A combined dynamic error correction method for multi-dimensional force sensors under dynamic support conditions

Abstract

This invention discloses a combined dynamic error correction method for multi-dimensional force sensors under dynamic support conditions. It achieves full dynamic error correction of the multi-dimensional force sensor by first dynamically correcting the sensor's own characteristics and then compensating for the inertia at the support end. First, a dynamic decoupling-compensator is designed through a dynamic calibration experiment of the multi-dimensional force sensor. Second, a six-dimensional acceleration measurement scheme for the support end is designed to obtain the six-dimensional acceleration at the support end. Then, the inertia compensation parameters for the support end are obtained through dynamic support experiments. Finally, for multi-dimensional force measurements under actual dynamic support conditions, the dynamic decoupling-compensator is first used to dynamically correct the sensor's own characteristics in the multi-dimensional force sensor measurement signal. Then, based on the six-dimensional acceleration at the support end and the inertia compensation parameters, the signal after dynamic error correction of the sensor's own characteristics is compensated for at the support end, thereby achieving combined dynamic error correction under dynamic support conditions.

Description

Technical Field

[0001] This invention relates to dynamic error correction technology for multidimensional force sensors, and in particular to a method for dynamic error correction of strain-type multidimensional force sensors when there is vibration or motion at the support end of the multidimensional force sensor. This method solves the problem that existing dynamic error correction methods for multidimensional force sensors cannot effectively reduce the dynamic error caused by the structural characteristics of the multidimensional force sensor itself, and the influence of the structural characteristics or motion state of the support mechanism on the dynamic characteristics of the multidimensional force sensor, resulting in incomplete dynamic error correction or even the basic failure of the dynamic decoupling-compensator when the support mechanism changes. Background Technology

[0002] Multidimensional force sensors, as measuring devices capable of simultaneously measuring force / torque components in multiple directions, are widely used in industrial automation, robotic sensing, aerospace, and biomedicine. Among them, strain gauge multidimensional force sensors dominate industrial production and scientific experiments due to their excellent static characteristics, stable performance, and mature static calibration and temperature compensation technologies. However, multidimensional force sensors suffer from low natural frequencies and small damping ratios, resulting in insufficient dynamic response speed, large overshoot, long settling time, and interdimensional dynamic coupling. Furthermore, in practical applications, the support mechanism, as an essential tooling condition, directly affects the dynamic characteristics of the multidimensional force sensor due to its structural characteristics and motion state; the vibration and motion of the support mechanism slows down the sensor's response speed, increases recovery time, expands dynamic errors, and narrows the measurement bandwidth. Therefore, improving the dynamic response speed and measurement accuracy of multidimensional force sensors is of great significance in high-precision dynamic force measurement applications such as high-precision machining, wind tunnel experiments, and robot force control. Currently, common dynamic error correction methods for multidimensional force sensors include dynamic correction methods based on the sensor's own characteristics and load-side inertial compensation methods. The sensor's own characteristic dynamic correction method involves constructing a dynamic decoupling-compensator cascaded to the sensor's output to reduce dynamic measurement errors. The load-end inertial compensation method compensates for all inertial forces / torques in the multi-dimensional force sensor's measurement signal based on the absolute acceleration and inertia matrix of the load end. However, the sensor's own characteristic dynamic correction method is only suitable for situations where the support end has no vibration or movement. Once the support mechanism is a movable part, this method struggles to address new errors introduced by support end movement or vibration. While the commonly used load-end inertial compensation method in practical applications can compensate for inertial errors in the multi-dimensional force sensor's measurement signal, it theoretically still retains the sensor's own damping error, and the compensation effect is affected by the load end structural stiffness and the accelerometer's installation position. To address the dynamic error correction problem of force sensors under dynamic support conditions, a Chinese invention patent discloses a combined dynamic compensation method for force sensors under dynamic support conditions (Yang Shuanglong, Ren Jie et al., application number: CN202210736824.X, application date: 2022.6.27). The method flow includes force sensor dynamic compensator design → force sensor support end inertia coefficient calibration → force sensor combined dynamic compensation. This combined dynamic compensation method achieves dynamic error correction of single-dimensional forces under dynamic support conditions, but it cannot be used for dynamic error correction of multi-dimensional force sensors under dynamic support conditions. In summary, for the dynamic measurement problem of multi-dimensional force sensors under dynamic support conditions, such as joint force measurement of robotic arms / mobile robots and aerodynamic force measurement under elastic support conditions, existing dynamic error correction methods all have certain limitations. A correction method that can comprehensively compensate for the dynamic characteristics of multi-dimensional force sensors themselves and the dynamic errors caused by the movement or vibration of their support ends is needed. Summary of the Invention

[0003] This invention primarily addresses situations where the support mechanism of a multidimensional force sensor is an elastic structure or the support end is subject to external control, resulting in vibration or movement during force measurement. It solves the problem that existing dynamic error correction methods for multidimensional force sensors cannot effectively remove errors introduced by the vibration or movement of the support mechanism from the measurement signal. The invention proposes a combined dynamic error correction method that integrates the dynamic error correction method based on the multidimensional force sensor's own characteristics with an inertial compensation method for the support end, thereby reducing the dynamic measurement error of multidimensional force sensors under dynamic support conditions.

[0004] The technical solution adopted in this invention is as follows: First, a dynamic decoupling-compensator for dynamic correction of the multidimensional force sensor's own characteristics is obtained through dynamic calibration experiments under fixed support conditions. Second, a six-dimensional acceleration calculation model for the support end is obtained by designing a measurement scheme for the six-dimensional acceleration at the support end. Then, multiple accelerometers are installed at the sensor support end, and dynamic excitation experiments are conducted under dynamic support conditions to obtain the six-dimensional acceleration transformation matrix and inertial compensation coefficient matrix in the multidimensional force sensor measurement coordinate system. Finally, in the actual multidimensional force measurement under dynamic support conditions, the dynamic decoupling-compensator for dynamic correction of the multidimensional force sensor's own characteristics is first used to correct the force sensor measurement signal. Then, based on the measurement values ​​of multiple accelerometers at the support end, the positional relationship between the accelerometers at the support end and the support mechanism and the multidimensional force sensor, and the inertial compensation coefficient matrix, the signal after correction by the dynamic decoupling-compensator for the sensor's own characteristics is inertially compensated at the support end to obtain the final combined dynamic error correction result. This effectively reduces the dynamic force measurement error of the multidimensional force sensor when there is vibration or movement at the support end, and improves the dynamic measurement accuracy.

[0005] The technical process of this invention is as follows: dynamic decoupling of multi-dimensional force sensor characteristics - compensator design 1 → support end acceleration measurement design 2 → support end inertial compensation parameter calibration 3 → multi-dimensional force sensor combined dynamic error correction 4. The method of this invention uses an inertial coordinate system {W}, a multi-dimensional force sensor measurement coordinate system {B}, a support mechanism coordinate system {S}, and an end load centroid coordinate system {E} for auxiliary explanation. Specifically, the inertial coordinate system {W} is a fixed reference coordinate system; the multi-dimensional force sensor measurement coordinate system {B} is calibrated and determined during the design and production of the multi-dimensional force sensor, with its origin located at the calibration center of the multi-dimensional force sensor; the support mechanism coordinate system {S} describes the motion state of the support mechanism in the inertial frame, moving with the movement of the support mechanism, with its origin defined at the intersection of the fastening contact surface between the support mechanism and the sensor and the z-axis of the multi-dimensional force sensor measurement coordinate system, and the coordinate axis direction is consistent with the direction of the multi-dimensional force sensor measurement coordinate system; the end load centroid coordinate system {E} describes the inertial parameters at the end load centroid.

[0006] The design 1 of the dynamic decoupling-compensator for the multidimensional force sensor's inherent characteristics involves designing a dynamic calibration experiment for the multidimensional force sensor in a calibration environment to obtain the input and output data of the multidimensional force sensor under different directional excitations; based on this, a dynamic decoupling-compensator is designed to achieve dynamic error correction of the multidimensional force sensor's inherent characteristics. The process is as follows: Multidimensional force sensor dynamic calibration experiment 5 → Dynamic decoupling-compensator design 6.

[0007] Experiment 5: Dynamic calibration of multi-dimensional force sensor. The multi-dimensional force sensor, along with a loading head simulating the actual sensor end workpiece, is mounted on a fixed calibration platform with stiffness much greater than the stiffness of each sensing element of the multi-dimensional force sensor. m sets of impact or step excitations in different directions are applied to the sensor end workpiece or loading head to obtain m sets of excitation inputs and corresponding outputs, where m ≥ n, and n is the dimension of the multi-dimensional force sensor.

[0008] Dynamic Decoupling-Compensator Design 6: Based on the input and output data obtained from the dynamic calibration experiment of the multidimensional force sensor in Experiment 5, a dynamic decoupling-compensator is designed using existing time-domain or frequency-domain decoupling-compensation methods.

[0009] The aforementioned support end acceleration measurement design 2 involves calculating the six-dimensional acceleration of the support end using measurements from multiple three-dimensional acceleration sensors installed on the support mechanism. The process is as follows: Accelerometer installation 7 → Accelerometer measurement of motion acceleration at sensor measurement points 8 → Six-dimensional acceleration calculation at the support end 9.

[0010] Accelerometer installation arrangement 7: Install q three-dimensional linear accelerometers on the support mechanism at the rigid connection point with the multi-dimensional force sensor, where q ≥ 3 and the accelerometers are not collinear, and the distance between each accelerometer is as large as possible.

[0011] Accelerometer measurement of motion acceleration at the measurement point: 8. When the support mechanism has no motion acceleration, the static bias of q three-dimensional linear accelerometers is eliminated by software offset removal. The measured value of the accelerometer is then the three-dimensional motion acceleration at the measurement point; the measured value of the three-dimensional linear accelerometer is denoted as a'. i =[a' ix ,a' iy ,a' iz ] T ,i=1,2,…,q.

[0012] Six-dimensional acceleration calculation at the support end (9): Based on the coordinate system orientation and measured values ​​of q three-dimensional linear accelerometers, calculate the six-dimensional motion acceleration of the origin of the support mechanism's coordinate system relative to the inertial coordinate system {W} within the support mechanism's coordinate system {S}. First, based on the coordinate axis relationship between the coordinate systems of the q accelerometers installed on the support mechanism and the support mechanism's coordinate system {S}, calculate the measured values ​​a' of the q three-dimensional linear accelerometers.i Transform them respectively to the coordinate axes of the support mechanism coordinate system {S}:

[0013]

[0014] In the above formula, a i =[a ix ,a iy ,a iz ] T R represents the three-dimensional linear acceleration at the i-th measurement point after rotation in the coordinate system; the rotation matrix R i In this context, "s" and "c" represent the simplified expressions for the sine and cosine functions, respectively, and α... i β i and γ i The coordinate system rotation angle, i.e., the support mechanism coordinate system {S} can be rotated by α around the x-axis from the measurement coordinate system of the three-dimensional accelerometer at the i-th measurement point. i Angle, then rotate β around the y-axis i Angle, and finally rotate γ around the z-axis. i The angle is obtained.

[0015] Then, based on the position vector of the i-th measurement point in the support mechanism coordinate system {S} Get a i Six-dimensional acceleration at the support end Relationship:

[0016]

[0017] in, For q a i The result of concatenating lines; Let be the six-dimensional acceleration at the support end to be calculated. The six-dimensional acceleration at the support end can be calculated using the least squares method according to the above formula:

[0018]

[0019] The calibration of the support end inertial compensation parameter 3 involves obtaining the transformation matrix from the six-dimensional acceleration of the support end to the six-dimensional acceleration of the multi-dimensional force sensor measurement coordinate system {B} based on the positional relationship between the support mechanism coordinate system {S} and the multi-dimensional force sensor measurement coordinate system {B}. The inertia coefficient matrix M of the end load in the multidimensional force sensor measurement coordinate system {B} was calibrated through a dynamic excitation experiment under dynamic support conditions. f The process is as follows: dynamic excitation experiment under dynamic support 10 → acquisition of six-dimensional acceleration of coordinate system by multi-dimensional force sensor 11 → calibration of inertial compensation coefficient matrix 12.

[0020] Dynamic excitation experiment 10 under dynamic support: Install the same workpiece or loading head as in the multidimensional force sensor dynamic calibration experiment 5 at the end of the force sensor; install the force sensor support end on the movable support; install q three-dimensional linear accelerometers according to the arrangement scheme in the accelerometer installation arrangement 7; install the movable support on a rigid calibration platform. Apply p groups (p≥n) of excitations in different directions to the workpiece or loading head at the end of the force sensor using negative step excitation or impact excitation to obtain the measurement signal of the multidimensional force sensor used for calibration and correction parameters. and the measurement signals of q three-dimensional linear accelerometers Where j = 1, 2, ..., p; negative step excitation refers to first applying a stable force or torque load to the multidimensional force sensor, and then suddenly unloading and removing the applied load from the multidimensional force sensor, making the load on the multidimensional force sensor zero, thereby realizing negative step excitation of the multidimensional force sensor; then the measurement signal of the multidimensional force sensor after negative step unloading or impact excitation. It only includes dynamic error.

[0021] Multi-dimensional force sensor measurement coordinate system six-dimensional acceleration acquisition 11: First, according to the design method in the support end acceleration measurement design 2, the dynamic excitation experiment 10 under the dynamic support condition p group excitation is obtained. Transformed into six-dimensional acceleration at the support end Then, because the inertial force component caused by the movement or vibration of the support end is the inertial property of the workpiece or loading head at the sensor end in the multi-dimensional force sensor measurement coordinate system {B} caused by the six-dimensional acceleration of the support end, it is necessary to transfer the six-dimensional acceleration of the support end to the force sensor measurement coordinate system {B}; therefore, according to Position vector of the multi-dimensional force sensor in the coordinate system {S} of the support mechanism The six-dimensional acceleration in the multi-dimensional force sensor measurement coordinate system {B} caused by the vibration of the support end is obtained from the following formula.

[0022]

[0023] Inertial compensation coefficient matrix calibration 12: Based on the output data of the multi-dimensional force sensor and q three-dimensional linear accelerometers obtained from the dynamic excitation experiment 10 under the dynamic support condition, the inertial compensation coefficient matrix is ​​calibrated using the time-domain least squares method based on truncation and splicing. The process is as follows: effective calibration data truncation and splicing → inertial compensation coefficient matrix estimation.

[0024] ① Effective calibration data capture and stitching: Using the dynamic decoupling-compensator design in section 6, the dynamic decoupling-compensator was used to measure the p groups of multidimensional force measurement signals in different directions obtained from the dynamic excitation experiment 10 under dynamic support conditions. Perform dynamic error correction on the sensor's own characteristics separately to obtain Then, from respectively and After the signal crosses zero following a negative step unloading or impact excitation, data of equal length for the same complete oscillation period are extracted, denoted as follows: and but This refers to the six-dimensional inertial force components remaining after a negative step unloading or impact excitation; the p groups of truncated six-dimensional inertial forces... and six-dimensional acceleration The inertial force component F in the valid calibration data is obtained by concatenating the data column by column. I cal and acceleration components

[0025] The inertial force component F in the valid calibration data I cal for:

[0026] Each element in the matrix express Inertial force / torque data in the o-th dimension. express The inertial force / torque value at the kth sampling point.

[0027] The acceleration component in the valid calibration data for:

[0028] Each element in the matrix express Linear / angular acceleration data in the o-th dimension of multidimensional acceleration. express The linear / angular acceleration value at the kth sampling point.

[0029] ② Estimation of inertial compensation coefficient matrix: based on the relationship between inertial force and acceleration. The inertia compensation coefficient matrix is ​​estimated using the least squares method:

[0030]

[0031] The multidimensional force sensor combined dynamic error correction 4, that is, in actual multidimensional force measurement, based on the dynamic decoupling-compensator designed in the multidimensional force sensor's own characteristics dynamic decoupling-compensator design 1, performs dynamic correction on the multidimensional force sensor measurement signal based on the sensor's own characteristics, and then based on the motion acceleration a' measured by q acceleration sensors. iThe method for calculating the six-dimensional acceleration at the support end in the support end acceleration measurement design 2, and the support end inertia compensation coefficient obtained in the support end inertia compensation parameter calibration 3, are used to perform support end inertia compensation on the signal after dynamic correction of the sensor's own characteristics; thereby improving the measurement accuracy and dynamic response speed of the multi-dimensional force sensor. The steps of the combined dynamic error correction are as follows:

[0032] Step ①: For multidimensional force measurement under actual working conditions, install q three-dimensional accelerometers on the actual movable support according to the arrangement scheme in the accelerometer installation arrangement 7; record the multidimensional force sensor output signal collected in the actual measurement as F, and the measurement signal of the q three-dimensional accelerometers as a'. i ,i=1,2,…,q.

[0033] Step ②: Based on the dynamic decoupling-compensator designed in the design 1 of the multidimensional force sensor's own characteristics, the multidimensional force sensor's measurement signal F is dynamically corrected according to the sensor's own characteristics, thereby obtaining the signal F after dynamic correction of the multidimensional force sensor's own characteristics. c .

[0034] Step ③: Based on q three-dimensional acceleration signals a' i The coordinate system rotation matrix R in the support end acceleration measurement design 2 i and the six-dimensional acceleration solution matrix at the support end The six-dimensional acceleration at the support end in actual measurement is obtained by solving the following formula:

[0035]

[0036] Step 4: Based on the six-dimensional acceleration coordinate transformation matrix in Calibration 3 using the support end inertial compensation parameters. and inertia compensation coefficient matrix M f The inertial force component F, which is caused by the vibration or motion of the support mechanism to the measurement signal of the multi-dimensional force sensor, is calculated using the following formula. I :

[0037]

[0038] Step 5: Dynamically correct the signal F based on the characteristics of the multidimensional force sensor obtained in Step 2. c and the inertial force component F obtained in step ④ I The final result of the combined dynamic error correction can be obtained using the following formula:

[0039] F ci =F c -F I

[0040] The advantages of this invention are: for multi-dimensional force signal measurement under dynamic support conditions, by first performing dynamic correction on the multi-dimensional force sensor measurement signal based on the force sensor's own characteristics, and then performing inertial compensation at the support end, all dynamic errors can be theoretically compensated, including inertial errors, damping errors, coupling errors caused by the force sensor's own structural characteristics, as well as inertial errors caused by the movement or vibration of the support mechanism; at the same time, since the accelerometer is directly installed at the rigid connection between the dynamic support mechanism and the multi-dimensional force sensor, the position installation requirements of the accelerometer and its impact on error correction are reduced. Attached Figure Description

[0041] Figure 1 This is a technical flowchart of the method of the present invention;

[0042] Figure 2 This is a schematic diagram of the multi-dimensional force sensor measurement system and its coordinate system according to the method of the present invention;

[0043] Figure 3 This is a schematic diagram of the installation of the multidimensional force sensor in the dynamic calibration experiment of the multidimensional force sensor according to a specific embodiment of the present invention;

[0044] Figure 4 This is a schematic diagram of the installation of a dynamic excitation experiment under dynamic support conditions according to a specific embodiment of the present invention;

[0045] Figure 5 This is a calibration effect diagram of a six-dimensional force sensor combined dynamic error correction main channel according to a specific embodiment of the present invention;

[0046] Figure 6 This is a diagram illustrating the correction effect of a six-dimensional force sensor combination dynamic error correction method with Fx-My directional loading, according to a specific embodiment of the present invention. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings:

[0048] The design concept of this invention is as follows: Addressing the problem that traditional dynamic error correction methods are incomplete or even ineffective due to vibration or motion in the support mechanism of a multi-dimensional force sensor during force measurement, the invention first obtains a dynamic decoupling-compensator based on the sensor's own characteristics from dynamic calibration experimental data. This compensator is used for dynamic error correction of the multi-dimensional force sensor's own characteristics under dynamic support conditions. Secondly, a measurement scheme for the six-dimensional acceleration at the support end is designed to calculate the six-dimensional acceleration. Then, relevant parameters for inertial compensation at the support end are obtained through a dynamic excitation experiment designed under dynamic support conditions. Finally, for multi-dimensional force measurement under actual dynamic support conditions, the force sensor measurement signal is first corrected for dynamic errors based on the dynamic decoupling-compensator. Then, the corrected signal is inertially compensated based on the calculated six-dimensional acceleration at the support end, the position vector of the multi-dimensional force sensor centering in the support mechanism coordinate system, and the calibrated inertial compensation coefficient matrix. This yields a final combined dynamic error correction result, thereby reducing the dynamic measurement error of the multi-dimensional force sensor under dynamic support conditions and improving its time-domain tracking performance.

[0049] The technical solution process of this invention is as follows: Figure 1 As shown. First, based on the dynamic calibration experimental data of the multi-dimensional force sensor, a dynamic decoupling-compensator for the sensor's own characteristics is designed through the design 1 of the multi-dimensional force sensor's own characteristics dynamic decoupling-compensator. Second, based on multiple three-dimensional accelerometers on the support mechanism, the six-dimensional acceleration of the support end is calculated through the design 2 of the support end acceleration measurement. Then, based on the dynamic excitation experiment under dynamic support conditions, the relevant parameters of the support end inertial compensation are obtained through the calibration 3 of the support end inertial compensation parameters. Finally, for the multi-dimensional force measurement under actual dynamic support conditions, the dynamic measurement output of the force sensor is combined with the dynamic error correction 4 of the multi-dimensional force sensor combination to perform combined dynamic error correction, so as to improve the dynamic measurement accuracy of the force sensor under dynamic support conditions. In the method of this invention, the inertial coordinate system {W}, the multi-dimensional force sensor measurement coordinate system {B}, the support mechanism coordinate system {S}, and the end load centroid coordinate system {E} are used to illustrate the method. Figure 2 As shown in the diagram. The inertial coordinate system {W} is a fixed reference coordinate system; the multi-dimensional force sensor measurement coordinate system {B} is calibrated and determined during the design and production of the multi-dimensional force sensor, with its origin located at the sensor's calibration center; the support mechanism coordinate system {S} describes the motion state of the support mechanism in the inertial frame, moving with the support mechanism; its origin is defined at the intersection of the fastening contact surface between the support mechanism and the sensor and the z-axis of the multi-dimensional force sensor measurement coordinate system, with the coordinate axis direction consistent with the direction of the multi-dimensional force sensor's measurement coordinate system; and the end-load centroid coordinate system {E} describes the inertial parameters at the end-load centroid.

[0050] The design 1 of the dynamic decoupling-compensator for the multidimensional force sensor's inherent characteristics involves designing a dynamic calibration experiment for the multidimensional force sensor in a calibration environment to obtain the input and output data of the multidimensional force sensor under different directional excitations; based on this, a dynamic decoupling-compensator is designed to achieve dynamic error correction of the multidimensional force sensor's inherent characteristics. The process is as follows: Multidimensional force sensor dynamic calibration experiment 5 → Dynamic decoupling-compensator design 6.

[0051] Multidimensional force sensor dynamic calibration experiment 5: The multidimensional force sensor, along with the actual sensor end workpiece or a loading head simulating the actual workpiece, is mounted on a fixed calibration platform with a stiffness much greater than the stiffness of each sensitive element of the multidimensional force sensor. Figure 3 As shown, m sets of impact excitations or step excitations in different directions are applied to the workpiece or loading head at the end of the sensor to obtain m sets of excitation inputs and corresponding outputs, where m ≥ n, and n is the dimension of the multidimensional force sensor.

[0052] Dynamic Decoupling-Compensator Design 6: This section describes the design of a dynamic decoupling-compensator based on the input and output data obtained from the multi-dimensional force sensor dynamic calibration experiment 5, using existing time-domain or frequency-domain decoupling-compensation methods. Time-domain decoupling-compensation methods include serial iterative dynamic decoupling-compensation, system identification, zero-pole placement, and neural networks; frequency-domain decoupling-compensation methods include frequency-domain decoupling correction based on frequency response function matrix inversion and inverse filtering dynamic error correction.

[0053] The aforementioned support end acceleration measurement design 2 involves calculating the six-dimensional acceleration of the support end using measurements from multiple three-dimensional acceleration sensors installed on the support mechanism. The process is as follows: Accelerometer installation 7 → Accelerometer measurement of motion acceleration at sensor measurement points 8 → Six-dimensional acceleration calculation at the support end 9.

[0054] Accelerometer sensor installation arrangement 7: Install q three-dimensional linear accelerometers on the support mechanism at the rigid connection point with the multi-dimensional force sensor, where q ≥ 3 and the accelerometers are not collinear, with the distance between each accelerometer as large as possible. When there are no suitable mounting points on the support mechanism, an accelerometer mounting plate with stiffness much greater than the stiffness of each sensitive element of the multi-dimensional force sensor can be installed between the force sensor support end and the support mechanism. Taking three three-dimensional linear accelerometers as an example, their installation arrangement on the accelerometer mounting plate is as follows. Figure 4 As shown.

[0055] Accelerometer measurement of motion acceleration at the measurement point: 8. When the support mechanism has no motion acceleration, the static bias of q three-dimensional linear accelerometers is eliminated by software offset removal. The measured value of the accelerometer is then the three-dimensional motion acceleration at the measurement point; the measured value of the three-dimensional linear accelerometer is denoted as a'. i =[a' ix ,a' iy ,a'iz ] T ,i=1,2,…,q.

[0056] Six-dimensional acceleration calculation at the support end (9): Based on the coordinate system orientation and measured values ​​of q three-dimensional linear accelerometers, calculate the six-dimensional motion acceleration of the origin of the support mechanism's coordinate system relative to the inertial coordinate system {W} within the support mechanism's coordinate system {S}. First, based on the coordinate axis relationship between the coordinate systems of the q accelerometers installed on the support mechanism and the support mechanism's coordinate system {S}, calculate the measured values ​​a' of the q three-dimensional linear accelerometers. i Transform them respectively to the coordinate axes of the support mechanism coordinate system {S}:

[0057]

[0058] In the above formula, a i =[a ix ,a iy ,a iz ] T R represents the three-dimensional linear acceleration at the i-th measurement point after rotation in the coordinate system; the rotation matrix R i In this context, "s" and "c" represent the simplified expressions for the sine and cosine functions, respectively, and α... i β i and γ i The coordinate system rotation angle, i.e., the support mechanism coordinate system {S} can be rotated by α around the x-axis from the measurement coordinate system of the three-dimensional accelerometer at the i-th measurement point. i Angle, then rotate β around the y-axis i Angle, and finally rotate γ around the z-axis. i The angle is obtained.

[0059] Then, based on the position vector of the i-th measurement point in the support mechanism coordinate system {S} Get a i Six-dimensional acceleration at the support end Relationship:

[0060]

[0061] in, For q a i The result of concatenating lines; Let be the six-dimensional acceleration at the support end to be calculated. The six-dimensional acceleration at the support end can be calculated using the least squares method according to the above formula:

[0062]

[0063] The calculation methods for the six-dimensional acceleration at the support end in the aforementioned support end acceleration measurement design 2 include, but are not limited to, using multiple three-dimensional linear accelerometers, multiple single-dimensional linear accelerometers, a combination of linear accelerometers and gyroscopes, or a single six-dimensional accelerometer.

[0064] The calibration of the support end inertial compensation parameter 3 involves obtaining the transformation matrix from the six-dimensional acceleration of the support end to the six-dimensional acceleration of the multi-dimensional force sensor measurement coordinate system {B} based on the positional relationship between the support mechanism coordinate system {S} and the multi-dimensional force sensor measurement coordinate system {B}. The inertia coefficient matrix M of the end load in the multidimensional force sensor measurement coordinate system {B} was calibrated through a dynamic excitation experiment under dynamic support conditions. f The process is as follows: dynamic excitation experiment under dynamic support 10 → acquisition of six-dimensional acceleration of coordinate system by multi-dimensional force sensor 11 → calibration of inertial compensation coefficient matrix 12.

[0065] Dynamic excitation experiment 10 under dynamic support: Install the same workpiece or loading head as in the multidimensional force sensor dynamic calibration experiment 5 at the end of the force sensor; install the force sensor support end on the movable support; install q three-dimensional linear accelerometers according to the arrangement scheme in the accelerometer installation arrangement 7; install the movable support on the rigid calibration platform, such as... Figure 4 As shown, p groups (p≥n) of excitations in different directions are applied to the workpiece or loading head at the end of the force sensor using negative step excitation or impact excitation, resulting in measurement signals for the multidimensional force sensor used to calibrate the calibration parameters. and the measurement signals of q three-dimensional linear accelerometers Where j = 1, 2, ..., p; negative step excitation refers to first applying a stable force or torque load to the multidimensional force sensor, and then suddenly unloading and removing the applied load from the multidimensional force sensor, making the load on the multidimensional force sensor zero, thereby realizing negative step excitation of the multidimensional force sensor; then the measurement signal of the multidimensional force sensor after negative step unloading or impact excitation. It only includes dynamic error.

[0066] Multi-dimensional force sensor measurement coordinate system six-dimensional acceleration acquisition 11: First, according to the design method in the support end acceleration measurement design 2, the dynamic excitation experiment 10 under the dynamic support condition p group excitation is obtained. Transformed into six-dimensional acceleration at the support end Then, because the inertial force component caused by the movement or vibration of the support end is the inertial property of the workpiece or loading head at the sensor end in the multi-dimensional force sensor measurement coordinate system {B} caused by the six-dimensional acceleration of the support end, it is necessary to transfer the six-dimensional acceleration of the support end to the force sensor measurement coordinate system {B}; therefore, according to Position vector of the multi-dimensional force sensor in the coordinate system {S} of the support mechanism The six-dimensional acceleration in the multi-dimensional force sensor measurement coordinate system {B} caused by the vibration of the support end is obtained from the following formula.

[0067]

[0068] Inertial compensation coefficient matrix calibration 12: Based on the output data of the multi-dimensional force sensor and q three-dimensional linear accelerometers obtained from the dynamic excitation experiment 10 under the dynamic support condition, the inertial compensation coefficient matrix is ​​calibrated using the time-domain least squares method based on truncation and splicing. The process is as follows: effective calibration data truncation and splicing → inertial compensation coefficient matrix estimation.

[0069] ① Effective calibration data capture and stitching: Using the dynamic decoupling-compensator design in section 6, the dynamic decoupling-compensator was used to measure the p groups of multidimensional force measurement signals in different directions obtained from the dynamic excitation experiment 10 under dynamic support conditions. Perform dynamic error correction on the sensor's own characteristics separately to obtain Then, from respectively and After the signal crosses zero following a negative step unloading or impact excitation, data of equal length for the same complete oscillation period are extracted, denoted as follows: and but This refers to the six-dimensional inertial force components remaining after a negative step unloading or impact excitation; the p groups of truncated six-dimensional inertial forces... and six-dimensional acceleration The inertial force component F in the valid calibration data is obtained by concatenating the data column by column. I cal and acceleration components

[0070] The inertial force component F in the valid calibration data I cal for:

[0071] Each element in the matrix express Inertial force / torque data in the o-th dimension. express The inertial force / torque value at the kth sampling point.

[0072] The acceleration component in the valid calibration data for:

[0073] Each element in the matrix express Linear / angular acceleration data in the o-th dimension of multidimensional acceleration. express The linear / angular acceleration value at the kth sampling point.

[0074] ② Estimation of inertial compensation coefficient matrix: based on the relationship between inertial force and acceleration. The inertia compensation coefficient matrix is ​​estimated using the least squares method:

[0075]

[0076] The multidimensional force sensor combined dynamic error correction 4, that is, in actual multidimensional force measurement, based on the dynamic decoupling-compensator designed in the multidimensional force sensor's own characteristics dynamic decoupling-compensator design 1, performs dynamic correction on the multidimensional force sensor measurement signal based on the sensor's own characteristics, and then based on the motion acceleration a' measured by q acceleration sensors. i The method for calculating the six-dimensional acceleration at the support end in the support end acceleration measurement design 2, and the support end inertia compensation coefficient obtained in the support end inertia compensation parameter calibration 3, are used to perform support end inertia compensation on the signal after dynamic correction of the sensor's own characteristics; thereby improving the measurement accuracy and dynamic response speed of the multi-dimensional force sensor. The steps of the combined dynamic error correction are as follows:

[0077] Step ①: For multidimensional force measurement under actual working conditions, install q three-dimensional accelerometers on the actual movable support according to the arrangement scheme in the accelerometer installation arrangement 7; record the multidimensional force sensor output signal collected in the actual measurement as F, and the measurement signal of the q three-dimensional accelerometers as a'. i ,i=1,2,…,q.

[0078] Step ②: Based on the dynamic decoupling-compensator designed in the design 1 of the multidimensional force sensor's own characteristics, the multidimensional force sensor's measurement signal F is dynamically corrected according to the sensor's own characteristics, thereby obtaining the signal F after dynamic correction of the multidimensional force sensor's own characteristics. c .

[0079] Step ③: Based on q three-dimensional acceleration signals a' i The coordinate system rotation matrix R in the support end acceleration measurement design 2 i and the six-dimensional acceleration solution matrix at the support end The six-dimensional acceleration at the support end in actual measurement is obtained by solving the following formula:

[0080]

[0081] Step 4: Based on the six-dimensional acceleration coordinate transformation matrix in Calibration 3 using the support end inertial compensation parameters. and inertia compensation coefficient matrix M fThe inertial force component F, which is caused by the vibration or motion of the support mechanism to the measurement signal of the multi-dimensional force sensor, is calculated using the following formula. I :

[0082]

[0083] Step 5: Dynamically correct the signal F based on the characteristics of the multidimensional force sensor obtained in Step 2. c and the inertial force component F obtained in step ④ I The final result of the combined dynamic error correction can be obtained using the following formula:

[0084] F ci =F c -F I

[0085] The method of this invention is used to perform combined dynamic error correction on the step response of a certain six-dimensional force sensor under elastic support, and the effect is as follows: Figure 5 , 6 As shown. Figure 5 This shows the calibration effect of the main channel of the multi-dimensional force sensor under loading in different directions; the left image is the time-domain effect before and after calibration, the middle image is a magnified view near the step jump point in the left image, and the right image is the frequency-domain effect near the resonant frequency points of each main channel before and after calibration; Figure 5 It can be seen that the combined dynamic error correction method greatly reduces the dynamic error of the main channel and significantly improves the dynamic characteristics of each main channel of the six-dimensional sensor. Figure 6 The figure shows the time-domain correction effect of each channel under the -Fx-My direction loading; it can be seen from the figure that the method of the present invention also achieves a good suppression effect on the dynamic error of the coupled channel.

Claims

1. A combined dynamic error correction method for a multi-dimensional force sensor under dynamic support conditions, which employs a combined dynamic error correction method by first performing dynamic error correction on the sensor's own characteristics and then performing inertial compensation on the support end, in order to reduce the dynamic measurement error of the multi-dimensional force sensor and thus improve the dynamic measurement performance under dynamic support conditions; the technical process includes: The design of the multi-dimensional force sensor's inherent characteristics, including dynamic decoupling and compensator design, support-end acceleration measurement design, support-end inertial compensation parameter calibration, and multi-dimensional force sensor combined dynamic error correction, is characterized by: First, a dynamic decoupling-compensator for dynamic correction of the multidimensional force sensor's own characteristics is obtained through dynamic calibration experiments under fixed support conditions. Second, a six-dimensional acceleration calculation model for the support end is obtained by designing a measurement scheme for the six-dimensional acceleration at the support end. Then, a dynamic excitation experiment is conducted under dynamic support conditions based on the aforementioned calculation model to obtain the six-dimensional acceleration transformation matrix and inertial compensation coefficient matrix in the multidimensional force sensor measurement coordinate system. Finally, in the actual multidimensional force measurement under dynamic support conditions, the dynamic error correction of the force sensor measurement signal is first performed based on the dynamic decoupling-compensator for the force sensor's own characteristics, thereby correcting the dynamic error caused by the multidimensional force sensor's own structural characteristics in the measurement signal. Then, based on the calculated six-dimensional acceleration at the support end, the six-dimensional acceleration transformation matrix in the multidimensional force sensor measurement coordinate system, and the inertial compensation coefficient matrix, the inertial compensation is performed on the signal after dynamic error correction of the sensor's own characteristics to further compensate for the inertial error caused by the motion or vibration of the support mechanism, thereby obtaining the final combined dynamic error correction result.

2. The combined dynamic error correction method for multi-dimensional force sensors under dynamic support conditions as described in claim 1, characterized in that: The design of a dynamic decoupling-compensator for the inherent characteristics of a multidimensional force sensor involves designing a dynamic calibration experiment for the multidimensional force sensor in a calibration environment to obtain the input and output data of the multidimensional force sensor under different directional excitations; based on this, a dynamic decoupling-compensator is designed to achieve dynamic error correction of the inherent characteristics of the multidimensional force sensor; the process is as follows: dynamic calibration experiment of multidimensional force sensor → design of dynamic decoupling-compensator. Dynamic calibration experiment of multidimensional force sensor: The multidimensional force sensor, together with the actual sensor end workpiece or the loading head simulating the actual workpiece, is mounted on a fixed calibration platform with stiffness much greater than that of each sensitive element of the multidimensional force sensor. Apply m sets of impact excitations or step excitations in different directions to the workpiece or loading head at the end of the sensor to obtain m sets of excitation inputs and corresponding outputs, where m ≥ n, and n is the dimension of the multidimensional force sensor; Dynamic decoupling-compensator design: This involves designing a dynamic decoupling-compensator based on the input and output data obtained from the dynamic calibration experiment of a multidimensional force sensor, using existing time-domain or frequency-domain decoupling-compensation methods.

3. The combined dynamic error correction method for multi-dimensional force sensors under dynamic support conditions as described in claim 1, characterized in that: The design of the support end acceleration measurement involves calculating the six-dimensional acceleration of the support end by measuring the values ​​of multiple three-dimensional acceleration sensors installed on the support mechanism. The process is as follows: installation and arrangement of acceleration sensors → measurement of the motion acceleration of the acceleration sensor measurement points → calculation of the six-dimensional acceleration of the support end. Accelerometer sensor installation and arrangement: Install q three-dimensional linear accelerometers on the support mechanism at the rigid connection point with the multi-dimensional force sensor, where q ≥ 3 and the accelerometers are not collinear, and the distance between each accelerometer is as large as possible; Accelerometer measurement of motion acceleration at the measurement point: When there is no motion acceleration in the support mechanism, the static bias of q three-dimensional linear accelerometers is eliminated by software offsetting. The measured value of the accelerometer is then the three-dimensional motion acceleration at the measurement point. The measured value of the three-dimensional linear accelerometer is denoted as a. i '=[a i ' x ,a i ' y ,a i ' z ] T i = 1, 2, ..., q; Six-dimensional acceleration calculation at the support end: This involves calculating the six-dimensional motion acceleration of the origin of the support mechanism's coordinate system within the support mechanism's coordinate system based on the coordinate system orientation and measured values ​​of q three-dimensional linear accelerometers. First, based on the coordinate axis orientation relationship between the coordinate systems of the q accelerometers installed on the support mechanism and the support mechanism's coordinate system, the measured values ​​a from the q three-dimensional linear accelerometers are... i 'Transform to the coordinate axes of the support mechanism coordinate system respectively:' In the above formula, a i =[a ix ,a iy ,a iz ] T R represents the three-dimensional linear acceleration at the i-th measurement point after rotation in the coordinate system; the rotation matrix R i In the text, "s" and "c" represent the simplified expressions for the sine and cosine functions, respectively, and α... i β i and γ i The coordinate system rotation angle is α, meaning the coordinate system of the support mechanism can be rotated by the coordinate system of the three-dimensional accelerometer at the i-th measurement point around the x-axis. i Angle, then rotate β around the y-axis i Angle, and finally rotate γ around the z-axis. i The angle is obtained; Then, based on the position vector of the i-th measurement point in the coordinate system of the support mechanism... Get a i Six-dimensional acceleration at the support end Relationship: in, For q a i The result of concatenating lines; The six-dimensional acceleration at the support end is to be calculated; the six-dimensional acceleration at the support end can be calculated using the least squares method according to the above formula:

4. The combined dynamic error correction method for multi-dimensional force sensors under dynamic support conditions as described in claim 1, characterized in that: The calibration of the inertial compensation parameters at the support end involves obtaining the transformation matrix from the six-dimensional acceleration at the support end to the six-dimensional acceleration in the multi-dimensional force sensor measurement coordinate system, based on the positional relationship between the support mechanism coordinate system and the multi-dimensional force sensor measurement coordinate system. The inertia coefficient matrix M of the end load in the multidimensional force sensor measurement coordinate system was calibrated through a dynamic excitation experiment under dynamic support conditions. f The process is as follows: dynamic excitation experiment under dynamic support conditions → six-dimensional acceleration acquisition of the coordinate system by multi-dimensional force sensor measurement → inertial compensation coefficient matrix calibration; Dynamic excitation experiment under dynamic support: Install the same workpiece as in the dynamic calibration experiment of the multidimensional force sensor at the end of the force sensor; install the support end of the force sensor on the movable support; install q three-dimensional linear accelerometers according to the arrangement scheme in the accelerometer installation layout; install the movable support on the rigid calibration platform; By applying p groups of excitations in different directions (p ≥ n) to the workpiece or loading head at the end of the force sensor using negative step excitation or impact excitation, the measurement signals of the multidimensional force sensor used for calibration parameters are obtained. and the measurement signals of q three-dimensional linear accelerometers Where j = 1, 2, ..., p; negative step excitation refers to first applying a stable force or torque load to the multidimensional force sensor, and then suddenly unloading and removing the applied load from the multidimensional force sensor, making the load on the multidimensional force sensor zero, thereby realizing negative step excitation of the multidimensional force sensor; then the measurement signal of the multidimensional force sensor after negative step unloading or impact excitation. It only contains dynamic error; The six-dimensional acceleration of the multi-dimensional force sensor measurement coordinate system is obtained as follows: First, according to the design method in the acceleration measurement design at the support end, the dynamic excitation experiment under the dynamic support condition is performed using p groups of excitation. Transformed into six-dimensional acceleration at the support end Then, because the inertial force component caused by the movement or vibration of the support end is the inertial property of the workpiece or loading head at the sensor end in the multi-dimensional force sensor measurement coordinate system caused by the six-dimensional acceleration of the support end, it is necessary to transfer the six-dimensional acceleration of the support end to the force sensor measurement coordinate system; therefore, according to Position vector of the multi-dimensional force sensor in the coordinate system of the support mechanism The following formula yields the six-dimensional acceleration in the multi-dimensional force sensor measurement coordinate system caused by the vibration of the support end. Inertial compensation coefficient matrix calibration: Based on the output data of the multi-dimensional force sensor and q three-dimensional linear accelerometers obtained from the dynamic excitation experiment under the dynamic support condition, the inertial compensation coefficient matrix is ​​calibrated using the time-domain least squares method based on truncation and splicing. The process is as follows: effective calibration data extraction and stitching → inertial compensation coefficient matrix estimation; ① Effective calibration data capture and stitching: Using the dynamic decoupling-compensator in the design of the dynamic decoupling-compensator, p groups of multidimensional force measurement signals in different directions were obtained from the dynamic excitation experiment under dynamic support conditions. Perform dynamic error correction on the sensor's own characteristics separately to obtain Then, from respectively and After the signal crosses zero following a negative step unloading or impact excitation, data of equal length for the same complete oscillation period are extracted, denoted as follows: and but This refers to the six-dimensional inertial force components remaining after a negative step unloading or impact excitation; the p groups of truncated six-dimensional inertial forces... and six-dimensional acceleration The inertial force component F in the valid calibration data is obtained by concatenating the data column by column. I cal and acceleration components The inertial force component F in the valid calibration data I cal for: Each element in the matrix express Inertial force / torque data in the o-th dimension. express The inertial force / torque value at the k-th sampling point; The acceleration component in the valid calibration data for: Each element in the matrix express Linear / angular acceleration data in the o-th dimension of multidimensional acceleration. express The linear / angular acceleration value at the k-th sampling point; ② Estimation of inertial compensation coefficient matrix: based on the relationship between inertial force and acceleration. The inertia compensation coefficient matrix is ​​estimated using the least squares method:

5. The combined dynamic error correction method for multi-dimensional force sensors under dynamic support conditions as described in claim 1, characterized in that: Multidimensional force sensor combined dynamic error correction, that is, in actual multidimensional force measurement, based on the characteristics of the multidimensional force sensor itself, the dynamic decoupling-compensator designed in the dynamic decoupling-compensator design performs dynamic correction on the multidimensional force sensor measurement signal according to the sensor's own characteristics, and then based on the motion acceleration a measured by q acceleration sensors. i The method for calculating the six-dimensional acceleration at the support end in the aforementioned support end acceleration measurement design, and the support end inertial compensation coefficient obtained in the calibration of the support end inertial compensation parameters, are used to perform support end inertial compensation on the signal after dynamic correction of the sensor's own characteristics; thereby improving the measurement accuracy and dynamic response speed of the multi-dimensional force sensor; the steps of the combined dynamic error correction are as follows: Step ①: For multidimensional force measurement under actual working conditions, install q three-dimensional accelerometers on the actual movable support according to the arrangement scheme in the accelerometer installation layout; record the multidimensional force sensor output signal collected in the actual measurement as F, and the measurement signal of the q three-dimensional accelerometers as a. i ', i = 1, 2, ..., q; Step ②: Based on the dynamic decoupling-compensator designed in the design of the multidimensional force sensor's own characteristics, the multidimensional force sensor's measurement signal F is dynamically corrected according to the sensor's own characteristics, thereby obtaining the dynamically corrected signal F of the multidimensional force sensor. c ; Step ③: Based on q three-dimensional acceleration signals a i The coordinate system rotation matrix R in the design of the support end acceleration measurement i and the six-dimensional acceleration solution matrix at the support end The six-dimensional acceleration at the support end in actual measurement is obtained by solving the following formula: Step 4: Based on the six-dimensional acceleration coordinate transformation matrix in the calibration of the support end inertial compensation parameters. and inertia compensation coefficient matrix M f The inertial force component F, which is caused by the vibration or motion of the support mechanism to the measurement signal of the multi-dimensional force sensor, is calculated using the following formula. I : Step 5: Dynamically correct the signal F based on the characteristics of the multidimensional force sensor obtained in Step 2. c The inertial force component F obtained in step ④ I Using F ci =F c -F I The final result of the combined dynamic error correction can then be obtained.

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