Self-adaptive cooperative mechanical arm damping identification method and device based on different loads

Abstract

The invention relates to a self-adaptive cooperative mechanical arm damping identification method and device based on different loads. Comprising nine core steps of no-load torque reference calibration, tail end load calculation, load grading, adaptive excitation matching, resonance signal acquisition, complete machine resonance parameter extraction, double-window damping identification and stability verification, damping precision verification and load drift adaptive compensation, and finally, accurate and stable damping ratios can be obtained under different loads. And reliable parameter support is provided for suppressing vibration and improving positioning precision.

Description

Technical Field

[0001] This invention relates to the field of robotic arm technology, specifically to an adaptive cooperative robotic arm damping identification method and device based on different loads. Background Technology

[0002] Collaborative robotic arms have been widely used in intelligent manufacturing, precision machining, and logistics sorting. Currently, collaborative robotic arms are gradually developing towards multi-functionality and flexible operation. To adapt to different operating scenarios, frequent changes of various end-effectors such as grippers, suction cups, and cutting tools are required. The unpredictable changes in the end-effector load mass and inertia make it impossible to maintain a fixed load state, leading to low-frequency flexible resonance during operation. This causes problems such as end-effector jitter, excessive trajectory deviation, and reduced operating accuracy, severely restricting the operating efficiency and application expansion of collaborative robotic arms. Damping parameters are the core parameters for flexible vibration suppression and active resonance control of collaborative robotic arms; the accuracy and stability of damping identification directly determine the vibration suppression effect. Current conventional damping identification technology has significant shortcomings in adaptability to variable load conditions of collaborative robotic arms, specifically as follows:

[0003] 1) The amplitude and frequency of the excitation signal were not adaptively adjusted according to the load size. Under light load, the excitation was too large and easily introduced interference, while under heavy load, the excitation was insufficient and could not effectively excite the resonance peak.

[0004] 2) The lack of a mechanism for verifying identification accuracy under conditions without a reference makes it impossible to determine whether the damping identification results are reliable;

[0005] 3) In actual operation, the load on the robotic arm changes transiently. The current excitation strategy and damping identification algorithm have not formed a collaborative optimization mechanism, making it difficult to continuously ensure high-precision damping identification under variable load conditions.

[0006] There is an urgent need for a novel identification method that can accurately measure the end load, adaptively match the excitation signal based on the end load, stably identify damping parameters, and has load drift compensation. Summary of the Invention

[0007] The purpose of this invention is to provide a method and device for damping identification of an adaptive collaborative robotic arm based on different loads, which can accurately measure the end load, adaptively match the excitation signal based on the end load, stably identify the damping parameters, and have load drift compensation.

[0008] In a first aspect, the adaptive cooperative robotic arm damping identification method based on different loads described in this invention includes the following steps:

[0009] No-load torque benchmark calibration: By collecting no-load joint torque data of the robotic arm in typical postures in the entire workspace, a no-load steady-state torque library is constructed. The no-load steady-state torque library consists of the joint benchmark torque generated by the robotic arm's own gravity and steady-state friction, and is used to characterize the dynamic change law of joint torque with working posture under no-load conditions.

[0010] End-load calculation: Based on the no-load steady-state torque library obtained from the no-load torque benchmark calibration, the equivalent end-load mass under the current working condition is calculated through attitude matching, torque separation and dynamic model mapping.

[0011] Load classification: Based on the magnitude of the equivalent load mass at the end obtained from the end load calculation, the working conditions are divided into three categories: light load, medium load, and heavy load.

[0012] Adaptive excitation matching: Based on the results of the load classification and the offset characteristics of the first-order resonant frequency of the robotic arm under variable load, an excitation frequency band and amplitude adapted to the current load are set to provide suitable excitation conditions for resonant signal acquisition.

[0013] Resonance signal acquisition: Select the dominant joint that dominates the vibration of the entire robotic arm, apply the adaptive excitation set by the adaptive excitation matching, and simultaneously acquire the joint torque and angle signals. Combine the no-load steady-state torque library to separate the high-frequency torque fluctuation component caused only by the flexible resonance of the entire machine.

[0014] Whole machine resonance parameter extraction: The high-frequency torque fluctuation component is processed to extract the resonance frequency and resonance peak value, and the equivalent damping ratio of the robotic arm is calculated based on the resonance frequency and resonance peak value;

[0015] Dual-window damping identification and stability verification: Dual-window synchronous damping identification is performed on the torque data of the main joint. The resonant frequency and resonant peak value are extracted from the whole machine resonance parameters. The damping ratio is calculated based on the half-power bandwidth method. A quantitative identification effectiveness judgment standard is established to determine the final equivalent damping ratio, measured resonant peak value, measured resonant frequency and model predicted frequency.

[0016] Damping accuracy verification: The model predicted resonance peak value is calculated based on the model predicted frequency and the final equivalent damping ratio. The model predicted frequency and the model predicted resonance peak value are compared with the measured resonance frequency and the measured resonance peak value to determine the accuracy of the damping ratio calculation results.

[0017] Load drift adaptive compensation: Real-time detection of end load changes; when a sudden change occurs in the load, a re-identification process is triggered and relevant data is cached.

[0018] One possible implementation method is as follows: the specific process of calibrating the no-load torque reference and calculating the end load is as follows:

[0019] The collaborative robotic arm is controlled to operate at a constant speed under no-load conditions. Multiple sets of joint torque data corresponding to several typical working postures in its entire workspace are collected. Based on the joint torque data, a no-load steady-state torque library is constructed.

[0020] When the robotic arm is in a loaded operation state, the joint torque signal and joint angle information under the current operation posture are collected in real time. The posture interpolation algorithm is used to match the unloaded steady-state torque library to obtain the unloaded torque reference value that completely corresponds to the current loaded posture.

[0021] Subtract the no-load torque reference value from the real-time collected loaded joint torque to obtain the pure load torque component caused only by the end load;

[0022] Substituting the pure load torque component into the Newton-Euler dynamics model, and combining it with the kinematic and dynamic parameters in the robotic arm's URDF file, the mapping calculation from joint torque to end-effector load is completed, yielding the equivalent end-effector load mass under the current working condition.

[0023] One possible implementation is that the selection of typical working postures should comprehensively cover the main spatial orientations of the robotic arm's routine operations; the joint torque data corresponding to each set of typical postures is obtained by repeated acquisition, and the arithmetic mean of the multiple acquisitions is taken as the no-load reference torque of each joint under that posture.

[0024] One possible implementation is that the specific criteria for matching the load grading with the adaptive excitation are:

[0025] Under light load conditions, a pseudo-random binary sequence micro-excitation with an amplitude of less than or equal to ±0.005 rad and covering the frequency band of 25 Hz to 50 Hz is used.

[0026] Under medium load conditions, a pseudo-random binary sequence micro-excitation with an amplitude greater than ±0.005 rad and less than ±0.01 rad, covering the frequency band of 10Hz to 30Hz, is used.

[0027] Under heavy load conditions, a pseudo-random binary sequence micro-excitation with an amplitude of ±0.01 rad and covering the frequency band of 5 Hz to 25 Hz is used.

[0028] One possible implementation is that the amplitude of the adaptive excitation is linearly and adaptively adjusted based on the equivalent end load mass, specifically according to the following adjustment rule:

[0029] For every 5kg increase in end load mass, the excitation amplitude increases linearly by 20%; at the same time, the upper limit threshold of the excitation amplitude is set to ±0.015rad.

[0030] One possible implementation method is as follows: The specific process for acquiring the resonant signal and extracting the overall resonant parameters is as follows:

[0031] The dominant joint that contributes the most to the end-effector vibration and dominates the overall flexible vibration of the robotic arm is selected as the excitation and signal acquisition object. Adaptive excitation is applied to the dominant joint, and its real-time joint torque signal and joint angle signal are acquired simultaneously.

[0032] The unloaded steady-state torque of the dominant joint in the current posture is obtained by interpolation of the unloaded steady-state torque library. The unloaded steady-state torque is then subtracted from the real-time collected torque of the loaded joint to obtain the high-frequency torque fluctuation component caused only by the flexible resonant vibration of the whole machine.

[0033] The high-frequency torque fluctuation component is processed to extract the overall resonance parameters, which include the resonance frequency and the resonance peak value.

[0034] If there is only a single dominant resonance peak in the spectrum, the damping ratio is calculated based on the half-power bandwidth method using the resonance peak value.

[0035] If there are multiple obvious resonant peaks formed by the superposition of multiple vibration modes in the spectrum, the resonant frequency and resonant peak value corresponding to each vibration mode are extracted, and the damping ratio of each mode is calculated by the half-power bandwidth method. Then, the resonant peak value of each mode is used as the basis for normalization and weighting to obtain the final equivalent damping ratio.

[0036] One possible implementation method is as follows: The specific operation of the dual-window damping identification and stability verification is as follows:

[0037] After applying excitation to a single dominant joint, under the condition that the robot arm posture, load and excitation parameters remain constant, the steady-state torque data of the dominant joint is continuously collected. The collected steady-state torque data is divided into two consecutive sliding windows, and damping identification is performed independently for the two sliding windows.

[0038] The two sliding windows use the same signal preprocessing and frequency domain analysis process to extract the resonant frequency and resonant peak value of each window, and calculate the damping ratio of the corresponding window using the half-power bandwidth method.

[0039] Calculate the relative deviation of the resonant frequency and the damping ratio deviation of the two sliding windows. When the relative deviation of the resonant frequency is <2% and the damping ratio deviation is <0.01, take the arithmetic mean of the damping ratios of the two sliding windows to obtain the final equivalent damping ratio. Take the average of the resonant peaks of the two windows as the measured resonant peak value. Take the average of the frequencies of the two sliding windows as the model predicted frequency. Take the average of the frequencies of the two sliding windows or the resonant frequency of a single sliding window as the measured resonant frequency. If the above deviation thresholds are not met, reapply the excitation and collect torque data until the validity judgment conditions are met.

[0040] One possible implementation includes, in the dual-window damping identification and stability verification step, adaptive adjustment of the window length based on the robot arm's movement speed. Specifically, when the robot arm's end-effector movement speed is greater than 0.5 m / s, the sliding window length is automatically shortened by 10%.

[0041] One possible implementation method is as follows: the specific process of damping accuracy verification and load drift adaptive compensation is as follows:

[0042] Based on the inherent characteristics of low-frequency flexible vibration of the collaborative robotic arm, it is equivalent to a typical second-order vibration system, which is a dynamic equivalent model for analyzing the vibration characteristics of the collaborative robotic arm. The model's predicted frequency and the final equivalent damping ratio are substituted into the preset second-order vibration system transfer function, and after conversion to the frequency domain, the model's predicted resonance peak value is calculated. The model's predicted resonance peak value is compared with the measured resonance peak value to obtain the relative frequency deviation, and the model's predicted frequency is compared with the measured resonance frequency to obtain the relative amplitude deviation.

[0043] When the measured resonant frequency is taken as the resonant frequency of a single sliding window, if the relative frequency deviation is <2% and the relative amplitude deviation is <5%, then the damping ratio calculation result is determined to be accurate.

[0044] When the measured resonant frequency is taken as the average of the two sliding windows, if the relative deviation of the amplitude is <5%, the damping ratio calculation result is considered accurate.

[0045] When a change in load at the end of the robotic arm is detected to be ≥0.5kg, the load matching identification process is immediately triggered, and multi-dimensional data of at least two sliding window lengths are cached simultaneously.

[0046] Secondly, the adaptive cooperative robotic arm damping identification device based on different loads according to the present invention includes a memory and a controller. The memory stores a computer-readable program. When the computer-readable program is invoked by the controller, it can execute the adaptive cooperative robotic arm damping identification method based on different loads as described in the present invention.

[0047] The present invention has the following advantages:

[0048] (1) The accuracy of load calculation is greatly improved: Through the full attitude no-load torque library and attitude interpolation algorithm, the load mass calculation error is stably controlled within ≤±0.2kg, which is far superior to the traditional calculation method. This provides accurate support for load classification and excitation matching, and improves the reliability of damping identification from the source.

[0049] (2) Significantly optimized excitation signal adaptability: The load-excitation parameter adaptive linkage is realized, with no jitter under light load and effective excitation under heavy load. Under the premise of not affecting the normal working trajectory of the robotic arm, the true resonance characteristics are accurately extracted, avoiding misjudgment of noise and interference signals.

[0050] (3) The damping identification results are stable and reliable: the dual-window quantitative verification mechanism first verifies the stability of the damping parameters, and then determines the identification accuracy after the stability is achieved.

[0051] (4) Low control cost and easy to implement in engineering: Only existing joint torque sensors are needed to collect signals. No additional sensors are required. Excitation is applied to a single dominant joint. The hardware modification is small and the amount of calculation is moderate. It is easy to integrate into the existing collaborative robotic arm control system and the threshold for engineering application is low. Attached Figure Description

[0052] Figure 1 This is a flowchart of the adaptive cooperative robotic arm damping identification method based on different loads in the embodiments of this application;

[0053] Figure 2 This is a detailed flowchart of the adaptive cooperative robotic arm damping identification method based on different loads in the embodiments of this application;

[0054] Figure 3 This is a block diagram illustrating the adaptive cooperative robotic arm damping identification based on different loads in an embodiment of this application. Detailed Implementation

[0055] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0056] Please see Figure 1 This application aims to provide an adaptive cooperative robotic arm damping identification method based on different loads, including the following steps:

[0057] No-load torque benchmark calibration: By collecting no-load joint torque data of the robotic arm in typical postures throughout the entire workspace, a no-load steady-state torque library is constructed. The no-load steady-state torque library consists of the joint benchmark torque generated by the robotic arm's own gravity and steady-state friction, and is used to characterize the dynamic change law of joint torque with working posture under no-load conditions.

[0058] End-load calculation: Based on the no-load steady-state torque library obtained from the no-load torque benchmark calibration, the equivalent end-load mass under the current working condition is calculated through attitude matching, torque separation and dynamic model mapping.

[0059] Load classification: Based on the magnitude of the equivalent load mass at the end obtained by the end load calculation, the working conditions are divided into three categories: light load, medium load, and heavy load.

[0060] Adaptive excitation matching: Based on the results of the load classification and the offset characteristics of the first-order resonant frequency of the robotic arm under variable load, an excitation frequency band and amplitude that are compatible with the current load are set to provide suitable excitation conditions for resonant signal acquisition.

[0061] Resonance signal acquisition: Select the dominant joint that drives the overall vibration of the robotic arm, apply the adaptive excitation set by the adaptive excitation matching, and simultaneously acquire the joint torque and angle signals. Combine the no-load steady-state torque library to separate the high-frequency torque fluctuation component caused only by the overall flexible resonance of the machine.

[0062] Whole machine resonance parameter extraction: The high-frequency torque fluctuation component is processed to extract the resonance frequency and resonance peak value, and the equivalent damping ratio of the robotic arm is calculated based on the resonance frequency and resonance peak value.

[0063] Dual-window damping identification and stability verification: Dual-window synchronous damping identification is performed on the torque data of the main joint. The resonant frequency and resonant peak value are extracted from the whole machine resonance parameters. The damping ratio is calculated based on the half-power bandwidth method. A quantitative identification effectiveness judgment standard is established to determine the final equivalent damping ratio, measured resonant peak value, measured resonant frequency and model predicted frequency.

[0064] Damping accuracy verification: The model predicted resonance peak value is calculated based on the model predicted frequency and the final equivalent damping ratio. The model predicted frequency and the model predicted resonance peak value are compared with the measured resonance frequency and the measured resonance peak value to determine the accuracy of the damping ratio calculation results.

[0065] Load drift adaptive compensation: Real-time detection of end load changes; when a sudden change occurs in the load, a re-identification process is triggered and relevant data is cached.

[0066] This method employs nine core steps: no-load torque benchmark calibration, end-load calculation, load grading, adaptive excitation matching, resonance signal acquisition, whole-machine resonance parameter extraction, dual-window damping identification and stability verification, damping accuracy verification, and load drift adaptive compensation. Ultimately, it achieves accurate and stable damping ratios under different loads, providing reliable parameter support for suppressing vibration and improving positioning accuracy.

[0067] 1.1 No-load torque benchmark calibration and end load calculation

[0068] The robotic arm is calibrated under no-load uniform speed operation. Multiple sets of joint torque data corresponding to several typical postures of the robotic arm in the entire workspace are collected to establish a no-load steady-state torque library covering the range of robotic arm operation postures. This no-load steady-state torque library is composed of joint reference torques generated by the robotic arm's own gravity and steady-state friction, which characterizes the dynamic change law of joint torque with operation posture under no-load conditions.

[0069] When the robotic arm is operating under load, it collects joint torque signals and joint angle information in real time under the current working posture. Using an attitude interpolation algorithm, it calculates a reference value of the no-load torque that perfectly matches the current loaded posture based on an established no-load steady-state torque library. Subtracting the interpolated no-load torque reference value from the real-time collected loaded joint torque yields the pure load torque component caused only by the end-effector load.

[0070] By substituting the pure load torque component into the Newton-Euler dynamics model and using the kinematic and dynamic parameters in the robotic arm's URDF file, the mapping calculation from joint torque to end-effector load is completed, yielding the equivalent end-effector load mass under the current working condition.

[0071] 1.2 Load grading and adaptive excitation matching

[0072] Based on the magnitude of the equivalent load mass, three types of operating conditions are classified: light load, medium load, and heavy load, providing a precise basis for subsequent adaptive excitation frequency band matching.

[0073] Dynamic modal analysis and frequency sweep experiments verified that under light load conditions, the first-order resonant frequency of the robotic arm is distributed in the high-frequency range of 25Hz to 50Hz; under heavy load conditions, the equivalent load inertia increases, and the first-order resonant frequency decreases to the low-frequency range of 5Hz to 25Hz; under medium load conditions, the resonant frequency is between the two. The first-order resonant frequency refers to the first principal modal frequency of the robotic arm's overall flexible vibration, which is the core vibration characteristic parameter, and its value dynamically shifts with changes in load inertia.

[0074] When the load at the end effector of a robotic arm changes, the arm's resonant frequency, inertia, and stiffness all change. If the excitation frequency band does not match the robotic arm's true resonant frequency band under the current load, the dominant flexible mode of the robotic arm cannot be effectively excited. In frequency domain analysis, the true resonant peak cannot be extracted, and noise or interference signals are easily misidentified as resonant characteristics, leading to distorted and incorrect damping identification results.

[0075] The core principle of adaptive excitation based on load grading is as follows: the lighter the load, the higher the resonant frequency, using small amplitude, high-frequency excitation to suppress end jitter and improve the signal-to-noise ratio; the heavier the load, the lower the resonant frequency, using large amplitude, low-frequency excitation to ensure effective excitation of the resonant peak. According to different load conditions, the baseline values ​​are set as follows: for light load conditions, a pseudo-random binary sequence (PRBS) micro-excitation with an amplitude less than or equal to ±0.005 rad is used, focusing on the high-frequency range of 25 Hz to 50 Hz; for medium load conditions, a pseudo-random binary sequence (PRBS) micro-excitation with an amplitude greater than ±0.005 rad and less than ±0.01 rad is used, covering the 10 Hz to 30 Hz range; for heavy load conditions, the excitation amplitude is adaptively increased to ±0.01 rad, focusing on the low-frequency range of 5 Hz to 25 Hz.

[0076] To improve the adaptability of the excitation signal under different loads, the excitation value is allowed to be linearly adjusted based on the reference value: for every 5kg increase in load mass, the excitation amplitude increases linearly by 20% based on the reference value, and the maximum value of the excitation amplitude does not exceed ±0.015rad, so as to avoid the excitation amplitude being too large and interfering with the normal trajectory movement of the robotic arm.

[0077] 1.3 Resonance Signal Acquisition and Whole Machine Resonance Parameter Extraction

[0078] For collaborative robotic arms, the dominant joint that contributes the most to the end effector vibration and dominates the overall vibration is selected. Adaptive excitation is applied to the dominant joint and the real-time torque and angle signals of the dominant joint are collected. The unloaded steady-state torque of the dominant joint in the current posture is obtained by interpolation through the unloaded steady-state torque library. The real-time loaded joint torque of the dominant joint is subtracted from the corresponding unloaded reference value (i.e., the unloaded steady-state torque), and the high-frequency torque fluctuation component caused only by the flexible resonant vibration of the whole machine is retained.

[0079] For the high-frequency torque fluctuation components separated after preprocessing, either Fast Fourier Transform (FFT) frequency domain analysis or Cross Power Spectral Density (CSD) analysis can be adaptively selected based on the actual working conditions to process the high-frequency torque fluctuation components and extract the overall machine resonance parameters. The two methods are complementary and logically consistent, and both can accurately extract the overall machine's flexible resonance characteristics through a single dominant joint signal. When using FFT frequency domain analysis, a Fast Fourier Transform is directly performed on the high-frequency torque fluctuation components to obtain the corresponding frequency domain power spectrum. Based on the spectral curve, the resonant frequency and resonant peak are quickly located. Sharp peaks in the spectrum correspond to the overall machine's flexible resonant frequency, and the peak amplitude is the overall machine's resonant peak amplitude. When using CSD cross power spectral density analysis, the PRBS pseudo-random micro-position perturbation applied by the system is used as the excitation signal. The corresponding high-frequency torque response signal of the dominant joint is simultaneously acquired. Cross power spectral density analysis is performed based on the two synchronous signals, effectively suppressing industrial environmental noise and irrelevant vibration interference, accurately extracting the frequency domain transfer characteristics between excitation and response, further sharpening the resonant peak, weakening clutter interference, and improving the stability and accuracy of resonant frequency and amplitude extraction. The two methods can be flexibly selected according to the differences in working conditions, so as to fully ensure the accuracy and reliability of the whole machine resonance characteristics extraction under different working scenarios.

[0080] If there is only a single dominant resonance peak in the spectrum, the damping ratio is directly calculated based on this resonance peak using the half-power bandwidth method. If there are multiple obvious resonance peaks formed by the superposition of multiple vibration modes in the spectrum, that is, when the superposition of multiple frequency vibrations is detected in the system, the resonance frequency and resonance peak corresponding to each vibration mode are extracted independently, and the damping ratio of each mode is calculated using the half-power bandwidth method. Based on the resonance peak of each mode, normalization and weighting are performed, with the larger the amplitude, the higher the weight. The final equivalent damping ratio is calculated through weighted fusion to improve the adaptation effect under multi-mode vibration conditions.

[0081] 1.4 Dual-Window Damping Identification and Stability Verification

[0082] After applying excitation to a single dominant joint, while keeping the robot arm's posture, load, and excitation unchanged, a steady-state torque data segment is continuously collected for the single dominant joint where the excitation is located. At the same time, this data segment is divided into two adjacent sliding windows, and damping identification is performed independently for each of the two sliding windows.

[0083] The continuously collected single-joint torque data is divided into two consecutive sliding windows (T1 and T2) in chronological order; the system's default sampling frequency is 1000Hz, and the number of sampling points per window is 1000.

[0084] To avoid identification errors caused by data lag during high-speed robotic arm movement, an adaptive window length adjustment mechanism is set up: when the end effector speed of the robotic arm is greater than 0.5m / s, the sliding window length is automatically shortened by 10%, achieving adaptive and reliable identification under different movement speeds.

[0085] A completely identical signal preprocessing, frequency domain analysis, and damping identification process is applied to both sliding windows. Frequency domain analysis is performed on each sliding window separately, extracting the resonant frequencies (f1, f2) and corresponding resonant peak values ​​(A1, A2) of each single resonant peak from their respective spectra. Based on each resonant peak, half-power points are located at positions with amplitudes half the peak value on both sides, and the half-power bandwidths (Δf1, Δf2) are calculated. The damping ratios (ζ1, ζ2) are obtained using the half-power bandwidth method ζ = Δf / (2f0). Where f1 is the resonant frequency corresponding to sliding window T1, A1 is the resonant peak value corresponding to sliding window T1, Δf1 is the half-power bandwidth corresponding to sliding window T1, ζ1 is the damping ratio corresponding to sliding window T1, f2 is the resonant frequency corresponding to sliding window T2, A2 is the resonant peak value corresponding to sliding window T2, Δf2 is the half-power bandwidth corresponding to sliding window T2, and ζ2 is the damping ratio corresponding to sliding window T2.

[0086] First, calculate the resonant frequency deviation Δf = |f1−f2| between the two sliding windows, and calculate the relative deviation Δf / f1. If Δf / f1 < 2%, the resonant frequency is considered stable under the same load; otherwise, it indicates that the current operating condition has not met the stability conditions required for identification, and the damping ratio stability determination is no longer performed. The identification is directly deemed invalid, and the excitation is reapplied and data is collected again. When the resonant frequency is stable, calculate the damping ratio deviation Δζ = |ζ1-ζ2|. If Δζ < 0.01, the damping ratio result is considered stable and reliable. At this time, the arithmetic mean of the damping ratios of the two sliding windows (i.e., ζ1 and ζ2) is taken to obtain the final equivalent damping ratio (i.e., ζ). The average of the resonant peak values ​​of the two sliding windows (i.e., A1 and A2) is taken as the measured resonant peak value (i.e., Aexp). The average of the resonant frequencies of the two sliding windows (i.e., f1 and f2) is taken as the measured resonant frequency (i.e., fexp) and the model predicted frequency (i.e., f0). If Δζ ≥ 0.01, the damping ratio result is considered unstable, and the excitation is reapplied and data is collected again.

[0087] 1.5 Damping accuracy verification and adaptive load drift compensation

[0088] The inherent physical characteristics of a collaborative robotic arm, comprised of link inertia, joint stiffness, and system damping, allow its low-frequency flexible vibrations to be equivalent to a typical second-order vibration system. This second-order vibration system serves as the dynamic equivalent model for analyzing the vibration characteristics of the collaborative robotic arm. Based on this characteristic, the model's predicted frequency (f0) and damping ratio (ζ) are substituted into the transfer function of the second-order vibration system. The amplitude at the resonant frequency is calculated by converting the signal to the frequency domain, and the model-predicted resonant peak value is obtained. The model-predicted frequency f0 is compared with the measured resonant frequency fexp (which can be the average of the two sliding windows or the resonant frequency of a single sliding window (e.g., f1 or f2)), and the model-predicted resonant peak value Apre is compared with the measured resonant peak value Aexp. When the measured resonant frequency is taken as the resonant frequency of a single sliding window, if the relative frequency deviation is <2% and the relative amplitude deviation is <5%, the damping ratio calculation is considered accurate. When the measured resonant frequency is taken as the average of the two sliding windows, the relative frequency deviation approaches 0, and only a relative amplitude deviation of <5% is needed to determine that the damping ratio calculation result is accurate.

[0089] Once a sudden change in the robotic arm load is detected (load change >= 0.5 kg), the load matching identification process is immediately triggered, and multi-dimensional data of at least two sliding window lengths are immediately cached to support the dual-window damping ratio stability verification. This ensures the reliability of the damping ratio update from the source and ensures that the damping identification is updated quickly after the load changes.

[0090] This application constructs a full-attitude, no-load steady-state torque library covering the entire workspace of a collaborative robotic arm. Combined with an attitude interpolation algorithm, it completely eliminates interference from joint gravity and steady-state friction, achieving high-precision calculation of the end-effector load error to no more than 0.2 kg. This effectively overcomes the technical bottlenecks of poor attitude adaptability and insufficient measurement accuracy in traditional load measurement methods, laying a precise and reliable data foundation for subsequent load grading and adaptive excitation strategies. Addressing the shift characteristics of the robotic arm's first-order resonant frequency under variable load conditions, this application sets an excitation frequency band and amplitude precisely matched to the current load level. Combined with a linear adjustment rule for the end-effector load mass and excitation amplitude, it achieves dynamic adaptation of excitation parameters and load state, effectively solving the technical problems of poor adaptability and misjudgment of resonance characteristics inherent in traditional fixed excitation methods. Simultaneously, a dual-window synchronous damping identification strategy is adopted, establishing a quantitative standard for determining identification effectiveness. The window length can be adaptively adjusted according to the robotic arm's end-effector speed, adapting to high-speed motion conditions and ensuring the stability and reliability of the damping identification results. This application achieves rapid adaptive re-identification by sensing sudden changes in end-load in real time and simultaneously caching multi-dimensional data, effectively avoiding signal acquisition delays and data gaps. For complex scenarios involving superimposed multimodal vibrations, it innovatively employs a composite weighting algorithm based on modal contribution and resonant peak weight. Using the peak amplitude and frequency domain coherence coefficient of each dominant resonant mode as weighting factors, it strengthens the weighting proportion of the dominant resonant mode and dynamically weights and fuses multiple identification results and multimodal damping parameters, significantly improving the accuracy and robustness of damping ratio identification under complex variable load conditions.

[0091] Please see Figure 2The following describes the implementation steps of the adaptive collaborative robotic arm damping identification method based on different loads, using a collaborative robotic arm with a rated load of 20kg and a precision material handling scenario.

[0092] 2.1 Establishment of the Unloaded Steady-State Torque Library

[0093] First, adjust the collaborative robotic arm to a completely unloaded state to ensure that there is no external load or additional external force interference at the end. Then, select 30 typical uniform speed operation postures evenly within the entire workspace of the robotic arm. The selected postures fully cover the main spatial orientations of conventional operations, taking into account both the representativeness of the working conditions and the integrity of the data.

[0094] Data is collected for each selected posture: First, the robotic arm is controlled to run smoothly to the first target posture and maintain a steady state for 3 seconds. After the torque values ​​of each joint have no obvious fluctuations and have completely entered the stable range, the steady-state torque data of the six joints are collected simultaneously through the joint torque sensor on the robotic arm. In order to avoid random collection errors, the posture data is collected three times and the arithmetic mean is taken as the no-load reference torque of each joint under the corresponding posture.

[0095] Following the unified data collection specifications and data processing procedures outlined above, the unloaded reference torques for the remaining 29 typical attitudes were collected and calculated sequentially. The unloaded reference torque data for the six joints corresponding to all attitudes were collected and archived one by one, ultimately forming a complete unloaded steady-state torque library, providing an accurate reference for the elimination of steady-state disturbance torques under subsequent loaded conditions.

[0096] 2.2 End-point load calculation and classification

[0097] The robotic arm performs loaded operations, collecting the current posture joint angle and torque signals in real time. It matches the no-load steady-state torque library through a posture interpolation algorithm to obtain the current posture no-load reference torque. After subtracting the reference torque, the pure load torque component is obtained. Substituting the parameters into the Newton-Euler dynamics model and combining the kinematic and dynamic parameters in the collaborative robotic arm's URDF file, the equivalent load mass at the end effector is calculated.

[0098] In this embodiment, the equivalent load at the end was measured to be 15kg, which was determined to be a heavy load condition.

[0099] 2.3 Adaptive Excitation Application

[0100] Based on preliminary calibration, the fifth joint is identified as the dominant joint contributing the most to the vibration at the end effector of the robotic arm, and adaptive excitation is applied only to the fifth joint. Under heavy load conditions, the excitation amplitude is set to ±0.01 rad, the excitation frequency band covers 5 Hz-25 Hz, and PRBS pseudo-random micro-position perturbation is used and superimposed on the joint target position. The excitation amplitude does not exceed the upper limit of ±0.015 rad and does not interfere with the normal handling trajectory.

[0101] 2.4 Resonance Signal Acquisition and Frequency Domain Analysis

[0102] The real-time torque signal of the fifth joint was collected at a sampling frequency of 1000Hz. After deducting the no-load reference torque, the high-frequency resonant fluctuation component was retained. Frequency domain analysis of this component showed a unique sharp peak in the spectrum. The first-order resonant frequency of the whole machine was measured to be 12Hz. The amplitude of the resonant peak was stable and there was no noise interference.

[0103] 2.5 Identification and Verification of Dual-Window Damping

[0104] Two consecutive 2000 sampling points are extracted and divided into two sliding windows, T1 and T2, with 1000 sampling points in each window. The current movement speed of the robotic arm is 0.3 m / s, so there is no need to shorten the window length. The resonant frequency of T1 is f1 = 12.1 Hz and the corresponding resonant peak value is A1 = 15.15. The half-power points fH1 and fL1 under T1 are determined, and the damping ratio ζ1 = 0.032 is calculated using the half-power bandwidth method. The resonant frequency of T2 is f2 = 11.9 Hz and the corresponding resonant peak value is A2 = 14.08. The half-power points fH2 and fL2 under T2 are determined, and the damping ratio ζ2 = 0.035 is calculated using the half-power bandwidth method.

[0105] Calculation deviation: Δf=0.2Hz, Δf / f1≈1.65%<2%; indicating that the resonant frequency is stable and can be used to determine the stability of the damping ratio. Δζ=0.003<0.01, indicating that the damping identification is stable and effective. The arithmetic mean of the damping ratios of the two sliding windows is taken to obtain the final equivalent damping ratio ζ=0.0335, f0=fexp=(f1+f2) / 2=12Hz, Aexp=(A1+A2) / 2=14.615.

[0106] 2.6 Damping accuracy verification

[0107] Substituting the resonant frequency of 12Hz and the damping ratio of 0.0335 into the second-order vibration system model, the predicted resonant peak value is approximately 14.93 (1 / 2 * 0.0335). Comparing this with the measured resonant peak value, the frequency deviation is approximately 0.83% (less than 2%) (using the single-window frequency as a reference), and the amplitude deviation is approximately 2.16% (less than 5%) (14.615 - 14.93) (less than 5%). Therefore, the damping identification result is accurate.

[0108] This embodiment verifies that the method of this application can achieve accurate and stable identification of the damping parameters of the collaborative robotic arm under variable load, effectively adapt to changes in working conditions, and the damping identification results can be directly used for vibration suppression control to improve the working accuracy of the robotic arm.

[0109] 3.1 Calculation of damping ratio ζ using the half-power bandwidth method

[0110] ζ=(f2-f1) / 2f0

[0111] Where: f0 is the model predicted frequency (the peak frequency found by frequency domain analysis); f1 and f2 are the frequencies corresponding to the half-power points on both sides of the resonance peak (the left and right frequencies at amplitude = Amax / 2, where Amax is the amplitude of the resonance peak).

[0112] 3.2 Frequency corresponding to the half-power points on both sides of the resonance peak

[0113] 1) Find the peak point in the frequency domain analysis spectrum: (f0, A_max);

[0114] 2) Calculate the half-power amplitude: Ahalf = Amax / 1.414 ( ≈1.414);

[0115] 3) Find two points with amplitude equal to Ahalf along the left and right sides of the resonance peak, corresponding to frequencies f1 and f2.

[0116] 3.3 Calculation process from transfer function to model prediction of resonance peak

[0117] 1) Transfer function of a second-order system

[0118] 2) Frequency domain conversion

[0119] Let s = jω (where j is the imaginary unit and ω = 2πf is the angular frequency), and substitute it into the transfer function to obtain the frequency domain response:

[0120] G( )

[0121] 3) Amplitude Calculation

[0122] The amplitude (gain) of the frequency domain response is equal to the magnitude:

[0123]

[0124] 4) Resonance peak position and amplitude

[0125] For a lightly damped system (ζ<0.5), the resonance peak appears near the natural frequency, ω≈ω0=2πf0 (ω0=2πf0: the natural angular frequency of the system when it is undamped).

[0126] Substituting ω=ω0, the denominator simplifies to 2ζf0 Therefore, the resonant peak value is:

[0127]

[0128] 3.4 PRBS pseudo-random micro-position perturbation

[0129] 1) Generate PRBS signal

[0130] The control unit generates a series of ±1 (or 0 / 1) pseudo-random sequences, switches them according to a set step size, and forms discrete position disturbance signals.

[0131] 2) Overlay onto the target location

[0132] qtarget(t)=qnominal(t)+ΔqPRBS(t)

[0133] Where: qnominal(t): the original target position of the operation;

[0134] ΔqPRBS(t): Small PRBS position perturbation (amplitude typically on the order of 0.01°~0.1°);

[0135] qtarget(t): The target request location after overlaying PRBS.

[0136] Since the damping ratio of a robotic arm cannot be directly measured, it is necessary to apply a suitable excitation to induce measurable weak vibrations in the robotic arm, extract the resonance characteristics from the vibration response, and indirectly achieve damping ratio identification. This application aims to improve the accuracy of damping ratio identification for collaborative robotic arms, and solves key technical problems affecting the damping ratio identification process, including low accuracy of end-effector load calculation, mismatch between excitation signal and variable load resonance characteristics, unstable damping identification results, and poor adaptability to sudden load changes.

[0137] 1) High-precision calculation of the equivalent load at the end of the entire attitude range, ensuring that the load mass calculation error is ≤0.2kg, providing an accurate basis for subsequent load classification and excitation matching;

[0138] 2) Based on the resonant frequency characteristics corresponding to different load levels, the excitation amplitude and frequency band can be adaptively adjusted. Without interfering with normal operation, the flexible resonant mode of the collaborative robotic arm can be effectively excited, avoiding misjudgment of resonant characteristics due to noise interference.

[0139] 3) Establish a stability verification mechanism for damping identification results to eliminate random errors in single identification, ensure that damping ratio identification results are stable and reliable, and optimize identification efficiency to adapt to high-speed motion conditions.

[0140] 4) Real-time sensing and adaptive compensation for load changes and drifts are achieved, ensuring continuous and uninterrupted damping identification under variable loads, adapting to multi-frequency vibration superposition scenarios, and improving vibration suppression and adaptation effects under complex working conditions.

[0141] Please see Figure 3In this embodiment of the application, an adaptive cooperative robotic arm damping identification device based on different loads includes a memory and a controller. The memory stores a computer-readable program. When the computer-readable program is called by the controller, it can execute the adaptive cooperative robotic arm damping identification method based on different loads as described in this invention.

[0142] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for identifying the damping of an adaptive cooperative robotic arm based on different loads, characterized in that, Includes the following steps: No-load torque benchmark calibration: By collecting no-load joint torque data of the robotic arm in typical postures in the entire workspace, a no-load steady-state torque library is constructed. The no-load steady-state torque library consists of the joint benchmark torque generated by the robotic arm's own gravity and steady-state friction, and is used to characterize the dynamic change law of joint torque with working posture under no-load conditions. End-load calculation: Based on the no-load steady-state torque library obtained from the no-load torque benchmark calibration, the equivalent end-load mass under the current working condition is calculated through attitude matching, torque separation and dynamic model mapping. Load classification: Based on the magnitude of the equivalent load mass at the end obtained from the end load calculation, the working conditions are divided into three categories: light load, medium load, and heavy load. Adaptive excitation matching: Based on the results of the load classification and the offset characteristics of the first-order resonant frequency of the robotic arm under variable load, an excitation frequency band and amplitude adapted to the current load are set to provide suitable excitation conditions for resonant signal acquisition. Resonance signal acquisition: Select the dominant joint that dominates the vibration of the entire robotic arm, apply the adaptive excitation set by the adaptive excitation matching, and simultaneously acquire the joint torque and angle signals. Combine the no-load steady-state torque library to separate the high-frequency torque fluctuation component caused only by the flexible resonance of the entire machine. Whole machine resonance parameter extraction: The high-frequency torque fluctuation component is processed to extract the resonance frequency and resonance peak value, and the equivalent damping ratio of the robotic arm is calculated based on the resonance frequency and resonance peak value; Dual-window damping identification and stability verification: Dual-window synchronous damping identification is performed on the torque data of the main joint. The resonant frequency and resonant peak value are extracted from the whole machine resonance parameters. The damping ratio is calculated based on the half-power bandwidth method. A quantitative identification effectiveness judgment standard is established to determine the final equivalent damping ratio, measured resonant peak value, measured resonant frequency and model predicted frequency. Damping accuracy verification: The model predicted resonance peak value is calculated based on the model predicted frequency and the final equivalent damping ratio. The model predicted frequency and the model predicted resonance peak value are compared with the measured resonance frequency and the measured resonance peak value to determine the accuracy of the damping ratio calculation results. Load drift adaptive compensation: Real-time detection of end load changes; when a sudden change occurs in the load, a re-identification process is triggered and relevant data is cached.

2. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 1, characterized in that, The specific implementation process for the no-load torque benchmark calibration and end load calculation is as follows: The collaborative robotic arm is controlled to operate at a constant speed under no-load conditions. Multiple sets of joint torque data corresponding to several typical working postures in its entire workspace are collected. Based on the joint torque data, a no-load steady-state torque library is constructed. When the robotic arm is in a loaded operation state, the joint torque signal and joint angle information under the current operation posture are collected in real time. The posture interpolation algorithm is used to match the unloaded steady-state torque library to obtain the unloaded torque reference value that completely corresponds to the current loaded posture. Subtract the no-load torque reference value from the real-time collected loaded joint torque to obtain the pure load torque component caused only by the end load; Substituting the pure load torque component into the Newton-Euler dynamics model, and combining it with the kinematic and dynamic parameters in the robotic arm's URDF file, the mapping calculation from joint torque to end-effector load is completed, yielding the equivalent end-effector load mass under the current working condition.

3. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 2, characterized in that, The selection of typical working postures should comprehensively cover the main spatial orientations of the robotic arm's routine operations; The joint torque data for each typical posture was obtained by repeated sampling, and the arithmetic mean of the multiple sampling data was taken as the no-load reference torque of each joint in that posture.

4. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 1, characterized in that, The specific criteria for load grading and adaptive excitation matching are as follows: Under light load conditions, a pseudo-random binary sequence micro-excitation with an amplitude of less than or equal to ±0.005 rad and covering the frequency band of 25 Hz to 50 Hz is used. Under medium load conditions, a pseudo-random binary sequence micro-excitation with an amplitude greater than ±0.005 rad and less than ±0.01 rad, covering the frequency band of 10Hz to 30Hz, is used. Under heavy load conditions, a pseudo-random binary sequence micro-excitation with an amplitude of ±0.01 rad and covering the frequency band of 5 Hz to 25 Hz is used.

5. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 4, characterized in that, The amplitude of the adaptive excitation is linearly and adaptively adjusted based on the equivalent load mass at the end, and the specific adjustment rule is as follows: For every 5kg increase in end load mass, the excitation amplitude increases linearly by 20%; at the same time, the upper limit threshold of the excitation amplitude is set to ±0.015rad.

6. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 1, characterized in that, The specific process for acquiring the resonant signal and extracting the resonant parameters of the whole machine is as follows: The dominant joint that contributes the most to the end-effector vibration and dominates the overall flexible vibration of the robotic arm is selected as the excitation and signal acquisition object. Adaptive excitation is applied to the dominant joint, and its real-time joint torque signal and joint angle signal are acquired simultaneously. The unloaded steady-state torque of the dominant joint in the current posture is obtained by interpolation of the unloaded steady-state torque library. The unloaded steady-state torque is then subtracted from the real-time collected torque of the loaded joint to obtain the high-frequency torque fluctuation component caused only by the flexible resonant vibration of the whole machine. The high-frequency torque fluctuation component is processed to extract the overall resonance parameters, which include the resonance frequency and the resonance peak value. If there is only a single dominant resonance peak in the spectrum, the damping ratio is calculated based on the half-power bandwidth method using the resonance peak value. If there are multiple obvious resonant peaks formed by the superposition of multiple vibration modes in the spectrum, the resonant frequency and resonant peak value corresponding to each vibration mode are extracted, and the damping ratio of each mode is calculated by the half-power bandwidth method. Then, the resonant peak value of each mode is used as the basis for normalization and weighting to obtain the final equivalent damping ratio.

7. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 1, characterized in that, The specific operations for the dual-window damping identification and stability verification are as follows: After applying excitation to a single dominant joint, under the condition that the robot arm posture, load and excitation parameters remain constant, the steady-state torque data of the dominant joint is continuously collected. The collected steady-state torque data is divided into two consecutive sliding windows, and damping identification is performed independently for the two sliding windows. The two sliding windows use the same signal preprocessing and frequency domain analysis process to extract the resonant frequency and resonant peak value of each window, and calculate the damping ratio of the corresponding window using the half-power bandwidth method. Calculate the relative deviation of the resonant frequency and the damping ratio deviation of the two sliding windows. When the relative deviation of the resonant frequency is <2% and the damping ratio deviation is <0.01, take the arithmetic mean of the damping ratios of the two sliding windows to obtain the final equivalent damping ratio. Take the average of the resonant peaks of the two windows as the measured resonant peak value. Take the average of the frequencies of the two sliding windows as the model predicted frequency. Take the average of the frequencies of the two sliding windows or the resonant frequency of a single sliding window as the measured resonant frequency. If the above deviation thresholds are not met, reapply the excitation and collect torque data until the validity judgment conditions are met.

8. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 7, characterized in that, The dual-window damping identification and stability verification step also includes adaptive adjustment of the window length according to the robot arm's movement speed. Specifically, when the robot arm's end-effector movement speed is greater than 0.5 m / s, the sliding window length is automatically shortened by 10%.

9. The adaptive cooperative robotic arm damping identification method based on different loads according to claim 7, characterized in that, The specific process of damping accuracy verification and load drift adaptive compensation is as follows: Based on the inherent characteristics of low-frequency flexible vibration of the collaborative robotic arm, it is equivalent to a typical second-order vibration system, which is a dynamic equivalent model for analyzing the vibration characteristics of the collaborative robotic arm. The model's predicted frequency and the final equivalent damping ratio are substituted into the preset second-order vibration system transfer function, and after conversion to the frequency domain, the model's predicted resonance peak value is calculated. The model's predicted resonance peak value is compared with the measured resonance peak value to obtain the relative frequency deviation, and the model's predicted frequency is compared with the measured resonance frequency to obtain the relative amplitude deviation. When the measured resonant frequency is taken as the resonant frequency of a single sliding window, if the relative frequency deviation is <2% and the relative amplitude deviation is <5%, then the damping ratio calculation result is determined to be accurate. When the measured resonant frequency is taken as the average of the two sliding windows, if the relative deviation of the amplitude is <5%, the damping ratio calculation result is considered accurate. When a change in load at the end of the robotic arm is detected to be ≥0.5kg, the load matching identification process is immediately triggered, and multi-dimensional data of at least two sliding window lengths are cached simultaneously.

10. An adaptive cooperative robotic arm damping identification device based on different loads, characterized in that, It includes a memory and a controller, wherein the memory stores a computer-readable program, which, when invoked by the controller, can execute the adaptive cooperative robotic arm damping identification method based on different loads as described in any one of claims 1 to 9.

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