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CN114505844A - Industrial robot-oriented residual vibration suppression system and method - Google Patents

Industrial robot-oriented residual vibration suppression system and method Download PDF

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CN114505844A
CN114505844A CN202210082583.1A CN202210082583A CN114505844A CN 114505844 A CN114505844 A CN 114505844A CN 202210082583 A CN202210082583 A CN 202210082583A CN 114505844 A CN114505844 A CN 114505844A
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residual vibration
industrial robot
filter
exponential
track
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CN114505844B (en
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邹焱飚
刘涛
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South China University of Technology SCUT
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/0081—Programme-controlled manipulators with master teach-in means
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J13/00—Controls for manipulators
    • B25J13/006—Controls for manipulators by means of a wireless system for controlling one or several manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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Abstract

The invention discloses a residual vibration suppression system and method for an industrial robot, which comprises an embedded industrial personal computer with a real-time control function, an acceleration sensor, an acceleration signal transmission device, the industrial robot and a servo controller thereof, wherein the acceleration sensor is arranged at the tail end of the industrial robot through an acceleration sensor fixing element, collected acceleration signals are accessed to a servo driver of the industrial robot through the acceleration signal transmission device, and the servo driver is connected with the embedded industrial personal computer through a gigabit industrial Ethernet interface. The residual vibration suppression system provided by the invention is simple and low in cost, the industrial robot control platform has a real-time function, and the residual vibration suppression method can realize the maximum suppression of residual vibration, further improve the smoothness of track running, reduce the impact on a motor in the running process and ensure the contour precision of an interpolation track.

Description

Industrial robot-oriented residual vibration suppression system and method
Technical Field
The invention relates to the field of residual vibration suppression, in particular to a residual vibration suppression system and method for an industrial robot.
Background
In industrial production, industrial robots often require rapid movement and precise positioning. However, due to the fact that the industrial robot has flexible structures such as a harmonic reducer and a belt, the tail end of the industrial robot can generate severe residual vibration after the movement is finished, and the terminal can be calmed after a certain time. Therefore, the suppression of the residual vibration at the tail end of the industrial robot is realized, and the method has great significance for improving the production efficiency and popularizing the application of the industrial robot.
Journal of mechanical design and manufacture published an academic paper entitled "research on residual vibration suppression and measurement mode of flexible loading of robot" in 2021, 11/8. Aiming at the working condition of flexible load of the six-degree-of-freedom industrial robot, the author designs a zero-vibration first-order differential input shaper (ZVD) for restraining residual vibration and designs an amplitude detection device based on a laser tracker. Although experiments show that the method can effectively suppress the residual vibration of the tail end of the industrial robot, the ZVD shaper only focuses on suppressing the residual vibration of the tail end of the robot, is not helpful to the vibration problem in the running process, and even causes the contour error of the running track to become large due to the time sequence change of each joint. In addition, the adopted laser tracker is high in price, greatly increases the technical cost, and is not suitable for actual production activities. Further, the industrial robot is a nonlinear time-varying system, and the postures of the robot are different according to different motion trajectories, and the corresponding residual vibration modes are also changed. The method has no self-adaptive adjustment capability, so the application range of the method is greatly limited.
In actual industrial production, people often hope to utilize limited equipment, and when the tail end of the robot is ensured not to generate residual vibration, the smoothness of track running can be further improved, the impact on a motor in the running process is reduced, and meanwhile the contour precision of the track is ensured. This requirement is very important in some industrial processes, such as spray robots, where the process can lead to uneven coatings if there is jitter, and to missing coatings in certain locations if there is profile error, which can seriously affect the quality of the product and even result in failure. Therefore, it is necessary to develop a new vibration suppression technology that can satisfy the above requirements.
Disclosure of Invention
The invention aims to provide a residual vibration suppression system for an industrial robot, which builds a real-time control platform, can solve the problem of lag in robot control and improves the flexibility. In addition, the adopted acceleration sensor does not need to have high-precision detection capability, so that hardware equipment can be simplified, the technical cost is reduced, and the technical feasibility is improved.
Another object of the present invention is to provide a method for suppressing residual vibration for an industrial robot, which can make full use of the advantages of a real-time control platform, realize online adaptive adjustment of the parameters of a shaper, further improve the smoothness of track running, reduce the impact on a motor during running, and ensure the contour accuracy of an interpolated track while realizing maximum suppression of residual vibration.
The invention is realized by at least one of the following technical schemes.
A residual vibration suppression method for an industrial robot comprises the following steps:
s1, manually teaching the industrial robot (4), determining interpolation track types and running time, and performing linear filtering track planning on the industrial robot to generate an initial interpolation track;
s2, controlling the industrial robot (4) to perform initial track interpolation motion, measuring an acceleration signal of the residual vibration of the tail end of the industrial robot after the motion is finished, and calculating the damping ratio and the undamped vibration angular frequency of the residual vibration;
s3, performing exponential filtering track planning on the industrial robot according to the residual vibration mode of the tail end of the industrial robot to generate a shaping interpolation track with a vibration suppression function;
s4, controlling the industrial robot (4) to perform shaping track interpolation motion, measuring an acceleration signal of the residual vibration of the tail end of the industrial robot after the motion is finished, and calculating the energy of the residual vibration;
and S5, adjusting the exponential filtering track planning parameters by using an iterative learning strategy, and re-performing exponential filtering track planning on the industrial robot to realize the maximum suppression of the residual vibration at the tail end of the industrial robot.
Further, in the linear filtering trajectory planning of step S1, the amplitude is determined by dividing the amplitude into two partsThe step signal with the value of total displacement h sequentially passes through two time lengths which are respectively T1、T2The first and second linear filters of (1) generate a total duration of Tot ═ T1+T2Wherein each linear filter M is a linear filteriThe transfer function of (a) is:
Figure BDA0003486491620000031
in the formula ,TiThe duration of the filter is set as i belongs to {1,2}, e is a natural base number, and s is an independent variable of a transfer function; in a discretized implementation, the linear filter MiThe difference equation of (a) is:
Figure BDA0003486491620000032
in the formula ,Ni＝[Ti/Ts]The number of times of sampling of the response of the linear filter, [ 2 ]]Denotes rounding up, TsIs a sampling period, qn(k) For the displacement of the output trajectory at the sampling instant k, qn-1(k) Is the displacement of the input trajectory at the sampling instant k.
Further, the process of linear filtering trajectory planning in step S1 includes the steps of:
s11, calculating the total displacement h of the interpolation track according to the position of the teaching point and the type of the interpolation track;
s12, determining the time length T of the first linear filter and the second linear filter according to the interpolation track running time length Tot1、T2To ensure that condition T is satisfied1≥T2；
S13, step signal r (t) h · u (t) is input to the first linear filter M1To obtain a first-order output trace q1(t) the discretization expression of which is:
Figure BDA0003486491620000033
wherein h is the total displacement of the interpolation locus, u (t) isUnit step function, q1(k) Is the displacement of the first-order output trace at the sampling time k, r (k) is the displacement of the input step signal at the sampling time k, N1The number of samples of the first linear filter response;
s14, converting the first-order track q1(t) input to a second linear filter M2To obtain a second-order output locus q2(t) the discretization expression of which is:
Figure BDA0003486491620000041
in the formula ,q2(k) Is the displacement of the second order output trajectory at the sampling instant k, q1(k) For the displacement of the first-order input trajectory at the sampling instant k, N2The number of samples of the second linear filter response.
Further, the damping ratio ζ and the undamped vibration angular frequency ω of the residual vibration are calculated in step S2nComprises the following steps:
s21, performing Fast Fourier Transform (FFT) on the collected residual vibration signal to obtain a spectrogram of the residual vibration signal;
s22, setting a frequency spectrum amplitude threshold value AvAnd frequency variation threshold omegavSelecting amplitude greater than AvPeak frequency ω ofiIf adjacent peak frequencies satisfy ωi+1-ωi＜ωvIf the two are the same modal frequency, the two are considered to be the same modal frequency;
s23, selecting all modal frequencies according to S22, and taking the modal frequency with the maximum amplitude as the main vibration frequency, namely the undamped vibration angular frequency omegan；
S24, low-pass filtering the collected residual vibration signal, and taking the cut-off frequency of the filter as fc＝2ωn；
S25, drawing the residual vibration signal after low-pass filtering, and extracting a peak point set (t) of the residual vibration signali,zi), wherein tiTime, z, corresponding to the ith peak point of the residual vibration signaliIs the ith wavePeak value corresponding to peak point and wave peak value ziLogarithmic operation, denoted as zi′＝ln(zi) To obtain a new point set (t)i,zi′)；
S26, point set (t) is aligned by least square methodi,zi') finding a fitted straight line
Figure BDA0003486491620000042
Figure BDA0003486491620000051
Figure BDA0003486491620000052
In the formula, N is the number of point concentration points,
Figure BDA0003486491620000053
is the slope of the straight line being fitted,
Figure BDA0003486491620000054
is the intercept of the fitted straight line;
s27, fitting straight line according to the step S26
Figure BDA0003486491620000055
The damping ratio ζ of the residual vibration is obtained as follows:
Figure BDA0003486491620000056
in the formula ,ωnUndamped vibration angular frequencies for residual vibration.
Further, in the exponential filtering trajectory planning of step S3, the step signal with the amplitude of the total displacement h is sequentially processed by two time durations T1、T2And a first and a second linear filter of time duration TJGenerating an exponential filter of total duration Tot ═ T1+T2+TJIn which the exponential filter MJThe transfer function of (a) is:
Figure BDA0003486491620000057
wherein α is the attenuation ratio, TJIs the filter duration, e is the natural base number, s is the independent variable of the transfer function;
in order to achieve complete suppression of residual vibrations, the following should be satisfied:
α＝-ζωn
Figure BDA0003486491620000058
where ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
in a discretized implementation, the exponential filter MJThe difference equation of (a) is:
Figure BDA0003486491620000061
in the formula ,NJ＝[TJ/Ts]Is the number of times of sampling of the response of the exponential filter, [ 2 ]]Denotes rounding up, TsIs a sampling period, qJ(k) For the displacement of the output trajectory at the sampling instant k, qn-1(k) Alpha is the decay rate of the exponential filter for the displacement of the input trajectory at the sampling instant k.
Further, the process of linear filtering trajectory planning in step S3 includes the steps of:
s31, calculating the total displacement h of the interpolation track according to the position of the teaching point and the type of the interpolation track;
s32, keeping the interpolation track motion time length Tot unchanged, and determining the time length T of the first linear filter and the second linear filter1、T2Sum exponential filter duration TJ：
Figure BDA0003486491620000062
T2＝TJ，T1＝Tot-T2-TJEnsure to satisfy T1≥T2+TJ and T2≥TJWhere ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
s33, step signal r (t) h · u (t) is input to the first linear filter M1To obtain a first-order output trace q1(t) the discretization expression of which is:
Figure BDA0003486491620000063
wherein h is the total displacement of the interpolation track, u (t) is the unit step function, q1(k) Is the displacement of the first-order output trace at the sampling time k, r (k) is the displacement of the input step signal at the sampling time k, N1The number of samples of the first linear filter response;
s34, converting the first-order track q1(t) input to a second linear filter M2To obtain a second-order output locus q2(t) the discretization expression of which is:
Figure BDA0003486491620000071
in the formula ,q2(k) Is the displacement of the second order output trajectory at the sampling instant k, q1(k) For the displacement of the first-order input trajectory at the sampling instant k, N2Is the number of samples of the second linear filter response;
s35, calculating the second-order track q2(t) input exponential Filter MJTo obtain a third order output trace q2e(t) the discretization expression of which is:
Figure BDA0003486491620000072
in the formula ,q2e(k) For the displacement of the third-order output trajectory at the sampling instant k, q2(k) Is the displacement of the second-order input track at the sampling time k, alpha is the attenuation rate of the exponential filter, NJIs the number of samples of the exponential filter response, TsIs the sampling period.
Further, the step S5 specifically includes:
s51, fixing the attenuation rate alpha of the exponential filter, and utilizing the gradient descent principle to carry out time length T on the exponential filterJPerforming iterative learning until an iteration stop condition is met;
s52 fixed exponential filter duration TJPerforming iterative learning on the attenuation rate alpha of the exponential filter by using a gradient descent principle until an iteration stop condition is met;
s53 optimal exponential filter attenuation rate alpha obtained by iterative learningoptSum duration TJoptAnd (4) for parameters, planning the exponential filtering track of the industrial robot again, and realizing the maximum inhibition of the residual vibration at the tail end of the industrial robot.
Further, the step S51 specifically includes:
s511, calculating the attenuation rate alpha of the initial exponential filter by taking the residual vibration mode parameter of the end of the industrial robot measured in the step S2 as a reference0And initial filter duration TJ0：
α0＝-ζωn
Figure BDA0003486491620000081
Where ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
s512, maintaining the attenuation rate alpha of the exponential filter0The time length of the next iteration parameter index filter is taken as TJ1＝(1+δ)TJ0And delta is a constant, the exponential filtering track planning is carried out on the industrial robot again, the industrial robot (4) is controlled to carry out interpolation motion, and the residual vibration signal at the tail end of the industrial robot after the motion is measured is countedCalculating residual vibration energy M1：
Figure BDA0003486491620000082
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s513, updating the index filter duration T by utilizing the gradient descent principleJ：
Figure BDA0003486491620000083
wherein ,
Figure BDA0003486491620000084
in the formula ,TJkFor exponential filter duration in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
s514, index filter parameter alpha obtained by utilizing updating0 and TJk+1Planning the exponential filtering track of the industrial robot again, controlling the industrial robot (4) to perform interpolation movement, measuring a residual vibration signal at the tail end of the industrial robot after the movement is finished, and calculating the residual vibration energy Mk+1；
S515, if the vibration energy M isk+1＜MkI.e. indicating a reduction in residual vibration, T is consideredJk+1Updating correctly; if M isk+1＞MkIf the residual vibration is larger, the current iteration is abandoned, and the T is updated by adopting the following ruleJk+1：
Figure BDA0003486491620000091
wherein ,
Figure BDA0003486491620000092
s516, judging | TJk+1-TJkThe | < epsilon >, and epsilon represents a preset error limit; if the condition is satisfied, the current iteration value T is considered to beJk+1For the optimum exponential filter duration, denoted TJoptStopping iteration; if the condition is not met, repeating the step S513 to the step S516, and continuing the iteration until the stop condition is met.
Further, the step S52 specifically includes:
s521, obtaining the optimal exponential filter duration T obtained by iteration of the step S51JoptKeeping the duration T of the exponential filterJoptThe attenuation rate of the next iteration parameter exponential filter is taken as alpha without change1＝(1+δ)α0Delta is a constant, alpha0For the attenuation rate of the initial exponential filter obtained in the step S511, the exponential filtering track of the industrial robot is planned again, the industrial robot (4) is controlled to perform interpolation motion, the residual vibration signal of the tail end of the industrial robot after the motion is finished is measured, and the residual vibration energy M is calculated1：
Figure BDA0003486491620000101
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s522, updating the attenuation rate alpha of the exponential filter by utilizing the gradient descent principle:
Figure BDA0003486491620000102
wherein ,
Figure BDA0003486491620000103
in the formula ,αkFor exponential filter decay Rate in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
s523, index filter parameter alpha obtained by updating is utilizedk+1 and TJoptPlanning the exponential filtering track of the industrial robot again, controlling the industrial robot (4) to perform interpolation movement, measuring a residual vibration signal at the tail end of the industrial robot after the movement is finished, and calculating the residual vibration energy Mk+1；
S524, if the vibration energy Mk+1＜MkI.e. indicating a reduction in residual vibration, alpha is consideredk+1Updating correctly; if M isk+1＞MkIf the residual vibration is larger, the current iteration is abandoned, and the following rule is adopted to update alphak+1：
Figure BDA0003486491620000104
wherein ,
Figure BDA0003486491620000111
s525, judging | alphak+1-αkThe | < epsilon >, and epsilon represents a preset error limit; if the condition is satisfied, the current iteration value alpha is considered to bek+1For optimum exponential filter duration, noted as αoptStopping iteration; if the condition is not met, repeating the steps S522 to S525, and continuing the iteration until the stop condition is met.
The system for realizing the method for inhibiting the residual vibration facing the industrial robot comprises an embedded industrial personal computer with a real-time control function, an acceleration sensor, an acceleration signal transmission device, the industrial robot and a servo driver thereof;
the acceleration sensor is installed at the tail end of the industrial robot through an acceleration sensor fixing element, collected acceleration signals are connected into a servo driver of the industrial robot through an acceleration signal transmission device, and the servo driver is connected with the embedded industrial personal computer through a gigabit industrial Ethernet interface.
Further, the acceleration sensor is used for measuring an acceleration signal and outputting the acceleration signal in an analog quantity form; the acceleration signal transmission device realizes an EtherCAT bus protocol stack, can convert analog signals of the acceleration sensor into EtherCAT bus communication messages, and realizes information interaction with an EtherCAT master station; the servo driver controls the industrial robot to move by adopting an EtherCAT bus protocol; the embedded industrial personal computer builds a real-time control platform based on Kithara software and can process each control signal in real time.
Compared with the prior art, the invention has the following advantages and effects:
(1) different from other shaping inhibition methods, the acceleration sensor does not need to accurately measure the vibration mode of the tail end of the industrial robot, and only needs to measure the vibration energy as feedback, so that the acceleration sensor with low precision can be adopted, the technical cost is reduced, and the technical feasibility is improved;
(2) hardware equipment of the residual vibration suppression system is simplified, the industrial robot control platform has a real-time control function, the problem of lag in robot control is avoided, and flexibility is improved;
(3) the proposed residual vibration suppression method can further improve the smoothness of track running, reduce the impact on the motor in the running process and ensure the contour accuracy of the interpolation track while realizing the maximum suppression of the residual vibration.
Drawings
Fig. 1 is a schematic structural diagram of a residual vibration suppression system for an industrial robot according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a residual vibration suppression method for an industrial robot according to an embodiment of the invention;
FIG. 3 is a schematic flow chart of a process for calculating vibration mode parameters in the residual vibration suppression method for the industrial robot according to the embodiment of the invention;
shown in the figure are: 1-an embedded industrial personal computer; 2-industrial robot servo controller; 3-acceleration signal transmission; 4-an industrial robot; 5-acceleration sensor.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Example 1
As shown in fig. 1, a method for suppressing residual vibration for an industrial robot, the method uses a residual vibration suppression system for an industrial robot, which comprises an embedded industrial personal computer 1 with a real-time control function, an acceleration sensor 5, an acceleration signal transmission device 3, an industrial robot 4 and a servo driver 2 thereof, wherein the acceleration sensor 5 is installed at the end 4 of the industrial robot through an acceleration sensor fixing element, collected acceleration signals are connected into the servo driver 2 of the industrial robot through the acceleration signal transmission device 3, and the servo driver 2 is connected with the embedded industrial personal computer 1 through a gigabit industrial ethernet interface; the acceleration sensor 5 is used for measuring an acceleration signal and outputting the acceleration signal in an analog quantity form; the acceleration signal transmission device 3 realizes an EtherCAT bus protocol stack, can convert the analog quantity signal of the acceleration sensor 5 into an EtherCAT bus communication message, and realizes information interaction with an EtherCAT master station; the servo driver 2 controls the industrial robot 4 to move by adopting an EtherCAT bus protocol; the embedded industrial personal computer 1 builds a real-time control platform based on Kithara software and can process each control signal in real time.
As a preferred embodiment 2, the embedded industrial personal computer 1 in this embodiment is a porphyry IPC-510 industrial personal computer with 4GB of memory configured with i 7-3770; the acceleration sensor 5 is a Type8395A three-dimensional acceleration sensor manufactured by KISTLER company; the acceleration sensor transmission device 3 is EK1100 and EL3104 modules of Beckhoff company; the industrial robot 4 is a six-degree-of-freedom industrial robot with the model number of RB03A1 of Guangzhou numerical control equipment; the servo controller 2 is a servo controller of the ASDA-A2-E series of Taida corporation.
The components described in the present embodiment may be selected as follows, but the selection is not limited thereto: an embedded industrial personal computer: other embedded controllers with the same function can be selected; an acceleration sensor: other acceleration sensors with the same function can be selected; acceleration sensor conveyer: the acceleration sensor transmission device can select other acceleration sensors with the same function; industrial robot: other types of industrial robots can be selected; a servo controller: other servo controllers of the same function may be selected.
Example 3
As shown in fig. 2, a residual vibration suppressing method for an industrial robot includes the steps of:
s1, manually teaching the industrial robot 4, determining the interpolation track type and the running time length, and performing linear filtering track planning on the industrial robot to generate an initial interpolation track;
s2, controlling the industrial robot 4 to perform initial track interpolation motion, measuring the acceleration signal of the residual vibration of the end of the industrial robot after the motion is finished, and calculating the damping ratio zeta and the undamped vibration angular frequency omega of the residual vibrationn；
S3, performing exponential filtering track planning on the industrial robot according to the residual vibration mode of the tail end of the industrial robot to generate a shaping interpolation track with a vibration suppression function;
s4, controlling the industrial robot 4 to perform shaping track interpolation motion, measuring an acceleration signal of the residual vibration of the tail end of the industrial robot after the motion is finished, and calculating the energy M of the residual vibration0：
Figure BDA0003486491620000131
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
and S5, adjusting the exponential filtering track planning parameters by using an iterative learning strategy, and re-performing exponential filtering track planning on the industrial robot to realize the maximum suppression of the residual vibration at the tail end of the industrial robot.
Specifically, in the linear filtering trajectory planning of step S1, the step signal with the amplitude of total displacement h is sequentially passed through two time periods T1、T2The first and second linear filters of (1) generate a total duration of Tot ═ T1+T2Wherein each linear filter M is a linear filteriThe transfer function of (a) is:
Figure BDA0003486491620000141
in the formula ,TiThe duration of the filter is set as i belongs to {1,2}, e is a natural base number, and s is an independent variable of a transfer function; in a discretized implementation, the linear filter MiThe difference equation of (a) is:
Figure BDA0003486491620000142
in the formula ,Ni＝[Ti/Ts]The number of times of sampling of the response of the linear filter, [ 2 ]]Denotes rounding up, TsIs a sampling period, qn(k) For the displacement of the output trajectory at the sampling instant k, qn-1(k) Is the displacement of the input trajectory at the sampling instant k.
Specifically, the process of linear filtering trajectory planning in step S1 includes the steps of:
s11, calculating the total displacement h of the interpolation track according to the position of the teaching point and the type of the interpolation track;
s12, determining the time length T of the first linear filter and the second linear filter according to the interpolation track running time length Tot1、T2To ensure that condition T is satisfied1≥T2；
S13, step signal r (t) h · u (t) is input to the first linear filter M1To obtain a first-order output trace q1(t) the discretization expression of which is:
Figure BDA0003486491620000151
wherein h is the total displacement of the interpolation track, u (t) is the unit step function, q1(k) Is the displacement of the first-order output trace at the sampling time k, r (k) is the displacement of the input step signal at the sampling time k, N1The number of samples of the first linear filter response;
s14, converting the first-order track q1(t) input to a second linear filter M2To obtain a second-order output locus q2(t) the discretization expression of which is:
Figure BDA0003486491620000152
in the formula ,q2(k) Is the displacement of the second order output trajectory at the sampling instant k, q1(k) For the displacement of the first-order input trajectory at the sampling instant k, N2The number of samples of the second linear filter response.
Specifically, as shown in fig. 3, the damping ratio ζ and undamped vibration angular frequency ω of the residual vibration are calculated in step S2nComprises the following steps:
s21, performing Fast Fourier Transform (FFT) on the collected residual vibration signal to obtain a spectrogram of the residual vibration signal;
s22, setting a frequency spectrum amplitude threshold value AvAnd frequency variation threshold omegavSelecting amplitude greater than AvPeak frequency ω ofiIf adjacent peak frequencies satisfy ωi+1-ωi＜ωvIf the two are the same modal frequency, the two are considered to be the same modal frequency;
s23, selecting all modal frequencies according to S22, and taking the modal frequency with the maximum amplitude as the main vibration frequency, namely the undamped vibration angular frequency omegan；
S24, low-pass filtering the collected residual vibration signal, and taking the cut-off frequency of the filter as fc＝2ωn；
S25, drawing the residual vibration signal after low-pass filtering, and extracting the wave of the residual vibration signalSet of peak points (t)i,zi), wherein tiTime, z, corresponding to the ith peak point of the residual vibration signaliThe peak value corresponding to the ith peak point and the wave peak value ziLogarithmic operation, denoted as zi′＝ln(zi) To obtain a new point set (t)i,zi′)；
S26, point set (t) is aligned by least square methodi,zi') finding a fitted straight line
Figure BDA0003486491620000161
Figure BDA0003486491620000162
Figure BDA0003486491620000163
In the formula, N is the number of point concentration points,
Figure BDA0003486491620000164
is the slope of the straight line being fitted,
Figure BDA0003486491620000165
the intercept of the fitted straight line;
s27 fitting straight line obtained according to S26
Figure BDA0003486491620000166
The damping ratio ζ of the available residual vibration is:
Figure BDA0003486491620000167
in the formula ,ωnThe undamped vibration angular frequency of the residual vibration,
Figure BDA0003486491620000168
is the slope of the fitted line.
Specifically, in the exponential filtering trajectory planning of step S3, the step signal with the amplitude of total displacement h is sequentially passed through two time periods T1、T2And a first and a second linear filter of time duration TJGenerating an exponential filter of total duration Tot ═ T1+T2+TJIn which the exponential filter MJThe transfer function of (a) is:
Figure BDA0003486491620000169
wherein α is the attenuation ratio, TJIs the filter duration, e is the natural base number, s is the independent variable of the transfer function;
in order to achieve complete suppression of residual vibrations, the following should be satisfied:
α＝-ζωn
Figure BDA0003486491620000171
where ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
in a discretized implementation, the exponential filter MJThe difference equation of (a) is:
Figure BDA0003486491620000172
in the formula ,NJ＝[TJ/Ts]Is the number of times of sampling of the response of the exponential filter, [ 2 ]]Denotes rounding up, TsIs a sampling period, qJ(k) For the displacement of the output trajectory at the sampling instant k, qn-1(k) Alpha is the decay rate of the exponential filter for the displacement of the input trajectory at the sampling instant k.
Specifically, the process of linear filtering trajectory planning in step S3 includes the steps of:
s31, calculating the total displacement h of the interpolation track according to the position of the teaching point and the type of the interpolation track;
s32, keeping the interpolation track motion time length Tot unchanged, and determining the time length T of the first linear filter and the second linear filter1、T2Sum exponential filter duration TJ：
Figure BDA0003486491620000173
T2＝TJ，T1＝Tot-T2-TJEnsure to satisfy T1≥T2+TJ and T2≥TJWhere ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
s33, step signal r (t) h · u (t) is input to the first linear filter M1To obtain a first-order output trace q1(t) the discretization expression of which is:
Figure BDA0003486491620000174
wherein h is the total displacement of the interpolation track, u (t) is the unit step function, q1(k) Is the displacement of the first-order output trace at the sampling time k, r (k) is the displacement of the input step signal at the sampling time k, N1The number of samples of the first linear filter response;
s34, converting the first-order track q1(t) input to a second linear filter M2To obtain a second-order output trajectory q2(t) the discretization expression of which is:
Figure BDA0003486491620000181
in the formula ,q2(k) Is the displacement of the second order output trajectory at the sampling instant k, q1(k) For the displacement of the first-order input trajectory at the sampling instant k, N2Is the number of samples of the second linear filter response;
s35, calculating the second-order track q2(t) input exponential Filter MJTo obtain a third order output trace q2e(t) the discretization expression of which is:
Figure BDA0003486491620000182
in the formula ,q2e(k) For the displacement of the third-order output trajectory at the sampling instant k, q2(k) Is the displacement of the second-order input track at the sampling time k, alpha is the attenuation rate of the exponential filter, NJIs the number of samples of the exponential filter response, TsIs the sampling period.
Specifically, step S5 specifically includes:
s51, fixing the attenuation rate alpha of the exponential filter, and utilizing the gradient descent principle to carry out time length T on the exponential filterJPerforming iterative learning until an iteration stop condition is met;
s52 fixed exponential filter duration TJPerforming iterative learning on the attenuation rate alpha of the exponential filter by using a gradient descent principle until an iteration stop condition is met;
s53 optimal exponential filter attenuation rate alpha obtained by iterative learningoptSum time length TJoptAnd (4) for parameters, planning the exponential filtering track of the industrial robot again, and realizing the maximum inhibition of the residual vibration at the tail end of the industrial robot.
Specifically, step S51 specifically includes:
s511, calculating the attenuation rate alpha of the initial exponential filter by taking the residual vibration mode parameter of the end of the industrial robot measured in the step S2 as a reference0And initial filter duration TJ0：
α0＝-ζωn
Figure BDA0003486491620000191
Where ζ is the damping ratio of the residual vibration at the end of the industrial robot, ωnAn undamped oscillation angular frequency;
s512, keeping exponential filteringAttenuation rate of device alpha0The time length of the next iteration parameter index filter is taken as TJ1＝(1+δ)TJ0And delta is a constant, the exponential filtering track planning is carried out on the industrial robot again, the industrial robot 4 is controlled to carry out interpolation motion, the residual vibration signal of the tail end of the industrial robot after the motion is measured, and the residual vibration energy M is calculated1：
Figure BDA0003486491620000192
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s513, updating the index filter duration T by utilizing the gradient descent principleJ：
Figure BDA0003486491620000193
wherein ,
Figure BDA0003486491620000194
in the formula ,TJkFor exponential filter duration in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
s514, index filter parameter alpha obtained by utilizing updating0 and TJk+1Planning the exponential filtering track of the industrial robot again, controlling the industrial robot 4 to perform interpolation motion, measuring a residual vibration signal at the tail end of the industrial robot after the motion is finished, and calculating the residual vibration energy Mk+1：
Figure BDA0003486491620000201
In the formulaV (t) is the acceleration signal of the residual oscillation at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s515, if the vibration energy M isk+1＜MkI.e. indicating a reduction in residual vibration, T is consideredJk+1Updating correctly; if M isk+1＞MkIf the residual vibration is larger, the current iteration is abandoned, and the T is updated by adopting the following ruleJk+1：
Figure BDA0003486491620000202
wherein ,
Figure BDA0003486491620000203
in the formula ,TJkFor exponential filter duration in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
s516, judging | TJk+1-TJkThe | < epsilon >, and epsilon represents a preset error limit; if the condition is satisfied, the current iteration value T is considered to beJk+1For the optimum exponential filter duration, denoted TJoptStopping iteration; if the condition is not met, repeating the step S513 to the step S516, and continuing the iteration until the stop condition is met.
Specifically, step S52 specifically includes:
s521, obtaining the optimal exponential filter duration T obtained by iteration of the step S51JoptKeeping the duration T of the exponential filterJoptThe attenuation rate of the next iteration parameter exponential filter is taken as alpha without change1＝(1+δ)α0Delta is a constant, alpha0For the attenuation rate of the initial exponential filter obtained in the step S511, the exponential filtering track of the industrial robot is planned again, the industrial robot 4 is controlled to perform interpolation motion, and the residual vibration signal of the tail end of the industrial robot after the motion is finished is measuredCalculating residual vibration energy M1：
Figure BDA0003486491620000211
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s522, updating the attenuation rate alpha of the exponential filter by utilizing the gradient descent principle:
Figure BDA0003486491620000212
wherein ,
Figure BDA0003486491620000213
in the formula ,αkFor exponential filter decay Rate in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
s523, index filter parameter alpha obtained by utilizing updatingk+1 and TJoptPlanning the exponential filtering track of the industrial robot again, controlling the industrial robot 4 to perform interpolation motion, measuring a residual vibration signal at the tail end of the industrial robot after the motion is finished, and calculating the residual vibration energy Mk+1：
Figure BDA0003486491620000221
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s524, if vibration energy Mk+1＜MkI.e. indicating a reduction in residual vibration, alpha is consideredk+1UpdatingCorrect; if M isk+1＞MkIf the residual vibration is larger, the current iteration is abandoned, and the following rule is adopted to update alphak+1：
Figure BDA0003486491620000222
wherein ,
Figure BDA0003486491620000223
in the formula ,αkFor exponential filter decay Rate in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
s525, judging | alphak+1-αkThe | < epsilon >, and epsilon represents a preset error limit; if the condition is satisfied, the current iteration value alpha is considered to bek+1For optimum exponential filter duration, noted as αoptStopping iteration; if the condition is not met, repeating the steps S522 to S525, and continuing the iteration until the stop condition is met.
According to the embodiment, after the industrial robot is taught, an initial interpolation track is generated by using a linear filtering track planning technology according to the interpolation track type and the running time length, and the industrial robot is controlled to perform initial track interpolation motion. After the motion of the industrial robot is finished, an acceleration signal of residual vibration is measured through an acceleration sensor, and a residual vibration mode of a current track is calculated and used as an index filter shaping parameter. Because the adopted acceleration sensor has lower precision and the measured vibration mode has certain error, the algorithm is utilized to make up the deficiency of the hardware. In the embodiment, modal parameters obtained by initial measurement are used as initial parameters, and an iterative learning strategy is used for repeatedly searching for optimal exponential filter parameters so as to realize the maximum suppression of residual vibration.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (10)

1. A residual vibration suppressing method for an industrial robot, characterized by comprising the steps of:
s1, manually teaching the industrial robot (4), determining interpolation track types and running time, and performing linear filtering track planning on the industrial robot to generate an initial interpolation track;
s2, controlling the industrial robot (4) to perform initial track interpolation motion, measuring an acceleration signal of the residual vibration of the tail end of the industrial robot after the motion is finished, and calculating the damping ratio and the undamped vibration angular frequency of the residual vibration;
s3, performing exponential filtering track planning on the industrial robot according to the residual vibration mode of the tail end of the industrial robot to generate a shaping interpolation track with a vibration suppression function;
s4, controlling the industrial robot (4) to perform shaping track interpolation motion, measuring an acceleration signal of the residual vibration of the tail end of the industrial robot after the motion is finished, and calculating the energy of the residual vibration;
and S5, adjusting the exponential filtering track planning parameters by using an iterative learning strategy, and re-performing exponential filtering track planning on the industrial robot to realize the maximum suppression of the residual vibration at the tail end of the industrial robot.
2. A residual vibration suppressing method for an industrial robot according to claim 1, characterized in that: in the linear filtering trajectory planning of step S1, the step signal with the amplitude of total displacement h is sequentially processed by two time lengths T1、T2The first and second linear filters of (1) generate a total duration of Tot ═ T1+T2Wherein each linear filter M is a linear filteriThe transfer function of (a) is:
Figure FDA0003486491610000011
in the formula ,TiThe duration of the filter is set as i belongs to {1,2}, e is a natural base number, and s is an independent variable of a transfer function;
in a discretized implementation, the linear filter MiThe difference equation of (a) is:
Figure FDA0003486491610000012
in the formula ,Ni＝[Ti/Ts]The number of times of sampling of the response of the linear filter, [ 2 ]]Denotes rounding up, TsIs a sampling period, qn(k) For the displacement of the output trajectory at the sampling instant k, qn-1(k) Is the displacement of the input trajectory at the sampling instant k.
3. A residual vibration suppressing method for an industrial robot according to claim 1, characterized in that: the process of linear filtering trajectory planning in step S1 includes the steps of:
s11, calculating the total displacement h of the interpolation track according to the position of the teaching point and the type of the interpolation track;
s12, determining the time length T of the first linear filter and the second linear filter according to the interpolation track running time length Tot1、T2To ensure that condition T is satisfied1≥T2；
S13, step signal r (t) h · u (t) is input to the first linear filter M1To obtain a first-order output trace q1(t) the discretization expression of which is:
Figure FDA0003486491610000021
wherein h is the total displacement of the interpolation track, u (t) is the unit step function, q1(k) Displacement of the first-order output trace at sampling time k, and input step signals r (k)Displacement at sampling time k, N1The number of samples of the first linear filter response;
s14, converting the first-order track q1(t) input to a second linear filter M2To obtain a second-order output locus q2(t) the discretization expression of which is:
Figure FDA0003486491610000022
in the formula ,q2(k) Is the displacement of the second order output trajectory at the sampling instant k, q1(k) For the displacement of the first-order input trajectory at the sampling instant k, N2The number of samples of the second linear filter response.
4. A residual vibration suppressing method for an industrial robot according to claim 1, characterized in that: the damping ratio ζ and the undamped vibration angular frequency ω of the residual vibration are calculated in step S2nComprises the following steps:
s21, performing Fast Fourier Transform (FFT) on the collected residual vibration signal to obtain a spectrogram of the residual vibration signal;
s22, setting a frequency spectrum amplitude threshold value AvAnd frequency variation threshold omegavSelecting amplitude greater than AvPeak frequency ω ofiIf the adjacent peak frequencies satisfy omegai+1-ωi＜ωvIf the two are the same modal frequency, the two are considered to be the same modal frequency;
s23, selecting all modal frequencies according to S22, and taking the modal frequency with the maximum amplitude as the main vibration frequency, namely the undamped vibration angular frequency omegan；
S24, low-pass filtering the collected residual vibration signal, and taking the cut-off frequency of the filter as fc＝2ωn；
S25, drawing the residual vibration signal after the low-pass filtering, and extracting a peak point set (t) of the residual vibration signali,zi), wherein tiCorresponding to the ith peak point of the residual vibration signalCarving, ziThe peak value corresponding to the ith peak point and the wave peak value ziIs calculated as z'i＝ln(zi) To obtain a new point set (t)i,z′i)；
S26, point set (t) is aligned by least square methodi,z′i) Calculating a fitted straight line
Figure FDA0003486491610000031
Figure FDA0003486491610000032
Figure FDA0003486491610000033
In the formula, N is the number of point concentration points,
Figure FDA0003486491610000034
is the slope of the straight line being fitted,
Figure FDA0003486491610000035
the intercept of the fitted straight line;
s27, fitting straight line according to the step S26
Figure FDA0003486491610000036
The damping ratio ζ of the residual vibration is obtained as follows:
Figure FDA0003486491610000037
in the formula ,ωnUndamped vibration angular frequencies for residual vibration.
5. A residual vibration suppressing method for an industrial robot according to claim 1, characterized in that:in the exponential filtering trajectory planning of step S3, the step signal with the amplitude of total displacement h is sequentially processed by two time lengths T1、T2And a first and a second linear filter of time duration TJGenerating an exponential filter of total duration Tot ═ T1+T2+TJIn which the exponential filter MJThe transfer function of (a) is:
Figure FDA0003486491610000041
wherein α is the attenuation ratio, TJIs the filter duration, e is the natural base number, s is the independent variable of the transfer function;
in order to achieve complete suppression of residual vibrations, the following should be satisfied:
α＝-ζωn
Figure FDA0003486491610000042
where ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
in a discretized implementation, the exponential filter MJThe difference equation of (a) is:
Figure FDA0003486491610000043
in the formula ,NJ＝[TJ/Ts]Is the number of times of sampling of the response of the exponential filter, [ 2 ]]Denotes rounding up, TsIs a sampling period, qJ(k) For the displacement of the output trajectory at the sampling instant k, qn-1(k) Alpha is the decay rate of the exponential filter for the displacement of the input trajectory at the sampling instant k.
6. A residual vibration suppressing method for an industrial robot according to claim 1, characterized in that: the process of linear filtering trajectory planning in step S3 includes the steps of:
s31, calculating the total displacement h of the interpolation track according to the position of the teaching point and the type of the interpolation track;
s32, keeping the interpolation track motion time length Tot unchanged, and determining the time length T of the first linear filter and the second linear filter1、T2Sum exponential filter duration TJ：
Figure FDA0003486491610000044
T2＝TJ，T1＝Tot-T2-TJEnsure to satisfy T1≥T2+TJ and T2≥TJWhere ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
s33, step signal r (t) h · u (t) is input to the first linear filter M1To obtain a first-order output trace q1(t) the discretization expression of which is:
Figure FDA0003486491610000051
wherein h is the total displacement of the interpolation track, u (t) is the unit step function, q1(k) Displacement of the first order output trace at sampling instant k, r (k) displacement of the input step signal at sampling instant k, N1The number of samples of the first linear filter response;
s34, converting the first-order track q1(t) input to a second linear filter M2To obtain a second-order output locus q2(t) the discretization expression of which is:
Figure FDA0003486491610000052
in the formula ,q2(k) Is the displacement of the second order output trajectory at the sampling instant k, q1(k) Bit at sampling time k for first order input traceMove, N2Is the number of samples of the second linear filter response;
s35, calculating the second-order track q2(t) input exponential Filter MJTo obtain a third order output trace q2e(t) the discretization expression of which is:
Figure FDA0003486491610000053
in the formula ,q2e(k) For the displacement of the third-order output trajectory at the sampling instant k, q2(k) Is the displacement of the second-order input trajectory at the sampling instant k, alpha is the attenuation ratio of the exponential filter, NJIs the number of samples of the exponential filter response, TsIs the sampling period.
7. The residual vibration suppression method for an industrial robot according to claim 1, wherein said step S5 specifically includes:
s51, fixing the attenuation rate alpha of the exponential filter, and utilizing the gradient descent principle to carry out time length T on the exponential filterJPerforming iterative learning until an iteration stop condition is met;
s52 fixed exponential filter duration TJPerforming iterative learning on the attenuation rate alpha of the exponential filter by using a gradient descent principle until an iteration stop condition is met;
s53 optimal exponential filter attenuation rate alpha obtained by iterative learningoptSum duration TJoptAnd (4) for parameters, planning the exponential filtering track of the industrial robot again, and realizing the maximum inhibition of the residual vibration at the tail end of the industrial robot.
8. The residual vibration suppression method for an industrial robot according to claim 7, wherein said step S51 specifically includes:
s511, calculating the attenuation rate alpha of the initial exponential filter by taking the residual vibration mode parameter of the end of the industrial robot measured in the step S2 as a reference0And initial filter duration TJ0：
α0＝-ζωn
Figure FDA0003486491610000061
Where ζ is the damping ratio of the residual vibration of the end of the industrial robot, ωnAn undamped oscillation angular frequency;
s512, maintaining the attenuation rate alpha of the exponential filter0The time length of the next iteration parameter index filter is taken as TJ1＝(1+δ)TJ0And delta is a constant, the exponential filtering track planning is carried out on the industrial robot again, the industrial robot (4) is controlled to carry out interpolation motion, the residual vibration signal of the tail end of the industrial robot after the motion is measured, and the residual vibration energy M is calculated1：
Figure FDA0003486491610000062
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s513, updating the duration T of the index filter by utilizing the gradient descent principleJ：
Figure FDA0003486491610000071
wherein ,
Figure FDA0003486491610000072
in the formula ,TJkFor exponential filter duration in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
S514using the updated exponential filter parameter alpha0 and TJk+1Planning the exponential filtering track of the industrial robot again, controlling the industrial robot (4) to perform interpolation movement, measuring a residual vibration signal at the tail end of the industrial robot after the movement is finished, and calculating the residual vibration energy Mk+1；
S515, if the vibration energy M isk+1＜MkI.e. indicating a reduction in residual vibration, T is consideredJk+1Updating correctly; if M isk+1＞MkIf the residual vibration is larger, the current iteration is abandoned, and the T is updated by adopting the following ruleJk+1：
Figure FDA0003486491610000073
wherein ,
Figure FDA0003486491610000081
s516, judging | TJk+1-TJkThe | < epsilon >, and epsilon represents a preset error limit; if the condition is satisfied, the current iteration value T is considered to beJk+1For the optimum exponential filter duration, noted TJoptStopping iteration; if the condition is not met, repeating the step S513 to the step S516, and continuing the iteration until the stop condition is met.
9. The method for suppressing residual vibration for an industrial robot according to claim 7, wherein said step S52 specifically includes:
s521, obtaining the optimal exponential filter duration T obtained by iteration of the step S51JoptKeeping the duration T of the exponential filterJoptThe attenuation rate of the next iteration parameter exponential filter is taken as alpha without change1＝(1+δ)α0Delta is a constant, alpha0For the attenuation rate of the initial exponential filter obtained in the step S511, the exponential filtering track planning is carried out again on the industrial robot, and the industrial robot (4) is controlled to carry out interpolation operationMeasuring the residual vibration signal of the end of the industrial robot after the motion is finished, and calculating the residual vibration energy M1：
Figure FDA0003486491610000082
In the formula, upsilon (t) is an acceleration signal of residual vibration at time t, t0 and tfRespectively the starting time and the ending time of the residual vibration;
s522, updating the attenuation rate alpha of the exponential filter by utilizing the gradient descent principle:
Figure FDA0003486491610000083
wherein ,
Figure FDA0003486491610000084
in the formula ,αkFor exponential filter decay Rate in the kth iteration, MkFor the residual vibration energy after the kth iterative learning, sat (x) is a self-defined function for controlling the convergence rate, and x is an independent variable of the sat function;
s523, index filter parameter alpha obtained by utilizing updatingk+1 and TJoptPlanning the exponential filtering track of the industrial robot again, controlling the industrial robot (4) to perform interpolation movement, measuring a residual vibration signal at the tail end of the industrial robot after the movement is finished, and calculating the residual vibration energy Mk+1；
S524, if the vibration energy Mk+1＜MkI.e. indicating a reduction in residual vibration, alpha is consideredk+1Updating correctly; if M isk+1＞MkIf the residual vibration is larger, the current iteration is abandoned, and the following rule is adopted to update alphak+1：
Figure FDA0003486491610000091
wherein ,
Figure FDA0003486491610000092
s525, judging | alphak+1-αkThe | < epsilon >, and epsilon represents a preset error limit; if the condition is satisfied, the current iteration value alpha is considered to bek+1For optimum exponential filter duration, noted as αoptStopping iteration; if the condition is not met, repeating the steps S522 to S525, and continuing the iteration until the stop condition is met.
10. The system for realizing the residual vibration suppression method for the industrial robot is characterized by comprising an embedded industrial personal computer (1) with a real-time control function, an acceleration sensor (5), an acceleration signal transmission device (3), the industrial robot (4) and a servo driver (2) thereof;
the acceleration sensor (5) is installed at the tail end (4) of the industrial robot through an acceleration sensor fixing element, collected acceleration signals are connected into a servo driver (2) of the industrial robot through an acceleration signal transmission device (3), and the servo driver (2) is connected with the embedded industrial personal computer (1) through a gigabit industrial Ethernet interface.
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