupling error modeling, comprising the following steps: Step 1: Collect voltage output data of each channel of the multi-dimensional force sensor when linear loading and unloading are performed individually. Repeat this process multiple times to obtain multiple sets of output voltage data, and add load information to form multiple sets of load and output voltage data matrices. Step 2: Calculate the data accuracy of each group of voltage data matrices, and select the matrix with higher overall accuracy as the sensor calibration matrix; Step 3: Use a variable-order polynomial piecewise to fit the coupling error between sensor channels, and introduce an adjustment coefficient of determination to evaluate the fitting effect of each order polynomial. Step 4: Perform the above fitting operation on the positive and negative directions of the sensor calibration matrix to obtain the positive correction coefficient matrix and the negative correction coefficient matrix of the loading value of each channel. Step 5: When decoupling the multi-dimensional force sensor, first obtain the coarse calculation value of each channel of the sensor; determine the sign of each channel value based on the output voltage of the main channel, and then select the correction coefficient from the positive or negative correction coefficient matrix according to its value to form a new decoupling matrix; multiply the multi-channel values ​​with the decoupling matrix to obtain the coupling error value on each channel; the load value of a certain channel of the sensor is the coarse calculation value minus the cumulative coupling error value of other channels in that channel.

[0007] Specifically, step 2 includes: calculating the data precision of each matrix group, including calculating linearity error, hysteresis error and repeatability error, and obtaining a comprehensive precision index by calculating the modulus of the three errors, and selecting the calibration matrix corresponding to the smallest comprehensive precision value as the final calibration matrix used.

[0008] Specifically, the linearity error is calculated as follows: take the output voltage and loading vector of each loading channel, perform linear fitting using the endpoint method, calculate the fitting error at each point, take the ratio of the maximum error value to the net increment of the full-load output of the corresponding channel of the sensor as the linearity error of that channel, and take the maximum value of all channels as the linearity error of the multi-dimensional force sensor.

[0009] Specifically, the hysteresis error is calculated as follows: take the net incremental voltage data during single-channel loading and unloading, subtract the values ​​at the same load point, take the ratio of the maximum value of the four error voltages to the net incremental value of the full-load output as the hysteresis error of a single channel, and take the maximum value of all channels as the maximum hysteresis error of the multi-dimensional force sensor.

[0010] Specifically, the method for calculating the repeatability error is as follows: extract the net increment data of the load segment voltage output of a certain channel from the same position in multiple calibration matrices to form a vector, calculate the difference, and take the ratio of the maximum value in the error vector to the net increment of the full-load output as the repeatability error of a single channel, and take the maximum value of all channels as the repeatability error of the multi-dimensional force sensor.

[0011] Specifically, when using a variable-order polynomial to fit the coupling error piecewise, the order of the polynomial ranges from 1 to k, where the maximum value of k is half the number of sample points, in order to avoid overfitting.

[0012] Specifically, the method for calculating the adjustment determination coefficient is as follows: the influence of the number of samples and the number of parameters is adjusted based on the determination coefficient R², wherein the determination coefficient R² is calculated by the sum of the squares of the actual output voltage value, the fitted predicted value and the mean of the actual output voltage, and the polynomial coefficient corresponding to the larger adjustment determination coefficient is taken as the final coupling polynomial coefficient.

[0013] Specifically, the adjustment determination coefficient

[0014] The calculation method is as follows:

[0015] in,

[0016] As the coefficient of determination, Let k be the number of sample points and k be the order of the polynomial.

[0017] In the above formula

[0018] The coefficient of determination is used to represent the quality of the fit; the closer its value is to 1, the better the fit. The method for calculating the coefficient of determination is as follows:

[0019] In the above formula,

[0020] This is the actual output voltage value;

[0021] These are the voltage prediction values ​​after multiple fittings;

[0022] This represents the average actual output voltage.

[0023] Specifically, in the construction of the positive correction coefficient matrix and the negative correction coefficient matrix, the non-main diagonal elements are the fitting polynomial coefficients of the coupling channel, and the main diagonal elements are the linear fitting coefficients of the output voltage and load of the main loading channel.

[0024] Specifically, during the decoupling process, row elements are selected from the positive or negative correction coefficient matrix according to the positive or negative output voltage to form a new decoupling matrix. The main channel load value and coupling error value are obtained through matrix multiplication, and finally the decoupled load vector is obtained through subtraction correction.

[0025] The method of the present invention has the following beneficial effects: (1) This application uses a comprehensive accuracy selection method to select the most stable data from multiple calibration matrices for calibration, thereby reducing the impact of bad data introduced by random errors; (2) The error of the same channel is fitted from both positive and negative directions, which reduces the impact of the difference between positive and negative directions caused by structural and process issues; (3) For a single error curve, polynomials of different orders were used for fitting. From the fitted curves of multiple orders, the one with the best effect was selected to reduce the error when using the fitted curve to predict the true value. Polynomials of different orders were used for fitting between all channels with coupling errors to further reduce the overall sensor decoupling error. (4) During decoupling, the direction of load force / torque (positive or negative) can be determined based on the actual output voltage of the sensor. The row vector can be directly selected from the corresponding correction coefficient matrix and stored in the corresponding row of the decoupling coefficient matrix. This can be achieved directly using matrix operations. The method is simple and the amount of computation is small. Attached Figure Description Figure 1 A schematic diagram of the input-output relationship of an ideal six-dimensional force sensor; Figure 2 This is a schematic diagram of the input-output relationship of a six-dimensional force sensor with interdimensional coupling. Figure 3 The output voltage of the main channel of the sensor calibration matrix is ​​compared with the voltage curve of the inter-dimensional coupling error. Figure 4 This is a schematic diagram of the multidimensional force decoupling method for modeling nonlinear coupling errors proposed in this invention. Detailed Implementation

[0026] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0027] This invention proposes a multidimensional force decoupling method based on piecewise variable-order polynomial nonlinear coupling error modeling, aiming to optimize the sensor calibration and decoupling processes and improve the measurement accuracy of multidimensional force sensors. The following explanation uses measurement data from a cross-beam type six-dimensional force sensor produced by the Shaanxi Electrical Research Institute. This sensor can measure load forces in the XYZ directions and load torques in the XYZ axes. The maximum range of the sensor's force channel is ±150N, and the maximum range of the torque channel is ±20N·m. The sensor was placed on a calibration platform, and the calibration process was repeated twice, yielding two sets of calibration data.

[0028] Figure 1 , Figure 2 This refers to the input-output relationship of an ideal six-dimensional force sensor and the input-output relationship of a six-dimensional force sensor with interdimensional coupling. Figure 3 The output voltage curve of the main channel of the sensor calibration matrix and the voltage curve of the inter-dimensional coupling error can intuitively show the nonlinear inter-dimensional coupling phenomenon and the linear output characteristics of the main channel.

[0029] The process of this solution is as follows: Figure 4 As shown, the specific steps include the following: Step 1: Collect voltage output data of each channel of the multi-dimensional force sensor during linear loading and unloading, repeat the process multiple times to obtain multiple sets of output voltage data, and add load information to form multiple sets of load and output voltage data matrices; the initial step is to build a high-quality calibration dataset.

[0030] This process involves not only simple data acquisition, but also rigorous loading / unloading process design, refined processing of voltage output data, and standardized construction of the final calibration matrix, laying a solid foundation for subsequent accuracy-based screening and piecewise variable-order polynomial fitting.

[0031] According to the aforementioned technical solution, the detailed operation of collecting voltage output data from each channel of the multi-dimensional force sensor during linear loading and unloading, repeating this process multiple times to obtain multiple sets of output voltage data, and adding load information to form multiple sets of load and output voltage data matrices is as follows: Independent channel linear loading and unloading: This process aims to obtain the sensor's response characteristics under a single main direction load, including the linear output of the main channel and the coupling error output of all unloaded channels.

[0032] 1. Independent loading operation: For multi-dimensional force sensors (e.g., six-dimensional force sensors, including...) Each of the six channels is loaded individually. In a particular channel (e.g., F...), the loading operation is performed separately. X When a load is applied to one channel, all other channels must remain unloaded throughout the entire process.

[0033] 2. Linear Loading Point Selection: Load application is typically carried out in a segmented, gradient-increasing manner to cover the entire measurement range of the sensor. Using F... X Taking a channel as an example, if its full scale is F 满 Multi-point calibration is usually chosen, such as the 5-point method: Five loads were applied sequentially.

[0034] After completing this step, you will get F. X A vector consisting of multiple loaded values:

[0035] F X During loading, the output voltage of its own channel and the coupled output voltage vector Uload generated on other channels are expressed as:

[0036] When the load value Fx takes different values, multiple coupled voltage output vectors can be obtained. These multiple vectors can form the coupled voltage output matrix of the sensor when Fx is applied, as follows:

[0037] because The actual value represents the net increment of the sensor load change, while here... The stored value in the vector represents the actual value of the sensor's output voltage. To facilitate calculations in subsequent calibration, the voltage vector is represented here using the incremental output voltage.

[0038] After the above calculations, the incremental value of the UFx_upload_net actual stored sensor output voltage is, for ease of calculation, rewritten as...

[0039] (The voltage matrices in the calibration matrix mentioned below are all net increments of the output voltage).

[0040] 3. Data Recording: Under each load condition, the loading channel needs to be recorded. The output voltage of the first channel and the output voltages of the other five unloaded channels due to coupling are recorded. These data together constitute the coupled output voltage vector under a certain load. At this time, no load is applied to the other channels. Six voltage data points are output for each load condition, which are summarized in the following table: at this time,

[0041] , It can be organized as follows: The output voltage converted to the voltage change after loading is: After summarizing the data from the Fx forward unloading segment, we have the following loading vector and voltage vector:

[0042] The linearity error of the Fx positive calibration matrix is ​​0.3241%, the hysteresis error is 0.2475%, and the repeatability error is 0.1619%.

[0043] Calculate the error of each channel in the entire calibration matrix, select the maximum error as the final selected error, and calculate the average to obtain the comprehensive error. Compare the comprehensive accuracy of the two sets of calibration data, and select the calibration data with the lower comprehensive accuracy as the fitting segment calibration data. The accuracy calculations for the two sets of calibration data are summarized as follows: Table 2 Summary of errors in the two sets of calibration data

[0044] As shown in the table above, calibration matrix 1 has better overall accuracy than matrix 2, and its overall data is more stable. Therefore, calibration matrix 1 is selected for error analysis and fitting. Plotting the output voltage of each channel in calibration matrix 1 against the applied load yields the following results: Figure 3 The output voltage characteristic curves of the main channel and the coupled channel are shown.

[0045] 4. Gradient unloading operation: After the loading operation is completed, the gradient unloading operation needs to be executed sequentially, and the data of the reverse run should be recorded for subsequent hysteresis error analysis.

[0046] 5. Repeated execution: The entire loading / unloading process of a single channel needs to be repeated multiple times (e.g., two calibration processes) to obtain multiple sets of output voltage data, which facilitates subsequent evaluation of data stability.

[0047] To facilitate subsequent calibration calculations, the acquired absolute output voltage needs to be converted into the voltage change (net increment) after loading. Absolute voltage vector: When a channel is positively loaded, the absolute output voltages under different load values ​​can form an absolute coupling voltage output matrix. Net increment calculation: The actual stored voltage value needs to be expressed as the increment of the sensor output voltage, that is, the voltage reading after deducting the zero load (0N).

[0048] Here This is the voltage output vector under zero load. After this calculation...

[0049] It stores the net increment value of the sensor output voltage.

[0050] The calibration matrix is ​​constructed by organizing the net incremental voltage data and corresponding load information into a standardized calibration matrix. Single-channel calibration matrix: The calibration data for a single channel is derived from its loading segment. and unload segment It is formed by merging the net voltage increment matrix.

[0051] Load matrix: and voltage matrix Correspondingly, the load information also constitutes a load vector F. x标定 This includes load values ​​during the loading and unloading processes. Final calibration matrix: for all channels. After performing the above operations, the complete calibration voltage output matrix of the sensor is obtained.

[0052] and the corresponding load matrix .

[0053]

[0054]

[0055] The purpose of obtaining multiple sets of matrices is to select the matrix with the highest overall accuracy and the most stable data for error fitting in subsequent steps, thereby reducing the impact of bad data introduced by random errors.

[0056] For example, in this instance, by repeating the calibration process twice, two sets of calibration data matrices are obtained, which will then proceed to the next step of precision calculation and filtering.

[0057] Step 2: Calculate the data accuracy of each matrix group and select the matrix with higher overall accuracy as the sensor calibration matrix; The screening process involves calculating the linearity error, hysteresis error, and repeatability error in the calibration matrix, and finally determining the magnitude of these three factors as a comprehensive accuracy index. .

[0058] 1. Overall accuracy indicators Composition and calculation After acquiring multiple sets of load and output voltage data matrices, it is necessary to calculate the comprehensive accuracy index of each matrix. The comprehensive accuracy index consists of the following three core error parameters: linearity error, hysteresis error, and repeatability error.

[0059] Overall accuracy The calculation method involves taking the modulus (Euclidean norm) of the three error data points, as shown in the following formula: Since this indicator measures the magnitude of error, the smaller the overall accuracy value, the higher the overall accuracy of the calibration data and the better the data stability.

[0060] 2. Detailed calculation method for core error parameters 2.1 Calculation of linearity error Linearity error refers to the maximum deviation between the actual output voltage curve of the sensor loading section and the ideal straight line fitted by the endpoint method.

[0061] Fitting and Deviation Calculation: Select the net output voltage increment and corresponding loading vector for each loading channel (considering only this channel). Use the endpoint method to perform linear fitting on the loading vector and voltage output value, and calculate the fitting error at each loading point. Maximum Error Determination: Take the maximum value among all fitting errors. Percentage: Percentage the ratio of the maximum fitting error value to the net full-load output increment of the corresponding channel of the sensor to obtain the linearity error of that channel. Sensor Bus Linearity Error: Calculate the linearity error of all channels of the multi-dimensional force sensor sequentially, and take the maximum value as the linearity error of the multi-dimensional force sensor. .

[0062] 2.2 Hysteresis Error Calculation Hysteresis error It describes the degree to which the input-output characteristic curves of a sensor do not coincide during the forward stroke (loading from small to large) and reverse stroke (unloading from large to small).

[0063] Data Selection: Taking a single channel of the multi-dimensional force sensor as the object, select the net incremental voltage data of that channel at the same load point in the loading and unloading sections. Error Voltage Calculation: Calculate the difference between the loading voltage and unloading voltage at the same load point to obtain the error voltage. Maximum Hysteresis: Take the maximum value among the error voltages (for example, in the 5-point calibration method, there are 4 error voltages at non-zero points, take the largest one). Percentage: Calculate the ratio of this maximum error voltage to the net incremental output of the sensor under full load to obtain the hysteresis error of this single channel. Total Sensor Hysteresis Error: Calculate the hysteresis error of all channels of the sensor, take the maximum value, and record it as the maximum hysteresis error of the multi-dimensional sensor. .

[0064] 2.3 Repeatability Error Calculation Repeatability error This refers to the degree of inconsistency in the output characteristics when the sensor input quantity is measured multiple times in the same direction across the entire measurement range.

[0065] Data Comparison: Extract the net voltage output increment data of a certain channel's loading segment from the same position in the two calibration matrices, forming two vectors. Error Vector: Obtain the error vector by subtracting these two vectors. Maximum Repeatability Error: Take the maximum value in the error vector and calculate its ratio to the net output increment at full load to obtain the repeatability error of that single channel. Total Sensor Repeatability Error: Calculate the repeatability error of each channel of the multi-dimensional force sensor separately, and select the one with the largest error value as the sensor repeatability error. .

[0066] 3. Selection of calibration matrix Complete the overall accuracy calculation for all calibration arrays (such as "calibration array 1" and "calibration array 2" obtained by repeating the calibration process twice). After calculation, the present invention uses the following criteria for screening: The calibration matrix corresponding to the smallest overall accuracy value is selected as the final calibration matrix used.

[0067] For example, in one embodiment, the overall accuracy of calibration matrix 1 for The overall accuracy of calibration matrix 2 for .because

[0068] Therefore, calibration matrix 1 was chosen for subsequent error analysis and fitting. This selection process ensured that the data used for coupling error modeling had the highest stability and the smallest internal error.

[0069] Step 3: Use a variable-order polynomial to piecewise fit the coupling error between sensor channels, and introduce an adjustment coefficient to evaluate the fitting effect of each order polynomial. Store the polynomial coefficients with good fitting effect in the off-diagonal element position of the coupling error correction coefficient matrix. Perform endpoint method linear fitting on the main channel loading value and output voltage value in the main direction, and fill the obtained channel coefficients into the main diagonal of the correction matrix.

[0070] In the calibration matrix, when the load on a certain channel changes, the output voltage of that channel and the output voltage of other channels will also change. This will be explained using Fx as an example.

[0071] When the Fx positive channel is loaded, the load change value for:

[0072] Sensor output voltage for:

[0073] If we plot the load change on the horizontal axis and the output voltage on the vertical axis,

[0074] and

[0075] By placing these values ​​into a two-dimensional coordinate system, we can obtain the variation trend of the output voltage of channel Fx with the load F; and the variation trend of the coupling error voltage of channels Fy, Fz, Mx, My, and Mz due to coupling phenomena with the load Fx. Analysis reveals that: (a) The output voltage of this channel, Fx, is linearly related to the load value; (b) The output voltage of other channels is affected by the loading of channel Fx, and there is a positive correlation. (c) The positive and negative coupling error curves are not symmetrical about the Y-axis. When performing line fitting, the positive and negative segments can be processed separately.

[0076] Because the trends of coupling error curves vary, traditional decoupling methods often use a single fitting method to handle the coupling error voltages of all channels during fitting, failing to differentiate the processing based on the specific coupling error characteristics of each channel.

[0077] Fitting operations are performed on the positive and negative data of the calibration matrix obtained through accuracy screening to obtain the correction coefficient matrix P used to correct the measurement error of the multidimensional force sensor. + and P - .

[0078] Since the positive and negative directions of the coupling error curve are often asymmetrical (i.e., not symmetrical along the Y-axis), processing the positive and negative segments separately can reduce the impact of differences in positive and negative directions caused by sensor structure and manufacturing processes on decoupling accuracy. Correction coefficient matrix The elements in the text are divided into two categories: main diagonal elements (P ii The main channel load is linearly calculated, while off-diagonal elements are used to correct nonlinear coupling errors between channels.

[0079] 1. Coupled channel variable-order polynomial error fitting (off-diagonal element P) ij ) The coupling error fitting is performed on the coupling error voltage data generated on the other unloaded channels when a certain channel in the calibration matrix is ​​loaded alone.

[0080] Variable-order polynomial fitting: For each coupling error voltage variation curve with applied force / torque, a polynomial of different orders is used for fitting. The order of the fitting polynomial ranges from 1 to k.

[0081] Order constraint: To avoid overfitting when the number of sample points is small (e.g., N=5 in 5-point calibration), the highest order used for fitting is constrained. Apply constraints: For example, for a six-dimensional force sensor calibrated using the 5-point method, the number of sample points... The order is 5, therefore the highest order is... The maximum value is 2.

[0082] Evaluation with Adjusted Coefficient of Determination: Introducing the Adjusted Coefficient of Determination The coefficients are used to evaluate the fitting effect on polynomials of orders 1-k, overcoming the limitations of the coefficient of determination Rk. 2 The inherent flaw of increasing with order is mitigated by adjusting the coefficient of determination to improve the optimality of the fitted model. The calculation method is as follows:

[0083] in,

[0084] is the coefficient of determination, n is the number of sample points, and k is the order of the polynomial.

[0085] In the above formula, R 2 The coefficient of determination (R-squared) is used to represent the quality of the fit; a value closer to 1 indicates a better fit. However, the coefficient of determination tends to increase with the order of the model, which can lead to the selection of a higher-order fit model. Therefore, this method uses an adjusted coefficient of determination to evaluate and improve the fit. The calculation method for the coefficient of determination is as follows:

[0086] In the above formula,

[0087] This is the actual output voltage value; These are the voltage prediction values ​​after multiple fittings;

[0088] This represents the average actual output voltage.

[0089] Optimal fit coefficient selection: Compare the fitting results obtained using polynomials of different orders. The larger of the values ​​is taken as the final coupling error polynomial coefficients Pij.

[0090] Off-diagonal element construction: The coefficients of the optimal fitting polynomial selected after adjusting the coefficients of determination are stored in the off-diagonal element positions Pij of the coupling error correction coefficient matrix (where ij is different). For a six-dimensional force sensor, there are 30 off-diagonal elements that need to be fitted and optimized.

[0091] 2. Main channel linear fitting (main diagonal element P) ii ) For the main load channel, its output voltage and the load it receives are usually linearly related.

[0092] Fitting method: The endpoint method is used to perform linear fitting of the load value and output voltage value of the main channel.

[0093] Linear coefficient acquisition: After fitting, the linear coefficients of each main channel are obtained. (where i takes values ​​from 1 to W).

[0094] Construction of main diagonal elements: the resulting linear coefficients Fill in the main diagonal of the correction coefficient matrix, that is .

[0095] Step 4: Perform the above fitting operation on the positive and negative directions of the calibration matrix respectively to obtain the positive correction coefficient matrix and the negative correction coefficient matrix of the loading values ​​of each channel. The fitting results were integrated, and correction coefficient matrices were constructed for the positive and negative calibration data respectively.

[0096] Positive correction coefficient matrix (P) + ): Perform the above coupled channel fitting (1.1) and main channel fitting (1.2) operations on the positive loading data of the calibration matrix to obtain the positive load correction coefficient matrix P. + .

[0097]

[0098] in, The coefficients are linear. These are the coefficients of the optimal polynomial (which can be first-order, second-order, or higher-order polynomials).

[0099] Negative correction coefficient matrix The negative load correction coefficient matrix can be obtained by processing the negative direction calibration data using the same method (i.e., performing coupled channel fitting and main channel fitting operations on the negative loading data).

[0100] These two matrices and Together, they form the correction coefficient library required for the decoupling algorithm, which will be selected and combined in real time according to the direction of the sensor output voltage during actual decoupling.

[0101] Step 5: When decoupling the multi-dimensional force sensor, firstly, calculate the output voltage of the main channel and the diagonal coefficients in the correction coefficient to obtain the rough calculated force / torque values ​​of each channel of the sensor; determine the sign of the force / torque value of each channel based on the output voltage of the main channel, and then select correction coefficients from the positive or negative correction coefficient matrix according to the value to form a new decoupling matrix; multiply the force values ​​of the multiple channels with the decoupling matrix to obtain the coupling error force value of each channel; the load value of a certain channel of the sensor is the rough calculated value minus the cumulative coupling error value of other channels in that channel; repeat the above operation until all channels of the multi-dimensional force sensor are corrected, thus completing the multi-dimensional force decoupling process.

[0102] The method for decoupling a multidimensional force sensor using a decoupling matrix is ​​specifically described as follows: Correction coefficients are selected based on the positive or negative load, and the final decoupling coefficients are combined. When a multi-dimensional force sensor is subjected to a combined load, all of its channels will output measured voltage values. Taking a six-dimensional force sensor as an example, a single combined load will produce a one-dimensional voltage vector V of length 6. U : in u i ( i Values ​​1 to 6 represent the six-dimensional force sensor. i The output voltage data of the channel shows that since the output voltage on each loading channel has a positive linear relationship with the load value, the positive or negative characteristics of the load can be directly determined based on the positive or negative value of the output voltage.

[0103] when u i When the value is greater than zero, it indicates that the load on the channel is positive, and the positive correction coefficient matrix is ​​used in this case. P + Select the first i Row elements are stored in a new decoupling matrix. P The i In the middle; when u i When the value is less than zero, it indicates that the load on the channel is negative. In this case, the negative correction coefficient matrix is ​​used. P - Select the first i Row elements are stored in a new decoupling matrix. P In the i-th row. After processing the 6 channels of the six-dimensional force sensor sequentially, the final combined decoupling coefficient matrix can be obtained. P Recombined as: Multiplying the correction coefficient matrix by the sensor output voltage yields the load value of the main channel and the load values ​​of other channels due to coupling, which can be represented by a matrix as follows: In the above E matrix f i The calculated load value for the main channel, e ji This represents the coupling error generated on channel j when channel i is loaded. The calculated load value is corrected for the coupling error, resulting in the decoupled corrected load value. Corrected load g i The calculation method is as follows: In the above formula, the value of W is determined based on the number of channels in the multi-dimensional force sensor. Here, a six-dimensional force sensor is used as an example, so W is set to 6. Each row of the E matrix is ​​corrected using a correction algorithm, ultimately yielding the decoupled load vector of the multi-dimensional force sensor. G : The elements 1 to 6 in the above G vector correspond to the load values ​​after final decoupling of the Fx, Fy, Fz, Mx, My, and Mz channels of the six-dimensional force sensor, respectively.

[0104] It should be understood that the processor in the embodiments of the present invention may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method embodiments can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor described above can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor, etc. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0105] It is understood that the memory in the embodiments of this application can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDR SDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). It should be noted that the memory used in the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0106] It should be understood that the above-described memory is exemplary but not restrictive. For example, the memory in the embodiments of this application may also be static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct memory bus RAM (DRRAM), etc. That is to say, the memory in the embodiments of this application is intended to include, but is not limited to, these and any other suitable types of memory.

[0107] This application also provides a computer-readable storage medium for storing computer programs.

[0108] Optionally, the computer-readable storage medium can be applied to the terminal device in the embodiments of this application, and the computer program causes the computer to execute the corresponding processes implemented by the mobile terminal / terminal device in the various methods of the embodiments of this application. For the sake of brevity, it will not be described in detail here.

[0109] This application also provides a computer program product, including computer program instructions.

[0110] Optionally, the computer program product can be applied to the terminal device in the embodiments of this application, and the computer program instructions cause the computer to execute the corresponding processes implemented by the mobile terminal / terminal device in the various methods of the embodiments of this application. For the sake of brevity, they will not be described in detail here.

[0111] This application also provides a computer program.

[0112] Optionally, the computer program can be applied to the vehicle autonomous driving device in the embodiments of this application. When the computer program is run on a computer, it causes the computer to execute the corresponding processes implemented by the terminal device in the various methods of the embodiments of this application. For the sake of brevity, it will not be described in detail here.

[0113] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

Claims

1. A multidimensional force decoupling method for nonlinear coupling error modeling, characterized in that, Includes the following steps: Step 1: Collect voltage output data of each channel of the multi-dimensional force sensor when linear loading and unloading are performed individually. Repeat this process multiple times to obtain multiple sets of output voltage data, and add load information to form multiple sets of load and output voltage data matrices. Step 2: Calculate the data accuracy of each group of voltage data matrices, and select the matrix with higher overall accuracy as the sensor calibration matrix; Step 3: Use a variable-order polynomial piecewise to fit the coupling error between sensor channels, and introduce an adjustment coefficient of determination to evaluate the fitting effect of each order polynomial. Step 4: Perform the above fitting operation on the positive and negative directions of the sensor calibration matrix to obtain the positive correction coefficient matrix and the negative correction coefficient matrix of the loading value of each channel. Step 5: When decoupling the multi-dimensional force sensor, first obtain the rough calculation values ​​of each channel of the sensor; The sign of each channel value is determined based on the output voltage of the main channel. Then, a correction coefficient is selected from the positive or negative correction coefficient matrix based on the value to form a new decoupling matrix. The multi-channel values ​​are multiplied by the decoupling matrix to obtain the coupling error value on each channel. The load value of a certain channel of the sensor is a rough calculated value minus the cumulative coupling error value of other channels on that channel.

2. The multidimensional force decoupling method according to claim 1, characterized in that, Step 2 specifically includes: calculating the data accuracy of each matrix group, including calculating linearity error, hysteresis error and repeatability error, and obtaining the comprehensive accuracy index by calculating the modulus of the three errors, and selecting the calibration matrix corresponding to the smallest comprehensive accuracy value as the final calibration matrix used.

3. The multidimensional force decoupling method according to claim 2, characterized in that, The linearity error is calculated as follows: take the output voltage and loading vector of each loading channel, use the endpoint method to perform linear fitting, calculate the fitting error at each point, take the ratio of the maximum error value to the net increment of the full-load output of the corresponding channel of the sensor as the linearity error of that channel, and take the maximum value of all channels as the linearity error of the multi-dimensional force sensor.

4. The multidimensional force decoupling method according to claim 2, characterized in that, The method for calculating the hysteresis error is as follows: take the net incremental voltage data during loading and unloading of a single channel, subtract the values ​​at the same load point, and take the ratio of the maximum value of the four error voltages to the net incremental value of the full-load output as the hysteresis error of a single channel, and take the maximum value of all channels as the maximum hysteresis error of the multi-dimensional force sensor.

5. The multidimensional force decoupling method according to claim 2, characterized in that, The calculation method for the repeatability error is as follows: take the net increment data of the load segment voltage output of a certain channel from the same position in multiple calibration matrices to form a vector, take the ratio of the maximum value in the error vector to the net increment of the full load output as the repeatability error of a single channel, and take the maximum value of all channels as the repeatability error of the multi-dimensional force sensor.

6. The multidimensional force decoupling method according to claim 1, characterized in that, When using a variable-order polynomial to fit the coupling error, the order of the polynomial ranges from 1 to k, where the maximum value of k is half the number of sample points, in order to avoid overfitting.

7. The multidimensional force decoupling method according to claim 1, characterized in that, The method for calculating the adjustment determination coefficient is as follows: the influence of the number of samples and the number of parameters is adjusted based on the determination coefficient R², wherein the determination coefficient R² is calculated by the sum of the squares of the actual output voltage value, the fitted predicted value and the mean of the actual output voltage, and the polynomial coefficient corresponding to the larger adjustment determination coefficient is taken as the final coupling polynomial coefficient.

8. The multidimensional force decoupling method according to claim 7, characterized in that, The adjustment determination coefficient The calculation method is as follows: in, The number of sample points. The order is the polynomial. In the above formula, R 2 The coefficient of determination is used to represent the quality of the fit; the closer its value is to 1, the better the fit. The method for calculating the coefficient of determination is as follows: In the above formula, This is the actual output voltage value; These are the voltage prediction values ​​after multi-factor fitting; This represents the average actual output voltage.

9. The multidimensional force decoupling method according to claim 1, characterized in that, In the construction of the positive and negative correction coefficient matrices, the non-main diagonal elements are the fitting polynomial coefficients of the coupling channel, and the main diagonal elements are the linear fitting coefficients of the output voltage and load of the main loading channel.

10. The multidimensional force decoupling method according to claim 1, characterized in that, During the decoupling process, row elements are selected from the positive or negative correction coefficient matrix according to the positive or negative output voltage to form a new decoupling matrix. The main channel load value and coupling error value are obtained through matrix multiplication, and finally the decoupled load vector is obtained through subtraction correction.

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