CN114368008A - Joint friction identification method of DELTA type parallel robot - Google Patents

Joint friction identification method of DELTA type parallel robot Download PDF

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CN114368008A
CN114368008A CN202111050226.9A CN202111050226A CN114368008A CN 114368008 A CN114368008 A CN 114368008A CN 202111050226 A CN202111050226 A CN 202111050226A CN 114368008 A CN114368008 A CN 114368008A
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motor
tau
speed reducer
friction torque
friction
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CN114368008B (en
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郭鹏
李景南
田坤淼
周文
杨医华
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Borunte Robot Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B25J19/0095—Means or methods for testing manipulators

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Abstract

The invention relates to a joint friction identification method of a DELTA type parallel robot, which is characterized in that after a physical prototype of the DELTA type parallel robot is manufactured, the joint friction torque tau of the physical prototype is required to be identifiedf＝τfm+τfbThe method comprises the following steps of performing 'disassembly-assembly' experiment on the DELTA type parallel robot, collecting corresponding data, and then using a conventional linear regression algorithm to finish the identification of the friction parameters of the motor and the speed reducer, thereby realizing the identification of the friction torque of the rotary joint of the main arm of the DELTA type parallel robot.

Description

Joint friction identification method of DELTA type parallel robot
Technical Field
The invention belongs to the field of robot control, and relates to a joint friction identification method of a DELTA type parallel robot.
Background
The DELTA type parallel robot shown in fig. 1 is one of the most successful parallel mechanisms at present, has the advantages of light weight, high movement speed and relatively large load self weight, and is widely applied to the fields of rapid sorting of articles, 3d printing and the like.
In order to develop the parallel robot, preliminary dynamic simulation needs to be carried out on the machine type in the design stage, and the motor working condition of the robot in the actual operation process is preliminarily simulated by setting parameters such as a rotating speed value and a torque value. According to the simulation result, core parts such as a motor, a speed reducer and the like of the robot prototype can be preliminarily selected. However, the preliminary dynamic simulation cannot evaluate the friction torque of the motor and the reducer, so the dynamic simulation is incomplete.
After the motor and the speed reducer are selected and the initial physical prototype is manufactured, joint friction identification needs to be carried out on the initial physical prototype. Specifically, a friction torque value generated when a motor and a speed reducer at a rotary joint operate is obtained through experiments, and a change rule of friction force along with joint speed is obtained through data processing, namely the change rule is the identification of the joint friction torque.
The joint friction identification method for the serial robot and the DELTA type parallel robot has the following prior applications:
according to the CN202010514746.X robot friction identification method, device, system and storage medium, the patent considers that different temperatures can affect friction torque, so that the robot needs to be fully heated before joint friction identification, and when the robot joint reaches thermal equilibrium, joint friction identification is carried out, so that a more accurate joint friction model can be obtained, and the problems of long time consumption and low efficiency in the existing robot friction identification process are solved.
CN201610966932.0 is a contact force detection method for robot based on torque observation and friction identification, which considers that the robot is increasingly in contact with the surrounding environment, and needs to strictly control the contact force, so it is first needed to detect the contact force that the end effector is subjected to during the operation of the robot. The constructed joint friction torque observed quantity is used for identifying the robot joint friction parameters, the observed quantity in a theoretical running state is regarded as a system model error, and an accurate contact force detection value is obtained after the influence of friction and the system model error is eliminated. In this patent, a friction model combining an exponential friction model and a sine and cosine function is used to identify friction parameters. The patent aims at solving the problems that a serial robot is not a parallel robot, and a friction model is a combination of an exponential friction model and a sine and cosine function, so that the serial robot is too complex, inconvenient to operate and high in requirement on theoretical knowledge of technicians.
There is CN201911221683.2 a delta robot control method based on fuzzy set theory, which discloses a method for identifying friction force, and uses stribeck friction force model, which is divided into definite item and uncertain item, the friction model established is extremely complex, it is difficult for general technicians to understand, and the calculated amount of control law is too large, and the real-time property cannot be guaranteed.
Disclosure of Invention
The invention aims to provide a joint friction identification method of a DELTA type parallel robot, which can greatly reduce the experimental difficulty, has moderate calculation amount, is easy to implement and is convenient to use.
The invention relates to a joint friction identification method of a DELTA type parallel robot, which is characterized in that after a physical prototype of the DELTA type parallel robot is manufactured, the friction torque tau of the physical prototype is required to be identifiedf＝τfm+τfb，τfmThe motor friction torque, tau, caused by internal bearing damping during rotation of the motor rotorfbThe friction torque of the speed reducer caused by the meshing of gears when the speed reducer rotates is simplified into the combination of static friction and viscous friction, and is defined as follows:
Figure BDA0003252652560000031
Figure BDA0003252652560000032
wherein: k is a radical offmIs the viscous damping coefficient, k, of the motorfbIs the viscous damping coefficient of the speed reducer, cfmMaximum static friction of the motor, cfbIs the maximum static friction force of the speed reducer,
Figure BDA0003252652560000033
the number of revolutions of the motor is,
Figure BDA0003252652560000034
for the rotating speed of the speed reducer, the identification of the joint friction torque is to solve the four coefficients, and the method specifically comprises the following steps:
step 1, carrying out experiments to identify the friction torque tau of the motorfm
Each horizontal joint is tested independently, a horizontal motor is disassembled independently, and the actual torque value tau of the motor is generated in the running process of the motorm' should be sufficient to overcome the motor friction torque taufmAnd moment of inertia τ of the rotorimAnd the three satisfy:
τm'＝τfm+τim (1.11)
the motor is tested separately and tested N1 times, in the ith experiment, i is 1,2, … and N1, a motor servo driver is used, and the maximum rotating speed of the motor is set to be
Figure BDA0003252652560000035
Wherein
Figure BDA0003252652560000036
The rated rotating speed of the motor;
setting angular acceleration amEnsuring that the motor operates in a reciprocating mode at a trapezoidal speed rule, acquiring a maximum current value by using servo debugging software during the operation period of the motor at least comprising a complete trapezoidal period, and converting the current value into a torque value taum' (i) obtaining the inertia moment value tau of the rotorim：
τim＝Im×αm (1.12)
Wherein, ImAs an electric motorThe rotor moment of inertia is obtained by consulting a motor manual;
calculating the motor friction torque taufm(i)：
τfm(i)＝τm'(i)-τim(1.13)
Recording the maximum rotation speed of the motor
Figure BDA0003252652560000041
Friction torque tau with motorfm(i)；
After N1 groups of numbers are tested according to the flow, the set maximum rotating speed value is sequentially
Figure BDA0003252652560000042
The motor friction torque is calculated to be tau through the formulas (1.11) to (1.13)fm(1)～τfm(N1)；
Will be provided with
Figure BDA0003252652560000043
And τfm(1)～τfm(N1) Linear regression was performed according to the formula (1.10) to find k in the formula (1.10)fmAnd cfm；
Step 2, identifying friction torque tau of speed reducer by experimentfb
The motor and the speed reducer are installed in a combined way and are fixedly connected, and the actual torque value tau of the motor is generated in the running process of the motorm"sufficient to overcome the motor friction torque taufmInertia moment tau of the rotor of the motorimFriction torque tau of speed reducerfbMoment of inertia τ of reducer rotoribAnd the five items satisfy:
τm”＝τfm+τim+τfb+τib (1.14)
the motor reducer combination was tested N2 times, and in the ith experiment, i was 1,2, …, and N2, and the maximum rotation speed of the motor was set using the motor servo driver
Figure BDA0003252652560000044
And angular acceleration am'＝αmEnsuring that the motor operates in a reciprocating mode at a trapezoidal speed rule, acquiring a maximum current value by using servo debugging software during the operation period of the motor at least comprising a complete trapezoidal period, and converting the current value into a torque value taum"(i), finding the moment of inertia τ of the reducer rotorib：
τib＝Ib×αm (1.15)
Wherein, IbThe moment of inertia of the rotor of the speed reducer is obtained by consulting a manual of the speed reducer or according to a three-dimensional model of the speed reducer provided by a manufacturer;
calculating friction torque tau of speed reducerfb(i)：
τfb(i)＝τm”(i)-τfm-τim-τib (1.16)
Recording the maximum rotation speed of the motor
Figure BDA0003252652560000051
Friction torque tau with speed reducerfb(i)；
After the N2 groups of data are tested according to the flow, the set maximum rotating speed of the motor is sequentially
Figure BDA0003252652560000052
The friction torque tau of the speed reducer is obtained through the formulas (1.14) to (1.16)fb(1)～τfb(N2)；
Will be provided with
Figure BDA0003252652560000053
And τfb(1)～τfb(N2) the k in the formula (1.11) is obtained by linear regression processing according to the formula (1.11)fbAnd cfb。
By adopting the technical scheme of the invention, the friction parameters of the motor and the speed reducer can be identified by carrying out the 'disassembly-combination' experimental step on the DELTA type parallel robot and using the conventional linear regression algorithm after acquiring corresponding data, so that the identification of the friction torque of the rotary joint of the main arm of the DELTA type parallel robot is realized.
Drawings
FIG. 1 is a DELTA type parallel robot;
FIG. 2 is a partial schematic view of a DELTA type parallel robot;
FIG. 3 is a schematic diagram of the driving part assembly of the driving arm joint of the DELTA type parallel robot;
FIG. 4 is a schematic torque diagram of the driving part assembly of the driving arm joint of the DELTA type parallel robot;
FIG. 5 is a schematic view of the horizontal motor alone test of the present invention;
FIG. 6 is a schematic view of a trapezoidal velocity curve during testing according to the present invention;
FIG. 7 is a schematic view of a reducer and motor combination test of the present invention;
fig. 8 is a working principle diagram of the present invention.
The invention is described in detail below with reference to the figures and specific embodiments.
Detailed Description
In the following description, numerous specific details are set forth to provide a thorough understanding of the present invention, and the described embodiments are merely a subset of the embodiments of the present invention, rather than a complete embodiment. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
As shown in figures 1 and 2, the Delta type parallel robot comprises a static platform 1, horizontal motors 2-1 to 2-3, a vertical motor 2-4, planetary speed reducers 3-1 to 3-3, driving arms 4-1 to 4-3, driven rods 5-1 to 5-6, a movable platform 6, a spline 7, a spline sleeve 8 and a tail end flange 9, wherein the Delta type parallel robot is provided with four motors in total, so that the Delta type parallel robot has four degrees of freedom, the direction of the degrees of freedom is X-Y-Z-phi, XYZ represents the position of a three-dimensional space, and phi represents the rotation angle of the tail end flange 9 relative to the movable platform. The whole machine can be considered to have three branched chains, and each branched chain consists of a horizontal motor, a speed reducer, a driving arm and 2 driven rods which are arranged on the same side.
The working principle of the Delta type parallel robot is as follows: the static platform 1 is fixedly arranged on the machine platform, the horizontal motors (2-1 to 2-3) and the speed reducers (3-1 to 3-3) are fixedly connected to the static platform 1, and the driving arms (4-1 to 4-3) are respectively arranged at the output ends of the speed reducers (3-1 to 3-3). The two driven rods are connected with the driving arm through spherical hinges, and the movable platform 6 is connected with the two driven rods through spherical hinges. The vertical motor (2-4) is arranged on the static platform 1, and when the vertical motor (2-4) rotates, the spline 7, the spline sleeve 8 and the tail end flange 9 are driven to rotate. When the horizontal motor rotates, the drive arm is driven by the reducer to rotate around the common axis (the "horizontal joint axis" in fig. 1) of the motor and the reducer. The driving arm drives the driven rod and finally the movable platform 6.
As shown in figure 3, a horizontal motor 2-1, a speed reducer 3-1 and a driving arm 4-1 of a branched chain of the Delta type parallel robot form a horizontal joint of the robot, a motor rotating shaft and a speed reducer rotating shaft share a common axis to jointly form a joint shaft, and joint friction provided by the invention is friction torque of the three horizontal joints. The friction torque mainly occurs when the motor rotor and the reducer rotate, and the friction resistance torque is caused by the internal bearing damping and the meshing of the gears.
As shown in FIG. 8, the joint friction identification method of the DELTA-type parallel robot of the present invention is to identify the friction torque tau of the physical prototype of the DELTA-type parallel robot shown in FIG. 1 after the physical prototype is manufacturedf＝τfm+τfb(as shown in FIG. 4), τfmThe motor friction torque, tau, caused by internal bearing damping during rotation of the motor rotorfbThe friction torque of the Delta robot is generated by the rotation of the motor and the speed reducer, is not a constant value and is equal to the rotation speed of the motor
Figure BDA0003252652560000071
Or speed of speed reducer
Figure BDA0003252652560000072
The relevant values, reduced to a combination of static and viscous friction, are defined as follows:
Figure BDA0003252652560000073
Figure BDA0003252652560000074
wherein: k is a radical offmIs the viscous damping coefficient, k, of the motorfbIs the viscous damping coefficient of the speed reducer, cfmMaximum static friction of the motor, cfbIs the maximum static friction force of the speed reducer,
Figure BDA0003252652560000081
the number of revolutions of the motor is,
Figure BDA0003252652560000082
for the rotating speed of the speed reducer, the identification of the friction torque is to solve the four coefficients, and the method specifically comprises the following steps:
step 1, carrying out experiments to identify the friction torque tau of the motorfm
Each horizontal joint is tested individually, as shown in fig. 5, a horizontal motor is disassembled individually, and the actual torque value tau of the motor is generated during the operation of the motorm' should be sufficient to overcome the motor friction torque taufmAnd moment of inertia τ of the rotorimAnd the three satisfy
τm'＝τfm+τim (1.11)
The motors were tested individually for 10 times, and in the ith experiment (i ═ 1,2, …, 10), the motor servo drive was used to set the maximum speed at which the motor operated at
Figure BDA0003252652560000083
Wherein
Figure BDA0003252652560000084
Is the rated rotating speed of the motor.
Setting angular acceleration amThe motor is caused to reciprocate with a trapezoidal velocity law (see fig. 6), and the angular acceleration a is setmThe principle is that the motor has a constant-speed section, the maximum current value is acquired by using servo debugging software during the running period of the motor at least comprising a complete trapezoidal period, and the current value is converted into a torque value taum' (i) obtaining the inertia moment value tau of the rotorim：
τim＝Im×αm (1.12)
Wherein, ImThe rotational inertia of the motor rotor is obtained by looking up a motor manual;
calculating the motor friction torque taufm(i)：
τfm(i)＝τm'(i)-τim (1.13)
Recording the maximum rotation speed of the motor
Figure BDA0003252652560000085
Friction torque tau with motorfm(i)；
After 10 groups of the rotation speed are tested according to the flow, the set maximum rotation speed values are sequentially
Figure BDA0003252652560000091
The motor friction torque is calculated to be tau through the formulas (1.11) to (1.13)fm(1)～τfm(10)；
Will be provided with
Figure BDA0003252652560000092
And τfm(1)～τfm(10) Linear regression is performed according to the formula (1.10) to obtain k in the formula (1.10)fmAnd cfm；
Step 2, identifying friction torque tau of speed reducer by experimentfb
The motor and the speed reducer are installed in a combined mode and are fixedly connected, as shown in figure 7. During the operation of the motor, the actual torque value tau of the motor is generatedm"sufficient to overcome the motor friction torque taufmInertia moment tau of the rotor of the motorimFriction torque tau of speed reducerfbMoment of inertia τ of reducer rotoribAnd the five items satisfy:
τm”＝τfm+τim+τfb+τib (1.14)
the motor reducer combination was tested 10 times, and in the ith experiment (i is 1,2, …, 10), the maximum rotation speed of the motor was set using the motor servo driver
Figure BDA0003252652560000093
And angular acceleration am'＝αmThe motor is made to reciprocate with a trapezoidal speed law (see fig. 6), the maximum current value is collected by using servo debugging software during the motor running period at least containing a complete trapezoidal period, and the current value is converted into a torque value taum"(i), finding the moment of inertia τ of the reducer rotorib：
τib＝Ib×αm (1.15)
Wherein, IbThe moment of inertia of the rotor of the speed reducer is obtained by consulting a manual of the speed reducer or according to a three-dimensional model of the speed reducer provided by a manufacturer;
calculating friction torque tau of speed reducerfb(i)：
τfb(i)＝τm”(i)-τfm-τim-τib (1.16)
Recording the maximum rotation speed of the motor
Figure BDA0003252652560000094
Friction torque tau with speed reducerfb(i)。
After testing 10 groups of data according to the above process, the set maximum rotation speed of the motor is sequentially
Figure BDA0003252652560000101
The friction torque tau of the speed reducer is obtained through the formulas (1.14) to (1.16)fb(1)～τfb(10)。
Will be provided with
Figure BDA0003252652560000102
And τfb(1)～τfb(10) The k in the formula (1.11) can be obtained by linear regression processing according to the formula (1.11)fbAnd cfb。
At this time, k is obtained by the above stepsfm,kfb，cfm,cfbThe four parameters are the friction parameters of the motor and the speed reducer, so that the friction torque of the rotary joint of the main arm of the DELTA type parallel robot is identified.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned. Furthermore, it is obvious that the word "comprising" does not exclude other elements or that the singular does not exclude the plural.
Finally, it should be noted that the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit scope of the technical solutions of the present invention.

Claims (1)

1. A joint friction identification method for a DELTA type parallel robot is characterized in that after a physical prototype of the DELTA type parallel robot is manufactured, joint friction torque tau of the physical prototype is required to be identifiedf＝τfm+τfb，τfmThe motor friction torque, tau, caused by internal bearing damping during rotation of the motor rotorfbThe friction torque of the speed reducer caused by the meshing of gears when the speed reducer rotates is simplified intoThe combination of static friction and viscous friction is defined as follows:
Figure FDA0003252652550000011
Figure FDA0003252652550000012
wherein: k is a radical offmIs the viscous damping coefficient, k, of the motorfbIs the viscous damping coefficient of the speed reducer, cfmMaximum static friction of the motor, cfbIs the maximum static friction force of the speed reducer,
Figure FDA0003252652550000013
the number of revolutions of the motor is,
Figure FDA0003252652550000014
for the rotating speed of the speed reducer, the identification of the joint friction torque is to solve the four coefficients, and the method is characterized by comprising the following steps:
step 1, carrying out experiments to identify the friction torque tau of the motorfm
Each horizontal joint is tested independently, a horizontal motor is disassembled independently, and the actual torque value tau of the motor is generated in the running process of the motorm' should be sufficient to overcome the motor friction torque taufmAnd moment of inertia τ of the rotorimAnd the three satisfy:
τm'＝τfm+τim (1.11)
the motor is tested separately and tested N1 times, in the ith experiment, i is 1,2, … and N1, a motor servo driver is used, and the maximum rotating speed of the motor is set to be
Figure FDA0003252652550000015
Wherein
Figure FDA0003252652550000016
The rated rotating speed of the motor;
setting angular acceleration amEnsuring that the motor operates in a reciprocating mode at a trapezoidal speed rule, acquiring a maximum current value by using servo debugging software during the operation period of the motor at least comprising a complete trapezoidal period, and converting the current value into a torque value taum' (i) obtaining the inertia moment value tau of the rotorim：
τim＝Im×αm (1.12)
Wherein, ImThe rotational inertia of the motor rotor is obtained by looking up a motor manual;
calculating the motor friction torque taufm(i)：
τfm(i)＝τm'(i)-τim (1.13)
Recording the maximum rotation speed of the motor
Figure FDA0003252652550000021
Friction torque tau with motorfm(i)；
After N1 groups of numbers are tested according to the flow, the set maximum rotating speed value is sequentially
Figure FDA0003252652550000022
The motor friction torque is calculated to be tau through the formulas (1.11) to (1.13)fm(1)～τfm(N1)；
Will be provided with
Figure FDA0003252652550000023
And τfm(1)～τfm(N1) Linear regression was performed according to the formula (1.10) to find k in the formula (1.10)fmAnd cfm；
Step 2, identifying friction torque tau of speed reducer by experimentfb
The motor and the speed reducer are installed in a combined way and are fixedly connected, and the actual torque value tau of the motor is generated in the running process of the motorm"sufficient to overcome the motor friction torque taufmMotor rotorMoment of inertia τ of the sonimFriction torque tau of speed reducerfbMoment of inertia τ of reducer rotoribAnd the five items satisfy:
τm”＝τfm+τim+τfb+τib (1.14)
the motor reducer combination was tested N2 times, and in the ith experiment, i was 1,2, …, and N2, and the maximum rotation speed of the motor was set using the motor servo driver
Figure FDA0003252652550000024
And angular acceleration am'＝αmEnsuring that the motor operates in a reciprocating mode at a trapezoidal speed rule, acquiring a maximum current value by using servo debugging software during the operation period of the motor at least comprising a complete trapezoidal period, and converting the current value into a torque value taum"(i), finding the moment of inertia τ of the reducer rotorib：
τib＝Ib×αm (1.15)
Wherein, IbThe moment of inertia of the rotor of the speed reducer is obtained by consulting a manual of the speed reducer or according to a three-dimensional model of the speed reducer provided by a manufacturer;
calculating friction torque tau of speed reducerfb(i)：
τfb(i)＝τm”(i)-τfm-τim-τib (1.16)
Recording the maximum rotation speed of the motor
Figure FDA0003252652550000031
Friction torque tau with speed reducerfb(i)；
After the N2 groups of data are tested according to the flow, the set maximum rotating speed of the motor is sequentially
Figure FDA0003252652550000032
The friction torque tau of the speed reducer is obtained through the formulas (1.14) to (1.16)fb(1)～τfb(N2)；
Will be provided with
Figure FDA0003252652550000033
And τfb(1)～τfb(N2) the k in the formula (1.11) is obtained by linear regression processing according to the formula (1.11)fbAnd cfb。
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH08249031A (en) * 1995-03-09 1996-09-27 Fanuc Ltd Inertia and frictional characteristic estimation method for motor-driven mechanical system
JP2006020487A (en) * 2004-06-04 2006-01-19 Yaskawa Electric Corp Identifying device and method for machine constants
CN202433735U (en) * 2011-12-29 2012-09-12 东北大学 Mechanical friction detection and compensation control device
CN105814506A (en) * 2013-12-06 2016-07-27 三菱电机株式会社 Friction identification method and friction identification device
CN106426174A (en) * 2016-11-05 2017-02-22 上海大学 Robot contact force detecting method based on torque observation and friction identification
CN107423515A (en) * 2017-08-01 2017-12-01 中科新松有限公司 Mechanical arm Friction identification method, apparatus, equipment and storage medium
CN113051673A (en) * 2020-12-14 2021-06-29 华南理工大学 Robot improved Stribeck friction model identification method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH08249031A (en) * 1995-03-09 1996-09-27 Fanuc Ltd Inertia and frictional characteristic estimation method for motor-driven mechanical system
JP2006020487A (en) * 2004-06-04 2006-01-19 Yaskawa Electric Corp Identifying device and method for machine constants
CN202433735U (en) * 2011-12-29 2012-09-12 东北大学 Mechanical friction detection and compensation control device
CN105814506A (en) * 2013-12-06 2016-07-27 三菱电机株式会社 Friction identification method and friction identification device
CN106426174A (en) * 2016-11-05 2017-02-22 上海大学 Robot contact force detecting method based on torque observation and friction identification
CN107423515A (en) * 2017-08-01 2017-12-01 中科新松有限公司 Mechanical arm Friction identification method, apparatus, equipment and storage medium
CN113051673A (en) * 2020-12-14 2021-06-29 华南理工大学 Robot improved Stribeck friction model identification method

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