Elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering

Abstract

The invention discloses an elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering, and belongs to the technical field of robot joint torque calibration. An integrated elastic joint is driven through PWM signals, angle values of joint double encoders are collected respectively, collected data are subjected to noise reduction processing through bidirectional Gaussian filtering, and the torque of the joint is calibrated. Meanwhile, sine calibration is carried out on different encoders; aiming at the problem of signal instability caused by physical factors such as joint vibration, encoder signals are decomposed into a limited number of internal mode functions based on an empirical mode decomposition method, and B-spline approximation is used as a time-varying filter, so that the accuracy of signal decomposition is improved; and through the filtered encoder angle value and the torque sensor measurement value, rigidity calibration of the elastic element is carried out, and the accurate output torque of the joint can be obtained through the angle measurement value and rigidity calculation, so that the requirements of high-precision torque tracking and control of the elastic joint are met.

Description

Technical Field

[0001] The invention belongs to the technical field of robot joint torque calibration, and in particular relates to an elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering. Background Art

[0002] As the core component of robot drive, robot joints determine the dynamic performance of the entire robot. With the development of robot technology, the demand for physical contact between robots and unknown non-structured environments has increased, such as human-machine interaction and human-machine collaboration. Robots not only need to achieve high-precision position control, but also need to accurately control their output torque to achieve a certain level of safe interaction capabilities to meet work needs.

[0003] In recent years, elastic joints represented by series elastic actuators have been widely studied due to their compact structure, impact resistance, low mechanical impedance and other advantages, and have been applied to many experimental robot platforms. Unlike the traditional robot joint method of measuring the output torque through torque sensors, elastic joints calculate the torque output by measuring the displacement of elastic elements. However, due to their own mechanical characteristics, the control of series elastic actuators is more complex and difficult, and due to design requirements, series elastic actuators are usually more expensive. These have affected the widespread application of series elastic actuators to a certain extent.

[0004] The integrated elastic joint integrates the motor, reducer and elastic element through spatial structure topology optimization, which effectively reduces the overall size of the joint and improves the energy density. However, due to the lack of internal sensors, the amount of feedback data of the elastic joint is reduced, and the control bandwidth is reduced and delayed due to the introduction of elastic elements, the control difficulty of the elastic joint is significantly increased. At the same time, due to the topological structure of the elastic joint and the errors caused by mechanical installation, the collected data is affected by the comprehensive errors of the motor, reducer and elastic element. Therefore, how to accurately decompose the required data from the noisy data, how to use the decomposed data to realize the torque calibration of the elastic joint, and improve the accuracy of torque tracking have become research problems. Summary of the invention

[0005] In order to solve the shortcomings of the prior art and achieve the purpose of accurately marking example sentences, the present invention adopts the following technical solutions:

[0006] The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering includes the following steps:

[0007] Step 1: By simulating the stress and strain of the elastic element under different loading conditions, the elastic joint is structurally optimized to select the appropriate elastic element structural design;

[0008] Step 2: Through the stm32 joint drive circuit, the motor control adopts the current-speed-position three-loop PID control principle, and the SVPWM control principle is used to perform sensorless drive control on the motor;

[0009] Step 3: Use the 16-bit magnetic encoder on the driver to collect the angle data of the motor end and the elastic element output end, and synchronize and align all elastic joints to ensure real-time transmission of communication;

[0010] Step 4: Collect the angle data of the motor end of the elastic joint and the output end of the elastic element under uniform rotation, and use bidirectional Gaussian filtering to perform preliminary calibration on the collected data;

[0011] Step 5: Collect the angle data and torque data of the dual encoders at the motor end of the elastic joint and the output end of the elastic element under step loading conditions, and perform preliminary decomposition of the collected angle data and torque data based on the empirical mode decomposition method of time-varying filtering. After removing the high-frequency components, reorganize the signals using the sinusoidal calibration information to obtain preliminary processed angle data and torque data; perform bidirectional Gaussian filtering on the decomposed data to remove the low-frequency components in the signal and reduce the delay caused by filtering. Perform linear fitting on the filtered data, and compare the obtained elastic element stiffness information with the simulation of the finite element analysis for calibration of the calculated torque and the actual torque.

[0012] Furthermore, the elastic element designed based on the Archimedean spiral is processed with maraging steel C300, which can produce a deformation of about 15° under a torque of 50Nm, and the safety factor is 1.512. The parameter equation of its outer ring profile is as follows:

[0013]

[0014] Among them, t 1 Represents the outer ring profile parameters, x 1 ,y 1 Represent the coordinates of the inner ring of the spring, x 2 ,y 2 They represent the coordinates of the outer ring of the spring respectively.

[0015] Furthermore, an elastic joint torque calibration platform is constructed, including an elastic joint, a torque sensor and a dynamometer connected in sequence. The coaxial installation error is compensated for by a plum blossom coupling to ensure that their axes are in the same position. Encoders are set at the motor end of the integrated elastic joint and the output end of the elastic element.

[0016] Furthermore, step 4 comprises the following steps:

[0017] Step 4.1: Use one-dimensional Gaussian filtering to perform preliminary processing on the encoder reading;

[0018] Step 4.2: The characteristics of Gaussian filtering will cause delay to the signal, so bidirectional Gaussian filtering is used, first filtering in the forward direction and then in the reverse direction, which effectively reduces the delay caused by filtering;

[0019] Step 4.3: Segment the filtered angle data according to the maximum value. The data of two adjacent extreme points are the complete data of the encoder in one circle. Then accumulate the data of multiple circles of encoders, and perform sinusoidal fitting with the angle data as the independent variable and the encoder data as the dependent variable to obtain the encoder sinusoidal calibration expression, the original angle data and the encoder angle data after sinusoidal calibration.

[0020] Furthermore, the one-dimensional Gaussian filter for the encoder in step 4.1 has the following function expression:

[0021]

[0022] Among them, x represents the angle data read by this encoder, σ represents the standard deviation, which controls the size of the weight; μ represents the average value, which actually represents the offset of the weight, which is generally 0. By setting the appropriate Gaussian kernel size and performing Gaussian convolution on the signal, the filtered data can be obtained. Gaussian kernel truncation is used for edge data, and adaptive endpoint data is used.

[0023] Furthermore, the empirical mode decomposition based on time-varying filtering in step 5 includes the following steps:

[0024] Step 5.1: Use B-spline approximation as a time-varying filter;

[0025] The Hilbert transform is used to calculate the instantaneous amplitude A(t) and instantaneous frequency of the input signal x(t):

[0026]

[0027] in, represents the instantaneous frequency, Represents the Hilbert transform of a signal;

[0028] The analytical signal z(t) of the multi-component signal represents the sum of the two signals, that is:

[0029]

[0030] Among them, j represents an imaginary number, a i (t) represent the amplitude and phase of the i-th component respectively, represents the instantaneous phase and therefore:

[0031]

[0032]

[0033] Among them, a 1 ′(t) and a 2 ′(t) is a 1 (t), a 2 The derivative of (t) is They are The derivative of ;

[0034] Since the nodes are unknown in practice, it is necessary to estimate the local cutoff frequency of the input signal according to the Hilbert change, so as to construct a B-spline time-varying filter. The local cutoff frequency is:

[0035] Step 5.2: Construct a time-varying filter;

[0036] By local cutoff frequency Get the signal Taking the extreme time point of the signal h(t) as the node m, a B-spline approximation time-varying filter is constructed to filter the input signal, and the approximation result is recorded as m(t);

[0037] Step 5.3: According to the criteria of time-varying filtering empirical mode decomposition, determine whether the residual signal meets the stopping criteria;

[0038] The criteria for time-varying filtering empirical mode decomposition are as follows:

[0039]

[0040] Where θ(t) represents the residual signal, B Loughlin (t) represents the instantaneous bandwidth, represents the weighted instantaneous frequency;

[0041] Select appropriate internal modal components to remove high-frequency information.

[0042] Furthermore, the formula of step 5.1 is as follows:

[0043]

[0044] Where x represents the input signal, [·] ↓m represents the downsampling operation, [·] ↑m Represents an upsampling operation; represents the prefilter, and represents the convolution operation, β n is the B-spline function, n represents the B-spline order, m represents the node, and t represents the time.

[0045] Furthermore, in step 5, the filtered data is recombined with the encoder sinusoidal calibration data to remove the influence of the encoder error; a bidirectional Gaussian filter is constructed, and the R-squared-determination coefficient is used as the judgment criterion to adjust the size of the Gaussian filter kernel to make the filtered data smoother.

[0046] Furthermore, in step 5, the angle data θ and the moment data T are fitted by using the overall least squares linear fitting method, and the expression is a*θ+b*T=d, and the minimum a, b, d is found so that Minimum, E represents the error, n represents the total amount of data, that is, find the minimum error from all data points to the straight line;

[0047] So find the minimum gradient:

[0048]

[0049] E=(UN) T (UN)

[0050]

[0051] in, Respectively represent θ i , T i The average value of

[0052] Use singular value decomposition SVD (singular value decomposition) to solve the second-order matrix U T The eigenvector corresponding to U is the solved N=[ab].

[0053] The invention discloses an elastic joint torque calibration system based on empirical mode decomposition and Gaussian filtering, comprising an elastic joint torque calibration platform composed of an elastic joint, a torque sensor and a dynamometer connected in sequence, wherein the elastic joint is an integrated elastic joint, and encoders are arranged at the motor end and the output end of the elastic element, and the torque calibration is performed by using the elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering.

[0054] The advantages and beneficial effects of the present invention are:

[0055] The present invention makes a lightweight torque calibration method for an integrated elastic joint. It only needs to collect data from dual encoders to realize torque calibration, and effectively eliminates the influence of joint operation noise on torque measurement calibration. It is mainly divided into three parts: joint drive, encoder error calibration and torque calibration. Among them, the empirical mode decomposition based on time-varying filtering removes the high-frequency components in the signal, and the bidirectional Gaussian filter is used for smoothing, while reducing the delay caused by filtering. Then, the data is linearly fitted by the total least squares method to obtain the stiffness information of the elastic element, thereby realizing accurate calibration of the torque. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flow chart of a method in an embodiment of the present invention.

[0057] Figure 2 Schematic diagram of the structure of the integrated joint in an embodiment of the present invention.

[0058] Figure 3 Schematic diagram of the structure of the elastic element in the embodiment of the present invention.

[0059] Figure 4 It is a diagram of the elastic joint drive and communication framework in an embodiment of the present invention.

[0060] Figure 5 Schematic diagram of the torque measurement platform structure in an embodiment of the present invention.

[0061] Figure 6 1 is an encoder error and compensation diagram in an embodiment of the present invention.

[0062] Figure 7 It is a stiffness fitting diagram in an embodiment of the present invention.

[0063] Figure 8 It is a diagram of the empirical mode decomposition result based on time-varying filtering in an embodiment of the present invention.

[0064] Fig. 9 It is a flow chart of torque calibration in an embodiment of the present invention.

[0065] Fig.10 2 is a diagram of torque calibration results in an embodiment of the present invention. DETAILED DESCRIPTION

[0066] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation described here is only used to illustrate and explain the present invention, and is not used to limit the present invention.

[0067] like Figure 1 As shown, the elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering includes the following steps:

[0068] Step 1: Perform structural topology optimization on the integrated elastic joint 1, such as Figure 2 A dual encoder design of an elastic joint motor end encoder 11 and an elastic joint output end encoder 13 is adopted, which are distributed at the elastic joint motor end and the elastic element output end. At the same time, the stress and strain of the elastic element under different loading conditions are simulated in the finite element analysis software to select a suitable elastic element structure design.

[0069] Elastic elements designed based on Archimedean spirals, such as Figure 3 As shown, when processing with maraging steel C300, a deformation of about 15° can be produced under a torque of 50Nm, and the safety factor is 1.512. The parameter equation of the outer ring profile is as follows:

[0070]

[0071] Among them, t 1 Represents the outer ring profile parameters, x 1 ,y 1 Represent the coordinates of the inner ring of the spring, x 2 ,y 2 They represent the coordinates of the outer ring of the spring respectively.

[0072] Step 2: Through the stm32 joint drive circuit, the motor control adopts the current-speed-position three-loop PID control principle, and uses the SVPWM control principle to perform sensorless drive control on the motor. The motor drive control architecture is as follows Figure 4 As shown;

[0073] Step 3: Read the angle value of the motor end through the 16-bit magnetic encoder on the driver, read the angle value of the 19-bit encoder on the elastic element end through RS485 communication, and transmit it to the driver. Specifically, the RS485 communication parameters are shown in Table 1:

[0074] Table 1 Serial communication parameter settings

[0075] Baud rate Transmission Type Byte length Parity Flow Control Stop bits 2.5M RS485 8 none none 1

[0076] The elastic joint driver and the host computer are connected through Ethercat communication. Following the ESI file writing rules of Ethercat, a six-channel SDO / PDO data transmission structure is designed. A multi-machine Ethercat communication network is built based on distributed clocks. The host computer clock is used to synchronize and align all elastic joints to ensure 1000 Hz real-time transmission of communication.

[0077] The dynamometer 3 and torque sensor 2 are used to build an elastic joint torque calibration test experimental platform, and the plum blossom coupling is used to compensate for the coaxiality installation error to ensure that the axes are in the same position, such as Figure 5 shown.

[0078] Step 4: Collect the angle data of the magnetic encoder at the motor end and output end of the elastic joint under uniform rotation, and use bidirectional Gaussian filtering to perform preliminary processing on the collected data.

[0079] Step 4.1: Use one-dimensional Gaussian filtering to perform preliminary processing on the encoder reading. The function expression is as follows

[0080]

[0081] Among them, x represents the angle data read by this encoder, σ represents the standard deviation, which controls the size of the weight; μ represents the average value, which actually represents the offset of the weight, which is generally 0. By setting the appropriate Gaussian kernel size and performing Gaussian convolution on the signal, the filtered data can be obtained, and the edge data is truncated by the Gaussian kernel and the endpoint data is adaptive.

[0082] Step 4.2: The characteristics of Gaussian filtering will cause delay to the signal, so bidirectional Gaussian filtering is used, that is, filtering is performed in the forward direction first, and then Gaussian filtering is performed in the reverse direction, which effectively reduces the delay caused by filtering.

[0083] Step 4.3: Segment the filtered angle data according to the maximum value. The data of two adjacent extreme points is the complete data of the encoder in one circle. Then accumulate the readings of the multi-circle encoder, and perform sine fitting with the angle value as the independent variable and the encoder value as the dependent variable to obtain the encoder sine calibration expression. The original data and the encoder data after sine calibration are as follows: Figure 6 shown.

[0084] Step 5: Collect the angle data and torque data of the dual encoders of the elastic joint under step loading, perform preliminary decomposition of the collected angle data and torque data based on the empirical mode decomposition method of time-varying filtering, and reorganize the signal using the sine calibration information after removing the high-frequency components to obtain the preliminary processed angle data and torque data; perform bidirectional Gaussian filtering on the decomposed data to remove the low-frequency components in the signal and reduce the delay caused by filtering, perform linear fitting on the filtered data to obtain the stiffness information of the elastic element, and compare it with the results of finite element analysis, such as Figure 7 shown.

[0085] In step 5, the empirical mode decomposition process based on time-varying filtering is as follows:

[0086] Step 5.1: Use the B-spline approximation as a time-varying filter, that is:

[0087]

[0088] Where x represents the input signal, [·] ↓mrepresents the downsampling operation, [·] ↑m Represents an upsampling operation; represents the prefilter, and (where: represents the convolution operation), β n is the B-spline function, n represents the B-spline order, m represents the node, and t represents the time.

[0089] The Hilbert transform is used to calculate the instantaneous amplitude A(t) and instantaneous frequency of the input signal x(t):

[0090]

[0091] in, represents the instantaneous frequency, Represents the Hilbert transform of a signal.

[0092] The analytical signal z(t) of the multi-component signal can be expressed as the sum of two signals, namely:

[0093]

[0094] Among them, j represents an imaginary number, a i (t) represent the amplitude and phase of the i-th component respectively, represents the instantaneous phase and therefore:

[0095]

[0096]

[0097] Among them, a 1 ′(t) and a 2 ′(t) is a 1 (t), a 2 The derivative of (t) is They are The derivative of ;

[0098] Since the nodes are unknown in practice, it is necessary to estimate the local cutoff frequency of the input signal according to the Hilbert change, so as to construct a B-spline time-varying filter. The local cutoff frequency is:

[0099] Step 5.2: Constructing a time-varying filter

[0100] Get the local cutoff frequency After that, we can get the signal h(t), The extreme time point of h(t) is used as the node m, and a B-spline approximation time-varying filter is constructed to filter the input signal. The approximation result is recorded as m(t).

[0101] Step 5.3: Determine whether the residual signal meets the stopping criteria

[0102] According to the criterion of time-varying filtering empirical mode decomposition: B Loughlin (t) represents the instantaneous bandwidth, represents the weighted instantaneous frequency, and the expression is:

[0103]

[0104] Here, θ(t) represents the residual signal.

[0105] Select appropriate internal modal components to remove high-frequency information. The original signal and the decomposed signal are as follows: Figure 8 shown.

[0106] Furthermore, the filtered data is recombined with the encoder sinusoidal calibration data to remove the influence of the encoder error. A bidirectional Gaussian filter is constructed, and the R-squared-coefficient of determination is used as the criterion. The size of the Gaussian filter kernel is adjusted to make the filtered data smoother. The signal processing flow is as follows: Fig. 9 shown.

[0107] Furthermore, the angle data θ and the torque data T are fitted by the overall least squares linear fitting method. The expression is a*θ+b*T=d. By finding the minimum a, b, d, Minimum, E represents error, n represents the total amount of data, that is, find the minimum error from all data points to the straight line.

[0108] So find the minimum gradient:

[0109]

[0110] E=(UN) T (UN)

[0111]

[0112] Among them, θ and T represent θ i , T i The average value of .

[0113] Therefore, singular value decomposition SVD (singular value decomposition) is used to solve the second-order matrix U T The eigenvector corresponding to U is the solved N = [ab]. The data to be fitted and the fitted straight line are as follows Figure 7 The final verification data results are shown as Fig.10 shown.

[0114] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. Elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering, characterized by The steps include: Step 1: Optimize the structure of the elastic joint by simulating the stress and strain of the elastic element under different loading conditions; Step 2: Use the joint drive circuit to control the motor without sensor. Step 3: Collect the angle data of the motor end and the output end of the elastic element, and perform synchronous alignment; Step 4: Collect the angle data of the motor end of the elastic joint and the output end of the elastic element under uniform rotation, and use bidirectional Gaussian filtering to perform preliminary calibration on the collected data; Step 5: Collect the angle data and torque data of the motor end of the elastic joint and the output end of the elastic element under step loading, and perform preliminary decomposition of the collected angle data and torque data based on the empirical mode decomposition method of time-varying filtering. After removing the high-frequency components, reorganize the signals using the calibration information to obtain preliminary processed angle data and torque data; perform bidirectional Gaussian filtering on the decomposed data to remove the low-frequency components in the signal, perform linear fitting on the filtered data, and compare the obtained elastic element stiffness information with the simulation for calibration of the calculated torque and the actual torque.

2. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 1, characterized in that: The elastic element designed based on the Archimedean spiral has the following outer ring profile parameter equation: Among them, t1 represents the outer ring profile parameter, x1 and y1 represent the coordinates of the inner ring of the spring, and x2 and y2 represent the coordinates of the outer ring of the spring.

3. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 1, characterized in that: An elastic joint torque calibration platform is constructed, comprising an elastic joint (1), a torque sensor (2) and a dynamometer (3) connected in sequence, wherein the coaxiality installation error is compensated for each other via a coupling, and encoders are arranged at the motor end of the elastic joint (1) and the output end of the elastic element.

4. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 3 is characterized in that: The step 4 comprises the following steps: Step 4.1: Use one-dimensional Gaussian filtering to perform preliminary processing on the encoder reading; Step 4.2: Use bidirectional Gaussian filtering, first filtering in the forward direction, and then filtering in the reverse direction; Step 4.3: Segment the filtered angle data according to the maximum value. The data of two adjacent extreme points are the complete data of the encoder in one circle. Then accumulate the data of multiple circles of encoders, and perform sinusoidal fitting with the angle data as the independent variable and the encoder data as the dependent variable to obtain the encoder sinusoidal calibration expression, the original angle data and the encoder angle data after sinusoidal calibration.

5. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 4 is characterized in that: The one-dimensional Gaussian filter for the encoder in step 4.1 has the following function expression: Among them, x represents the angle data read by this encoder, σ represents the standard deviation, which controls the size of the weight; μ represents the average value, which actually represents the offset of the weight. By setting the appropriate Gaussian kernel size and performing Gaussian convolution on the signal, the filtered data can be obtained. Gaussian kernel truncation and adaptive endpoint data are used for edge data.

6. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 1, characterized in that: The empirical mode decomposition based on time-varying filtering in step 5 includes the following steps: Step 5.1: Use B-spline approximation as a time-varying filter; The Hilbert transform is used to calculate the instantaneous amplitude A(t) and instantaneous frequency of the input signal x(t): in, represents the instantaneous frequency, Represents the Hilbert transform of a signal; The analytical signal z(t) of the multi-component signal represents the sum of the two signals, that is: Among them, j represents an imaginary number, a i (t) represent the amplitude and phase of the i-th component respectively, represents the instantaneous phase and therefore: Among them, a1′(t) and a2′(t) are the derivatives of a1(t) and a2(t), They are The derivative of ; The local cutoff frequency of the input signal is estimated according to the Hilbert change, so as to construct a B-spline time-varying filter. The local cutoff frequency is: Step 5.2: Construct a time-varying filter; By local cutoff frequency Get the signal Taking the extreme time point of the signal h(t) as the node m, a B-spline approximation time-varying filter is constructed to filter the input signal, and the approximation result is recorded as m(t); Step 5.3: According to the criteria of time-varying filtering empirical mode decomposition, determine whether the residual signal meets the stopping criteria; The criteria for time-varying filtering empirical mode decomposition are as follows: Where θ(t) represents the residual signal, B Loughlin (t) represents the instantaneous bandwidth, represents the weighted instantaneous frequency; Select appropriate internal modal components to remove high-frequency information.

7. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 6, characterized in that: The formula of step 5.1 is as follows: Where x represents the input signal, [·] ↓m represents the downsampling operation, [·] ↑m Represents an upsampling operation; represents the prefilter, and : represents the convolution operation, β n is the B-spline function, n represents the B-spline order, m represents the node, and t represents the time.

8. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 1, characterized in that: In step 5, the filtered data and the calibration data are recombined; a bidirectional Gaussian filter is constructed, and the R-squared-coefficient of determination is used as a criterion to adjust the size of the Gaussian filter kernel to make the filtered data smoother.

9. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering according to claim 1, characterized in that: In step 5, the angle data θ and the moment data T are fitted by the overall least squares linear fitting method, and the expression is a*θ+b*T=d. By finding the minimum a, b, d, Minimum, E represents the error, n represents the total amount of data, that is, find the minimum error from all data points to the straight line; So find the minimum gradient: E=(UN) T (A) in, Respectively represent θ i 、T i The average value of Solve the second-order matrix U using singular value decomposition T The eigenvector corresponding to U is the solved N=[ab].

10. An elastic joint torque calibration system based on empirical mode decomposition and Gaussian filtering, comprising an elastic joint torque calibration platform composed of an elastic joint (1), a torque sensor (2) and a dynamometer (3) connected in sequence, characterized in that: The elastic joint (1) is an integrated elastic joint, and encoders are provided at both the motor end and the elastic element output end thereof. The elastic joint torque calibration method based on empirical mode decomposition and Gaussian filtering described in claim 1 is used for torque calibration.

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