A multi-axis robot control method and system suitable for clean environments

Abstract

The application discloses a multi-axis robot control method and system suitable for a clean environment, and particularly relates to the technical field of robot program control, and is used for solving the problem that the end of an existing multi-axis robot is unexpectedly vibrated due to the mismatch of a fixed parameter friction model in a track containing steering and micro-amplitude reciprocating adjustment; a symbol change rate of an original counting signal of an encoder is counted, a statistical mode is transitioned from a single-peak distribution to a double-peak distribution, a joint accompanied by counting symbol flipping is identified as a target joint, a micro-amplitude bidirectional exploratory motion is superimposed before the motion direction of the target joint is reversed, and exploratory asymmetry is calculated; when the exploratory asymmetry exceeds a preset threshold, a driving torque feedback value in a reverse period is extracted to perform time-frequency transformation, a shift of an energy ratio of sidebands on both sides of an engagement frequency before and after the reverse is compared to evaluate a lubrication state deviation degree, a coulomb friction term in a feedforward friction compensation model is modified according to the lubrication state deviation degree, and is used for multi-axis linkage control in a next period.

Description

Technical Field

[0001] This invention relates to the field of robot program control technology, and more specifically, to a multi-axis robot control method and system suitable for clean environments. Background Technology

[0002] In applications where multi-axis industrial robots are used for precision transport in clean environments, the robot's trajectory stability directly affects the quality of the work. To suppress speed fluctuations and end effector jitter during low-speed operation, existing control methods typically use a friction model with fixed parameters to feedforward compensate for the joint drive torque. The friction models used are mostly based on Stribeck curves, identifying the steady-state friction characteristics of the reducer and transmission mechanism under specific speed and load conditions. These characteristics are then superimposed as feedforward terms into the torque command to counteract the influence of nonlinear resistance on motion accuracy. This approach achieves good compensation results in the normal speed range and unidirectional motion, meeting the stability requirements of general industrial material handling tasks.

[0003] However, when multi-axis linkage executes trajectories that include steering and micro-amplitude reciprocating adjustments, the fluidity state of the lubricating medium inside each joint reducer will differ from the steady-state identification conditions due to the change in the direction of motion. This causes the actual change law of friction to deviate from the compensation curve originally established based on the assumption of constant characteristics. The feedforward model with fixed parameters cannot match this time-varying characteristic, resulting in deviations in torque compensation. After the deviations accumulate, they cause unexpected vibrations at the end of the multi-axis trajectory linkage process, directly restricting the improvement of the stability of precision transmission in clean rooms. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention provides a multi-axis robot control method and system suitable for clean environments to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A multi-axis robot control method suitable for clean environments includes: S1. Acquire the raw counting signals from the encoders of each joint of the multi-axis robot; S2. Perform sign change rate statistics on the original counting signal within a sliding window. When the sign change rate statistics mode of a certain joint transitions from a single-peak distribution to a double-peak distribution and the counting sign of one of the double peaks flips, the corresponding joint is identified as the target joint whose motion direction has reversed. S3. Control the target joint to perform a micro-amplitude bidirectional trial motion before reversing the direction of motion, record the peak values ​​of the driving torque response of the forward trial segment and the reverse trial segment, and calculate the trial asymmetry. S4. When the asymmetry of the test exceeds the preset threshold, extract the driving torque feedback value of the target joint during the period of reversal of the movement direction. S5. Perform time-frequency transformation on the driving torque feedback value, extract the energy ratio of the sidebands on both sides of the meshing frequency, compare the offset of the energy ratio before and after the reversal of the motion direction, and evaluate the degree of deviation of the lubrication state of the target joint. S6. Based on the degree of deviation of the lubrication state, the Coulomb friction term in the feedforward friction compensation model of the target joint is corrected, and the corrected feedforward friction compensation model is used for the multi-axis linkage control in the next cycle.

[0006] Furthermore, the raw counting signals from the encoders of each joint of the multi-axis robot are acquired, including: The output of the photoelectric encoder mounted on the joint motor shaft reads the raw pulse count value without position interpolation processing in real time. The sign difference between the original pulse count values ​​of adjacent control cycles is used as the sign change event; The original counting signal is formed by the sequence of events that change the symbol of each control cycle.

[0007] Furthermore, the sign change rate of the original counting signal is statistically analyzed within a sliding window. When the statistical pattern of the sign change rate of a certain joint transitions from a single-peak distribution to a bi-peak distribution and the counting sign of one of the bi-peaks flips, the corresponding joint is identified as the target joint whose motion direction has reversed, including: A sliding window is established on the sequence of sign change events of the original counting signal, with a fixed number of events as the window length; Calculate the ratio of the number of positive symbol events to the number of negative symbol events in the symbol change events within the sliding window, and use it as the symbol change rate; The frequency distribution of the rate of change of the statistical sign in each value interval yields the statistical pattern of the rate of change of the sign. The range of values ​​corresponding to the maximum frequency in the statistical pattern of the rate of change of sign is taken as a single peak, and the range of values ​​with two frequency maxima located in the positive ratio region and the negative ratio region, respectively, is taken as a double peak. When the statistical pattern of the rate of change of the sign transitions from a unimodal distribution to a bimodal distribution, and the frequency maxima corresponding to the inverse ratio region in the bimodal distribution exceed the frequency maxima corresponding to the forward ratio region for the first time, the corresponding joint is identified as the target joint.

[0008] Furthermore, the frequency distribution of the statistical sign change rate across various value intervals includes: dividing the range of sign change rate values ​​into a positive value interval group and a negative value interval group, centered at zero and with a preset step size as the interval; counting the frequency of the sign change rate falling into each value interval in the positive value interval group and the negative value interval group within the sliding window; and arranging the frequency of each value interval in the positive value interval group and the negative value interval group in ascending order of the value interval to form a statistical pattern of the sign change rate.

[0009] Furthermore, before reversing the direction of motion, a micro-amplitude bidirectional trial motion is superimposed on the target joint. The peak values ​​of the driving torque response during the forward and reverse trial segments are recorded, and the trial asymmetry is calculated, including: An offset signal with an amplitude not exceeding the product of the encoder's minimum resolution step size and the reducer's transmission ratio is superimposed on the target position trajectory of the target joint in the joint space. First, apply a positive bias along the original direction of motion to form a positive test segment, and then apply a reverse bias in the opposite direction of the original direction of motion to form a reverse test segment. During the duration of the positive test phase, the actual output torque value is collected from the joint actuator of the target joint, and the maximum absolute value of the actual output torque value during the duration of the positive test phase is taken as the peak value of the driving torque response of the positive test phase. During the duration of the reverse test segment, the actual output torque value is collected from the joint actuator of the target joint, and the maximum absolute value of the actual output torque value during the duration of the reverse test segment is taken as the peak value of the driving torque response of the reverse test segment. The ratio of the peak value of the driving torque response in the forward test section to the peak value of the driving torque response in the reverse test section is calculated as the test asymmetry.

[0010] Furthermore, when the tested asymmetry exceeds a preset threshold, the driving torque feedback value of the target joint during the period of reversal of the motion direction is extracted, including: When the asymmetry of the trial exceeds the preset threshold, the motion direction reversal period is defined as the time from the start of the transition of the statistical pattern of the sign change rate of the target joint from a unimodal distribution to a bimodal distribution, until the time when the statistical pattern of the sign change rate returns to a unimodal distribution after the motion direction reversal is completed. During the period of reversal of the motion direction, the actual output torque value is continuously collected from the joint actuator of the target joint; All actual output torque values ​​collected during the period of reverse motion direction are used as driving torque feedback values.

[0011] Furthermore, the driving torque feedback value is subjected to time-frequency transformation to extract the energy ratio of the sidebands on both sides of the meshing frequency. The shift in the energy ratio before and after the reversal of the motion direction is compared to assess the degree of deviation in the lubrication state of the target joint, including: Obtain the number of reducer teeth of the joint to which the target joint belongs; The meshing frequency is obtained by multiplying the number of teeth in the reducer by the average rotational speed of the target joint during the period when the direction of motion reverses. A short-time Fourier transform is performed on the driving torque feedback value to obtain the torque spectrum; In the torque spectrum, the difference between the meshing frequency and the meshing frequency corresponding to the number of teeth of the reducer is taken as the center frequency of the lower sideband, and the sum of the meshing frequency and the meshing frequency corresponding to the number of teeth of the reducer is taken as the center frequency of the upper sideband. The sum of the power values ​​within the preset bandwidth range of the lower sideband center frequency and the upper sideband center frequency is calculated and divided by the power values ​​within the preset bandwidth range of the meshing frequency to obtain the energy ratio. The energy ratio of the first part of the period when the direction of motion is reversed is taken as the energy ratio before reversal, and the energy ratio of the second part of the period when the direction of motion is reversed is taken as the energy ratio after reversal. The absolute value of the difference between the energy ratio after reversal and the energy ratio before reversal is taken as the energy ratio offset. The degree of deviation in lubrication condition is determined based on the magnitude of the energy ratio deviation.

[0012] Further, the power value within the preset bandwidth range of the lower sideband center frequency is calculated, including: using the lower sideband center frequency as a reference, extending the half-octave width of the meshing frequency corresponding to the number of reducer teeth in both low-frequency and high-frequency directions as the statistical range of the lower sideband; within the statistical range of the lower sideband, summing the squared amplitudes of all frequency points in the torque spectrum to obtain the lower sideband power value; the lower sideband power value is used as the power value within the preset bandwidth range of the lower sideband center frequency; the calculation method for the power value within the preset bandwidth range of the upper sideband center frequency is the same as the calculation method for the power value within the preset bandwidth range of the lower sideband center frequency.

[0013] Furthermore, based on the degree of deviation in lubrication condition, the Coulomb friction term in the feedforward friction compensation model of the target joint is modified, and the modified feedforward friction compensation model is used for the multi-axis linkage control in the next cycle, including: Multiply the degree of deviation in lubrication condition by the corresponding correction coefficient in the preset correction coefficient table to obtain the correction amount for the Coulomb friction term; The Coulomb friction term correction is added to the current Coulomb friction term in the feedforward friction compensation model of the target joint to obtain the corrected Coulomb friction term. The corrected Coulomb friction term replaces the current Coulomb friction term in the feedforward friction compensation model, forming the corrected feedforward friction compensation model. In the next cycle of multi-axis linkage control, the feedforward torque output by the corrected feedforward friction compensation model is superimposed on the torque command of the target joint.

[0014] On the other hand, the present invention provides a multi-axis robot control system suitable for clean environments, comprising: The signal acquisition module is used to acquire the raw counting signals from the encoders of each joint of the multi-axis robot; The reversal recognition module is used to perform sign change rate statistics on the original counting signal within a sliding window. When the sign change rate statistics mode of a certain joint transitions from a single-peak distribution to a double-peak distribution and the counting sign of one of the double peaks is flipped, the corresponding joint is identified as the target joint whose motion direction has been reversed. The bidirectional probing module is used to control the target joint to superimpose micro-amplitude bidirectional probing motions before performing a reversal of the motion direction, record the peak values ​​of the driving torque response of the forward and reverse probing segments, and calculate the probing asymmetry. The torque extraction module is used to extract the driving torque feedback value of the target joint during the period of reversal of the motion direction when the probe asymmetry exceeds a preset threshold. The deviation assessment module is used to perform time-frequency transformation on the driving torque feedback value, extract the energy ratio of the sidebands on both sides of the meshing frequency, compare the deviation of the energy ratio before and after the reversal of the motion direction, and assess the degree of deviation of the lubrication state of the target joint. The feedforward correction module is used to correct the Coulomb friction term in the feedforward friction compensation model of the target joint based on the degree of deviation of the lubrication state, and then use the corrected feedforward friction compensation model for the multi-axis linkage control in the next cycle.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. By extracting the statistical distribution characteristics of the sign change rate from the original encoder counting signal, the statistical pattern of the sign change rate is transitioned from a single-peak distribution to a bi-peak distribution accompanied by counting sign reversal. This serves as the basis for identifying joints with reversed motion direction. It can directly capture the microscopic motion state changes during the reducer backlash crossing stage using the encoder's inherent signal. It can accurately lock the target joint before the actual reversal of motion direction without relying on zero-crossing detection of the speed command, providing sufficient time margin for subsequent compensation. After identifying the target joint, a micro-amplitude bidirectional trial motion that does not affect the end effector pose is actively superimposed before the motion direction reverses, and the trial asymmetry is calculated. Subsequent lubrication state deviation evaluation is only triggered when the trial asymmetry exceeds a preset threshold, thus avoiding full-process processing for each reversal event and reducing the online computational load of the controller while ensuring compensation accuracy.

[0016] 2. Utilizing the frequency domain characteristics of the driving torque feedback value during the motion direction reversal period, the degree of deviation in the lubrication state of the target joint is assessed by comparing the shift in the ratio of sideband energy on both sides of the meshing frequency before and after reversal. Quantitative information on the time-varying characteristics of the lubricating medium inside the reducer is indirectly obtained from the sideband energy migration of the torque signal, without the need to introduce additional sensors or change the hardware configuration in the cleanroom. Based on the degree of lubrication state deviation, the Coulomb friction term in the feedforward friction compensation model is corrected, enabling the model to adaptively adjust with real-time changes in lubrication state. The corrected model directly applies the torque command in the next cycle of multi-axis linkage control, fundamentally suppressing unexpected judder at the end of the multi-axis trajectory caused by the mismatch of the fixed-parameter friction model, and improving the stability of the robot when executing trajectories including steering and micro-amplitude reciprocating adjustments in a clean environment. Attached Figure Description

[0017] Figure 1 This is a flowchart of a multi-axis robot control method suitable for clean environments according to the present invention; Figure 2 This is a schematic diagram of a multi-axis robot control system suitable for clean environments according to the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1: Figure 1 This invention provides a multi-axis robot control method suitable for clean environments, comprising: S1. Acquire the raw counting signals from the encoders of each joint of the multi-axis robot; S2. Perform sign change rate statistics on the original counting signal within a sliding window. When the sign change rate statistics mode of a certain joint transitions from a single-peak distribution to a double-peak distribution and the counting sign of one of the double peaks flips, the corresponding joint is identified as the target joint whose motion direction has reversed. S3. Control the target joint to perform a micro-amplitude bidirectional trial motion before reversing the direction of motion, record the peak values ​​of the driving torque response of the forward trial segment and the reverse trial segment, and calculate the trial asymmetry. S4. When the asymmetry of the test exceeds the preset threshold, extract the driving torque feedback value of the target joint during the period of reversal of the movement direction. S5. Perform time-frequency transformation on the driving torque feedback value, extract the energy ratio of the sidebands on both sides of the meshing frequency, compare the offset of the energy ratio before and after the reversal of the motion direction, and evaluate the degree of deviation of the lubrication state of the target joint. S6. Based on the degree of deviation of the lubrication state, the Coulomb friction term in the feedforward friction compensation model of the target joint is corrected, and the corrected feedforward friction compensation model is used for the multi-axis linkage control in the next cycle.

[0020] In a multi-axis robot control method suitable for clean environments, the specific implementation of the steps for acquiring the original counting signals of the encoders of each joint of the multi-axis robot is as follows.

[0021] The multi-axis robot is installed in an ISO Class 1000 cleanroom environment. Each joint of the robot is driven by a servo motor, which is connected to the joint output end via a reducer. A photoelectric encoder is coaxially mounted on the non-load-bearing end face of each joint motor axis. The photoelectric encoder is an incremental photoelectric encoder with a dustproof and sealed structure. The housing material of the photoelectric encoder is a cleanroom-compatible material with low gas release properties to prevent the release of volatile pollutants into the clean environment. The grating disk of the photoelectric encoder is rigidly connected to the joint motor axis and rotates synchronously with it. The reading head of the photoelectric encoder is fixed to the joint motor axis by a bracket, maintaining a non-contact working gap with the grating disk. When the joint motor axis rotates, the grating lines on the grating disk pass sequentially through the beam path of the reading head, and the reading head outputs two orthogonal raw pulse signals.

[0022] During the servo control cycle of the robot controller, the two orthogonal raw pulse signals output by the photoelectric encoder are sampled at four times the frequency. Four times the frequency means that a counting pulse is generated at each edge transition of the orthogonal signal, thereby amplifying the inherent linear resolution of the grating disk by a factor of four. At the end of each servo control cycle, the accumulated pulse count value at the output of the photoelectric encoder is read. The accumulated pulse count value is the total number of pulses accumulated since the photoelectric encoder was powered on. The read accumulated pulse count value is not processed by any position interpolation, subdivision algorithm, low-pass filtering or smoothing filtering, and is not compared or fused with the position command value; it is directly used as the raw pulse count value.

[0023] Subtract the original pulse count value read in the current control cycle from the original pulse count value read in the previous control cycle to obtain the difference. Determine the sign of the difference: if the result of subtracting the original pulse count value read in the previous control cycle from the original pulse count value read in the current control cycle is greater than zero, the difference is positive, indicating that the joint motor shaft rotated in the forward direction relative to the previous control cycle in the current control cycle; if the result of subtracting the original pulse count value read in the previous control cycle from the original pulse count value read in the current control cycle is less than zero, the difference is negative, indicating that the joint motor shaft rotated in the reverse direction relative to the previous control cycle in the current control cycle; if the result of subtracting the original pulse count value read in the previous control cycle is equal to zero, the difference is zero, indicating that the joint motor shaft did not undergo a discernible angular change relative to the previous control cycle in the current control cycle.

[0024] The determined sign (positive, negative, or zero) is treated as a sign change event. The sign change event's value range includes only three states: positive, negative, and zero. One sign change event is generated for each control cycle, and there is a one-to-one correspondence between the sign change events and the control cycles that generated them.

[0025] The symbol change events generated by multiple consecutive control cycles are arranged sequentially according to the order of the control cycles to form a symbol change event sequence, which is used as the original counting signal. Logically, the original counting signal is a discrete sequence consisting of positive, negative, and zero signs, and the position index of each element in the original counting signal sequence corresponds to the sequence number of the control cycle.

[0026] Because the photoelectric encoder directly outputs the unprocessed raw pulse count values, the raw counting signal completely preserves all the informational characteristics of the joint motion under low-speed conditions. When the joint operates at extremely low angular velocities, the nonlinear creeping effect of friction within the reducer causes the actual motion of the joint motor shaft to be not a uniform, continuous rotation, but rather a micro-motion pattern alternating between brief pauses and sudden, minute jumps. This micro-motion pattern of alternating brief pauses and sudden, minute jumps manifests in the raw counting signal as an alternating distribution of positive and zero signs or negative and zero signs in the sequence of sign change events, rather than a continuous distribution of the same sign. If the raw pulse count values ​​are interpolated or filtered, the micro-motion characteristics of alternating brief pauses and sudden, minute jumps will be smoothed out or blurred by the algorithm, thus losing the crucial information needed in subsequent steps to identify the transition of the sign change rate statistical pattern from a single-peak distribution to a double-peak distribution. Therefore, it is essential to collect the raw pulse count values ​​without position interpolation processing as the signal source.

[0027] For each joint of the multi-axis robot, its original counting signal is acquired independently using the same acquisition method. The original counting signals of each joint are acquired synchronously in time, and the acquisition time is aligned with the sampling edge of the same servo control cycle to ensure the time consistency of the original counting signals between the joints.

[0028] The specific implementation method for identifying the target joint whose motion direction has reversed by statistically analyzing the sign change rate within a sliding window of the original counting signal is as follows.

[0029] The original count signals of each joint have already been obtained in the step of acquiring the original count signals of the encoders of each joint of the multi-axis robot. The original count signals are a sequence of sign change events generated by multiple consecutive control cycles, arranged in the order of the control cycles. The step of performing sign change rate statistics within a sliding window on the original count signals further processes the original count signals.

[0030] A sliding window is established on the sequence of sign change events of the original counting signal. The window length is defined by a fixed number of events, meaning the number of sign change events included within the sliding window is fixed. The fixed number of events is set based on the following principle: the time span covered by the fixed number of events is sufficient to include multiple sign changes of the encoder output signal during the reducer backlash crossing process, while avoiding the introduction of irrelevant motion features outside the motion direction reversal period due to an excessively large time span. The specific value of the fixed number of events is determined during the robot debugging phase as follows: when the joint performs a complete motion direction reversal operation at the minimum task speed, record the number of continuous events from the appearance of the first zero sign in the sign change event sequence to the resumption of consecutive same signs in the sign change event sequence. Round this number down to twice its original value as the fixed number of events. For example, if the number of continuous events recorded in a debugging session is 25, then the fixed number of events is set to 50. Once determined, the fixed number of events remains unchanged during subsequent robot operation.

[0031] The sliding window slides forward one event step at a time along the sequence of symbolic change events. Each time the sliding window slides forward one event step, the set of symbolic change events within the sliding window is updated once. The updated set of symbolic change events discards the earliest symbolic change event that entered the original set of symbolic change events and adds the new symbolic change event that immediately follows the end of the original set of symbolic change events.

[0032] After each sliding window update, the ratio of the number of positive sign events to the number of negative sign events within the sliding window is calculated as: R = Np / Nn; where R represents the sign change rate, Np represents the number of positive signs appearing within the sliding window, and Nn represents the number of negative signs appearing within the sliding window. When Nn equals 0, a substitute value is assigned to R. The substitute value is set based on the following: the substitute value must be greater than the maximum value that R may have under normal operating conditions to ensure that the substitute value will not be confused with the normally calculated sign change rate. The specific value of the substitute value is determined based on the joint reduction ratio and the task speed range. For example, under the condition of a reduction ratio of 100 and a minimum task angular velocity of 0.01 radians per second, the substitute value is 1000. The physical meaning of the sign change rate is: a sign change rate greater than 1 indicates that positive rotation is dominant, a sign change rate less than 1 indicates that negative rotation is dominant, a sign change rate equal to 1 indicates that the number of positive and negative rotations is equal, and a sign change rate equal to the substitute value indicates that there is no negative rotation within the sliding window.

[0033] The range of the sign rate of change is divided into multiple intervals to statistically analyze its frequency distribution across these intervals. The division method is as follows: centering on zero, and using a preset step size, the complete range of the sign rate of change is divided into positive and negative interval groups. The preset step size is set based on the following criteria: it is small enough to distinguish the distribution characteristics of small fluctuations in the sign rate of change around 1, while being large enough to ensure that the frequency falling into each interval is statistically significant without being overly sparse. The preset step size is determined as follows: With the joint in a stable, positive, unloaded state, the sign rate of change obtained from continuous sliding window updates forms a sample set. The number of samplings is determined based on a fixed number of events, and is 20 times the fixed number of events, ensuring the sample size is sufficient to cover the complete fluctuation range of the sign rate of change. The standard deviation of the sample set is calculated, and 1 / 10 of the standard deviation is taken as the preset step size. For example, if the number of fixed events is 50 and the number of data collections is 1000, the standard deviation of the sample set is calculated to be 0.3, then the preset step size is 0.03.

[0034] The positive value interval group is divided starting from the point where the rate of change of sign equals 1, increasing sequentially in the direction greater than 1 with a preset step size. The negative value interval group is divided starting from the point where the rate of change of sign equals 1, decreasing sequentially in the direction less than 1 with a preset step size. The case where the rate of change of sign is exactly 1 is assigned to a separate value interval. The value interval corresponding to the case where the rate of change of sign is exactly 1 belongs to neither the positive value interval group nor the negative value interval group, serving as the boundary interval between the positive and negative value interval groups.

[0035] For each new sign rate of change generated, determine which value interval in the positive or negative value interval group it falls into, and increment the frequency count of the corresponding value interval by 1. Arrange the frequencies corresponding to each value interval in the positive and negative value interval groups in ascending order of value intervals to form a frequency distribution sequence. This frequency distribution sequence is the statistical pattern of the sign rate of change.

[0036] When the joint is in a stable unidirectional motion state, the rate of change of sign continuously falls within a certain range of values ​​in the positive ratio region or near a certain range of values ​​in the negative ratio region, exhibiting a unimodal distribution. The unimodal distribution is determined as follows: in the rate of change of sign statistical pattern, the range corresponding to the maximum frequency is the peak position. The frequency of the ranges on both sides of the peak position decreases monotonically towards both sides, and there is no other range whose frequency reaches a local maximum comparable to the maximum frequency. The maximum frequency is determined by taking the maximum value after traversing all ranges in the rate of change of sign statistical pattern. Comparability with the maximum frequency is determined by a pre-set percentage threshold. The percentage threshold is determined based on the fluctuation range of the rate of change of sign in the stable unidirectional motion state of the joint. The percentage threshold is set as follows: when the joint is in a stable unidirectional motion state, continuously record the ratio of the frequency of each range (excluding the peak position) to the maximum frequency in the frequency distribution sequence. Take the maximum value of the ratio plus a safety margin as the percentage threshold. The safety margin is 20% of the maximum value of the ratio. For example, if the maximum ratio recorded under a stable unidirectional motion state is 0.65 and the safety margin is 0.13, then the percentage threshold is set to 0.78. When there exists another range of values ​​with a frequency greater than the maximum frequency multiplied by the percentage threshold, it is considered that there is another local maximum comparable to the maximum frequency. In this case, the statistical pattern of the sign rate of change does not meet the conditions of a unimodal distribution.

[0037] When the joint is about to enter the reversal phase of motion, the tooth surface inside the reducer changes from a forward contact state to a separation and then contact with the reverse tooth surface. In the gap of tooth surface separation, the motion of the joint motor shaft is affected by the sudden decrease in friction force, resulting in a brief alternating micro-motion between forward and reverse directions. The sign change rate fluctuates around 1, and the statistical pattern of the sign change rate transitions from a single-peak distribution to a double-peak distribution.

[0038] The determination method for a bimodal distribution is as follows: In the statistical model of the rate of change of sign, two frequency maxima appear. The first frequency maxima is located in the positive ratio region, and the second frequency maxima is located in the negative ratio region. Furthermore, there is a frequency minimum between the two frequency maxima. The positive ratio region is defined as the range of values ​​where the rate of change of sign is greater than 1, and the negative ratio region is defined as the range where the rate of change of sign is less than 1. The determination criterion for a frequency maxima is: the frequency of a certain interval is greater than the frequency of the number of adjacent intervals to its left and right. The number of adjacent intervals is determined based on the number of fixed events within the sliding window and a preset step size. The number of adjacent intervals is calculated by multiplying the number of fixed events within the sliding window by the preset step size, and the number of adjacent intervals is not less than 2. The frequency minimum is the frequency of the interval with the lowest frequency among all intervals between the two frequency maxima.

[0039] The transition from a unimodal to a bimodal distribution in the statistical pattern of the sign rate of change reflects the physical process of a joint moving from stable unidirectional motion to interdental clearance. The relative trends of the two frequency maxima within the bimodal distribution are monitored simultaneously. When the statistical pattern of the sign rate of change transitions from a unimodal to a bimodal distribution, and the frequency maxima corresponding to the reverse ratio region in the bimodal distribution first exceed the frequency maxima corresponding to the forward ratio region, it indicates that the reverse motion trend of the corresponding joint has become dominant, and the actual motion direction of the corresponding joint is about to reverse. At this point, the corresponding joint is identified as the target joint whose motion direction has reversed.

[0040] The method of identifying target joints whose motion direction has reversed by analyzing the peak transition of the statistical pattern of the sign change rate does not rely on zero-crossing detection of the speed command signal or speed feedback signal. Instead, it directly utilizes the microscopic statistical characteristics of the original counting signal to capture the precursors of reversal. Because the original counting signal completely preserves the sign sequence characteristics caused by frictional crawling at extremely low speeds, the transition pattern from a single-peak distribution to a double-peak distribution has a much higher sensitivity for detecting precursors of reversal than the speed zero-crossing detection method. It can identify the target joint in advance during the transition stage before the speed command has crossed zero and before the motion direction has actually reversed, providing an accurate starting point for the trial motion superposition and lubrication status assessment in subsequent steps.

[0041] The specific implementation steps for controlling the target joint to superimpose a micro-amplitude bidirectional trial motion before performing a reversal of the motion direction, recording the peak values ​​of the driving torque response of the forward trial segment and the reverse trial segment, and calculating the trial asymmetry are as follows.

[0042] The target joint has been identified in the step of identifying the target joint whose motion direction is about to reverse. The target joint is the joint that is about to undergo a reversal of motion direction. The step of controlling the target joint to superimpose a micro-amplitude bidirectional trial motion before performing the motion direction reversal is used to further process the target joint.

[0043] The target position trajectory of the target joint in joint space is generated in real time by the trajectory planner of the multi-axis robot. The target position trajectory defines the desired angular position of the target joint in each servo control cycle. Before the target joint performs a motion direction reversal action along the target position trajectory, an offset signal is superimposed on the target position trajectory. The amplitude of the offset signal does not exceed the product of the encoder's minimum resolution step distance and the reducer's transmission ratio. The encoder's minimum resolution step distance is the angular displacement of the joint motor shaft corresponding to each pulse after the photoelectric encoder is sampled at 4 times the frequency. The encoder's minimum resolution step distance is calculated as: θ = 360 / (L × 4); where θ represents the encoder's minimum resolution step distance in degrees, and L represents the number of inherent lines of the grating disk. For example, if the number of inherent lines of the grating disk is 2000, then the encoder's minimum resolution step distance is 360 divided by 2000 and then divided by 4, resulting in 0.045 degrees. The reducer's transmission ratio is the ratio of the input shaft speed to the output shaft speed of the reducer to which the target joint belongs. The reducer's transmission ratio is calibrated at the robot's factory and stored in the parameter table of the robot controller. The upper limit of the bias signal amplitude is the product of the encoder's minimum resolvable step size and the reducer's transmission ratio. The actual amplitude of the bias signal is between 1 / 2 and 2 / 3 of the upper limit to ensure that the displacement of the joint output end caused by the bias signal does not exceed the elastic deformation range of the reducer's tooth backlash, thus not changing the actual pose of the target joint's end effector in the workspace. At the same time, the amplitude of the bias signal is large enough to generate a torque change in the joint motor shaft that can be distinguished by the torque sensor in the joint actuator. For example, if the encoder's minimum resolvable step size is 0.045 degrees and the reducer's transmission ratio is 100, then the upper limit of the bias signal amplitude is 4.5 degrees, and the actual amplitude of the bias signal is between 2.25 degrees and 3 degrees.

[0044] The bias signal is applied as follows: first, a positive bias is applied along the original direction of motion to form a positive probe segment, and then a reverse bias is applied in the opposite direction of motion to form a reverse probe segment. The original direction of motion is the direction of motion that the target joint is executing at the moment the target joint is identified. The original direction of motion is obtained from the slope sign of the target position trajectory of the target joint; when the slope is positive, the original direction of motion is positive, and when the slope is negative, the original direction of motion is reverse. The positive bias is applied after the statistical pattern of the rate of change of the target joint's sign transitions from a single-peak distribution to a double-peak distribution, and before the target joint actually executes the motion direction reversal action. The durations of both the positive and reverse biases are preset. The settings for the durations of the positive and reverse biases are based on the following: the duration is long enough so that the torque response of the joint actuator can reach a steady-state value, and the duration is short enough so that the total duration of the bidirectional probe motion does not exceed the time window between when the target joint is identified as the target joint and when it actually executes the motion direction reversal action. The duration of both the forward bias and the reverse bias is set to half the duration corresponding to the fixed number of events, which is the fixed number of events multiplied by the servo control cycle. For example, if the fixed number of events is 50 and the servo control cycle is 1 millisecond, then the duration corresponding to the fixed number of events is 50 milliseconds, and the duration of both the forward bias and the reverse bias is set to 25 milliseconds.

[0045] During the forward trial phase, actual output torque values ​​are acquired from the joint actuator of the target joint. The joint actuator contains a torque sensor or torque observer. The torque sensor directly measures the output torque of the joint motor shaft, while the torque observer indirectly estimates the output torque of the joint motor shaft using motor current and a motor model. The acquisition frequency of the actual output torque values ​​is synchronized with the servo control cycle, with one actual output torque value acquired per servo control cycle. The absolute values ​​of all actual output torque values ​​acquired during the forward trial phase are taken, and the maximum value is selected from the set of absolute values. This maximum value is used as the peak value of the driving torque response during the forward trial phase.

[0046] During the duration of the reverse testing phase, actual output torque values ​​are collected from the joint actuators of the target joint. The method for collecting actual output torque values ​​during the reverse testing phase is the same as that for the forward testing phase. The absolute values ​​of all actual output torque values ​​collected during the reverse testing phase are taken, and the maximum value is selected from the set of actual output torque values ​​after taking the absolute values. This maximum value is taken as the peak value of the driving torque response during the reverse testing phase.

[0047] The ratio of the peak driving torque response of the forward test segment to the peak driving torque response of the reverse test segment is calculated as: A = Tp / Tn; where A represents the test asymmetry, which is dimensionless; Tp represents the peak driving torque response of the forward test segment, in Newton-meters (N·m); and Tn represents the peak driving torque response of the reverse test segment, in Newton-meters (N·m). When Tn equals 0, it indicates that no measurable torque response is generated in the reverse test segment. A is assigned a substitute value, which is set based on the same criteria as the substitute value for the sign change rate, and is set to 1000. The physical meaning of the test asymmetry is: a test asymmetry of 1 indicates good symmetry of the internal friction torque of the target joint during the forward and reverse test movements, and normal lubrication; the greater the deviation of the test asymmetry from 1, the greater the asymmetry of the internal friction torque of the target joint and the greater the deviation of the lubrication condition.

[0048] By superimposing micro-amplitude bidirectional trial motions and calculating the trial asymmetry, the symmetry characteristics of the forward and reverse torques of the target joint before the reversal of the motion direction were actively acquired. By actively injecting a micro-amplitude offset signal that does not affect the end-effector pose, bidirectional torque response information was acquired in advance within the time window before the actual reversal of the motion direction. This provides an active and quantifiable screening criterion for determining whether to trigger lubrication status assessment in subsequent steps. The introduction of trial asymmetry allows subsequent steps to perform frequency domain analysis and compensation correction only on target joints where the torque asymmetry exceeds a preset threshold, thus avoiding full-process processing for every reversal of the motion direction and reducing the online computational overhead of the controller while ensuring compensation accuracy.

[0049] The specific implementation method for extracting the driving torque feedback value of the target joint during the reversal period of the motion direction when the probe asymmetry exceeds the preset threshold is as follows.

[0050] The trial asymmetry has been obtained in the step of superimposing a small-amplitude bidirectional trial motion and calculating the trial asymmetry before controlling the target joint to reverse the direction of motion. The trial asymmetry is then compared with a preset threshold.

[0051] A preset threshold is used to distinguish whether the lubrication state of the target joint has deviated sufficiently to affect the accuracy of feedforward friction compensation. The preset threshold is set as follows: Under the condition that all robot joints are in a known normal lubrication state, execute multiple standard task trajectories containing motion direction reversals. Before each motion direction reversal, calculate the trial asymmetry using the aforementioned steps to obtain the statistical distribution range of the trial asymmetry under normal lubrication conditions. The preset threshold is a value between 1.2 and 1.5 times the upper limit of the statistical distribution range. The condition of a known normal lubrication state refers to the joint reducer being fully run-in after the robot's first operation following factory manufacturing or after the lubricating medium has been replaced according to maintenance procedures. The upper limit of the statistical distribution range is the maximum value of the trial asymmetry obtained from multiple calculations. For example, if 50 standard task trajectories containing motion direction reversals are executed consecutively under the condition of known normal lubrication, and the maximum value of the trial asymmetry obtained from the 50 calculations is 1.15, then the preset threshold is a value between 1.38 and 1.73, for example, 1.5. Once the preset threshold is determined, it remains unchanged during subsequent robot operations until recalibration is performed after the lubricating medium is replaced.

[0052] When the trial asymmetry exceeds the preset threshold, it indicates a significant asymmetry in the torque of the target joint during forward and reverse trial movements, suggesting that the lubrication state of the target joint has deviated from the normal range. In this case, the driving torque feedback value of the target joint during the reversal of the movement direction needs to be extracted for subsequent frequency domain analysis. When the trial asymmetry does not exceed the preset threshold, it indicates that the lubrication state of the target joint is still within the normal range. No further steps are required; the Coulomb friction term in the current feedforward friction compensation model can be directly used to continue the multi-axis linkage control for the next cycle.

[0053] Under the condition that the asymmetry exceeds a preset threshold, a motion direction reversal period is defined. The start time of the motion direction reversal period is the start time when the statistical pattern of the sign change rate recorded in the step of identifying the target joint where the motion direction has reversed transitions from a unimodal distribution to a bimodal distribution. The specific method for determining the start time of the transition from a unimodal distribution to a bimodal distribution in the statistical pattern of sign change rate is as follows: In the statistical pattern of sign change rate, when a local maximum value interval is first detected from the unimodal distribution state, excluding the value interval corresponding to the peak position, with a frequency comparable to the maximum frequency, and the value interval corresponding to the local maximum value is located in the ratio interval opposite to the ratio interval where the peak position is located in the positive ratio region or the negative ratio region, then the moment when the local maximum value is first detected is taken as the start time of the transition to a bimodal distribution. The end time of the motion direction reversal period is the moment when the statistical pattern of sign change rate returns to a unimodal distribution after the motion direction reversal is completed. The specific method for determining the moment when the statistical pattern of the rate of change of sign returns to a unimodal distribution is as follows: In a bimodal distribution, when one of the two frequency maxima located in the positive ratio region and the negative ratio region gradually decreases until it no longer meets the frequency maxima determination condition, while the other frequency maxima continues to be maintained and the frequency of the value intervals on both sides decreases monotonically, the moment when the frequency maxima that no longer meets the frequency maxima determination condition disappears is taken as the moment when the distribution returns to a unimodal distribution.

[0054] During the motion direction reversal period, the actual output torque value is continuously acquired from the joint actuator of the target joint. The method of acquiring the actual output torque value during the motion direction reversal period is the same as the method of acquiring the actual output torque value from the joint actuator of the target joint during the duration of the forward trial phase in the step of superimposing a micro-amplitude bidirectional trial motion before the motion direction reversal is performed. The actual output torque value is acquired once in each servo control cycle. All actual output torque values ​​acquired during the motion direction reversal period form a timing sequence. Each actual output torque value in the timing sequence corresponds to one acquisition time, and the acquisition time is marked by the sequence number of the servo control cycle.

[0055] All actual output torque values ​​collected during the motion direction reversal period are used as driving torque feedback values. These driving torque feedback values ​​are stored in the robot controller's memory as a time sequence for subsequent time-frequency transformation processing. The length of the time sequence is determined by the time span of the motion direction reversal period and the servo control cycle; the time span of the motion direction reversal period dynamically changes according to the specific operating conditions of each motion direction reversal.

[0056] By extracting the driving torque feedback value within the motion direction reversal period after filtering by a preset threshold, the scope of lubrication state assessment is limited to the motion direction reversal period of the target joint where deviation actually occurs. This avoids the computational overhead of performing subsequent frequency domain analysis on all motion direction reversal events. Furthermore, the motion direction reversal period is defined using the kurtosis of the sign rate of change statistical pattern as the start and end markers. This ensures that the extracted driving torque feedback value fully covers the torque change information throughout the entire process from tooth surface separation, backlash crossing, to re-contact of the reverse tooth surface. This provides signal data with a complete time window and clear boundaries for capturing the energy migration of the meshing frequency sidebands in subsequent frequency domain analysis.

[0057] The specific implementation steps for performing time-frequency transformation on the driving torque feedback value, extracting the energy ratio of the sidebands on both sides of the meshing frequency, comparing the shift of the energy ratio before and after the reversal of the motion direction, and evaluating the degree of deviation of the lubrication state of the target joint are as follows.

[0058] In the step of extracting the driving torque feedback value of the target joint during the motion direction reversal period when the tested asymmetry exceeds a preset threshold, the driving torque feedback value has already been obtained. The driving torque feedback value is a time series composed of all actual output torque values ​​collected during the motion direction reversal period. The step of performing time-frequency transformation on the driving torque feedback value further processes the driving torque feedback value.

[0059] Obtain the number of reducer teeth of the joint to which the target joint belongs. The number of reducer teeth refers to the number of meshing teeth between the flexible and rigid gears inside the reducer connected to the target joint. The number of reducer teeth is calibrated and stored in the parameter table of the robot controller when the robot leaves the factory. Calculate the average rotational speed of the target joint during the motion direction reversal period. The average rotational speed is calculated as follows: read the joint motor shaft angular velocity value of each servo control cycle during the motion direction reversal period from the joint driver of the target joint, sum all the joint motor shaft angular velocity values ​​during the motion direction reversal period, and divide by the number of servo control cycles included in the motion direction reversal period. Multiply the number of reducer teeth by the average rotational speed to obtain the meshing frequency. The meshing frequency is calculated as: fg = Z × n; where fg represents the meshing frequency in Hertz, Z represents the number of reducer teeth (dimensionless), and n represents the average rotational speed in revolutions per second. The physical meaning of the meshing frequency is the number of times the internal tooth surfaces of the reducer mesh per unit time. The meshing frequency is a characteristic frequency directly related to the tooth surface contact state in the driving torque feedback value.

[0060] A short-time Fourier transform (SFT) is performed on the driving torque feedback value to obtain the torque spectrum. The SFT parameters are set as follows: a Hanning window is used as the window function, and the window length is determined based on the frequency resolution requirements of the meshing frequency in the frequency domain. The window length must cover at least five complete cycles of the meshing frequency to ensure sufficient frequency domain resolution in the torque spectrum. The window length is calculated by multiplying the sampling frequency by 5 and then dividing by the meshing frequency, where the sampling frequency is the servo control frequency, which is the reciprocal of the servo control cycle. The window sliding step is 1 / 4 of the window length to achieve a balance between time resolution and frequency resolution. For example, if the servo control frequency is 1000 Hz and the meshing frequency is 20 Hz, then the window length must be at least 250 sampling points, and the window sliding step must be 62 sampling points. The output of the SFT is a two-dimensional complex matrix. The rows of the two-dimensional complex matrix correspond to time frames, and the columns correspond to frequency points. The magnitude of each element in the two-dimensional complex matrix represents the torque spectrum amplitude at the corresponding time frame and frequency point.

[0061] In the torque spectrum, determine the center frequencies of the lower and upper sidebands. The center frequency of the lower sideband is the difference between the meshing frequency and the meshing frequency corresponding to the number of reducer teeth, while the center frequency of the upper sideband is the sum of the meshing frequency and the meshing frequency corresponding to the number of reducer teeth. The meshing frequency corresponding to the number of reducer teeth is the meshing frequency fg calculated above, with the lower sideband center frequency calculated as 0 and the upper sideband center frequency calculated as 2fg. The center frequencies of the lower and upper sidebands are located on either side of the meshing frequency and are equidistant from it.

[0062] The power ratio is obtained by summing the power values ​​within the preset bandwidth of the lower sideband center frequency and the upper sideband center frequency, and dividing the sum by the power value within the preset bandwidth of the meshing frequency. The power ratio is calculated as: E = (Pl + Pu) / Pc; where E represents the power ratio (dimensionless), Pl represents the power value within the preset bandwidth of the lower sideband center frequency (in watts), Pu represents the power value within the preset bandwidth of the upper sideband center frequency (in watts), and Pc represents the power value within the preset bandwidth of the meshing frequency (in watts).

[0063] The power value within the preset bandwidth of the lower sideband center frequency is calculated as follows: Using the lower sideband center frequency as a reference, the statistical range of the lower sideband is defined as the half-octave width of the meshing frequency corresponding to the number of reducer teeth, extending towards both low and high frequencies. The half-octave width of the meshing frequency corresponding to the number of reducer teeth is half the meshing frequency fg. Within the lower sideband statistical range, the amplitudes of all frequency points in the torque spectrum are squared and summed. The amplitude of each frequency point in the torque spectrum is in Newton-meters (N·m), and the squared value is in N·m². The summation result is taken as the lower sideband power value, which is then used as the power value within the preset bandwidth of the lower sideband center frequency.

[0064] The calculation method for the power value within the preset bandwidth range of the upper sideband center frequency is the same as that for the power value within the preset bandwidth range of the lower sideband center frequency. The upper sideband center frequency is 2fg, and the upper sideband statistical range is defined as the half-octave width of the meshing frequency extended in both the low-frequency and high-frequency directions of the upper sideband center frequency. Within the upper sideband statistical range, the squared amplitudes of all frequency points in the torque spectrum are summed, and the sum is taken as the upper sideband power value. This upper sideband power value is used as the power value within the preset bandwidth range of the upper sideband center frequency. Since all frequency points in the torque spectrum are non-negative frequencies, when 0 Hz is less than 0.5fg Hz, the frequency range from 0 Hz to 0.5fg Hz is not included in the statistical range. The lower limit of the lower sideband statistical range is 0 Hz, and the upper limit of the upper sideband statistical range is determined by the sum of the meshing frequency fg and the half-octave width.

[0065] The power value within the preset bandwidth of the meshing frequency is calculated as follows: taking the meshing frequency fg as the reference, the half-octave width of the meshing frequency is extended in both the low-frequency and high-frequency directions to form the statistical range of the meshing frequency. Within the statistical range of the meshing frequency, the amplitudes of all frequency points in the torque spectrum are squared and summed, and the sum is taken as the power value within the preset bandwidth of the meshing frequency.

[0066] The energy ratio of the first segment of the motion direction reversal period is taken as the energy ratio before reversal, and the energy ratio of the second segment of the motion direction reversal period is taken as the energy ratio after reversal. The division of the first and second segments of the motion direction reversal period is as follows: the motion direction reversal period is divided into a first segment and a second segment, with the midpoint of the motion direction reversal period as the boundary. The midpoint of the motion direction reversal period is determined by the arithmetic mean of the start and end times of the motion direction reversal period. Short-time Fourier transforms are performed on the driving torque feedback values ​​of the first and second segments respectively, and the energy ratios are calculated to obtain the energy ratios before and after reversal.

[0067] The absolute value of the difference between the energy ratio after reversal and the energy ratio before reversal is taken as the energy ratio offset. The energy ratio offset is calculated as: D = |Ea - Eb|; where D represents the energy ratio offset (dimensionless), Ea represents the energy ratio after reversal (dimensionless), and Eb represents the energy ratio before reversal (dimensionless). The physical meaning of the energy ratio offset is that it reflects the change in the energy distribution of the sidebands on both sides of the meshing frequency relative to the meshing frequency energy during the reversal of the motion direction. Under normal lubrication conditions, the energy ratios before and after the reversal of the motion direction are close, and the energy ratio offset approaches 0. When the lubrication conditions deviate, the tooth surface contact stiffness undergoes time-varying modulation due to fluctuations in oil film thickness. This modulation effect causes a significant shift in energy between the upper and lower sidebands before and after the reversal of the motion direction, increasing the energy ratio offset.

[0068] The degree of deviation in lubrication condition is determined based on the magnitude of the energy ratio deviation. The mapping relationship between the degree of lubrication state deviation and the energy ratio offset is established as follows: Under the condition that all joints of the robot are in a known normal lubrication state, execute multiple standard task trajectories that include reversal of motion direction, and record the reference range of energy ratio offset under normal lubrication state. The reference range of energy ratio offset under normal lubrication state is obtained by: under the condition that the lubrication state is known to be normal, continuously execute standard task trajectories that include reversal of motion direction, calculate the energy ratio offset for each reversal of motion direction, and take the maximum value of multiple energy ratio offsets as the upper limit of the reference range of energy ratio offset under normal lubrication state; under the condition that all joints of the robot are in different known levels of lubrication state deviation, execute the same standard task trajectory, and record the energy ratio offset range corresponding to each level of lubrication state deviation; divide the energy ratio offset range into multiple intervals, each interval corresponding to one level of lubrication state deviation, and set the interval boundary values ​​as follows: take the upper limit of the reference range of energy ratio offset under normal lubrication state as the boundary value between the first interval and the second interval, take twice the upper limit of the reference range of energy ratio offset under normal lubrication state as the boundary value between the second interval and the third interval, and so on. The deviation level of lubrication condition starts from 1 and increases. Level 1 corresponds to normal lubrication condition, and the higher the level, the more serious the deviation of lubrication condition.

[0069] For example, if the upper limit of the energy ratio deviation from the baseline range under normal lubrication conditions is 0.065, then an energy ratio deviation less than or equal to 0.065 corresponds to lubrication condition deviation level 1, an energy ratio deviation greater than 0.065 and less than or equal to 0.13 corresponds to lubrication condition deviation level 2, and an energy ratio deviation greater than 0.13 corresponds to lubrication condition deviation level 3. The lubrication condition deviation level is a quantitative expression of the degree of deviation from the lubrication condition.

[0070] The method utilizes the modulation effect of oil film thickness change on meshing frequency by extracting the ratio of sideband energy on both sides of the meshing frequency through time-frequency transformation and comparing the offset before and after the reversal of motion direction. Conventional methods assess lubrication status by identifying friction model parameters or observing the distortion of friction force and velocity curves. However, the above method captures the characteristic information of lubrication status deviation from the frequency domain structure change of torque signal. Meshing frequency sideband energy migration is a sensitive indicator for identifying gear wear and poor lubrication. Introducing it into the real-time control scenario of robot joints, online quantitative assessment of the degree of lubrication status deviation is achieved without adding any external sensors and only using the existing torque signal of the joint actuator. This provides a precise quantitative basis for determining the Coulomb friction term correction in subsequent steps.

[0071] The specific implementation steps for correcting the Coulomb friction term in the feedforward friction compensation model of the target joint based on the degree of deviation of the lubrication state, and then using the corrected feedforward friction compensation model for the multi-axis linkage control in the next cycle are as follows.

[0072] The degree of deviation in the lubrication condition of the target joint has been obtained in the step of assessing the deviation, and is expressed as a numerical value of the energy ratio offset. The energy ratio offset is a dimensionless scalar, and its calculation method has been explained in detail in the step of assessing the degree of deviation in the lubrication condition of the target joint.

[0073] Correcting the Coulomb friction term based on the degree of deviation from lubrication conditions requires a preset correction coefficient table. This table stores multiple correction coefficients, each corresponding to a range of values ​​for the energy ratio offset. The preset correction coefficient table is established as follows: under three conditions—normal lubrication at each robot joint, slight deviation from lubrication, and significant deviation from lubrication—a standard task trajectory is executed, and the end-effector jitter amplitude is recorded after each direction reversal. The end-effector jitter amplitude is obtained by bandpass filtering the acceleration signal from the accelerometer installed at the joint output, or by bandpass filtering the angular acceleration signal obtained by differentiating the joint encoder signal. Under each lubrication condition, the Coulomb friction term in the feedforward friction compensation model is iteratively adjusted, and the value of the Coulomb friction term that minimizes the end-effector jitter amplitude is recorded. The difference between the optimal Coulomb friction term obtained under the condition of slight deviation from the known lubrication state and the optimal Coulomb friction term obtained under the condition of normal lubrication state is denoted as the first Coulomb friction term increment. The difference between the optimal Coulomb friction term obtained under the condition of significant deviation from the known lubrication state and the optimal Coulomb friction term obtained under the condition of normal lubrication state is denoted as the second Coulomb friction term increment.

[0074] Simultaneously, the average value of the energy ratio deviation is calculated under three lubrication conditions. The average value under the condition of normal lubrication is denoted as the first deviation reference value; the average value under the condition of slight deviation is denoted as the second deviation reference value; and the average value under the condition of significant deviation is denoted as the third deviation reference value. The first correction factor is calculated as the increment of the first coulomb friction term divided by the difference between the second and first deviation reference values. The second correction factor is calculated as the increment of the second coulomb friction term divided by the difference between the third and first deviation reference values, thus establishing a mapping table from the energy ratio deviation interval to the correction factor.

[0075] For example, if the experimentally measured first offset reference value is 0.03, second offset reference value is 0.08, third offset reference value is 0.18, first coulomb friction term increment is 0.15 N·m, and second coulomb friction term increment is 0.45 N·m, then the first correction factor is 0.15 / 0.05 = 3.0 N·m, and the second correction factor is 0.45 / 0.10 = 4.5 N·m. The preset correction factor table includes entries where the correction factor is 3.0 N·m when the energy ratio offset is less than or equal to 0.08, and 4.5 N·m when the energy ratio offset is greater than 0.08.

[0076] Using a preset correction factor table, the corresponding correction factor is obtained by looking up the table based on the calculated deviation of the lubrication state, i.e., the energy ratio shift. The Coulomb friction term correction is calculated as: ΔTc = k × D; where ΔTc represents the Coulomb friction term correction in Newton-meters (N·m), k represents the correction factor obtained from the preset correction factor table in N·m, and D represents the energy ratio shift, which is dimensionless. The Coulomb friction term correction is directly proportional to the deviation of the lubrication state, and the proportionality coefficient is determined by experimental calibration.

[0077] In the feedforward friction compensation model of the target joint, the current Coulomb friction term is either the initial Coulomb friction term calibrated and stored in the parameter table after the robot leaves the factory or after lubrication maintenance, or the Coulomb friction term corrected in the previous cycle. The corrected Coulomb friction term is obtained by adding the correction amount to the current Coulomb friction term in the feedforward friction compensation model of the target joint, calculated as: Tcnew = Tc0 + ΔTc; where Tcnew represents the corrected Coulomb friction term in Newton-meters (N·m), and Tc0 represents the current Coulomb friction term in the feedforward friction compensation model of the target joint in Newton-meters (N·m).

[0078] The current Coulomb friction term in the feedforward friction compensation model is replaced with the modified Coulomb friction term to form the modified feedforward friction compensation model. In the modified feedforward friction compensation model, all parts except the Coulomb friction term, including the viscous friction term and the Stribeck curve portion, remain unchanged.

[0079] In the next cycle of multi-axis linkage control, the feedforward torque output by the modified feedforward friction compensation model is superimposed on the torque command of the target joint. The feedforward torque is calculated by the modified feedforward friction compensation model based on the current angular velocity command of the target joint and the modified Coulomb friction term. The superposition method is that the torque command equals the sum of the feedback control torque and the feedforward torque. The torque command of the target joint already includes the Coulomb friction compensation component corrected according to the deviation of the real-time lubrication state, thereby compensating for the friction torque asymmetry caused by the change in lubrication state in the next cycle after the reversal of the motion direction and in subsequent motions.

[0080] Based on the dynamic correction of the Coulomb friction term in the feedforward friction compensation model according to the degree of lubrication state deviation, the mapping relationship between the energy ratio shift and the correction coefficient was established through experimental calibration. This ensures that the compensation amount is proportional to the degree of lubrication state deviation, and the calibration guarantees the rationality of the correction gain. The corrected feedforward friction compensation model can compensate for the friction torque change caused by lubrication state deviation in advance in the next multi-axis linkage, avoiding the accumulation of unexpected end-effector vibrations and improving the trajectory stability of the multi-axis robot in clean environments, including steering and micro-amplitude reciprocating trajectories.

[0081] It is worth noting that the feedforward friction compensation model is a compensation algorithm used in robot joint torque control to counteract the influence of friction on motion accuracy. The basic form of the feedforward friction compensation model includes a Coulomb friction term, a viscous friction term, and a Stribeck curve portion. The Coulomb friction term is a physical quantity in the feedforward friction compensation model that describes a constant frictional torque component related to the motion direction but largely independent of the velocity magnitude. Mathematically, the Coulomb friction term is represented as the product of a sign function and the Coulomb friction coefficient, with the sign function taking the positive or negative sign of the joint angular velocity command. During operation, the feedforward friction compensation model calculates the Coulomb friction torque corresponding to the Coulomb friction term, the viscous friction torque corresponding to the viscous friction term, and the low-speed nonlinear friction torque corresponding to the Stribeck curve portion, based on the angular velocity command of the target joint in the current control cycle. The sum of these three is then added as the feedforward torque to the torque command of the target joint.

[0082] In this method, the Coulomb friction term in the feedforward friction compensation model is no longer kept constant, but is corrected in real time based on the degree of lubrication state deviation obtained in the step of evaluating the deviation of the target joint's lubrication state. The correction amount of the Coulomb friction term is obtained by multiplying the degree of lubrication state deviation by a correction coefficient obtained from a preset correction coefficient table. The corrected Coulomb friction term replaces the current Coulomb friction term in the feedforward friction compensation model, enabling the feedforward friction compensation model to adaptively adjust the compensation amount according to the time-varying characteristics of the lubrication state. The calculation methods of the Coulomb friction term correction amount, the corrected Coulomb friction term, and the corrected feedforward friction compensation model have been explained in detail in the step of correcting the Coulomb friction term in the feedforward friction compensation model of the target joint based on the degree of lubrication state deviation.

[0083] Example 2: Figure 2 A schematic diagram of a multi-axis robot control system suitable for clean environments is provided according to the present invention. The multi-axis robot control system suitable for clean environments includes: The signal acquisition module is used to acquire the raw counting signals from the encoders of each joint of the multi-axis robot; The reversal recognition module is used to perform sign change rate statistics on the original counting signal within a sliding window. When the sign change rate statistics mode of a certain joint transitions from a single-peak distribution to a double-peak distribution and the counting sign of one of the double peaks is flipped, the corresponding joint is identified as the target joint whose motion direction has been reversed. The bidirectional probing module is used to control the target joint to superimpose micro-amplitude bidirectional probing motions before performing a reversal of the motion direction, record the peak values ​​of the driving torque response of the forward and reverse probing segments, and calculate the probing asymmetry. The torque extraction module is used to extract the driving torque feedback value of the target joint during the period of reversal of the motion direction when the probe asymmetry exceeds a preset threshold. The deviation assessment module is used to perform time-frequency transformation on the driving torque feedback value, extract the energy ratio of the sidebands on both sides of the meshing frequency, compare the deviation of the energy ratio before and after the reversal of the motion direction, and assess the degree of deviation of the lubrication state of the target joint. The feedforward correction module is used to correct the Coulomb friction term in the feedforward friction compensation model of the target joint based on the degree of deviation of the lubrication state, and then use the corrected feedforward friction compensation model for the multi-axis linkage control in the next cycle.

[0084] All calculations involved in the embodiments are performed using dimensionless numerical values, and the preset parameters and thresholds in the calculations can be set by those skilled in the art according to actual conditions.

[0085] This technical solution can be flexibly deployed, for example, as embedded software running on device hardware, or installed on personal computers or other smart terminals with user interfaces, thus adapting to various hardware environments and usage requirements.

[0086] The above solutions can be implemented in software, hardware, firmware, or a combination thereof. When implemented in software, they are presented, in whole or in part, as a computer program product, containing one or more computer instructions or programs. When these instructions or programs are loaded and executed on a computer, results are produced corresponding to the processes or functions of the embodiments of this application. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. Computer instructions can be stored in a computer-readable storage medium or transmitted from one medium to another via wired or wireless means, such as from a website, server, or data center via wired means such as fiber optic cables, twisted-pair cables, or coaxial cables, or wireless means such as infrared or microwaves to another site. A computer-readable storage medium refers to any usable medium that a computer can access or a data storage device such as a server or data center that contains one or more usable media, including magnetic media such as floppy disks, hard disks, and magnetic tapes, optical media such as DVDs, and semiconductor media such as solid-state drives.

[0087] The specific working process of the system, device and module can be found in the method embodiment, and will not be repeated here.

[0088] The disclosed systems, devices, and methods can be implemented in other ways. The device embodiments are for illustrative purposes only, and the module division is only a logical division. In practice, different divisions can be implemented, such as merging or integrating multiple modules or components, or omitting some features. Coupling, direct coupling, or communication connections between the components can be achieved through interfaces, while indirect coupling or communication connections can take electrical, mechanical, or other forms.

[0089] The modules described as separate components may or may not be physically separated. The components shown as modules can be physical hardware or software, and can be deployed centrally or distributed across multiple network nodes. Some or all of the modules can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0090] The functional modules in each embodiment can be integrated into one processing module, or they can exist independently, or two or more modules can be integrated into one.

[0091] If the functionality is implemented as a software module and used as an independent product, it can be stored in a computer-readable storage medium. Under this understanding, the substantial contribution of the technical solution of this application can be embodied in the form of a software product. This computer software product is stored in a storage medium and contains instructions to cause a computer device, such as a personal computer, server, or network device, to execute all or part of the steps of the methods in the embodiments of this application. The storage medium includes any medium capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory, random access memory, magnetic disk, or optical disk.

[0092] The above are merely specific embodiments of this application, and the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should fall within the scope of protection of this application.

Claims

1. A multi-axis robot control method suitable for clean environments, characterized in that, include: S1. Acquire the raw counting signals from the encoders of each joint of the multi-axis robot; S2. Perform sign change rate statistics on the original counting signal within a sliding window. When the sign change rate statistics mode of a certain joint transitions from a single-peak distribution to a double-peak distribution and the counting sign of one of the double peaks flips, the corresponding joint is identified as the target joint whose motion direction has reversed. S3. Control the target joint to perform a micro-amplitude bidirectional trial motion before reversing the direction of motion, record the peak values ​​of the driving torque response of the forward trial segment and the reverse trial segment, and calculate the trial asymmetry. S4. When the asymmetry of the test exceeds the preset threshold, extract the driving torque feedback value of the target joint during the period of reversal of the movement direction. S5. Perform time-frequency transformation on the driving torque feedback value, extract the energy ratio of the sidebands on both sides of the meshing frequency, compare the offset of the energy ratio before and after the reversal of the motion direction, and evaluate the degree of deviation of the lubrication state of the target joint. S6. Based on the degree of deviation of the lubrication state, the Coulomb friction term in the feedforward friction compensation model of the target joint is corrected, and the corrected feedforward friction compensation model is used for the multi-axis linkage control in the next cycle.

2. The multi-axis robot control method suitable for clean environments according to claim 1, characterized in that, Acquire the raw counting signals from the encoders of each joint of the multi-axis robot, including: The output of the photoelectric encoder mounted on the joint motor shaft reads the raw pulse count value without position interpolation processing in real time. The sign difference between the original pulse count values ​​of adjacent control cycles is used as the sign change event; The original counting signal is formed by the sequence of events that change the symbol of each control cycle.

3. The multi-axis robot control method suitable for clean environments according to claim 1, characterized in that, The sign change rate of the original counting signal is statistically analyzed within a sliding window. When the statistical pattern of the sign change rate of a certain joint transitions from a unimodal distribution to a bimodal distribution and the counting sign of one of the bimodal peaks flips, the corresponding joint is identified as the target joint whose motion direction has reversed, including: A sliding window is established on the sequence of sign change events of the original counting signal, with a fixed number of events as the window length; Calculate the ratio of the number of positive symbol events to the number of negative symbol events in the symbol change events within the sliding window, and use it as the symbol change rate; The frequency distribution of the rate of change of the statistical sign in each value interval yields the statistical pattern of the rate of change of the sign. The range of values ​​corresponding to the maximum frequency in the statistical pattern of the rate of change of sign is taken as a single peak, and the range of values ​​with two frequency maxima located in the positive ratio region and the negative ratio region, respectively, is taken as a double peak. When the statistical pattern of the rate of change of the sign transitions from a unimodal distribution to a bimodal distribution, and the frequency maxima corresponding to the inverse ratio region in the bimodal distribution exceed the frequency maxima corresponding to the forward ratio region for the first time, the corresponding joint is identified as the target joint.

4. The multi-axis robot control method suitable for clean environments according to claim 3, characterized in that, The frequency distribution of the statistical rate of change of the sign in each value interval includes: dividing the range of the rate of change of the sign into a positive value interval group and a negative value interval group with zero as the center and a preset step size as the interval; counting the frequency of the rate of change of the sign falling into each value interval in the positive value interval group and the negative value interval group within the sliding window; and arranging the frequency of each value interval in the positive value interval group and the negative value interval group in ascending order of the value interval to form a statistical pattern of the rate of change of the sign.

5. The multi-axis robot control method suitable for clean environments according to claim 1, characterized in that, Before reversing the direction of motion, a small-amplitude bidirectional trial motion is superimposed on the target joint. The peak values ​​of the driving torque response during the forward and reverse trial segments are recorded, and the trial asymmetry is calculated, including: An offset signal with an amplitude not exceeding the product of the encoder's minimum resolution step size and the reducer's transmission ratio is superimposed on the target position trajectory of the target joint in the joint space. First, apply a positive bias along the original direction of motion to form a positive test segment, and then apply a reverse bias in the opposite direction of the original direction of motion to form a reverse test segment. During the duration of the positive test phase, the actual output torque value is collected from the joint actuator of the target joint, and the maximum absolute value of the actual output torque value during the duration of the positive test phase is taken as the peak value of the driving torque response of the positive test phase. During the duration of the reverse test segment, the actual output torque value is collected from the joint actuator of the target joint, and the maximum absolute value of the actual output torque value during the duration of the reverse test segment is taken as the peak value of the driving torque response of the reverse test segment. The ratio of the peak value of the driving torque response in the forward test section to the peak value of the driving torque response in the reverse test section is calculated as the test asymmetry.

6. The multi-axis robot control method suitable for clean environments according to claim 1, characterized in that, When the tested asymmetry exceeds a preset threshold, the driving torque feedback value of the target joint during the period of reversal of the motion direction is extracted, including: When the asymmetry of the trial exceeds the preset threshold, the motion direction reversal period is defined as the time from the start of the transition of the statistical pattern of the sign change rate of the target joint from a unimodal distribution to a bimodal distribution, until the time when the statistical pattern of the sign change rate returns to a unimodal distribution after the motion direction reversal is completed. During the period of reversal of the motion direction, the actual output torque value is continuously collected from the joint actuator of the target joint; All actual output torque values ​​collected during the period of reverse motion direction are used as driving torque feedback values.

7. The multi-axis robot control method suitable for clean environments according to claim 1, characterized in that, The driving torque feedback value is subjected to time-frequency transformation to extract the energy ratio of the sidebands on both sides of the meshing frequency. The shift in the energy ratio before and after the reversal of the motion direction is compared to assess the degree of deviation in the lubrication state of the target joint, including: Obtain the number of reducer teeth of the joint to which the target joint belongs; The meshing frequency is obtained by multiplying the number of teeth in the reducer by the average rotational speed of the target joint during the period when the direction of motion reverses. A short-time Fourier transform is performed on the driving torque feedback value to obtain the torque spectrum; In the torque spectrum, the difference between the meshing frequency and the meshing frequency corresponding to the number of teeth of the reducer is taken as the center frequency of the lower sideband, and the sum of the meshing frequency and the meshing frequency corresponding to the number of teeth of the reducer is taken as the center frequency of the upper sideband. The sum of the power values ​​within the preset bandwidth range of the lower sideband center frequency and the upper sideband center frequency is calculated and divided by the power values ​​within the preset bandwidth range of the meshing frequency to obtain the energy ratio. The energy ratio of the first part of the period when the direction of motion is reversed is taken as the energy ratio before reversal, and the energy ratio of the second part of the period when the direction of motion is reversed is taken as the energy ratio after reversal. The absolute value of the difference between the energy ratio after reversal and the energy ratio before reversal is taken as the energy ratio offset. The degree of deviation in lubrication condition is determined based on the magnitude of the energy ratio deviation.

8. A multi-axis robot control method suitable for clean environments according to claim 7, characterized in that, The calculation of the power value within the preset bandwidth range of the lower sideband center frequency includes: using the lower sideband center frequency as a reference, extending the half-octave width of the meshing frequency corresponding to the number of reducer teeth in both low-frequency and high-frequency directions as the statistical range of the lower sideband; within the statistical range of the lower sideband, summing the squared amplitudes of all frequency points in the torque spectrum to obtain the lower sideband power value; the lower sideband power value is used as the power value within the preset bandwidth range of the lower sideband center frequency; the calculation method for the power value within the preset bandwidth range of the upper sideband center frequency is the same as the calculation method for the power value within the preset bandwidth range of the lower sideband center frequency.

9. A multi-axis robot control method suitable for clean environments according to claim 1, characterized in that, Based on the degree of deviation from the lubrication condition, the Coulomb friction term in the feedforward friction compensation model of the target joint is modified, and the modified feedforward friction compensation model is used for the multi-axis linkage control in the next cycle, including: Multiply the degree of deviation in lubrication condition by the corresponding correction coefficient in the preset correction coefficient table to obtain the correction amount for the Coulomb friction term; The Coulomb friction term correction is added to the current Coulomb friction term in the feedforward friction compensation model of the target joint to obtain the corrected Coulomb friction term. The corrected Coulomb friction term replaces the current Coulomb friction term in the feedforward friction compensation model, forming the corrected feedforward friction compensation model. In the next cycle of multi-axis linkage control, the feedforward torque output by the corrected feedforward friction compensation model is superimposed on the torque command of the target joint.

10. A multi-axis robot control system suitable for clean environments, used to implement the multi-axis robot control method suitable for clean environments as described in any one of claims 1-9, characterized in that, include: The signal acquisition module is used to acquire the raw counting signals from the encoders of each joint of the multi-axis robot; The reversal recognition module is used to perform sign change rate statistics on the original counting signal within a sliding window. When the sign change rate statistics mode of a certain joint transitions from a single-peak distribution to a double-peak distribution and the counting sign of one of the double peaks is flipped, the corresponding joint is identified as the target joint whose motion direction has been reversed. The bidirectional probing module is used to control the target joint to superimpose micro-amplitude bidirectional probing motions before performing a reversal of the motion direction, record the peak values ​​of the driving torque response of the forward and reverse probing segments, and calculate the probing asymmetry. The torque extraction module is used to extract the driving torque feedback value of the target joint during the period of reversal of the movement direction when the tested asymmetry exceeds a preset threshold. The deviation assessment module is used to perform time-frequency transformation on the driving torque feedback value, extract the energy ratio of the sidebands on both sides of the meshing frequency, compare the deviation of the energy ratio before and after the reversal of the motion direction, and assess the degree of deviation of the lubrication state of the target joint. The feedforward correction module is used to correct the Coulomb friction term in the feedforward friction compensation model of the target joint based on the degree of deviation of the lubrication state, and then use the corrected feedforward friction compensation model for the multi-axis linkage control in the next cycle.

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