An active vibration suppression method and system for robotic arm end effector based on predictive compensation

Abstract

This application relates to the technical field of vibration suppression for robotic arms, and in particular to an active vibration suppression method and system for the end effector of a robotic arm based on predictive compensation. The method includes the following steps: S1, real-time acquisition of triaxial acceleration, angular velocity, and vibration spectrum data of the robotic arm using a high-frequency IMU sensor, monitoring the roll angle, pitch angle, and yaw angle of the base attitude using an auxiliary IMU sensor, and then fusing the dual IMU data using a Kalman filter algorithm; S2, generation of a pre-compensation torque based on the fused data, and optimization of the model gain coefficient by combining the real-time deviation between the measured spectrum from the high-frequency IMU sensor and the model's predicted spectrum, real-time correction, and output of the pre-compensation torque; S3, injection of the corrected compensation torque into the feedforward channel of the joint motor control loop, and output of the vibration suppression torque to the joint actuator through a high-gain controller to real-time offset residual vibration at the end effector of the robotic arm. This application can construct an active vibration suppression system to solve the real-time vibration suppression problem under the aforementioned multi-source disturbance coupling.

Description

Technical Field

[0001] This application relates to the technical field of vibration suppression for robotic arms, and in particular to an active vibration suppression method and system for the end effector of a robotic arm based on predictive compensation. Background Technology

[0002] As a core actuator in industrial automation, the robotic arm's end-effector positioning accuracy directly affects the quality of machining, assembly, and other processes. Under high-speed movement or directional changes, the robotic arm will experience three types of vibrations due to its inherent structural characteristics:

[0003] 1. Joint transmission flexible vibration: Joint transmission flexible vibration originates from the elastic deformation characteristics of the harmonic reducer. As the core transmission component of the robotic arm, the flexible wheel of the harmonic reducer undergoes periodic elastic deformation under high-speed start-stop conditions, resulting in a micron-level angular hysteresis between the joint output shaft and the input shaft. This hysteresis energy is transmitted to the end effector through the connecting rod, forming low-frequency residual vibration, which affects the positioning accuracy of the robotic arm end effector.

[0004] 2. Mechanical Resonance: Mechanical resonance is caused by the frequency domain coupling between lightweight structure and motion excitation. Modern robotic arms widely use carbon fiber composite materials to reduce weight, but the density of natural modes in the 80-150Hz frequency band of thin-walled structures increases significantly. When the acceleration changes abruptly in trajectory planning or the external excitation frequency is close to the natural frequency, the system's kinetic energy is converted into deformation potential energy, forming standing waves at specific nodes with amplitude amplification of more than 3 times, resulting in displacement shift in the vibration energy concentration area at the end of the robotic arm.

[0005] 3. Multi-source coupled vibration: Multi-source coupled vibration is the nonlinear superposition result of base disturbance, load change, and thermal deformation. Base disturbance is transmitted through the kinematic chain. According to the DH coordinate system transformation model, the base attitude angle deviation is amplified by the Jacobian matrix, and the end pose error can reach 3mm. Load change causes transient joint torque, which breaks the dynamic balance and produces low-frequency shaking of 2-10Hz for up to 400ms. Thermal deformation is due to the thermal expansion characteristics of the material. After 4 hours of continuous operation, the connecting rod thermally elongates by 0.1mm, which changes the natural frequency of the structure and makes the original vibration suppression strategy ineffective. After the three are coupled, the vibration energy will be greatly increased, further reducing the positioning accuracy.

[0006] A search revealed Chinese Patent Publication No. CN106737857B, which discloses a vibration suppression method for the end effector of a robotic arm. The method includes the following steps: collecting the acceleration and / or amplitude of the robotic arm's end effector; when the acceleration is greater than or equal to a critical acceleration, slowing the movement of the robotic arm until the acceleration is at a safe level; and / or, when the amplitude is greater than or equal to a critical amplitude, slowing the movement of the robotic arm until the amplitude is at a safe level; when the acceleration is greater than or equal to an alarm acceleration, stopping the movement of the robotic arm and triggering an alarm; and / or, when the amplitude is greater than or equal to a critical amplitude, stopping the movement of the robotic arm and triggering an alarm. Using this method, the end effector vibration of a multi-joint robotic arm can be effectively and quantitatively suppressed, ensuring that the vibration of the robotic arm's end effector is within a reasonable range, effectively guaranteeing the detection quality and equipment safety of the X-ray machine.

[0007] A search revealed Chinese Patent Publication No. CN114347018B, which discloses a method for compensating for disturbances in a robotic arm based on a wavelet neural network. This method mainly consists of two parts: disturbance signal prediction and feedforward feedback compensation. The disturbance signal prediction part addresses the low accuracy and poor real-time performance of nonlinear signal prediction by employing an online prediction model for time-varying near-period disturbance signals analyzed by wavelet neural networks, thereby improving the accuracy of disturbance prediction. The feedforward feedback compensation part addresses the low positioning accuracy of the robot's end effector by using a combined feedforward and feedback compensation control method. Through the established robotic arm dynamics model, joint compensation angles are calculated and added to the feedforward control system to improve the compensation effect, thus enhancing the positioning accuracy of the robotic arm's end effector.

[0008] While prior art 1 (CN106737857B) and prior art 2 (CN114347018B) have unilaterally solved the problem of robotic arm vibration, the aforementioned prior art still has the following technical defects under high-speed or variable load conditions:

[0009] 1. Disconnect between vibration monitoring and compensation: For example, the existing technology 1 relies on the passive vibration suppression strategy of triggering deceleration or stopping based on the end acceleration and amplitude threshold. Its feedback delay causes the failure to suppress high-frequency vibrations >100Hz. Although the existing technology 2 predicts the base disturbance through wavelet neural network, the base IMU cannot capture the high-frequency residual vibration at the end. Moreover, its joint angle compensation requires Jacobian matrix transformation, which introduces a 3-5ms calculation delay. It is difficult to match the phase requirements of the vibration energy concentration area, thus failing to solve the real-time vibration suppression problem.

[0010] 2. Insufficient adaptability of the dynamic model: The weights of the offline trained neural network in the existing technology 2 are fixed, which cannot correct the stiffness matrix drift caused by sudden load changes or the link size changes caused by thermal deformation in real time. This results in a mismatch between the compensation command and the actual dynamic parameters, thus failing to solve the problem of real-time vibration suppression.

[0011] 3. Real-time performance defects in vibration suppression: Existing technologies lack a direct mechanism to cancel high-frequency vibrations. For example, the vibration suppression of existing technology 1 relies on the overall speed reduction of the robotic arm, and the joint angle feedforward of existing technology 2 requires a closed loop of motor PI control. The response bandwidth is insufficient and cannot cover the third harmonic domain of the vibration fundamental frequency (e.g., a 150Hz resonance requires a control bandwidth of more than 450Hz), thus failing to solve the problem of real-time vibration suppression. Summary of the Invention

[0012] In order to construct an active vibration suppression system to solve the real-time vibration suppression problem under the above-mentioned multi-source disturbance coupling, this application provides an active vibration suppression method and system for the end effector of a robotic arm based on predictive compensation.

[0013] Firstly, this application provides an active vibration suppression method for the end effector of a robotic arm based on predictive compensation, employing the following technical solution: An active vibration suppression method for the end effector of a robotic arm based on predictive compensation includes the following steps:

[0014] S1. Collaborative acquisition and fusion of vibration data: A high-frequency IMU sensor is installed on the end flange of the robotic arm to collect the three-axis acceleration, angular velocity and vibration spectrum data of the robotic arm in real time; at the same time, an auxiliary IMU sensor is installed on the base of the robotic arm to monitor the roll angle, pitch angle and yaw angle of the base attitude; then, the high-frequency IMU sensor data and the auxiliary IMU sensor data are fused by the Kalman filter algorithm to improve the signal-to-noise ratio and achieve spatiotemporal synchronization.

[0015] S2. Structural Flexible Vibration Suppression: Based on the vibration data fused in step S1, a pre-compensation torque is generated through the rigid-flexible coupling dynamic model of the robotic arm. The real-time deviation between the measured spectrum of the high-frequency IMU sensor and the predicted spectrum of the model is combined with the Lyapunov stability algorithm to dynamically optimize the gain coefficient in the rigid-flexible coupling dynamic model, correct the output accuracy of the pre-compensation torque in real time, and output the corrected compensation torque.

[0016] S3. Vibration suppression command execution: The corrected compensation torque output in step S2 is injected into the feedforward channel of the joint motor control circuit. Through a high-gain controller whose response bandwidth covers the three-fold harmonic domain of the vibration fundamental frequency, the vibration suppression torque is output to the joint actuator to cancel the residual vibration at the end of the robotic arm in real time.

[0017] Optionally, the dual IMU data fusion method in step S1 includes the following steps:

[0018] S11. Based on the precise time synchronization protocol, achieve microsecond-level time alignment between the high-frequency IMU sensor and the auxiliary IMU sensor, and establish a time domain foundation for subsequent frequency domain processing;

[0019] S12. Using the data synchronized in step S11, perform wavelet threshold denoising on the raw data collected by the high-frequency IMU sensor to eliminate high-frequency interference components above 200Hz. At the same time, use principal component analysis algorithm to separate the effective vibration signal from the environmental temperature drift noise and output a pure vibration signal.

[0020] S13. Calculate the real-time vibration energy value based on the pure vibration signal output in step S12, and dynamically allocate data weights according to the energy threshold. The specific method is as follows:

[0021] When the vibration energy is greater than 0.1 times the gravitational acceleration, the high-frequency IMU sensor data is used as the dominant output.

[0022] When the vibration energy is less than or equal to 0.1 times the gravitational acceleration, the output is switched to auxiliary IMU sensor data for compensation.

[0023] Optionally, the pre-compensation torque generation in step S2 is step S21, which includes the following steps:

[0024] S211. Based on the vibration data fused in step S1, a step-loading experiment of the harmonic reducer is conducted in a constant temperature environment of 25℃ to establish a three-dimensional mapping relationship between joint stiffness and load and velocity; when the joint velocity is greater than 1m / s, the following dynamic adjustments are performed synchronously based on the basic mapping relationship:

[0025] The stiffness compensation coefficient is increased based on the velocity increment gradient to enhance the joint's resistance to deformation and suppress high-frequency vibration.

[0026] The preload output value is reduced according to the inverse proportional function of joint speed to avoid the risk of resonance caused by over-constraint;

[0027] The preload reference value is refreshed every 100ms, and the stiffness compensation coefficient and preload output value are integrated to generate real-time stiffness compensation parameters.

[0028] S212. Based on the real-time stiffness compensation parameters generated in step S211, the 80 to 150 Hz resonance frequency band is identified through finite element modal analysis to locate the concentrated area of ​​vibration energy in the robotic arm; based on the diagnostic results of this resonance frequency band, a band-stop filter command is injected into the pre-compensation torque to suppress the transmission of resonance energy to the end of the robotic arm.

[0029] S213, the real-time stiffness compensation parameters from the dynamic coupling step S211, and the band-stop filtering command from step S212 form a composite vibration suppression strategy that combines time-domain stiffness enhancement and frequency-domain energy blocking. The convergence of the composite vibration suppression strategy is verified using the Lyapunov stability condition to ensure that the torque command input to the module used for gain correction satisfies global asymptotic stability. Then, the composite vibration suppression strategy is optimized based on the verification results. The specific method is as follows:

[0030] Strengthen stiffness compensation weight when high-frequency vibration dominates;

[0031] Increase the weight of the band-stop filter when the resonant frequency band is concentrated.

[0032] S214. The optimized composite vibration suppression strategy is encapsulated into a pre-compensation torque instruction package and transmitted to the module used for gain correction via the standard industrial bus protocol.

[0033] Optionally, step S2 further includes step S22, which suppresses discontinuous vibrations of the trajectory, and includes the following steps:

[0034] S221. The target motion trajectory of the robotic arm is reprogrammed using a fifth-order polynomial, and the acceleration is limited to 300 mm / s² using a time scaling algorithm. 2 Within this range, eliminate acceleration steps at trajectory corners;

[0035] S222. Insert a sinusoidal function transition segment at the corner of the trajectory to make the acceleration curve have a smooth and gradual change characteristic, which directly reduces the impact vibration component in the high-frequency IMU sensor data input in step S1.

[0036] S223. The optimized trajectory command is input to the vibration data collaborative acquisition and fusion module used to implement step S1 as the motion reference for high-frequency IMU sensor data acquisition. At the same time, it is linked with the structural flexible vibration suppression module used to implement step S2 to dynamically generate pre-compensation torque based on trajectory characteristics. The specific method is as follows:

[0037] The stiffness compensation weight is increased in the high-speed section to enhance the joint's resistance to deformation.

[0038] The corner section increases the intensity of the band-stop filter command, blocking the transmission of resonant energy.

[0039] Optionally, step S2 further includes step S23, which suppresses base disturbance transmission, and includes the following steps:

[0040] S231. The roll angle, pitch angle and yaw angle deviations of the base attitude are measured in real time using the auxiliary IMU sensor in step S1.

[0041] S232. Establish a kinematic transformation model of the robotic arm based on spatial vector chain multiplication. By transposing the Jacobian matrix, the end pose offset caused by the base attitude angle deviation in step S231 is mapped to the joint space compensation torque, thereby eliminating the end pose kinematic transmission error of the robotic arm caused by base disturbance.

[0042] S233. The joint space compensation torque of step S232 is proportionally superimposed on the corrected compensation torque output in step S2, wherein the gain coefficient of step S2 is directly proportional to the attitude angle deviation in step S231; then the superimposed total compensation torque is synchronously input into the high-gain controller of step S3, and the end drift caused by the base disturbance is offset in real time through the feedforward channel of step S3 to achieve base disturbance suppression.

[0043] Optionally, step S2 further includes step S24, which suppresses sudden load vibrations, and includes the following steps:

[0044] S241. By installing a torque sensor at the output end of the joint harmonic reducer, the load change rate is detected in real time. When the load change rate is detected to exceed 50 N·m / ms, based on the three-dimensional mapping relationship between joint stiffness and load and speed established in step S211, the stiffness compensation coefficient in step S211 is increased according to the load change intensity ratio. The stiffness matrix value in the rigid-flexible coupling dynamic model in step S2 is updated synchronously, so that the rigid-flexible coupling dynamic model matches the change condition in real time and eliminates the low-frequency resonance caused by dynamic mismatch.

[0045] S242, the linkage module used to implement the composite vibration suppression strategy generation module in step S213, regenerates the pre-compensation torque based on the stiffness matrix value updated in step S241, performs frequency domain spread spectrum processing on the pre-compensation torque through the high-gain controller in step S3 to cover the low-frequency swaying frequency band, and then injects the spread vibration suppression torque into the joint actuator in step S3 through the feedforward channel in step S3 to offset the low-frequency swaying caused by load change in real time and suppress the residual amplitude.

[0046] Optionally, step S2 further includes step S25, dynamic model thermal deformation correction, which includes the following steps:

[0047] S251. Deploy a temperature sensor network on the joints and links of the robotic arm to monitor the temperature change from -10℃ to 60℃ in real time. At the same time, calculate the thermal deformation of the robotic arm links based on the thermal expansion coefficient of the material, analyze the impact of thermal deformation on the vibration data acquisition accuracy of step S1, and quantify the end-positioning error caused by thermal drift.

[0048] S252. Adjust the link size parameters in the rigid-flexible coupling dynamic model in step S2 proportionally according to the amount of thermal deformation, and update the geometric parameters in the three-dimensional mapping relationship between joint stiffness and load and velocity established in step S211 to eliminate the dynamic model mismatch caused by thermal deformation and suppress the model prediction spectrum shift.

[0049] S253. The core parameters of the rigid-flexible coupling dynamic model database in step S2 are automatically calibrated every 30 minutes. This is linked to the composite vibration suppression strategy generation module used in step S213. Based on the updated rigid-flexible coupling dynamic model in step S2, the pre-compensation torque is regenerated. The high-gain controller in step S3 is used to offset the low-frequency drift at the end caused by thermal deformation in real time.

[0050] Optionally, after step S3, step S4 is performed to verify the vibration suppression effect in a closed loop, which includes the following steps:

[0051] S41. Based on the high-frequency IMU sensor data from step S1 and the pure vibration signal output from step S12, extract the acceleration amplitude before and after vibration suppression to calculate the vibration suppression rate. When the vibration suppression rate is less than 70%, execute step S42. When the vibration suppression rate is greater than or equal to 90%, execute step S43.

[0052] S42. Increase the sampling frequency of the high-frequency IMU sensor and the auxiliary IMU sensor in step S1 to enhance the microsecond-level time synchronization accuracy of the high-frequency IMU sensor and the auxiliary IMU sensor; increase the dynamic adjustment frequency of the stiffness compensation weight and band-stop filter intensity in step S213 to improve the convergence speed of the composite vibration suppression strategy; activate the trajectory replanning module used to implement step S221 to reduce the joint speed of the robotic arm to a safe threshold.

[0053] S43. Reduce the torque output of the joint motor through the standard industrial bus protocol in step S214, while maintaining a vibration suppression rate of more than 85% and reducing the total power consumption of the system.

[0054] Secondly, this application provides an active vibration damping system for the end effector of a robotic arm, which adopts the following technical solution: An active vibration damping system for the end effector of a robotic arm, comprising:

[0055] The multi-sensor fusion module includes a high-frequency IMU sensor, an auxiliary IMU sensor, and a joint strain gauge network. The high-frequency IMU sensor is mounted on the end flange of the robotic arm to collect triaxial acceleration, angular velocity, and vibration spectrum data in real time. The auxiliary IMU sensor is mounted on the base of the robotic arm to synchronously monitor roll angle, pitch angle, and yaw angle. The joint strain gauge network is used to form a dual-frequency monitoring network to cover the vibration frequency domain of 0-500Hz.

[0056] The dual-loop control module includes a prediction unit and a correction unit. The prediction unit stores the rigid-flexible coupling dynamics model of the robotic arm and outputs pre-compensation torque commands. The correction unit dynamically optimizes the gain coefficient in the rigid-flexible coupling dynamics model using the Lyapunov stability algorithm.

[0057] The execution module includes a high-gain controller, which outputs a damping torque to the joint actuator, with a response bandwidth covering the third harmonic of the vibration fundamental frequency.

[0058] In summary, this application includes the following beneficial technical effects:

[0059] 1. This application constructs a high-precision vibration monitoring network by integrating dual IMU collaborative acquisition with Kalman filtering. This network accurately captures the three-axis acceleration, angular velocity, and 0-500Hz vibration spectrum at the end of the robotic arm, while eliminating base disturbance interference. Based on a rigid-flexible coupling dynamic model and Lyapunov real-time optimization, a pre-compensation torque is dynamically generated and the output accuracy is corrected, effectively suppressing joint flexibility deformation and mechanical resonance. A high-gain feedforward controller directly injects the vibration suppression torque into the joint actuator, offsetting residual vibration in the 2-150Hz frequency band in real time. This significantly improves stability and processing quality under high-speed operation conditions, thereby constructing an active vibration suppression system to solve the real-time vibration suppression problem under the above-mentioned multi-source disturbance coupling.

[0060] 2. In the multi-source sensing layer, a high-precision vibration monitoring network is constructed by combining dual IMU collaborative acquisition with Kalman filtering. The microsecond-level time synchronization protocol eliminates phase shift caused by transmission delay. Combined with sym8 wavelet basis 5-layer decomposition and soft thresholding, high-frequency interference above 200Hz is suppressed. PCA principal component analysis separates environmental temperature drift noise, outputting a pure vibration signal with residual noise of less than 0.05g. Based on the dynamic weight allocation mechanism of vibration energy threshold, the high-frequency vibration details at the end are preserved under high-energy conditions, and the micro-vibration interference of the base is suppressed under low-energy conditions, providing a highly reliable data foundation for vibration suppression decision-making.

[0061] 3. In the dynamic modeling layer, the step loading experiment of the harmonic reducer establishes a three-dimensional mapping between joint stiffness and load / velocity. Based on the velocity increment gradient, the stiffness compensation coefficient is increased and the preload output is dynamically reduced. Real-time stiffness compensation parameters are refreshed every 100ms to enhance high-speed deformation resistance. Finite element modal analysis accurately locates the 80-150Hz resonant frequency band, and a band-stop filter command is injected to block resonant energy transfer. Lyapunov stability verification dynamically optimizes the time-domain stiffness weight and frequency-domain filter intensity to form a globally stable composite vibration suppression strategy. For discontinuous trajectory vibration, five-fold polynomial... Reprogramming eliminates acceleration steps, and the insertion of a sinusoidal transition segment achieves smooth and gradual acceleration changes, reducing impact vibration energy; base disturbance suppression derives end-positional offset through a spatial vector chain model, generates joint compensation torque through Jacobian transpose mapping, and injects total vibration suppression torque through dynamic gain superposition; load mutation response is detected in real time by a torque sensor, and the stiffness compensation coefficient is increased according to the mutation intensity, and frequency domain spread spectrum processing suppresses low-frequency swaying; thermal deformation correction calculates the connecting rod deformation based on the material's thermal expansion coefficient, dynamically adjusts the model's geometric parameters, and periodic calibration ensures long-term high matching degree of the model.

[0062] 4. In the optimization layer, the high-gain feedforward controller directly injects the vibration suppression torque into the joint actuator, covering the full frequency band of 2-150Hz vibration suppression. The closed-loop verification of the vibration suppression effect is achieved by real-time diagnosis of performance through vibration suppression rate. When the vibration suppression rate is less than 70%, the sampling frequency is increased to 2kHz, the synchronization accuracy is enhanced to 0.5μs, the strategy optimization frequency is increased to 20 times / second, and the joint speed is reduced to 0.8m / s. When the vibration suppression rate is greater than or equal to 90%, the joint torque is reduced by 10%, the power consumption is reduced by 15%, and the vibration suppression rate is maintained at greater than 85%. Attached Figure Description

[0063] Figure 1 This is a flowchart of the active vibration suppression method according to an embodiment of this application;

[0064] Figure 2 This is a flowchart of step S1 of the active vibration suppression method according to an embodiment of this application;

[0065] Figure 3 This is a flowchart of step S2 of the active vibration suppression method in the embodiments of this application;

[0066] Figure 4 This is a flowchart of step S21 of the active vibration suppression method in an embodiment of this application;

[0067] Figure 5 This is a flowchart of step S22 of the active vibration suppression method in the embodiments of this application;

[0068] Figure 6 This is a flowchart of step S23 of the active vibration suppression method in the embodiments of this application;

[0069] Figure 7 This is a flowchart of step S24 of the active vibration suppression method in this application embodiment;

[0070] Figure 8 This is a flowchart of step S25 of the active vibration suppression method in this application embodiment;

[0071] Figure 9 This is a flowchart of step S4 of the active vibration suppression method in this application embodiment;

[0072] Figure 10 This is a diagram illustrating the composition of the active vibration damping system according to an embodiment of this application;

[0073] Figure 11 This is a flowchart of the multi-sensor fusion module in the active vibration suppression system of this application embodiment;

[0074] Figure 12 This is a flowchart of the dual-loop control module in the active vibration damping system of this application embodiment;

[0075] Figure 13This is a flowchart of the execution module in the active vibration damping system of this application embodiment. Detailed Implementation

[0076] The following is in conjunction with the appendix Figure 1-13 This application will be described in further detail.

[0077] This application discloses an active vibration suppression method for the end effector of a robotic arm based on predictive compensation. For example... Figure 1 As shown, an active vibration suppression method for the end effector of a robotic arm based on predictive compensation includes the following steps:

[0078] S1. Collaborative acquisition and fusion of vibration data: A high-frequency IMU sensor is installed on the end flange of the robotic arm to collect the three-axis acceleration, angular velocity, and vibration spectrum data of the robotic arm in real time. The sampling frequency must be greater than 1kHz. At the same time, an auxiliary IMU sensor is installed on the base of the robotic arm to monitor the roll angle, pitch angle, and yaw angle of the base attitude. Then, the high-frequency IMU sensor data and the auxiliary IMU sensor data are fused by the Kalman filter algorithm to improve the signal-to-noise ratio and achieve spatiotemporal synchronization.

[0079] S2. Structural Flexible Vibration Suppression: Based on the vibration data fused in step S1, a pre-compensation torque is generated through the rigid-flexible coupling dynamic model of the robotic arm. The real-time deviation between the measured spectrum of the high-frequency IMU sensor and the predicted spectrum of the model is combined with the Lyapunov stability algorithm to dynamically optimize the gain coefficient in the rigid-flexible coupling dynamic model, correct the output accuracy of the pre-compensation torque in real time, and output the corrected compensation torque.

[0080] S3. Vibration suppression command execution: The corrected compensation torque output in step S2 is injected into the feedforward channel of the joint motor control circuit to avoid the phase delay of traditional PID control. A high-gain controller with a response bandwidth covering three times the frequency domain of the vibration fundamental frequency (response delay ≤ 0.5ms) outputs the vibration suppression torque to the joint actuator to cancel the residual vibration in the 2-150Hz frequency band at the end of the robotic arm in real time.

[0081] This method constructs a high-precision vibration monitoring network by combining dual IMU collaborative acquisition with Kalman filtering. It accurately captures the three-axis acceleration, angular velocity, and vibration spectrum of the robotic arm end effector in the 0-500Hz range, while eliminating base disturbance interference. Based on a rigid-flexible coupling dynamic model and Lyapunov real-time optimization, it dynamically generates pre-compensation torque and corrects the output accuracy, effectively suppressing joint flexibility deformation and mechanical resonance. Through a high-gain feedforward controller, the vibration suppression torque is directly injected into the joint actuator to cancel residual vibration in the 2-150Hz frequency band in real time, significantly improving stability and processing quality under high-speed operating conditions.

[0082] like Figure 2 As shown, the dual IMU data fusion method in step S1 includes the following steps:

[0083] S11. Based on the precise time synchronization protocol, microsecond-level time alignment between the high-frequency IMU sensor and the auxiliary IMU sensor is achieved. The sampling time is marked by hardware timestamps to eliminate phase shift caused by transmission delay, and a time domain reference is established for subsequent frequency domain analysis. The synchronized data stream is transmitted in parallel to the data processing unit at a sampling rate of 1kHz to ensure time domain consistency.

[0084] S12. Based on the data synchronized in step S11, the raw data collected by the high-frequency IMU sensor is decomposed into 5 levels using the sym8 wavelet basis to separate vibration components of different frequency bands. Soft thresholding is applied to high-frequency components above 200Hz to eliminate electromagnetic interference and high-frequency noise, retaining the denoised signal with effective vibration characteristics. PCA decomposition is performed on the denoised data to extract the first three principal components with an energy ratio of more than 95% as effective vibration signals. Environmental temperature drift noise is separated, and the triaxial acceleration and angular velocity signals are reconstructed based on the principal components. The residual noise is less than 0.05 times the gravitational acceleration, and then a clean vibration signal is output.

[0085] S13. Squaring and summing the triaxial acceleration components of the pure vibration signal output in step S12, then taking the square root of the sum to obtain the real-time vibration energy scalar, and then dynamically allocating data weights according to the energy threshold, as follows:

[0086] When the vibration energy is greater than 0.1 times the gravitational acceleration, the high-frequency IMU sensor data is used as the main output, and the high-frequency vibration details at the end are preserved. That is, the high-frequency IMU sensor data accounts for 80% and the auxiliary IMU sensor data accounts for 20%.

[0087] When the vibration energy is less than or equal to 0.1 times the gravitational acceleration, the output is switched to auxiliary IMU sensor data for compensation to suppress micro-vibration interference of the base. That is, the high-frequency IMU sensor data accounts for 60% and the auxiliary IMU sensor data accounts for 40%.

[0088] S14. The dynamic weight allocation results are fused through a Kalman filter to output the final vibration suppression reference signal.

[0089] The fusion method in step S14 is as follows:

[0090] S141. Based on the time correlation of the vibration signal, predict the vibration state at the next moment. For example, if there is an upward acceleration trend at present, predict that the upward motion inertia will still be maintained at the next moment.

[0091] S142. As the prediction step size increases, the state confidence is reduced to simulate prediction uncertainty. The attenuation magnitude is calibrated by static sensor testing.

[0092] S143. Compare the predicted state with the weighted fused observation data and calculate the difference value;

[0093] S144. If the difference exceeds the sensor calibration error (e.g., >0.005g), increase the correction strength (up to 90%) to quickly bring the predicted value closer to the observed value; if the difference is small (<0.001g), decrease the correction strength (down to 10%) to avoid over-adjustment oscillation.

[0094] S145. The corrected residual is superimposed on the predicted state, and the optimized true value of the vibration signal is output.

[0095] S146. Improve the state confidence based on the correction effect to provide a more reliable starting point for the next round of prediction.

[0096] Step S1 eliminates phase shift caused by transmission delay through a microsecond-level time synchronization protocol, ensuring time-domain consistency of dual IMU data and establishing a high-precision benchmark for frequency-domain analysis. A 5-layer decomposition of the sym8 wavelet basis and soft thresholding are employed to effectively suppress high-frequency interference above 200Hz. Combined with PCA principal component analysis, the first three principal components are extracted to separate environmental temperature drift noise, outputting a pure vibration signal with residual noise less than 0.05g. Based on a dynamic weight allocation mechanism for vibration energy thresholds, high-frequency IMU sensor data dominates to preserve end-vibration details under high-energy conditions, while auxiliary IMU sensor data is switched to suppress micro-vibration interference from the base under low-energy conditions. Finally, a Kalman filter is used to fuse and output a vibration suppression benchmark signal, significantly improving vibration monitoring accuracy and adaptability to different operating conditions.

[0097] like Figure 3 and Figure 4 As shown, the pre-compensation torque generated in step S2 is step S21, which includes the following steps:

[0098] S211. Based on the vibration data fused in step S1, a stepped loading experiment of the harmonic reducer was conducted in a constant temperature environment of 25℃. The load gradient increased from 0-20kg in increments of 2kg, and the speed range covered from 0.1-3m / s. A three-dimensional mapping relationship between joint stiffness and load and speed was established. When the joint speed was greater than 1m / s, the following dynamic adjustments were performed synchronously based on the basic mapping relationship:

[0099] a. The stiffness compensation coefficient is increased based on the velocity increment gradient (the stiffness compensation coefficient increases by 15% for every 0.5 m / s increase in velocity) to enhance the joint's resistance to deformation and suppress high-frequency vibrations. The formula for calculating the stiffness compensation amount brought about by the velocity increment is as follows:

[0100]

[0101] in, This represents the stiffness compensation due to the velocity increment, where v is the real-time joint velocity. The basic value of joint stiffness output from the stepped loading experiment in step S211;

[0102] b. Reduce the preload output value according to the inverse proportional function of joint velocity to avoid the risk of resonance caused by over-constraint. The formula for calculating the preload output value is:

[0103]

[0104] in, This is the real-time preload output value. 0.2 is the reference preload (calibrated value at low speed ≤ 1m / s), and 0.2 is the speed influence factor (to suppress resonance caused by over-constraint).

[0105] c. The preload reference value is refreshed every 100ms. The stiffness compensation coefficient and the preload output value are integrated to generate real-time stiffness compensation parameters to support high-frequency vibration suppression. The calculation formula for the real-time stiffness compensation parameters is as follows:

[0106]

[0107] in, These are the parameters for real-time stiffness compensation.

[0108] S212. Based on the real-time stiffness compensation parameters generated in step S211, the 80 to 150 Hz resonance frequency band is identified through finite element modal analysis to locate the concentrated area of ​​vibration energy in the robotic arm; based on the diagnostic results of this resonance frequency band, a band-stop filter command is injected into the pre-compensation torque to suppress the transmission of resonance energy to the end of the robotic arm.

[0109] S213, the real-time stiffness compensation parameters from the dynamic coupling step S211, and the band-stop filtering command from step S212 form a composite vibration suppression strategy that combines time-domain stiffness enhancement and frequency-domain energy blocking. The convergence of the composite vibration suppression strategy is verified using the Lyapunov stability condition to ensure that the torque command input to the module used for gain correction satisfies global asymptotic stability. Then, the composite vibration suppression strategy is optimized based on the verification results. The specific method is as follows:

[0110] When high-frequency vibration dominates, the stiffness compensation weight is increased. That is, when the proportion of components greater than 100Hz is greater than 60%, the stiffness compensation weight is increased to 1.2-1.5 times.

[0111] When the resonant frequency band is concentrated, the weight of the band-stop filter is increased. That is, when the energy of 80-150Hz is greater than 70% of the total energy, the weight of the band-stop filter is increased to 1.3 times.

[0112] S214. The optimized composite vibration suppression strategy is encapsulated into a pre-compensation torque instruction package and transmitted to the module used for gain correction via the standard industrial bus protocol.

[0113] Step S21 constructs a high-precision three-dimensional mapping of joint stiffness with load and velocity through a stepped loading experiment of a harmonic reducer. The stiffness compensation coefficient is increased based on the velocity increment gradient, and the preload output is dynamically reduced. Real-time stiffness compensation parameters are refreshed every 100ms, significantly enhancing the deformation resistance under high-speed conditions. Based on finite element modal analysis, the 80-150Hz resonant frequency band is accurately located, and a band-stop filter command is injected to block the resonant energy transfer. Through Lyapunov stability verification, the time-domain stiffness weight and frequency-domain filter intensity are dynamically optimized to form a globally stable composite vibration suppression strategy. Finally, the transmission command is encapsulated and transmitted to the gain correction module using a standard industrial bus protocol, achieving highly reliable, low-delay closed-loop control of the pre-compensation torque. This solves the multi-frequency vibration coupling problem under high-speed, high-load conditions and suppresses residual vibration at the end.

[0114] like Figure 3 and Figure 5 As shown, step S2 further includes step S22, which suppresses discontinuous vibrations of the trajectory, and includes the following steps:

[0115] S221. The target motion trajectory of the robotic arm is reprogrammed using a fifth-order polynomial, and the acceleration is limited to 300 mm / s² using a time scaling algorithm. 2 Within this range, eliminate acceleration steps at trajectory corners;

[0116] S222. Insert a sinusoidal function transition segment at the corner of the trajectory to make the acceleration curve have a smooth and gradual change characteristic, which directly reduces the impact vibration component in the high-frequency IMU sensor data input in step S1.

[0117] S223. The optimized trajectory command is input to the vibration data collaborative acquisition and fusion module used to implement step S1 as the motion reference for high-frequency IMU sensor data acquisition. At the same time, it is linked with the structural flexible vibration suppression module used to implement step S2 to dynamically generate pre-compensation torque based on trajectory characteristics. The specific method is as follows:

[0118] The stiffness compensation weight is increased in the high-speed section to enhance the joint's resistance to deformation.

[0119] The corner section increases the strength of the band-stop filter command, blocking the transmission of resonant energy in the 80-150Hz range.

[0120] Step S22 eliminates acceleration steps at corners through fifth-order polynomial trajectory replanning, and combines the insertion of a sinusoidal transition segment to make the acceleration curve smooth and gradual, directly suppressing the impact vibration component greater than 100Hz in the high-frequency IMU sensor data; the optimized trajectory is used as the motion reference input to the vibration acquisition module, and the vibration suppression module is linked to strengthen the stiffness compensation weight in the high-speed section to improve the joint's resistance to deformation, and strengthen the band-stop filtering intensity in the corner section to block the transmission of resonance energy, significantly reducing the impact vibration and resonance risk caused by trajectory discontinuity, and suppressing the residual amplitude at the end.

[0121] like Figure 3 and Figure 6 As shown, step S2 further includes step S23, which suppresses the transmission of base disturbances, and includes the following steps:

[0122] S231. The roll angle, pitch angle and yaw angle deviations of the base attitude are measured in real time using the auxiliary IMU sensor in step S1.

[0123] S232. Establish a kinematic transformation model of the robotic arm based on spatial vector chain multiplication. By transposing the Jacobian matrix, the end pose offset caused by the base attitude angle deviation in step S231 is mapped to the joint space compensation torque, thereby eliminating the end pose kinematic transmission error of the robotic arm caused by base disturbance.

[0124] S233. The joint space compensation torque of step S232 is proportionally superimposed on the corrected compensation torque output in step S2, wherein the gain coefficient of step S2 is directly proportional to the attitude angle deviation in step S231; then the superimposed total compensation torque is synchronously input into the high-gain controller of step S3, and the end drift caused by the base disturbance is offset in real time through the feedforward channel of step S3 to achieve base disturbance suppression.

[0125] Step S23 uses the base IMU to capture the roll angle, pitch angle and yaw angle deviations in real time through high-precision attitude monitoring. The end pose offset is derived based on the spatial vector chain dynamics model, and the joint compensation torque is generated by the transpose mapping of the Jacobian matrix to accurately eliminate the kinematic transmission error caused by the base disturbance. The compensation torque is injected into the total vibration damping torque in proportion through the dynamic gain superposition mechanism. Combined with high-gain feedforward control, the end drift is offset in real time, thereby improving the positioning accuracy under the condition of base disturbance.

[0126] like Figure 3 and Figure 7 As shown, step S2 further includes step S24, which suppresses sudden load vibrations, and includes the following steps:

[0127] S241. By installing a torque sensor at the output end of the joint harmonic reducer, the load change rate is detected in real time. When the load change rate is detected to exceed 50 N·m / ms, based on the three-dimensional mapping relationship between joint stiffness and load and speed established in step S211, the stiffness compensation coefficient in step S211 is increased according to the load change intensity ratio. The stiffness matrix value in the rigid-flexible coupling dynamic model in step S2 is updated synchronously, so that the rigid-flexible coupling dynamic model matches the change condition in real time and eliminates the low-frequency resonance caused by dynamic mismatch.

[0128] S242, the linkage module used to implement the composite vibration suppression strategy generation module in step S213, regenerates the pre-compensation torque based on the stiffness matrix value updated in step S241, performs frequency domain spread spectrum processing on the pre-compensation torque through the high-gain controller in step S3, expands the vibration suppression frequency band to 2-10Hz, covers the low-frequency shaking caused by load change, and then injects the spread vibration suppression torque into the joint actuator in step S3 through the feedforward channel in step S3, to offset the low-frequency shaking caused by load change in real time and suppress the residual amplitude.

[0129] Step S24 uses a high-precision torque sensor to detect the load change rate in real time, dynamically increases the stiffness compensation coefficient based on the three-dimensional stiffness mapping relationship, and synchronously updates the stiffness matrix of the rigid-flexible coupling dynamic model to eliminate the 6-10Hz low-frequency resonance caused by sudden load changes. The linkage composite vibration suppression strategy module regenerates the pre-compensation torque, which is then spread in the frequency domain by a high-gain controller to generate a vibration suppression torque. This torque is then injected into the joint actuator in real time through a feedforward channel to suppress the low-frequency swaying amplitude caused by sudden load changes, significantly improving the end-effector stability under heavy-load gripping conditions.

[0130] like Figure 3 and Figure 8 As shown, step S2 also includes step S25, thermal deformation correction of the dynamic model, which includes the following steps:

[0131] S251. Deploy a temperature sensor network on the joints and links of the robotic arm to monitor the temperature change from -10℃ to 60℃ in real time. At the same time, calculate the thermal deformation of the robotic arm links based on the thermal expansion coefficient of the material, analyze the impact of thermal deformation on the vibration data acquisition accuracy of step S1, and quantify the end-positioning error caused by thermal drift.

[0132] S252. Adjust the link size parameters in the rigid-flexible coupling dynamic model in step S2 proportionally according to the amount of thermal deformation, and update the geometric parameters in the three-dimensional mapping relationship between joint stiffness and load and velocity established in step S211 to eliminate the dynamic model mismatch caused by thermal deformation and suppress the model prediction spectrum shift.

[0133] S253. The core parameters of the rigid-flexible coupling dynamic model database in step S2 are automatically calibrated every 30 minutes. This is linked to the composite vibration suppression strategy generation module used in step S213. Based on the updated rigid-flexible coupling dynamic model in step S2, the pre-compensation torque is regenerated. The high-gain controller in step S3 is used to offset the low-frequency drift at the end caused by thermal deformation in real time.

[0134] Step S25 monitors the temperature change from -10℃ to 60℃ in real time through a temperature sensor network, accurately calculates the thermal deformation of the robotic arm link based on the material's thermal expansion coefficient, and quantifies the end-effector positioning error caused by thermal drift; dynamically adjusts the link size parameters of the rigid-flexible coupling dynamic model according to the deformation amount and simultaneously updates the geometric parameters of the joint stiffness and the mapping relationship between load and velocity to eliminate model mismatch caused by thermal deformation; refreshes the core parameters of the model database through a 30-minute periodic calibration mechanism, regenerates the pre-compensation torque in conjunction with the composite vibration suppression strategy module, and cancels the low-frequency drift of the end-effector in real time through a high-gain controller bandpass filter, thereby improving the positioning accuracy of the robotic arm under continuous operation for 8 hours.

[0135] like Figure 1 and Figure 9 As shown, after step S3, step S4 is performed to verify the vibration suppression effect in a closed loop, which includes the following steps:

[0136] S41. Based on the high-frequency IMU sensor data from step S1 and the pure vibration signal output from step S12, extract the acceleration amplitude before and after vibration suppression to calculate the vibration suppression rate. When the vibration suppression rate is less than 70%, execute step S42. When the vibration suppression rate is greater than or equal to 90%, execute step S43.

[0137] S42. Increase the sampling frequency of the high-frequency IMU sensor and the auxiliary IMU sensor in step S1 to 2kHz, and enhance the microsecond-level time synchronization accuracy of the high-frequency IMU sensor and the auxiliary IMU sensor to 0.5μs; increase the dynamic adjustment frequency of the stiffness compensation weight and band-stop filter intensity in step S213 to 20 times / second, so as to improve the convergence speed of the composite vibration suppression strategy; activate the trajectory replanning module used to implement step S221, and reduce the joint speed of the robotic arm to a safe threshold of 0.8m / s;

[0138] S43. Reduce the torque output of the joint motor by 10% using the standard industrial bus protocol in step S214, while maintaining a vibration suppression rate of greater than 85% and reducing the total power consumption of the system by 15%.

[0139] Step S4 quantifies and evaluates the vibration suppression efficiency in real time. When the vibration suppression rate is less than 70%, step S42 is executed, the sampling frequency is increased to 2kHz, the synchronization accuracy is enhanced to 0.5μs, the high-frequency vibration capture capability is improved, the strategy optimization frequency is increased to 20 times / second, the convergence of the composite vibration suppression strategy is accelerated, the joint speed is reduced to 0.8m / s, and the impact energy is suppressed. When the vibration suppression rate is greater than or equal to 90%, step S43 is executed, the joint torque output is reduced by 10% through the standard industrial bus protocol, the system power consumption is reduced by 15%, and the vibration suppression rate is maintained at greater than 85%, so as to achieve a dynamic balance between vibration suppression efficiency and energy consumption and improve the end positioning accuracy under all working conditions.

[0140] This application significantly improves the positioning accuracy and stability of the robotic arm end effector under high-speed and high-load conditions through multi-source sensing, dynamic modeling, and execution optimization, as detailed below:

[0141] In the multi-source sensing layer, a high-precision vibration monitoring network is constructed by combining dual IMU collaborative acquisition with Kalman filtering. The microsecond-level time synchronization protocol eliminates phase shift caused by transmission delay. Combined with sym8 wavelet basis 5-layer decomposition and soft thresholding, high-frequency interference above 200Hz is suppressed. PCA principal component analysis separates environmental temperature drift noise, outputting a pure vibration signal with residual noise of less than 0.05g. Based on the dynamic weight allocation mechanism of vibration energy threshold, the high-frequency vibration details at the end are preserved under high-energy conditions, and the micro-vibration interference of the base is suppressed under low-energy conditions, providing a highly reliable data foundation for vibration suppression decision-making.

[0142] In the dynamic modeling layer, the stepped loading experiment of the harmonic reducer establishes a three-dimensional mapping between joint stiffness and load / velocity. Based on the velocity increment gradient, the stiffness compensation coefficient is increased and the preload output is dynamically reduced. Real-time stiffness compensation parameters are refreshed every 100ms to enhance high-speed deformation resistance. Finite element modal analysis accurately locates the 80-150Hz resonant frequency band, and a band-stop filter command is injected to block resonant energy transfer. Lyapunov stability verification dynamically optimizes the time-domain stiffness weight and frequency-domain filter intensity to form a globally stable composite vibration suppression strategy. For discontinuous trajectory vibration, a fifth-order polynomial... The replanning eliminates acceleration steps, and the insertion of a sinusoidal transition segment achieves smooth and gradual acceleration changes, reducing impact vibration energy; the base disturbance suppression derives the end pose offset through a spatial vector chain model, generates joint compensation torque through Jacobian transpose mapping, and injects total vibration suppression torque through dynamic gain superposition; the load mutation response is detected in real time by a torque sensor, and the stiffness compensation coefficient is increased according to the mutation intensity, and low-frequency sway is suppressed through frequency domain spread spectrum processing; the thermal deformation correction calculates the connecting rod deformation based on the material's thermal expansion coefficient, dynamically adjusts the model's geometric parameters, and periodically calibrates to ensure the model's long-term high matching degree.

[0143] At the optimization layer, the high-gain feedforward controller directly injects the vibration suppression torque into the joint actuator, covering the full frequency band of 2-150Hz vibration suppression. The closed-loop verification of the vibration suppression effect is achieved by real-time diagnosis of performance through vibration suppression rate. When the vibration suppression rate is less than 70%, the sampling frequency is increased to 2kHz, the synchronization accuracy is enhanced to 0.5μs, the strategy optimization frequency is increased to 20 times / second, and the joint speed is reduced to 0.8m / s. When the vibration suppression rate is greater than or equal to 90%, the joint torque is reduced by 10%, the power consumption is reduced by 15%, and the vibration suppression rate is maintained at greater than 85%.

[0144] In summary, this application constructs an active vibration suppression system, solving the real-time vibration suppression problem under multi-source disturbance coupling in the prior art, and providing core technical support for high-precision operation scenarios such as precision manufacturing and semiconductor assembly. The specific effects are as follows:

[0145] 1. Improved precision: The positioning accuracy of the robotic arm end effector reaches ±0.03mm, the thermal drift suppression rate is ≥90%, and the positioning drift is <0.1mm after 8 hours of continuous operation;

[0146] 2. Vibration suppression performance: The residual vibration suppression rate of 2-150Hz is ≥92%, of which the resonance energy of 150Hz is reduced by 40dB, and the low-frequency sway amplitude of 10Hz is reduced from 0.25mm to 0.02mm;

[0147] 3. Dynamic response: The delay from vibration occurrence to vibration suppression execution is less than 5ms, and the convergence speed of the composite strategy is improved by 60%;

[0148] 4. Energy efficiency balance: When the vibration suppression rate is greater than or equal to 90%, the power consumption is reduced by 15%, and the vibration suppression rate is maintained above 85%;

[0149] 5. Operating condition adaptability: Covers multiple disturbance scenarios such as high speed, heavy load, track corners, and base disturbance, improving stability under all operating conditions.

[0150] Example 2

[0151] This embodiment discloses an active vibration damping system at the end effector of a robotic arm. For example... Figure 10 As shown, an active vibration damping system at the end of a robotic arm includes a multi-sensor fusion module, a dual-loop control module, and an execution module.

[0152] like Figure 11 As shown, the multi-sensor fusion module includes a high-frequency IMU sensor, an auxiliary IMU sensor, and a joint strain gauge network. The high-frequency IMU sensor is installed on the end flange of the robotic arm; the auxiliary IMU sensor is installed on the base of the robotic arm; and the joint strain gauge network is installed in a circumferentially distributed manner at the output end of the harmonic reducer.

[0153] The multi-sensor fusion module accurately captures triaxial acceleration, angular velocity, and 0-500Hz vibration spectrum data at the end effector of the robotic arm using a high-frequency IMU sensor, and monitors high-frequency micro-vibration components above 100Hz in real time. An auxiliary IMU sensor, combined with a temperature drift compensation mechanism, synchronously monitors base attitude disturbance data to eliminate base drift interference. A network of joint strain gauges detects ±0.15mm elastic deformation in a circumferentially distributed manner and sets a 50N·m / ms load mutation trigger threshold, achieving high-sensitivity deformation sensing. These three components form a dual-frequency monitoring network through microsecond-level time synchronization based on the PTP protocol: the 0-10Hz low-frequency band is covered by the joint strain gauge network and auxiliary IMU sensor, while the 80-500Hz high-frequency band is dominated by the high-frequency IMU sensor, improving the signal-to-noise ratio and reducing residual noise. This provides a full-frequency, high-precision, and low-latency vibration sensing foundation for vibration suppression control, significantly enhancing operational adaptability and the reliability of vibration suppression decisions.

[0154] like Figure 12As shown, the dual-loop control module includes a prediction unit and a correction unit. The prediction unit is used to store the rigid-flexible coupling dynamic model of the robotic arm and integrates a three-dimensional mapping database of stiffness and load, velocity, and a finite element modal analysis engine.

[0155] The dual-loop control module generates joint stiffness compensation coefficients in real time through a three-dimensional mapping database of stiffness, load, and velocity of the prediction unit, dynamically refreshing parameters every 100ms, significantly enhancing the joint's resistance to deformation under high-speed conditions. The finite element modal analysis engine accurately identifies the 80-150Hz resonant frequency band, generating band-stop filtering commands with a stopband attenuation of ≥40dB, effectively blocking the transmission of resonant energy. The correction unit uses the Lyapunov stability algorithm to construct an energy function, ensuring global asymptotic stability, and dynamically optimizes the weight of the composite vibration suppression strategy according to the vibration conditions: when high-frequency vibration dominates (energy proportion greater than 100Hz > 60%), the stiffness compensation weight is increased to 1.5 times to enhance the joint's resistance to high-frequency impact; when the resonant frequency band is concentrated (energy proportion greater than 70% in the 80-150Hz range), the band-stop filtering intensity is increased to 1.3 times to improve the resonant energy suppression rate.

[0156] like Figure 13 As shown, the execution module includes a high-gain controller and a joint actuator. The high-gain controller has a response bandwidth covering three times the frequency of the vibration fundamental frequency and injects the vibration damping torque into the feedforward channel of the joint motor. The joint actuator adopts a harmonic reducer vibration damping structure, which includes a double-row crossed roller bearing integrated piezoelectric ceramic actuator and a preload dynamic control mechanism.

[0157] The execution module directly injects the damping torque into the feedforward channel of the joint motor through a high-gain controller, avoiding the phase delay problem of traditional PID closed loops. The current loop control accuracy reaches ±0.5%, significantly improving the real-time performance and accuracy of the damping command. The joint actuator adopts an innovative harmonic reducer damping structure, which directly cancels the elastic deformation detected by the joint strain gauge network (response delay <0.2ms) through a double-row crossed roller bearing integrated piezoelectric ceramic actuator, achieving real-time compensation for micron-level deformation and improving the attenuation of 150Hz resonance energy. The preload dynamic adjustment mechanism maintains the benchmark preload at low speed (≤1m / s) to ensure the smooth operation of the joint, and increases the preload output by 40% at high speed (>1m / s), enhancing the joint's resistance to deformation and suppressing the inertial impact caused by high-speed start-stop. The dual technologies work together to cover residual vibration suppression across the entire 2-150Hz frequency band, resulting in more stable amplitude. At the same time, the instantaneous torque injection through the feedforward channel solves the response lag problem of traditional damping systems under high-speed variable load conditions, improving the positioning accuracy of the robotic arm end effector.

[0158] The implementation principle of the active vibration suppression system at the end of a robotic arm in this embodiment is as follows: A multi-sensor fusion module achieves full-frequency vibration sensing, namely, a high-frequency IMU sensor precisely captures the vibration spectrum of the end effector from 0-500Hz, monitors high-frequency micro-vibration components above 100Hz in real time, an auxiliary IMU sensor combined with a temperature drift compensation mechanism eliminates base drift interference, and a joint strain gauge network detects elastic deformation and sets a load mutation trigger threshold. The three are synchronized at the microsecond level to form a dual-frequency monitoring network, providing a high-precision, low-latency sensing basis for vibration suppression control; a dual-loop control module generates joint stiffness compensation coefficients in real time based on a three-dimensional mapping database of stiffness, load, and velocity, enhancing high-speed resistance to deformation. The finite element modal analysis engine accurately identifies the 80-150Hz resonant frequency band and generates band-stop filtering commands. The correction unit constructs an energy function using the Lyapunov stability algorithm to ensure global asymptotic stability and dynamically optimizes the vibration suppression strategy weights to improve the resonance suppression rate. The high-gain controller of the execution module injects the vibration suppression torque into the feedforward channel to avoid PID phase delay. The double-row crossed roller bearing integrated piezoelectric ceramic actuator of the joint actuator directly cancels elastic deformation. The preload dynamic control mechanism maintains the reference preload under low-speed conditions and increases the output by 40% under high-speed conditions to enhance the anti-deformation capability. The dual technologies work together to cover vibration suppression across the entire 2-150Hz frequency band. In summary, this application constructs an active vibration suppression system to solve the real-time vibration suppression problem under multi-source disturbance coupling in the prior art.

[0159] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A method for active vibration suppression at the end effector of a robotic arm based on predictive compensation, characterized in that: Includes the following steps: S1. Collaborative acquisition and fusion of vibration data: A high-frequency IMU sensor is installed on the end flange of the robotic arm to collect the three-axis acceleration, angular velocity and vibration spectrum data of the robotic arm in real time; at the same time, an auxiliary IMU sensor is installed on the base of the robotic arm to monitor the roll angle, pitch angle and yaw angle of the base attitude; then, the high-frequency IMU sensor data and the auxiliary IMU sensor data are fused by the Kalman filter algorithm to improve the signal-to-noise ratio and achieve spatiotemporal synchronization. S2. Structural Flexible Vibration Suppression: Based on the vibration data fused in step S1, a pre-compensation torque is generated through the rigid-flexible coupling dynamic model of the robotic arm. The real-time deviation between the measured spectrum of the high-frequency IMU sensor and the predicted spectrum of the model is combined with the Lyapunov stability algorithm to dynamically optimize the gain coefficient in the rigid-flexible coupling dynamic model, correct the output accuracy of the pre-compensation torque in real time, and output the corrected compensation torque. S3. Vibration suppression command execution: The corrected compensation torque output in step S2 is injected into the feedforward channel of the joint motor control circuit. Through a high-gain controller whose response bandwidth covers the three-fold harmonic domain of the vibration fundamental frequency, the vibration suppression torque is output to the joint actuator to cancel the residual vibration at the end of the robotic arm in real time.

2. The active vibration suppression method for a robotic arm end effector based on predictive compensation according to claim 1, characterized in that: The dual IMU data fusion method in step S1 includes the following steps: S11. Based on the precise time synchronization protocol, achieve microsecond-level time alignment between the high-frequency IMU sensor and the auxiliary IMU sensor, and establish a time domain foundation for subsequent frequency domain processing; S12. Using the data synchronized in step S11, perform wavelet threshold denoising on the raw data collected by the high-frequency IMU sensor to eliminate high-frequency interference components above 200Hz. At the same time, use principal component analysis algorithm to separate the effective vibration signal from the environmental temperature drift noise and output a pure vibration signal. S13. Calculate the real-time vibration energy value based on the pure vibration signal output in step S12, and dynamically allocate data weights according to the energy threshold. The specific method is as follows: When the vibration energy is greater than 0.1 times the gravitational acceleration, the high-frequency IMU sensor data is used as the dominant output. When the vibration energy is less than or equal to 0.1 times the gravitational acceleration, the output is switched to auxiliary IMU sensor data for compensation.

3. The active vibration suppression method for the end effector of a robotic arm based on predictive compensation according to claim 1, characterized in that: The pre-compensation torque generation in step S2 is step S21, which includes the following steps: S211. Based on the vibration data fused in step S1, a step-loading experiment of the harmonic reducer is conducted in a constant temperature environment of 25℃ to establish a three-dimensional mapping relationship between joint stiffness and load and velocity; when the joint velocity is greater than 1m / s, the following dynamic adjustments are performed synchronously based on the basic mapping relationship: The stiffness compensation coefficient is increased based on the velocity increment gradient to enhance the joint's resistance to deformation and suppress high-frequency vibration. The preload output value is reduced according to the inverse proportional function of joint speed to avoid the risk of resonance caused by over-constraint; The preload reference value is refreshed every 100ms, and the stiffness compensation coefficient and preload output value are integrated to generate real-time stiffness compensation parameters. S212. Based on the real-time stiffness compensation parameters generated in step S211, the 80 to 150 Hz resonance frequency band is identified through finite element modal analysis to locate the concentrated area of ​​vibration energy in the robotic arm; based on the diagnostic results of this resonance frequency band, a band-stop filter command is injected into the pre-compensation torque to suppress the transmission of resonance energy to the end of the robotic arm. S213, the real-time stiffness compensation parameters from the dynamic coupling step S211, and the band-stop filtering command from step S212 form a composite vibration suppression strategy that combines time-domain stiffness enhancement and frequency-domain energy blocking. The convergence of the composite vibration suppression strategy is verified using the Lyapunov stability condition to ensure that the torque command input to the module used for gain correction satisfies global asymptotic stability. Then, the composite vibration suppression strategy is optimized based on the verification results. The specific method is as follows: Strengthen stiffness compensation weight when high-frequency vibration dominates; Increase the weight of the band-stop filter when the resonant frequency band is concentrated. S214. The optimized composite vibration suppression strategy is encapsulated into a pre-compensation torque instruction package and transmitted to the module used for gain correction via the standard industrial bus protocol.

4. The active vibration suppression method for a robotic arm end effector based on predictive compensation according to claim 3, characterized in that: Step S2 further includes step S22, which suppresses discontinuous vibrations of the trajectory, and includes the following steps: S221. The target motion trajectory of the robotic arm is reprogrammed using a fifth-order polynomial, and the acceleration is limited to 300 mm / s² using a time scaling algorithm. 2 Within this range, eliminate acceleration steps at trajectory corners; S222. Insert a sinusoidal function transition segment at the corner of the trajectory to make the acceleration curve have a smooth and gradual change characteristic, which directly reduces the impact vibration component in the high-frequency IMU sensor data input in step S1. S223. The optimized trajectory command is input to the vibration data collaborative acquisition and fusion module used to implement step S1 as the motion reference for high-frequency IMU sensor data acquisition. At the same time, it is linked with the structural flexible vibration suppression module used to implement step S2 to dynamically generate pre-compensation torque based on trajectory characteristics. The specific method is as follows: The stiffness compensation weight is increased in the high-speed section to enhance the joint's resistance to deformation. The corner section increases the intensity of the band-stop filter command, blocking the transmission of resonant energy.

5. The active vibration suppression method for the end effector of a robotic arm based on predictive compensation according to claim 4, characterized in that: Step S2 further includes step S23, which suppresses the transmission of base disturbances, and includes the following steps: S231. The roll angle, pitch angle and yaw angle deviations of the base attitude are measured in real time using the auxiliary IMU sensor in step S1. S232. Establish a kinematic transformation model of the robotic arm based on spatial vector chain multiplication. By transposing the Jacobian matrix, the end pose offset caused by the base attitude angle deviation in step S231 is mapped to the joint space compensation torque, thereby eliminating the end pose kinematic transmission error of the robotic arm caused by base disturbance. S233. The joint space compensation torque of step S232 is proportionally superimposed on the corrected compensation torque output in step S2, wherein the gain coefficient of step S2 is directly proportional to the attitude angle deviation in step S231; then the superimposed total compensation torque is synchronously input into the high-gain controller of step S3, and the end drift caused by the base disturbance is offset in real time through the feedforward channel of step S3 to achieve base disturbance suppression.

6. The active vibration suppression method for the end effector of a robotic arm based on predictive compensation according to claim 5, characterized in that: Step S2 further includes step S24, which suppresses sudden load vibrations, and includes the following steps: S241. By installing a torque sensor at the output end of the joint harmonic reducer, the load change rate is detected in real time. When the load change rate is detected to exceed 50 N·m / ms, based on the three-dimensional mapping relationship between joint stiffness and load and speed established in step S211, the stiffness compensation coefficient in step S211 is increased according to the load change intensity ratio. The stiffness matrix value in the rigid-flexible coupling dynamic model in step S2 is updated synchronously, so that the rigid-flexible coupling dynamic model matches the change condition in real time and eliminates the low-frequency resonance caused by dynamic mismatch. S242, the linkage module used to implement the composite vibration suppression strategy generation module in step S213, regenerates the pre-compensation torque based on the stiffness matrix value updated in step S241, performs frequency domain spread spectrum processing on the pre-compensation torque through the high-gain controller in step S3 to cover the low-frequency swaying frequency band, and then injects the spread vibration suppression torque into the joint actuator in step S3 through the feedforward channel in step S3 to offset the low-frequency swaying caused by load change in real time and suppress the residual amplitude.

7. The active vibration suppression method for the end effector of a robotic arm based on predictive compensation according to claim 1, characterized in that: Step S2 further includes step S25, thermal deformation correction of the dynamic model, which includes the following steps: S251. Deploy a temperature sensor network on the joints and links of the robotic arm to monitor the temperature change from -10℃ to 60℃ in real time. At the same time, calculate the thermal deformation of the robotic arm links based on the thermal expansion coefficient of the material, analyze the impact of thermal deformation on the vibration data acquisition accuracy of step S1, and quantify the end-positioning error caused by thermal drift. S252. Adjust the link size parameters in the rigid-flexible coupling dynamic model in step S2 proportionally according to the amount of thermal deformation, and update the geometric parameters in the three-dimensional mapping relationship between joint stiffness and load and velocity established in step S211 to eliminate the dynamic model mismatch caused by thermal deformation and suppress the model prediction spectrum shift. S253. The core parameters of the rigid-flexible coupling dynamic model database in step S2 are automatically calibrated every 30 minutes. This is linked to the composite vibration suppression strategy generation module used in step S213. Based on the updated rigid-flexible coupling dynamic model in step S2, the pre-compensation torque is regenerated. The high-gain controller in step S3 is used to offset the low-frequency drift at the end caused by thermal deformation in real time.

8. The active vibration suppression method for a robotic arm end effector based on predictive compensation according to claim 1, characterized in that: After step S3, step S4 is performed to verify the vibration suppression effect in a closed loop, which includes the following steps: S41. Based on the high-frequency IMU sensor data from step S1 and the pure vibration signal output from step S12, extract the acceleration amplitude before and after vibration suppression to calculate the vibration suppression rate. When the vibration suppression rate is less than 70%, execute step S42. When the vibration suppression rate is greater than or equal to 90%, execute step S43. S42. Increase the sampling frequency of the high-frequency IMU sensor and the auxiliary IMU sensor in step S1 to enhance the microsecond-level time synchronization accuracy of the high-frequency IMU sensor and the auxiliary IMU sensor; increase the dynamic adjustment frequency of the stiffness compensation weight and band-stop filter intensity in step S213 to improve the convergence speed of the composite vibration suppression strategy; activate the trajectory replanning module used to implement step S221 to reduce the joint speed of the robotic arm to a safe threshold. S43. Reduce the torque output of the joint motor through the standard industrial bus protocol in step S214, while maintaining a vibration suppression rate of more than 85% and reducing the total power consumption of the system.

9. An active vibration damping system for the end effector of a robotic arm, used to implement the active vibration damping method according to any one of claims 1 to 8, characterized in that: include: The multi-sensor fusion module includes a high-frequency IMU sensor, an auxiliary IMU sensor, and a joint strain gauge network. The high-frequency IMU sensor is mounted on the end flange of the robotic arm to collect triaxial acceleration, angular velocity, and vibration spectrum data in real time. The auxiliary IMU sensor is mounted on the base of the robotic arm to synchronously monitor roll angle, pitch angle, and yaw angle. The joint strain gauge network is used to form a dual-frequency monitoring network to cover the vibration frequency domain of 0-500Hz. The dual-loop control module includes a prediction unit and a correction unit. The prediction unit stores the rigid-flexible coupling dynamics model of the robotic arm and outputs pre-compensation torque commands. The correction unit dynamically optimizes the gain coefficient in the rigid-flexible coupling dynamics model using the Lyapunov stability algorithm. The execution module includes a high-gain controller, which outputs a damping torque to the joint actuator, with a response bandwidth covering the third harmonic of the vibration fundamental frequency.

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