Dynamic simulation damping parameter solving method based on gravity compensation mechanism

Abstract

The invention relates to the technical field of industrial robots, in particular to a dynamic simulation damping parameter solving method based on a gravity compensation mechanism, which comprises the following steps of: acquiring a joint basic parameter set of a to-be-tested industrial robot, and determining a test boundary condition according to the joint basic parameter set, and constructing a test task sequence based on the test boundary conditions. According to the method, the fusion weight of the static stiffness and the dynamic stiffness is intelligently adjusted according to the characteristics of the movement speed, the acceleration or the force control frequency band in a specific application task, and the limitation of a single parameter under complex and changeable working conditions is avoided. According to the parameter fusion mechanism aiming at the specific task characteristics, the generated joint comprehensive rigidity parameters can truly reflect the physical response of the robot in different operation stages, and the prediction error between the physical simulation environment and the actual physical operation is reduced; and the strict requirements of high-precision scenes such as semiconductor packaging and the like on micron-level positioning precision and force control stability are met.

Description

Technical Field

[0001] This invention relates to the field of industrial robot technology, and in particular to a method for solving damping parameters in dynamic simulation based on a gravity compensation mechanism. Background Technology

[0002] As industrial robots develop towards "precision and force control" (such as the ±0.1mm positioning accuracy required for semiconductor packaging), high-precision physical simulation has become a core support. By simulating and verifying trajectory accuracy and force control stability, actual debugging costs and risks can be reduced. Joint stiffness is a key parameter that determines the accuracy of simulation.

[0003] Current technologies for obtaining robot joint stiffness parameters generally rely on theoretical design parameters provided by manufacturers or experimental values ​​obtained through general static testing platforms. Manufacturer-provided theoretical values ​​are typically based on average design standards for batch products, neglecting the individual characteristics of individual robots due to manufacturing tolerances, assembly clearance differences, and wear and aging caused by long-term operation. This leads to inherent deviations between the physical properties of simulation models and actual physical objects. Furthermore, traditional testing methods overemphasize static loading tests under steady-state conditions, only characterizing the linear deformation resistance of joints at rest or extremely low speeds, failing to capture the nonlinear dynamic characteristics and frequency domain response differences exhibited by robot joints during high-speed dynamic operation or high-frequency force-controlled tasks. Therefore, improvements are needed. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a method for solving damping parameters in dynamic simulation based on a gravity compensation mechanism.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for solving damping parameters in dynamic simulation based on a gravity compensation mechanism, comprising the following steps: Obtain the set of basic joint parameters of the industrial robot under test, determine the test boundary conditions based on the set of basic joint parameters, and construct a test task sequence based on the test boundary conditions; Zero-load posture calibration is performed on the industrial robot under test, the end-effector posture change data is monitored, and the zero-load deformation reference position is determined based on the end-effector posture change data. Based on the zero-load deformation reference position, a graded static load is applied to the industrial robot under test, and a static response data sequence under the graded static load is collected. The static response data sequence is then processed using the weighted least squares method to obtain the joint static stiffness coefficient. A dynamic frequency domain excitation is applied to the industrial robot under test, and the dynamic time domain response signal of the industrial robot under test under the dynamic frequency domain excitation is collected. The joint dynamic stiffness characteristics corresponding to the dynamic time domain response signal are extracted by cross power spectral density analysis. Obtain the task feature parameters of the target simulation scene, construct an adaptive weighted fusion model based on the task feature parameters, and use the adaptive weighted fusion model to fuse the static stiffness coefficient and dynamic stiffness characteristics of the joint to obtain the comprehensive stiffness parameters of the joint for physical simulation.

[0006] Preferably, the steps of performing zero-load posture calibration on the industrial robot under test, monitoring end-effector pose change data, and determining the zero-load deformation reference position based on the end-effector pose change data include: Control the industrial robot under test to move to the preset initial test posture and lock the joint brakes of non-test axes; A preset standard micro-test load is applied to the end effector of the industrial robot under test in the initial test posture, and the end effector pose change data is collected in real time using a displacement sensor. Calculate the displacement deviation in the end-effector pose change data and compare the displacement deviation with a preset rigid body deformation threshold. If the displacement deviation is greater than the preset rigid body deformation threshold, the joint angle of the industrial robot under test is adjusted, and the steps of applying the standard micro-test load and collecting the end pose change data are repeated until the displacement deviation is less than or equal to the preset rigid body deformation threshold. The joint angle at which the displacement deviation is less than or equal to the preset rigid body deformation threshold is determined as the zero-load deformation reference position, and the joint state at this time is recorded as the anti-coupling interference reference state.

[0007] Preferably, the step of applying graded static loads to the industrial robot under test based on the zero-load deformation reference position and collecting static response data sequences under the graded static loads includes: Based on the rated load parameters in the set of basic joint parameters, set the graded loading step size and the maximum loading threshold. Starting from the zero-load deformation reference position, the control torque loading device gradually increases the load torque according to the graded loading step size until the maximum loading threshold is reached; During the loading and holding phase of each load torque level, the joint input torque data and joint output angle data are recorded synchronously using a data acquisition card. Monitor the time-domain fluctuation variance of the joint output angle data. When the time-domain fluctuation variance is less than the preset steady-state judgment index, extract the steady-state torque value and steady-state angle value at the current moment. Iterate through all loading levels to generate the static response data sequence containing multiple sets of the steady-state torque values ​​and the steady-state angle values.

[0008] Preferably, the step of processing the static response data sequence using the weighted least squares method to obtain the joint static stiffness coefficients relies on a static stiffness calculation formula that includes stability weights. The static stiffness calculation formula is as follows: , in, This represents the static stiffness coefficient of the joint. This represents the total number of data sampling points in the static response data sequence. This represents the index of the current data sampling point. Indicates the first The steady-state torque value at each sampling point This represents the average of all the aforementioned steady-state torque values. Indicates the first The steady-state angle value at each sampling point, This represents the average of all the aforementioned steady-state angle values. Indicates the first Confidence weighting coefficients for each sampling point; The formula for calculating the confidence weight coefficient is as follows: ,in Represented by natural constant An exponential function with base 0. Indicates the first The residual values ​​of each sampling point relative to the straight line obtained by linear regression fitting of the static response data sequence based on ordinary least squares method. This represents the inherent noise variance of the measurement sensor.

[0009] Preferably, the steps of applying dynamic frequency domain excitation to the industrial robot under test, acquiring the dynamic time domain response signal of the industrial robot under test under the dynamic frequency domain excitation, and extracting the joint dynamic stiffness characteristics corresponding to the dynamic time domain response signal through cross power spectral density analysis include: A sinusoidal sweep frequency signal covering a frequency range of 0.1Hz to 5Hz is generated, and the sinusoidal sweep frequency signal is input as a torque command to the servo controller of the industrial robot under test. Set the signal sampling frequency to at least 10 times the highest frequency of the excitation signal, and synchronously acquire the dynamic time-domain response signal containing the dynamic torque time-domain sequence and the dynamic angle time-domain sequence; The Hanning window function is used to window and truncate the dynamic torque time-domain sequence and the dynamic angle time-domain sequence to suppress spectral leakage. Based on the windowed dynamic torque time-domain sequence and the dynamic angle time-domain sequence, the cross power spectral density function and the self power spectral density function are calculated. The frequency response function is calculated based on the cross power spectral density function and the self power spectral density function, and the joint dynamic stiffness characteristics corresponding to different frequency points are extracted from the frequency response function.

[0010] Preferably, the step of extracting the joint dynamic stiffness characteristics corresponding to the dynamic time-domain response signal through cross-power spectral density analysis relies on the dynamic stiffness frequency domain calculation formula, which is: , in, Indicates at a specific frequency The joint dynamic stiffness characteristics described below, This represents the operation of taking the real part of a complex number. This represents the cross-power spectral density between the dynamic torque time-domain sequence and the dynamic angle time-domain sequence. This represents the auto-power spectral density of the dynamic angle time-domain sequence. This represents the dynamic hardening correction factor, used to compensate for nonlinear hardening effects at high frequencies. Represents the logarithmic function with base 10. This represents the system's inherent frequency reference value, used to normalize frequency variables.

[0011] Preferably, the steps of obtaining task feature parameters of the target simulation scene, constructing an adaptive weighted fusion model based on the task feature parameters, and using the adaptive weighted fusion model to fuse the joint static stiffness coefficient and the joint dynamic stiffness characteristics include: Analyze the robot motion trajectory file in the target simulation scene and extract the velocity vector set and acceleration vector set of the trajectory points; Calculate the root mean square velocity value of the velocity vector set, and perform spectral analysis on the velocity vector set to identify the dominant frequency component. Use the root mean square velocity value and the dominant frequency component together as the task feature parameter. An adaptive weight allocation strategy based on the Sigmoid function is constructed, and dynamic weight coefficients are calculated based on the root mean square velocity value in the task feature parameters. The joint's static stiffness coefficient and dynamic stiffness characteristics are linearly interpolated using the dynamic weighting coefficient to generate the joint's comprehensive stiffness parameters; The adaptive weighted fusion model is specifically as follows: , in, This represents the overall stiffness parameter of the joint. This represents the dynamic weighting coefficient. This represents the dominant frequency component; The dynamic weighting coefficient The calculation formula is: , in, This represents the root mean square velocity value. This represents the critical speed threshold that distinguishes between static and dynamic scenes. This represents the sensitivity coefficient for weight switching.

[0012] Preferably, before obtaining the set of basic joint parameters of the industrial robot under test, a sensor calibration and adjustment step is also included: An external torque sensor and an external displacement sensor used for data acquisition are connected in series to a standard measuring device to obtain a standard reading sequence; Calculate the linear deviation rate between the measured value of the external torque sensor and the standard reading sequence; If the linear deviation rate exceeds the preset accuracy tolerance range, a calibration compensation matrix is ​​generated, and the internal parameters of the external torque sensor are updated using the calibration compensation matrix. Check the timestamp synchronization protocol of the external torque sensor and the external displacement sensor to ensure that the clock synchronization error when acquiring the static response data sequence and the dynamic time domain response signal is less than a preset microsecond threshold.

[0013] Preferably, after obtaining the joint composite stiffness parameters for physical simulation, the process also includes parameter verification and optimization steps: The joint composite stiffness parameters are imported into the physics simulation engine to construct a virtual robot model; The loading conditions corresponding to the static response data sequence are reproduced in the physical simulation engine, and the simulated deformation is output. Calculate the relative error rate between the simulated deformation and the actual measured deformation; If the relative error rate is greater than the preset simulation accuracy standard, the model parameters in the adaptive weighted fusion model are corrected, and the parameter fusion step is re-executed until the relative error rate meets the preset simulation accuracy standard.

[0014] Preferably, the set of basic joint parameters includes a joint type identifier, a rated torque parameter, a reduction ratio parameter, and a motor inertia parameter, wherein the joint type identifier is used to distinguish between rotary joints and linear joints; When the joint type identifier indicates a rotary joint, the unit of the joint static stiffness coefficient is configured to be Newton-meter per degree. When the joint type identifier indicates a linear joint, the unit of the joint static stiffness coefficient is configured to be Newtons per millimeter; The step of constructing the test task sequence also includes automatically matching the corresponding load loading direction and displacement measurement dimension according to the joint type identifier to ensure that the test coordinate system is consistent with the direction of joint motion degrees of freedom.

[0015] Compared with the prior art, the advantages and positive effects of the present invention are as follows: This invention establishes rigorous constraints for subsequent data acquisition by acquiring the basic joint parameters of the industrial robot under test and constructing a task sequence with clear test boundaries. Zero-load attitude calibration and real-time monitoring of end-effector pose changes lock the zero-load deformation reference position, eliminating initial coupling interference caused by uneven weight distribution and accumulated assembly tolerances, thus establishing a measurement reference that closely matches the actual physical state. Based on this reference, a graded static load is applied and the response data sequence is acquired. Weighted least squares is used for processing, and a weighting mechanism is introduced to reduce the influence of random measurement noise and outlier data points, improving the fitting accuracy and robustness of the static stiffness coefficient. Dynamic frequency domain excitation is applied and time-domain response signals are acquired. Cross-power spectral density analysis is used to extract dynamic stiffness characteristics. This logic utilizes the correlation between signals to suppress incoherent noise introduced by environmental vibration or motor control ripple, ensuring the purity and completeness of the dynamic frequency domain feature extraction. Further, task feature parameters of the target simulation scene are obtained to construct an adaptive weighted fusion model. Based on the motion velocity, acceleration, or force control frequency band characteristics in the specific application task, the fusion weights of static and dynamic stiffness are intelligently adjusted to avoid the limitations of a single parameter under complex and variable working conditions. This parameter fusion mechanism, tailored to specific task characteristics, enables the generated joint comprehensive stiffness parameters to realistically reflect the robot's physical response at different operation stages, reducing the prediction error between the physical simulation environment and actual physical operation, and meeting the stringent requirements of micron-level positioning accuracy and force control stability in high-precision scenarios such as semiconductor packaging. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the steps of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0018] Please see Figure 1 This invention provides a technical solution: a method for solving damping parameters in dynamic simulation based on a gravity compensation mechanism, comprising the following steps: Obtain the set of basic joint parameters of the industrial robot under test, determine the test boundary conditions based on the set of basic joint parameters, and construct a test task sequence based on the test boundary conditions; Perform zero-load attitude calibration on the industrial robot under test, monitor the end-effector pose change data, and determine the zero-load deformation reference position based on the end-effector pose change data; Based on the zero-load deformation reference position, a graded static load is applied to the industrial robot under test. Static response data sequence under graded static load is collected. The static response data sequence is processed by weighted least squares method to obtain the joint static stiffness coefficient. A dynamic frequency domain excitation is applied to the industrial robot under test, and the dynamic time domain response signal of the industrial robot under test under the dynamic frequency domain excitation is collected. The joint dynamic stiffness characteristics corresponding to the dynamic time domain response signal are extracted by cross power spectral density analysis. Obtain the task feature parameters of the target simulation scene, construct an adaptive weighted fusion model based on the task feature parameters, and use the adaptive weighted fusion model to fuse the static stiffness coefficient and dynamic stiffness characteristics of the joint to obtain the comprehensive stiffness parameters of the joint for physical simulation.

[0019] In this embodiment, the steps of performing zero-load posture calibration on the industrial robot under test, monitoring end-effector posture change data, and determining the zero-load deformation reference position based on the end-effector posture change data include: controlling the industrial robot under test to move to a preset initial test posture and locking the joint brakes of non-test axes; applying a preset standard micro-test load to the end of the industrial robot under test in the initial test posture; collecting end-effector posture change data in real time using a displacement sensor; calculating the displacement deviation in the end-effector posture change data; comparing the displacement deviation with a preset rigid body deformation threshold; if the displacement deviation is greater than the preset rigid body deformation threshold, adjusting the joint angle of the industrial robot under test; and repeating the steps of applying the standard micro-test load and collecting end-effector posture change data until the displacement deviation is less than or equal to the preset rigid body deformation threshold. The joint angle when the displacement deviation is less than or equal to the preset rigid body deformation threshold is determined as the zero-load deformation reference position, and the joint state at this time is recorded as the anti-coupling interference reference state.

[0020] Specifically, the robot under test is controlled to move to a preset initial test posture. This initial posture, based on the robot's kinematic model, is set so that each joint is in a mechanical zero position or a horizontally extended state conducive to force application. By sending a low-level servo lock command to the robot controller, the brakes of non-test axes are energized or de-energized to achieve mechanical locking, preventing coupling motion interference from non-test joints during the test. While maintaining a stable initial test posture, a preset standard micro-test load is applied to the end effector of the robot under test using a force-controlled end effector. The standard micro-test load is set between 1% and 2% of the joint's rated load; for example, 0.5 Nm to 1 Nm for a joint with a rated load of 50 Nm, ensuring that the resulting deformation is only in the initial stage of elastic deformation and does not enter the plastic deformation zone. High-precision displacement measurement equipment such as laser displacement sensors or grating rulers are used to collect end-effector pose change data in real time at a sampling frequency of no less than 1000 Hz. The end-effector pose change data is then calculated in three-dimensional space. The displacement deviation is obtained by measuring the Euclidean distance between the points. This displacement deviation is then compared with a preset rigid body deformation threshold, which is calculated based on the robot's link material properties and structural stiffness matrix. This threshold is typically set between 0.001 mm and 0.005 mm. If the real-time monitored displacement deviation is greater than the preset rigid body deformation threshold, it indicates nonlinear loosening caused by gravitational torque or assembly gaps in the current posture. The joint angles of the industrial robot under test are adjusted in 0.01-degree increments using fine-tuning commands. After each adjustment, the load application and data collection actions are re-executed, entering a closed-loop feedback adjustment process. This continues until the monitored displacement deviation converges to less than or equal to the preset rigid body deformation threshold. At this point, the joint is considered to be in a tight contact state where the internal gaps of the mechanism are completely eliminated and the forces are balanced. The joint angle values ​​at this moment are locked, and the joint angles that satisfy the condition that the displacement deviation is less than or equal to the preset rigid body deformation threshold are determined as the zero-load deformation reference position. The joint state at this point is recorded as the anti-coupling interference reference state.

[0021] In this embodiment, the steps of loading graded static loads onto the industrial robot under test based on the zero-load deformation reference position and collecting static response data sequences under graded static loads include: setting graded loading step size and maximum loading threshold according to the rated load parameters in the joint basic parameter set; starting from the zero-load deformation reference position, controlling the torque loading device to increase the load torque step size step by step until the maximum loading threshold is reached; during the loading and holding phase of each load torque level, using a data acquisition card to synchronously record joint input torque data and joint output angle data; monitoring the time domain fluctuation variance of the joint output angle data; when the time domain fluctuation variance is less than the preset steady-state judgment index, extracting the steady-state torque value and steady-state angle value at the current moment; traversing all loading levels to generate a static response data sequence containing multiple sets of steady-state torque values ​​and steady-state angle values.

[0022] Specifically, based on the rated load parameters in the joint's basic parameter set, the maximum allowable torque value recorded on the motor nameplate or in the controller configuration file is read. A 5% increment of this value is used to set the graded loading step size, and 100% of this value is set as the maximum loading threshold. For example, if the rated torque is 100 Nm, the step size is set to 5 Nm. Starting from the zero-load deformation reference position, a high-dynamic-response torque loading device is driven to gradually increase the load torque to the joint output shaft according to the graded loading step size. During the loading process, a torque closed-loop control mode is used to ensure the accuracy of the loading force until the maximum loading threshold is reached. During the loading holding phase of each load torque level, the holding time is set to 10 to 20 seconds to allow the mechanical structure and material stress distribution to reach equilibrium. A multi-channel high-speed data acquisition card is used to synchronously record... The system records joint input torque data and joint output angle data, setting the sampling frequency to above 500 Hz to capture subtle fluctuations. It calculates the variance of the collected joint output angle data using a sliding window, with the window size set to 50 sampling points. It monitors the temporal variance of the joint output angle data. When the temporal variance of three consecutive time windows is less than a preset steady-state judgment index (typically set to three times the sensor resolution, e.g., 0.003 degrees), it determines that the current loading level has reached mechanical steady state. The average value within the current time window is extracted as the steady-state torque and angle values. Following the same logic, all loading levels are traversed, and the data acquired at each level is sequentially stored in a memory array, generating a static response data sequence containing multiple sets of steady-state torque and angle values.

[0023] In this embodiment, the step of processing the static response data sequence using the weighted least squares method to obtain the joint static stiffness coefficients relies on the static stiffness calculation formula that includes stability weights. The static stiffness calculation formula is as follows: ,in, This represents the static stiffness coefficient of the joint. This represents the total number of data sampling points in the static response data sequence. This represents the index of the current data sampling point. Indicates the first Steady-state torque values ​​at each sampling point This represents the average of all steady-state torque values. Indicates the first Steady-state angle values ​​at each sampling point This represents the average of all steady-state angle values. Indicates the first The confidence weight coefficient for each sampling point is calculated using the following formula: ,in Represented by natural constant An exponential function with base 0. Indicates the first The residual values ​​of each sampling point relative to the straight line obtained by linear regression fitting of the static response data sequence based on ordinary least squares method. This represents the inherent noise variance of the measurement sensor.

[0024] Specifically, the step of processing the static response data sequence using the weighted least squares method to obtain the joint static stiffness coefficients relies on a static stiffness calculation formula that includes stability weights. This calculation process aims to eliminate the influence of measurement noise on stiffness parameter identification through a mathematical regression model. Specifically, it introduces a confidence weight coefficient to weight data points with different degrees of deviation. Data points that deviate far from the fitted line are given lower weights, while reliable data points that closely follow the fitted trend line are given higher weights, thereby improving the robustness of the fitting results to outliers. The static stiffness calculation formula is as follows: ,in, This represents the static stiffness coefficient of the joint. This represents the total number of data sampling points in the static response data sequence. This represents the index of the current data sampling point. Indicates the first Steady-state torque values ​​at each sampling point This represents the average of all steady-state torque values. Indicates the first Steady-state angle values ​​at each sampling point This represents the average of all steady-state angle values. Indicates the first The confidence weight coefficient for each sampling point is calculated using the following formula: ,in Represented by natural constant An exponential function with base 0. Indicates the first The residual values ​​of each sampling point relative to the straight line obtained by linear regression fitting of the static response data sequence based on ordinary least squares method. This represents the inherent noise variance of the measurement sensor, which is obtained by statistically analyzing the variance of sensor data collected over a long period of time while the sensor is stationary.

[0025] In this embodiment, the steps of applying dynamic frequency domain excitation to the industrial robot under test, acquiring the dynamic time domain response signal of the industrial robot under test under dynamic frequency domain excitation, and extracting the joint dynamic stiffness characteristics corresponding to the dynamic time domain response signal through cross power spectral density analysis include: generating a sinusoidal sweep frequency signal covering a frequency range of 0.1Hz to 5Hz, and inputting the sinusoidal sweep frequency signal as a torque command to the servo controller of the industrial robot under test; setting the signal sampling frequency to at least 10 times the highest frequency of the excitation signal; synchronously acquiring the dynamic time domain response signal containing the dynamic torque time domain sequence and the dynamic angle time domain sequence; using the Hanning window function to window and truncate the dynamic torque time domain sequence and the dynamic angle time domain sequence to suppress spectral leakage; calculating the cross power spectral density function and the autopower spectral density function based on the windowed dynamic torque time domain sequence and the dynamic angle time domain sequence; calculating the frequency response function based on the cross power spectral density function and the autopower spectral density function; and extracting the joint dynamic stiffness characteristics corresponding to different frequency points from the frequency response function.

[0026] Specifically, a sinusoidal sweep signal with a frequency range of 0.1Hz to 5Hz is generated using a signal generator. The sinusoidal sweep signal employs a logarithmic sweep method to ensure a balanced distribution of test points in both low and high frequency bands. This sinusoidal sweep signal is then input to the servo controller of the industrial robot under test via a real-time communication bus as a torque feedforward command or current command. This drives the motor to generate dynamically changing electromagnetic torque. According to the Nyquist sampling theorem, the signal sampling frequency is set to at least 10 times the highest frequency of the excitation signal, for example, a sampling rate of 100 Hz or higher. A synchronous triggering mechanism is used to synchronously acquire dynamic time-domain response signals containing dynamic torque and dynamic angle time-domain sequences, ensuring strict alignment of the torque and position signals on the time axis. This is achieved using a [missing information - likely a Chinese language tool or similar]. The windowing function performs windowing and truncation on the dynamic torque time-domain sequence and the dynamic angle time-domain sequence. By smoothing and attenuating both ends of the time-domain signal, it can effectively reduce spectral leakage caused by signal truncation and improve the accuracy of frequency domain analysis. Based on the windowed dynamic torque time-domain sequence and the dynamic angle time-domain sequence, the fast Fourier transform algorithm is applied to convert the time-domain signal into a frequency-domain complex sequence. The cross-power spectral density function of the input signal and the output signal, as well as the self-power spectral density function of the output signal, are calculated. The frequency response function is calculated by dividing the cross-power spectral density by the self-power spectral density. This method can effectively filter out unrelated random noise mixed in during the measurement process and extract the joint dynamic stiffness characteristics corresponding to different frequency points from the frequency response function.

[0027] In this embodiment, the step of extracting the joint dynamic stiffness characteristics corresponding to the dynamic time-domain response signal through cross-power spectral density analysis relies on the dynamic stiffness frequency domain calculation formula, which is as follows: ,in, Indicates at a specific frequency The dynamic stiffness characteristics of the joint under these conditions This represents the operation of taking the real part of a complex number. This represents the cross-power spectral density between the dynamic torque time-domain sequence and the dynamic angle time-domain sequence. This represents the self-power spectral density of a dynamic angular time-domain sequence. This represents the dynamic hardening correction factor, used to compensate for nonlinear hardening effects at high frequencies. Represents the logarithmic function with base 10. This represents the system's inherent frequency reference value, used to normalize frequency variables.

[0028] Specifically, the step of extracting the joint dynamic stiffness characteristics corresponding to the dynamic time-domain response signal through cross-power spectral density analysis relies on the dynamic stiffness frequency domain calculation formula. This formula comprehensively considers the real part of the frequency domain transfer function and the nonlinear hardening phenomenon that occurs with increasing frequency. By applying a logarithmic correction to the basic frequency domain stiffness, the dynamic hardening behavior of the actual physical joint under high-frequency excitation is fitted. The dynamic stiffness frequency domain calculation formula is as follows: ,in, Indicates at a specific frequency The dynamic stiffness characteristics of the joint under these conditions This represents the operation of taking the real part of a complex number. This represents the cross-power spectral density between the dynamic torque time-domain sequence and the dynamic angle time-domain sequence. This represents the self-power spectral density of a dynamic angular time-domain sequence. This represents the dynamic hardening correction factor, used to compensate for nonlinear hardening effects at high frequencies. This factor is obtained by fitting the deviation between theoretical predictions and experimental values ​​in the high-frequency range. Represents the logarithmic function with base 10. This represents the system's natural frequency reference value, used to normalize frequency variables, and is usually taken as the system's first natural frequency value.

[0029] In this embodiment, the steps of obtaining task feature parameters of the target simulation scene, constructing an adaptive weighted fusion model based on the task feature parameters, and fusing parameters of the joint static stiffness coefficient and joint dynamic stiffness characteristics using the adaptive weighted fusion model include: parsing the robot motion trajectory file in the target simulation scene, extracting the velocity vector set and acceleration vector set of the trajectory points, calculating the root mean square velocity value of the velocity vector set, performing spectral analysis on the velocity vector set to identify the dominant frequency component, using the root mean square velocity value and the dominant frequency component together as task feature parameters, constructing an adaptive weight allocation strategy based on the Sigmoid function, calculating dynamic weight coefficients based on the root mean square velocity values ​​in the task feature parameters, and using the dynamic weight coefficients to perform linear interpolation on the joint static stiffness coefficient and joint dynamic stiffness characteristics to generate joint comprehensive stiffness parameters. The adaptive weighted fusion model is specifically as follows: ,in, This represents the overall joint stiffness parameter. Indicates the dynamic weighting coefficient. Represents the dominant frequency component, dynamic weighting coefficient The calculation formula is: ,in, This represents the root mean square velocity value. This represents the critical speed threshold that distinguishes between static and dynamic scenes. This represents the sensitivity coefficient for weight switching.

[0030] Specifically, the robot motion trajectory file in the target simulation scene is analyzed. This file typically contains time-series data such as timestamps, joint angles, joint velocities, and torque commands. The velocity vector set and acceleration vector set of the trajectory points are extracted through numerical differentiation or direct reading. The root mean square velocity value of the velocity vector set is calculated, reflecting the average motion intensity throughout the entire operation cycle. Simultaneously, a fast Fourier transform spectral analysis is performed on the velocity vector set to identify the frequency point with the highest energy proportion as the dominant frequency component. The root mean square velocity value and the dominant frequency component are used together as task feature parameters to construct an adaptive weight allocation strategy based on the Sigmoid function. The core of this strategy is to construct a weight curve that smoothly changes with velocity. Dynamic weight coefficients are calculated based on the root mean square velocity value in the task feature parameters. When the velocity is low, the weights tend to favor static stiffness; when the velocity is high, the weights tend to favor dynamic stiffness. The dynamic weight coefficients are used to linearly interpolate the joint static stiffness coefficient and joint dynamic stiffness characteristics to generate the joint comprehensive stiffness parameters. The adaptive weighted fusion model is as follows: ,in, This represents the overall joint stiffness parameter. Indicates the dynamic weighting coefficient. Represents the dominant frequency component, dynamic weighting coefficient The calculation formula is: ,in, This represents the root mean square velocity value. This indicates the critical speed threshold that distinguishes between static and dynamic scenes. This threshold is typically set to 10% to 20% of the joint's rated maximum speed. This represents the sensitivity coefficient for weight switching, which is empirically set between 0.5 and 1.0 to control the steepness of weight switching.

[0031] In this embodiment, before obtaining the set of basic joint parameters of the industrial robot under test, a sensor calibration and calibration step is also included: connecting the external torque sensor and the external displacement sensor used for data acquisition in series to a standard metrology device, obtaining a standard reading sequence, calculating the linear deviation rate between the measured value of the external torque sensor and the standard reading sequence, and if the linear deviation rate exceeds a preset accuracy tolerance range, generating a calibration compensation matrix, updating the internal parameters of the external torque sensor using the calibration compensation matrix, checking the timestamp synchronization protocol of the external torque sensor and the external displacement sensor, and ensuring that the clock synchronization error when acquiring static response data sequences and dynamic time-domain response signals is less than a preset microsecond threshold.

[0032] Specifically, external torque and displacement sensors used for data acquisition are connected in series to a standard metrology device, which is a national standard torque meter and laser interferometer with higher precision. By synchronously applying a series of standard physical quantities, a standard reading sequence is obtained. The linear deviation rate between the measured value of the external torque sensor and the standard reading sequence is calculated. The linear deviation rate is obtained by dividing the absolute value of the difference between the measured value and the standard value by the standard value. If the linear deviation rate exceeds the preset accuracy tolerance range, such as exceeding 0.1% of the full-scale error, a calibration compensation matrix is ​​generated based on the least squares principle. The matrix includes the zero-point offset and gain correction coefficient. The calibration compensation matrix is ​​used to update the internal parameters of the external torque sensor or the correction configuration of the data acquisition software. The timestamp synchronization protocol of the external torque and displacement sensors is checked to verify whether synchronization is achieved through a hardware trigger line or the PTP precision clock protocol. This ensures that the clock synchronization error when acquiring static response data sequences and dynamic time-domain response signals is less than a preset microsecond threshold, such as less than 10 microseconds, to prevent stiffness calculation errors caused by phase lag.

[0033] In this embodiment, after obtaining the joint composite stiffness parameters for physical simulation, the method further includes parameter verification and optimization steps: importing the joint composite stiffness parameters into the physical simulation engine, constructing a virtual robot model, reproducing the loading conditions corresponding to the static response data sequence in the physical simulation engine, outputting the simulated deformation, calculating the relative error rate between the simulated deformation and the actual measured deformation, and if the relative error rate is greater than the preset simulation accuracy standard, then correcting the model parameters in the adaptive weighted fusion model and re-executing the parameter fusion step until the relative error rate meets the preset simulation accuracy standard.

[0034] Specifically, the joint composite stiffness parameters are imported into a physical simulation engine, such as MuJoCo, PyBullet, or commercial robot simulation software. A virtual robot model is constructed based on the robot's URDF or DH parameters. The loading conditions corresponding to the static response data sequence are reproduced in the physical simulation engine, that is, the same torque sequence is applied in the virtual environment, and the simulated deformation is output. The relative error rate between the simulated deformation and the actual measured deformation is calculated. The relative error rate is the ratio of the absolute value of the difference between the two to the actual measured value. If the relative error rate is greater than the preset simulation accuracy standard, for example, greater than 5%, the model parameters in the adaptive weighted fusion model are corrected according to the direction and magnitude of the error. This mainly involves adjusting the weight switching sensitivity coefficient or the critical velocity threshold, and the parameter fusion step is re-executed. The model continuously approaches the real physical characteristics through iterative optimization until the relative error rate meets the preset simulation accuracy standard.

[0035] In this embodiment, the set of basic joint parameters includes joint type identifier, rated torque parameter, reduction ratio parameter, and motor inertia parameter. The joint type identifier is used to distinguish between rotary joints and linear joints. When the joint type identifier indicates a rotary joint, the unit of the joint static stiffness coefficient is configured as Newton-meter per degree. When the joint type identifier indicates a linear joint, the unit of the joint static stiffness coefficient is configured as Newton-millimeter per millimeter. The step of constructing the test task sequence also includes automatically matching the corresponding load loading direction and displacement measurement dimension according to the joint type identifier to ensure that the test coordinate system is consistent with the direction of joint motion degrees of freedom.

[0036] Specifically, the set of basic joint parameters includes joint type identifier, rated torque parameter, reduction ratio parameter, and motor inertia parameter. The joint type identifier is used to distinguish between rotary joints and linear joints, and is usually defined through enumerated variables or specific state bits in the configuration file. When the joint type identifier indicates a rotary joint, the unit of the joint static stiffness coefficient is configured to Newton-meter per degree, which corresponds to the torsional resistance of angular displacement. When the joint type identifier indicates a linear joint, the unit of the joint static stiffness coefficient is configured to Newton-millimeter per millimeter, which corresponds to the compressive or tensile resistance of linear displacement. The steps of constructing the test task sequence also include automatically matching the corresponding load loading direction and displacement measurement dimension according to the joint type identifier. For rotary joints, the loading torque direction is set to be perpendicular to the rotation axis, and the displacement measurement is angular displacement; for linear joints, the loading force direction is set to be parallel to the motion axis, and the displacement measurement is linear displacement, ensuring that the test coordinate system is consistent with the direction of the joint's degrees of freedom.

[0037] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for solving damping parameters in dynamic simulation based on a gravity compensation mechanism, characterized in that, Includes the following steps: Obtain the set of basic joint parameters of the industrial robot under test, determine the test boundary conditions based on the set of basic joint parameters, and construct a test task sequence based on the test boundary conditions; Zero-load posture calibration is performed on the industrial robot under test, the end-effector posture change data is monitored, and the zero-load deformation reference position is determined based on the end-effector posture change data. Based on the zero-load deformation reference position, a graded static load is applied to the industrial robot under test, and a static response data sequence under the graded static load is collected. The static response data sequence is then processed using the weighted least squares method to obtain the joint static stiffness coefficient. A dynamic frequency domain excitation is applied to the industrial robot under test, and the dynamic time domain response signal of the industrial robot under test under the dynamic frequency domain excitation is collected. The joint dynamic stiffness characteristics corresponding to the dynamic time domain response signal are extracted by cross power spectral density analysis. Obtain the task feature parameters of the target simulation scene, construct an adaptive weighted fusion model based on the task feature parameters, and use the adaptive weighted fusion model to fuse the static stiffness coefficient and dynamic stiffness characteristics of the joint to obtain the comprehensive stiffness parameters of the joint for physical simulation.

2. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 1, characterized in that, The steps of performing zero-load attitude calibration on the industrial robot under test, monitoring end-effector pose change data, and determining the zero-load deformation reference position based on the end-effector pose change data include: Control the industrial robot under test to move to the preset initial test posture and lock the joint brakes of non-test axes; A preset standard micro-test load is applied to the end effector of the industrial robot under test in the initial test posture, and the end effector pose change data is collected in real time using a displacement sensor. Calculate the displacement deviation in the end-effector pose change data and compare the displacement deviation with a preset rigid body deformation threshold. If the displacement deviation is greater than the preset rigid body deformation threshold, the joint angle of the industrial robot under test is adjusted, and the steps of applying the standard micro-test load and collecting the end pose change data are repeated until the displacement deviation is less than or equal to the preset rigid body deformation threshold. The joint angle at which the displacement deviation is less than or equal to the preset rigid body deformation threshold is determined as the zero-load deformation reference position, and the joint state at this time is recorded as the anti-coupling interference reference state.

3. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 1, characterized in that, The steps of applying graded static loads to the industrial robot under test based on the zero-load deformation reference position and collecting static response data sequences under the graded static loads include: Based on the rated load parameters in the set of basic joint parameters, set the graded loading step size and the maximum loading threshold. Starting from the zero-load deformation reference position, the control torque loading device gradually increases the load torque according to the graded loading step size until the maximum loading threshold is reached; During the loading and holding phase of each load torque level, the joint input torque data and joint output angle data are recorded synchronously using a data acquisition card. Monitor the time-domain fluctuation variance of the joint output angle data. When the time-domain fluctuation variance is less than the preset steady-state judgment index, extract the steady-state torque value and steady-state angle value at the current moment. Iterate through all loading levels to generate the static response data sequence containing multiple sets of the steady-state torque values ​​and the steady-state angle values.

4. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 3, characterized in that, The step of processing the static response data sequence using the weighted least squares method to obtain the joint static stiffness coefficients relies on a static stiffness calculation formula that includes stability weights. The static stiffness calculation formula is as follows: ， in, This represents the static stiffness coefficient of the joint. This represents the total number of data sampling points in the static response data sequence. This represents the index of the current data sampling point. Indicates the first The steady-state torque value at each sampling point This represents the average of all the aforementioned steady-state torque values. Indicates the first The steady-state angle value at each sampling point, This represents the average of all the aforementioned steady-state angle values. Indicates the first Confidence weighting coefficients for each sampling point; The formula for calculating the confidence weight coefficient is as follows: ,in Represented by natural constant An exponential function with base 0. Indicates the first The residual values ​​of each sampling point relative to the straight line obtained by linear regression fitting of the static response data sequence based on ordinary least squares method. This represents the inherent noise variance of the measurement sensor.

5. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 1, characterized in that, The steps include: applying dynamic frequency domain excitation to the industrial robot under test, acquiring the dynamic time domain response signal of the industrial robot under test under the dynamic frequency domain excitation, and extracting the joint dynamic stiffness characteristics corresponding to the dynamic time domain response signal through cross power spectral density analysis, including: A sinusoidal sweep frequency signal covering a frequency range of 0.1Hz to 5Hz is generated, and the sinusoidal sweep frequency signal is input as a torque command to the servo controller of the industrial robot under test. Set the signal sampling frequency to at least 10 times the highest frequency of the excitation signal, and synchronously acquire the dynamic time-domain response signal containing the dynamic torque time-domain sequence and the dynamic angle time-domain sequence; The Hanning window function is used to window and truncate the dynamic torque time-domain sequence and the dynamic angle time-domain sequence to suppress spectral leakage. Based on the windowed dynamic torque time-domain sequence and the dynamic angle time-domain sequence, the cross power spectral density function and the self power spectral density function are calculated. The frequency response function is calculated based on the cross power spectral density function and the self power spectral density function, and the joint dynamic stiffness characteristics corresponding to different frequency points are extracted from the frequency response function.

6. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 5, characterized in that, The step of extracting the joint dynamic stiffness characteristics corresponding to the dynamic time-domain response signal through cross-power spectral density analysis relies on the dynamic stiffness frequency domain calculation formula, which is: ， in, Indicates at a specific frequency The joint dynamic stiffness characteristics described below, This represents the operation of taking the real part of a complex number. This represents the cross-power spectral density between the dynamic torque time-domain sequence and the dynamic angle time-domain sequence. This represents the auto-power spectral density of the dynamic angle time-domain sequence. This represents the dynamic hardening correction factor, used to compensate for nonlinear hardening effects at high frequencies. Represents the logarithmic function with base 10. This represents the system's inherent frequency reference value, used to normalize frequency variables.

7. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 1, characterized in that, The steps of obtaining task feature parameters of the target simulation scene, constructing an adaptive weighted fusion model based on the task feature parameters, and using the adaptive weighted fusion model to fuse the static stiffness coefficient and dynamic stiffness characteristics of the joint include: Analyze the robot motion trajectory file in the target simulation scene and extract the velocity vector set and acceleration vector set of the trajectory points; Calculate the root mean square velocity value of the velocity vector set, and perform spectral analysis on the velocity vector set to identify the dominant frequency component. Use the root mean square velocity value and the dominant frequency component together as the task feature parameter. An adaptive weight allocation strategy based on the Sigmoid function is constructed, and dynamic weight coefficients are calculated based on the root mean square velocity value in the task feature parameters. The joint's static stiffness coefficient and dynamic stiffness characteristics are linearly interpolated using the dynamic weighting coefficient to generate the joint's comprehensive stiffness parameters; The adaptive weighted fusion model is specifically as follows: ， in, This represents the overall stiffness parameter of the joint. This represents the dynamic weighting coefficient. This represents the dominant frequency component; The dynamic weighting coefficient The calculation formula is: ， in, This represents the root mean square velocity value. This represents the critical speed threshold that distinguishes between static and dynamic scenes. This represents the sensitivity coefficient for weight switching.

8. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 1, characterized in that, Before obtaining the set of basic joint parameters of the industrial robot under test, sensor calibration and adjustment steps are also included: An external torque sensor and an external displacement sensor used for data acquisition are connected in series to a standard measuring device to obtain a standard reading sequence; Calculate the linear deviation rate between the measured value of the external torque sensor and the standard reading sequence; If the linear deviation rate exceeds the preset accuracy tolerance range, a calibration compensation matrix is ​​generated, and the internal parameters of the external torque sensor are updated using the calibration compensation matrix. Check the timestamp synchronization protocol of the external torque sensor and the external displacement sensor to ensure that the clock synchronization error when acquiring the static response data sequence and the dynamic time domain response signal is less than a preset microsecond threshold.

9. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 1, characterized in that, After obtaining the joint composite stiffness parameters for physical simulation, the process also includes parameter verification and optimization steps: The joint composite stiffness parameters are imported into the physics simulation engine to construct a virtual robot model; The loading conditions corresponding to the static response data sequence are reproduced in the physical simulation engine, and the simulated deformation is output. Calculate the relative error rate between the simulated deformation and the actual measured deformation; If the relative error rate is greater than the preset simulation accuracy standard, the model parameters in the adaptive weighted fusion model are corrected, and the parameter fusion step is re-executed until the relative error rate meets the preset simulation accuracy standard.

10. The method for solving damping parameters in dynamic simulation based on gravity compensation mechanism according to claim 1, characterized in that, The set of basic joint parameters includes joint type identifier, rated torque parameter, reduction ratio parameter, and motor inertia parameter. The joint type identifier is used to distinguish between rotary joints and linear joints. When the joint type identifier indicates a rotary joint, the unit of the joint static stiffness coefficient is configured to be Newton-meter per degree. When the joint type identifier indicates a linear joint, the unit of the joint static stiffness coefficient is configured to be Newtons per millimeter; The step of constructing the test task sequence also includes automatically matching the corresponding load loading direction and displacement measurement dimension according to the joint type identifier to ensure that the test coordinate system is consistent with the direction of joint motion degrees of freedom.

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