CN107942683A - Modularization robot joint power parameter identification precision improves method - Google Patents
Modularization robot joint power parameter identification precision improves method Download PDFInfo
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Abstract
The present invention provides a kind of modularization robot joint power parameter identification precision and improves method, Dynamic Modeling is carried out using Newton-Euler method, improved Fourier space excitation track is applied to modularization robot joint power parameter identification precision improves device；Utilize sensor unit acquisition angle angle value, magnitude of angular velocity and moment values；The magnitude of angular velocity measured by tachometer carries out differential and obtains angular acceleration values, tentatively pre-processes information；Parameter Estimation is carried out, parameter is brought into kinetics equation and estimates kinetic parameter.The present invention uses multi-sensor fusion technology, directly measures joint end and motor side angle in real time respectively by two absolute type encoders, enhances the security of device.Mode measured directly reduces the calculation amount of control unit, is easy to implement real-time control, and solves the problems such as measurement causes interference to increase with error indirectly, improves parameter identification precision.
Description
Technical field
The present invention relates to a kind of modularization robot joint power parameter identification precision to improve method.
Background technology
Robot plays an increasingly important role in present production, life, especially the stronger module of versatility
Change robot.Modularization robot be one kind based on modularized joint, connecting rod and standard electrical interface, can be according to environment
Robot that is automatic or artificially changing itself configuration is needed with task.Since the features such as modularization robot configuration is variable, causes machine
The uncertain enhancing of device people, causes traditional control method to be unsatisfactory for the requirement of current manipulator trajectory tracking, to improve robot
Performance is, it is necessary to establish the method for considering the accurate joint power model of robot, in the case, joint of robot parameter identification
It is particularly important, but existing parameter identification method and device accuracy are poor at present.
The main reason for measurement of existing parameter identification is inaccurate be：Generally encoded in existing joint measurment using electric machine built-in
Device obtains joint angle angle value, and angular speed needs to obtain by mathematical differentiation with angle acceleration figure, which increase noise jamming and error,
Harmonic wave is installed in partial robotic joint and reduces the device such as device, the factor such as the flexibility of introducing, gap, sluggishness certainly will influence tradition
The precision of measurement method.Joint moment value is usually obtained by detecting the indirect mode of current of electric, and measurement accuracy relies on motor
Performance, it is clear that inaccurate.
There are the shortcomings that Optimization Steps complexity, inefficiency, big starting and ending stage noise jamming for existing excitation track.
In existing parameter identification method and device, the process without verification discrimination method accuracy, it is even more impossible to optimize renewal identification side
Method and device.
The above problem should pay attention to and solve during modularization robot joint power parameter identification
Problem.
The content of the invention
Method is improved the object of the present invention is to provide a kind of modularization robot joint power parameter identification precision to solve
Joint moment value existing in the prior art is usually obtained by detecting the indirect mode of current of electric, and measurement accuracy relies on motor
Performance, it is clear that it is inaccurate, cause existing parameter identification to measure the problem of inaccurate.
The present invention technical solution be：
A kind of modularization robot joint power parameter identification precision improves the modularization robot joint power of device
Learn parameter identification precision and improve method, comprise the following steps,
S1, using Newton―Leibniz formula carry out Dynamic Modeling, obtain kinetics equation：
In formula,Represent observing matrix, be onPolynomial form, q is joint angle angle value,For angle
Velocity amplitude,For angular acceleration values, x represents parameter vector to be identified；τ represents the moment values of torque sensor measurement；
S2, by improved Fourier space excitation track be applied to modularization robot joint power parameter identification precision
Improve device；
S3, utilize sensor unit acquisition angle angle value, magnitude of angular velocity and moment values；
S4, the magnitude of angular velocity measured by tachometer carry out differential and obtain angular acceleration values, tentatively pre-process information；
S5, carry out parameter Estimation, brings parameter into kinetics equation and estimates kinetic parameter.
Further, step S6 is further included, step S6 brings the identified parameters of acquisition into model specifically, experimental verification
Trajectory Tracking Control test is carried out, identification result validity is verified by tracking error, and identification dress is continued to optimize according to result
Put, treat that track following test reaches sets requirement, stop optimization, obtain final identified parameters.
Further, excitation lopcus function is in step S2：
Wherein, tf=2 π/ωf, j=INT (t/tf), q (0)=qinit,q(tf)=qinit,
In formula, h represents harmonic wave number, and t represents the time, and m is integer, and i represents the i-th joint number, ωfRepresent fundamental frequency, N is represented
The number of harmonic wave, j represent j-th of cycle, and INT () represents bracket function,Represent coefficient, qinitRepresent initial to close
The angular amount of section,Represent initial joint angular velocity vector, a cycle terminates, and joint of robot returns to initial pose, tfFor week
Phase；
Excitation track is write in the upper computer software of PC industrial personal computers in the form of C language, the transmission in the form of instruction
To motion control card, motion control card sends commands to driver by communication bus.
Further, step S3 is specifically, 20 absolute type encoder measurement motor end angles, 16 absolute type encoders
Joint loads end angle is measured, tachometer measures joint angular speed in real time, and torque sensor measurement obtains moment values.
Further, information is tentatively pre-processed in step S4, specifically, the gathered data that sensor unit is obtained passes through
Communication bus feeds back to control unit, carries out data preliminary treatment, and filtering process is first carried out to the angular speed amount of tachometer measurement
Signal-to-noise ratio is improved, differential process is then carried out and obtains joint angular acceleration values, by the joint of acquisitionValue is processed into observation
The parameter form of matrix Y.
Further, step S5 carries out parameter Estimation, specifically,
According toDeformation can obtain：(YTY)-1YTτ=x；
By in step S4, preprocessed obtained joint angles q, angular speed is measured by sensor unitAngular acceleration
Value is brought into observing matrix Y, and parameter identification value x is obtained using weighted least-squares method.
Further, step S6 in the case of unloaded, installation aluminum connecting rod, three kinds of steel connecting rod specifically, repeat respectively
Above-mentioned steps carry out 3 groups of experiments, and every group of experiment is several times；Aluminium connecting rod is established by Solidworks softwares and steel connecting rod is several
What model, obtains the inertia parameter of connecting rod by CAD methods and the identified parameters of experiment acquisition contrasts, theory is provided for identification result
Support；Bring identification result into kinetic model and carry out Trajectory Tracking Control test, verify that identification result has by tracking error
Effect property, and device for identifying is continued to optimize according to result, treat that track following test reaches sets requirement, stop optimization, obtain final
Identified parameters.
A kind of modularization robot joint power parameter identification precision improves the modularization robot joint power of device
Learn parameter identification precision and improve method, comprise the following steps,
S1, establish rigidity identification equation according to torsional spring principle：
τ=K Δ q=K (q-q0)
Wherein, Δ q represents torsion angle deflection, and q represents joint angle angle value, q0Represent motor side angle value；
S2, by improved Fourier space excitation track be applied to modularization robot joint power parameter identification precision
Improve device；Excitation lopcus function is in step S2：
Wherein, tf=2 π/ωf, j=INT (t/tf), q (0)=qinit,q(tf)=qinit,
In formula, i represents the i-th joint number, and t represents the time, and m is integer, ωfRepresent fundamental frequency, N represents the number of harmonic wave, j tables
Showing j-th of cycle, INT () represents bracket function,Represent coefficient, qinitRepresent initial joint angle vector,Table
Show initial joint angular velocity vector, a cycle terminates, and joint of robot returns to initial pose；
Excitation track is write in PC industrial personal computer upper computer softwares in the form of C language, is passed in the form of instruction
Motion control card, motion control card send commands to motor and driver by communication bus；
S3, utilize the direct motor in real time end angle value q of 20 absolute type encoders0, torque sensor is directly real-time
Gather joint moment value τi, 16, joint end absolute type encoder directly in real time collection joint angle angle value q, is passed by communication bus
Control unit is defeated by, according to formula τi=K (q-q0) joint equivalent stiffness coefficients K is calculated；
S4, repeat the above steps under different steel and aluminum connecting rod loading condition, does experiment several times respectively and makes even
Average, tries to achieve final joint equivalent stiffness coefficients K.
The present invention establishes joint of robot kinetic model using Newton-Euler Method first, and improved Fourier is encouraged
Track is applied to parameter identification precision and improves device.Improve in parameter identification precision and tested on device, adopted using sensor
Collect the data such as angle value, magnitude of angular velocity and moment values, then preprocessed data, identification ginseng is solved using cum rights least square method
Number, is finally applied to Identification Platform to examine discrimination method validity and Optimal Identification device by identification result.Parameter identification essence
Degree, which improves device, includes control unit, driving unit, sensing unit and load unit, and each unit is connected by communication bus.Adopt
The direct measurement in real time of joint information is realized with tachometer, encoder and torque sensor multi-sensor fusion technology, avoids noise
Interference and error.
The beneficial effects of the invention are as follows：
First, this kind of modularization robot joint power parameter identification precision improves method, using multi-sensor fusion technology,
By two absolute type encoders, directly there is power-off to remember for measurement joint end and motor side angle, absolute type encoder in real time respectively
Recall function, enhance the security of device.Joint angular speed is directly measured with tachometer, is directly measured in real time with torque sensor
Joint moment, mode measured directly reduce the calculation amount of control unit, are easy to implement real-time control, and solve measurement indirectly
The problems such as causing interference to increase with error, improves parameter identification precision.
2nd, the present invention establishes kinetics equation using Newton-Euler iterative formula, and calculation amount is small, reduces run time and protects
Demonstrate,prove control system real-time.
3rd, the present invention solves existing excitation track and there is optimization by the use of improved Fourier space as excitation track
The shortcomings that step is complicated, inefficiency, it is ensured that excitation track meets speed, acceleartion boundary condition, improves sampled data
Signal-to-noise ratio is so as to improve parameter measurement precision.
4th, the present invention obtains load connecting rod inertia parameter using CAD methods, is identified parameters by solidworks softwares
Reliable theoretical foundation is provided.
5th, present invention configuration is identical, and the different connecting rod of material loads, can be constant in geometric parameter, what quality changed
In the case of, analysis compares the parameter identification result under different loads quality condition fully to verify the effective of discrimination method and device
Property.
Brief description of the drawings
Fig. 1 is the explanation signal that modularization robot joint power of embodiment of the present invention parameter identification precision improves device
Figure；
Fig. 2 is that the flow of one modularization robot joint power parameter identification precision of embodiment of the present invention raising method is shown
It is intended to；
Wherein：1- control units, 2-PC industrial personal computers, 3- motion control cards, 4- platform fixed cells, 5- drivers, 6-20
The code-disc of position absolute type encoder, the reading head of 7-20 absolute type encoders, 8- communication buses one, 9- communication buses two, 10-
The reading head of 16 absolute type encoders, the code-disc of 11-16 absolute type encoders, 12- motors, 13- adjustable flanges one, 14-
Harmonic speed reducer, 15- torque sensors, 16- adjustable flanges two, the reading head of 17- tachometers, the code-disc of 18- tachometers, 19-
Load unit.
Embodiment
The preferred embodiment that the invention will now be described in detail with reference to the accompanying drawings.
A kind of modularization robot joint power parameter identification precision improves device, such as Fig. 1, including control unit, drive
Moving cell, sensor unit and load unit, control unit connect driving unit, sensor unit by communication bus respectively,
Driving unit connects load unit by sensor unit, and control unit is made of PC industrial personal computers and motion control card, and driving is single
Member be made of motor, driver and harmonic speed reducer, sensor unit by tachometer, 16 absolute type encoders, 20 definitely
Formula encoder and torque sensor composition.Load unit uses aluminium connecting rod or steel connecting rod.
This kind of modularization robot joint power parameter identification precision improves device, using multi-sensor fusion technology, leads to
Crossing two absolute type encoders, directly measurement joint end and motor side angle, absolute type encoder have power-fail memory function in real time respectively
Function, enhances the security of device.Joint angular speed is directly measured with tachometer, directly measurement is closed in real time with torque sensor
Torque is saved, mode measured directly reduces the calculation amount of control unit, is easy to implement real-time control, and solves measurement indirectly and draw
The problems such as interference increases with error is played, improves parameter identification precision.
Embodiment one
A kind of modularization robot joint power parameter identification precision improves the modularization robot joint power of device
Learning parameter identification precision and improve method, such as Fig. 2, specifically includes following steps,
S1, using Newton―Leibniz formula carry out Dynamic Modeling.Step S1 is specifically included：
S11, setting coordinate system, joint power model is established according to newton-Euler's formula：
In formula, F represents the power on barycenter, and m represents Rigid Mass,Represent acceleration, I represents rigid body in a coordinate system
Inertial tensor, ω represent the angular speed of Rigid Body in Rotation With,Represent the angular acceleration of Rigid Body in Rotation With.
S12, by above formula derivation abbreviation obtain joint power equation universal equivalent form：
S13, by above formula linearisation be rewritten into following form：
In formula,Represent observing matrix, be onPolynomial form, x represent parameter to be identified to
The amount, " kinetic parameter, for example, joint of robot inertia parameter, joint of robot load that parameter x to be identified can be recognized
Mass parameter etc..
S2, by improved Fourier space excitation track be applied to modularization robot joint power parameter identification precision
Improve device；Excitation lopcus function is in step S2：
Wherein, tf=2 π/ωf, j=INT (t/tf), q (0)=qinit,q(tf)=qinit,
In formula, i represents the i-th joint number, and t represents the time, and m is integer, ωfRepresent fundamental frequency, N represents the number of harmonic wave, j tables
Showing j-th of cycle, INT () represents bracket function,Represent coefficient, qinitRepresent initial joint angle vector,Represent
Initial joint angular velocity vector, a cycle terminate, and joint of robot returns to initial pose.
Excitation track is write in PC industrial personal computer upper computer softwares in the form of C language, is passed in the form of instruction
Motion control card, motion control card send commands to motor and driver by communication bus.
S3, utilize sensor unit acquisition angle angle value, magnitude of angular velocity and moment values；Step S3 specifically,
The direct motor in real time end angle of 20 absolute type encoders, 16 absolute type encoders directly measure joint and bear
End angle is carried, tachometer directly measures joint angular speed, and moment values directly measure acquisition by torque sensor.Above-mentioned data are led to
Cross communication bus and pass to control unit, using mode measured directly, avoid caused by the factors such as noise jamming by mistake
Difference, improves parameter identification accuracy.
S4, the magnitude of angular velocity measured by tachometer carry out differential and obtain angular acceleration values, tentatively pre-process information；Step
In S4, information is tentatively pre-processed, specifically, gathered data is fed back into parameter identification device control units by communication bus,
Data preliminary treatment is carried out, filtering process raising signal-to-noise ratio is first carried out to the angular speed amount of tachometer measurement, then carries out differential
Processing obtains joint angular acceleration values.By the joint of acquisitionValue is processed into the parameter form of observing matrix Y.
S5, carry out parameter Estimation, brings parameter into kinetics equation and estimates kinetic parameter；In step S5, carry out
Parameter Estimation, specifically, step S4 is obtained parameter brings kinetics equation intoEstimate power
Learn parameter：
According toDeformation can obtain：(YTY)-1YTτ=x
By in step S4, preprocessed obtained joint angles q, angular speed are measured by sensorAngular accelerationIt is worth band
Enter in observing matrix Y, the τ that torque sensor measurement obtainsiValue brings τ into, and parameter identification value is obtained using weighted least-squares method
x。
S6, experimental verification, by the identified parameters of acquisition bring into kinetic model carry out Trajectory Tracking Control test, by with
Track error validity identification result validity, and device for identifying is continued to optimize according to result, it is, in many experiments, analysis
Compare Trajectory Tracking Control as a result, finding out factor (such as the joint angle angle value or motor angle value for influencing Trajectory Tracking Control result
It is inaccurate Deng measurement), as the case may be, correct Optimal Parameters device for identifying and be allowed to obtain precise angle value so as to reach optimization
The purpose of device, treats that track following test reaches sets requirement, stops optimization, obtain final identified parameters.Specially：
Repeat the above steps respectively under unloaded, installation aluminium connecting rod, steel connecting rod and carry out 3 groups of experiments.Pass through
Solidworks softwares establish aluminium connecting rod and steel connecting rod geometrical model, and the inertia parameter and reality of connecting rod are obtained by CAD methods
The identified parameters contrast of acquisition is tested, theory support is provided for identification result.Bring identification result into kinetic model and carry out track
Tracing control is tested, and identification result validity is verified by tracking error, and continues to optimize device for identifying according to result, treats track
Tracking and testing reaches sets requirement, stops optimization, obtains final identified parameters.
Embodiment two
A kind of modularization robot joint power parameter identification precision improves the modularization robot joint power of device
Learn parameter identification precision and improve method, specifically include following steps,
S1, establish rigidity identification equation according to torsional spring principle：
τ=K Δ q=K (q-q0)
Wherein, Δ q represents torsion angle deflection, and q represents joint angle angle value, q0Represent motor side angle value.
S2, by improved Fourier space excitation track be applied to modularization robot joint power parameter identification precision
Improve device；Excitation lopcus function is in step S2：
Wherein, tf=2 π/ωf, j=INT (t/tf), q (0)=qinit,q(tf)=qinit,
In formula, i represents the i-th joint number, and t represents the time, and m is integer, ωfRepresent fundamental frequency, N represents the number of harmonic wave, j tables
Showing j-th of cycle, INT () represents bracket function,Represent coefficient, qinitRepresent initial joint angle vector,Table
Show initial joint angular velocity vector, a cycle terminates, and joint of robot returns to initial pose.
Excitation track is write in PC industrial personal computer upper computer softwares in the form of C language, is passed in the form of instruction
Motion control card, motion control card send commands to motor and driver by communication bus.
S3, ignore the influence of the factors such as gap, utilizes the direct motor in real time end angle value q of 20 absolute type encoders0,
Torque sensor directly gathers joint moment value τ in real timei, 16, joint end absolute type encoder directly gathers joint angles in real time
Value q.Control unit is transferred to by communication bus, according to formula τi=K (q-q0) joint equivalent stiffness coefficients K is calculated.
S4, repeat the above steps under different steel and aluminum connecting rod loading condition, does 5 experiments respectively and is averaged
Value, tries to achieve final joint equivalent stiffness coefficients K.
Claims (8)
1. a kind of modularization robot joint power parameter identification precision improves the modularization robot joint power of device
Parameter identification precision improves method, it is characterised in that：Comprise the following steps,
S1, using Newton―Leibniz formula carry out Dynamic Modeling, obtain kinetics equation：
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In formula,Represent observing matrix, be onPolynomial form, q is joint angle angle value,For angular speed
Value,For angular acceleration values, x represents parameter vector to be identified；τ represents the moment values of torque sensor measurement；
S2, by improved Fourier space excitation track be applied to modularization robot joint power parameter identification precision raising
Device；
S3, utilize sensor unit acquisition angle angle value, magnitude of angular velocity and moment values；
S4, the magnitude of angular velocity measured by tachometer carry out differential and obtain angular acceleration values, tentatively pre-process information；
S5, carry out parameter Estimation, brings parameter into kinetics equation and estimates kinetic parameter.
2. modularization robot joint power parameter identification precision as claimed in claim 1 improves method, it is characterised in that：
Step S6 is further included, step S6 brings the identified parameters of acquisition into model and carry out Trajectory Tracking Control survey specifically, experimental verification
Examination, identification result validity is verified by tracking error, and continues to optimize device for identifying according to result, treats that track following test reaches
To sets requirement, stop optimization, obtain final identified parameters.
3. modularization robot joint power parameter identification precision as claimed in claim 1 improves method, it is characterised in that：
Excitation lopcus function is in step S2：
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In formula, h represents harmonic wave number, and t represents the time, and m is integer, and i represents the i-th joint number, ωfRepresent fundamental frequency, N represents harmonic wave
Number, j represent j-th of cycle, INT () represent bracket function,Represent coefficient, qinitRepresent initial joint angle
Vector,Represent initial joint angular velocity vector, a cycle terminates, and joint of robot returns to initial pose, tfFor the cycle；
Excitation track is write in the upper computer software of PC industrial personal computers in the form of C language, fortune is passed in the form of instruction
Dynamic control card, motion control card send commands to driver by communication bus.
4. such as claim 1-3 any one of them modularization robot joint powers parameter identification precision improves method, its
It is characterized in that：Step S3 is specifically, 20 absolute type encoder measurement motor end angles, 16 absolute type encoders measure joint
Load end angle, tachometer measure joint angular speed in real time, and torque sensor measurement obtains moment values.
5. modularization robot joint power parameter identification precision as claimed in claim 4 improves method, it is characterised in that：
Information is tentatively pre-processed in step S4, specifically, the gathered data that sensor unit is obtained feeds back to control by communication bus
Unit processed, carries out data preliminary treatment, and filtering process raising signal-to-noise ratio, Ran Houjin are first carried out to the angular speed amount of tachometer measurement
Row differential process obtains joint angular acceleration values, by the joint of acquisitionValue is processed into the parameter shape of observing matrix Y
Formula.
6. modularization robot joint power parameter identification precision as claimed in claim 5 improves method, it is characterised in that：
Step S5 carries out parameter Estimation, specifically,
According toDeformation can obtain：(YTY)-1YTτ=x；
By in step S4, preprocessed obtained joint angles q, angular speed is measured by sensor unitAngular accelerationIt is worth band
Enter in observing matrix Y, parameter identification value x is obtained using weighted least-squares method.
7. modularization robot joint power parameter identification precision as claimed in claim 6 improves method, it is characterised in that：
Step S6 is specifically, 3 groups of the progress that repeats the above steps respectively in the case of unloaded, installation aluminum connecting rod, three kinds of steel connecting rod is real
Test, every group of experiment is several times；Aluminium connecting rod and steel connecting rod geometrical model are established by Solidworks softwares, pass through CAD methods
The identified parameters contrast that the inertia parameter of connecting rod is obtained with experiment is obtained, theory support is provided for identification result；By identification result
Bring kinetic model into and carry out Trajectory Tracking Control test, identification result validity is verified by tracking error, and according to result
Device for identifying is continued to optimize, treats that track following test reaches sets requirement, stops optimization, obtain final identified parameters.
8. a kind of modularization robot joint power parameter identification precision improves the modularization robot joint power of device
Parameter identification precision improves method, it is characterised in that：Comprise the following steps,
S1, establish rigidity identification equation according to torsional spring principle：
τ=K Δ q=K (q-q0)
Wherein, Δ q represents torsion angle deflection, and q represents joint angle angle value, q0Represent motor side angle value；
S2, by improved Fourier space excitation track be applied to modularization robot joint power parameter identification precision raising
Device；Excitation lopcus function is in step S2：
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<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<msubsup>
<mi>a</mi>
<mi>h</mi>
<mi>i</mi>
</msubsup>
<mrow>
<msub>
<mi>&omega;</mi>
<mi>f</mi>
</msub>
<mi>h</mi>
</mrow>
</mfrac>
<mi>sin</mi>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>&omega;</mi>
<mi>f</mi>
</msub>
<mi>h</mi>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>b</mi>
<mi>h</mi>
<mi>i</mi>
</msubsup>
<mrow>
<msub>
<mi>&omega;</mi>
<mi>f</mi>
</msub>
<mi>h</mi>
</mrow>
</mfrac>
<mi>cos</mi>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mi>&omega;</mi>
<mi>f</mi>
</msub>
<mi>h</mi>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>+</mo>
<munderover>
<mi>&Sigma;</mi>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>5</mn>
</munderover>
<msubsup>
<mi>c</mi>
<mi>m</mi>
<mi>i</mi>
</msubsup>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<msub>
<mi>t</mi>
<mi>f</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mi>m</mi>
</msup>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, tf=2 π/ωf, j=INT (t/tf), q (0)=qinit,q(tf)=qinit,
<mrow>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mi>i</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>,</mo>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mo>(</mo>
<msub>
<mi>t</mi>
<mi>f</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mover>
<mi>q</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mi>i</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>,</mo>
</mrow>
In formula, i represents the i-th joint number, and t represents the time, and m is integer, ωfRepresent fundamental frequency, N represents the number of harmonic wave, and j represents jth
A cycle, INT () represent bracket function,Represent coefficient, qinitRepresent initial joint angle vector,Represent initial
Joint angular velocity vector, a cycle terminate, and joint of robot returns to initial pose；
Excitation track is write in PC industrial personal computer upper computer softwares in the form of C language, movement is passed in the form of instruction
Control card, motion control card send commands to motor and driver by communication bus；
S3, utilize the direct motor in real time end angle value q of 20 absolute type encoders0, torque sensor directly close in real time by collection
Save moment values τi, 16, joint end absolute type encoder directly in real time collection joint angle angle value q, control is transferred to by communication bus
Unit processed, according to formula τi=K (q-q0) joint equivalent stiffness coefficients K is calculated；
S4, repeat the above steps under different steel and aluminum connecting rod loading condition, does experiment several times respectively and is averaged,
Try to achieve final joint equivalent stiffness coefficients K.
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