CN113977579A - Joint friction modeling method for improving tracking precision of robot track - Google Patents

Joint friction modeling method for improving tracking precision of robot track Download PDF

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CN113977579A
CN113977579A CN202111255895.XA CN202111255895A CN113977579A CN 113977579 A CN113977579 A CN 113977579A CN 202111255895 A CN202111255895 A CN 202111255895A CN 113977579 A CN113977579 A CN 113977579A
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speed
joint
friction
robot
torque
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刘玮
万平
徐之豪
周廷玉
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Yancheng Institute of Technology
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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
    • B25J9/16—Programme controls
    • 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

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  • Robotics (AREA)
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Abstract

The invention relates to the technical field of robot track modeling, and discloses a joint friction modeling method for improving the tracking precision of a robot track, which comprises the following steps of S1: dividing the speed reducer into a high-speed side and a low-speed side according to the speed, wherein a motor shaft is a high-speed shaft, an output side shaft of the harmonic speed reducer is a low-speed shaft, obtaining a joint transmission chain mechanism through analysis, and obtaining a dynamic model of the robot joint through modeling the high-speed shaft and the low-speed shaft respectively; s2, modeling joint nonlinear friction; s3, identifying friction force model parameters; s4, experimental procedure. According to the joint friction modeling method for improving the tracking precision of the robot track, the tracking precision of each joint of the robot is improved, the joint friction is a key factor influencing the dynamic characteristic of the robot, the dynamic characteristic of the robot is analyzed, an accurate robot dynamics model is established, the control precision of the robot is improved, the system is simplified and processed, and the control precision of the system is improved.

Description

Joint friction modeling method for improving tracking precision of robot track
Technical Field
The invention relates to the technical field of robot track modeling, in particular to a joint friction modeling method for improving the tracking precision of a robot track.
Background
The robot track tracking is a key problem for limiting the high-precision application of the robot, and modeling and compensating the friction of the joints of the robot are effective ways for improving the track tracking precision of the robot. Aiming at the problem that the conventional friction modeling method cannot be applied in an actual scene due to the influence of non-linear factors such as discontinuity in reversing, modeling error and the like, a friction modeling and compensating method based on a Radial Basis Function Neural Network (RBFNN) is provided.
At present, the existing joint friction modeling method with robot track tracking precision has the following problems: the tracking precision of each joint of the robot cannot be improved, joint friction is a key factor influencing the dynamic characteristic of the robot, the control precision is low, and the system processing is complex. For this reason, a corresponding technical scheme needs to be designed for solution.
Disclosure of Invention
Technical problem to be solved
Aiming at the defects of the prior art, the invention provides a joint friction modeling method for improving the tracking precision of a robot track, and solves the technical problems that the tracking precision of each joint of the robot cannot be improved, the joint friction is a key factor influencing the dynamic characteristic of the robot, the control precision is low, and the system processing is complex.
(II) technical scheme
In order to achieve the purpose, the invention is realized by the following technical scheme: a joint friction modeling method for improving the tracking precision of a robot track comprises the following steps,
s1, joint friction modeling: dividing a speed reducer into a high-speed side and a low-speed side according to the speed, wherein a motor shaft is a high-speed shaft, an output side shaft of a harmonic speed reducer is a low-speed shaft, obtaining a joint transmission chain mechanism through analysis, obtaining a dynamic model of a robot joint through modeling the high-speed shaft and the low-speed shaft respectively, firstly, carrying out high-speed shaft modeling, and obtaining a high-speed shaft dynamic equation according to an input and output torque balance principle
Figure BDA0003324095230000021
Then modeling the low-speed shaft, and obtaining a dynamic equation of the low-speed shaft in the same way as
Figure BDA0003324095230000022
Based on the Lagrangian equation, the load τ r can be expressed as
Figure BDA0003324095230000023
The relationship between the high-speed shaft rotation angle thetam and the low-speed shaft rotation angle q is q ═ thetamAnd/n. The dynamic model of the robot joint can be obtained as
Figure BDA0003324095230000024
S2, modeling joint nonlinear friction: based on the Stribeck model in the static friction model, the joint friction torque can be expressed as,
Figure BDA0003324095230000025
equation of joint friction torque tau f and motor current i
Figure BDA0003324095230000026
When the robot joint is in a no-load and uniform motion state, the electromagnetic torque and the friction torque generated by the robot joint friction modeling and self-adaptive RBF neural network compensation calculation torque control motor are equal, and tau can be obtained f＝Kmi. Calculating to obtain an equivalent friction torque tau f at a high-speed end, wherein tau f comprises tau fm and tau fr;
s3, identifying friction force model parameters: in order to identify the parameters of the friction model, a parameter identification experiment is carried out on the robot joint, a joint transmission system mainly comprises a brushless servo motor and a harmonic reducer, a motor shaft is directly connected with an input shaft of the reducer, and meanwhile, a rotary encoder is arranged on one side of the joint to measure the rotation angle of the joint;
s4, experimental method: the robot joint is set in an idle state, the output torque of the motor at different speeds is recorded, in MATLAB, data obtained by experiment measurement are utilized, a least square method is used for identifying friction model parameters in the positive direction and the negative direction, and modeling errors are identified and compensated on line.
Preferably, in step S1, τ motor represents an electromagnetic torque, Nm; j1 denotes the moment of inertia of the high speed shaft, kg · m 2; τ fm is high speed end friction torque, Nm; θ m is the high-speed end corner, rad; τ m is the torque output from the high-speed end and the torque input from the low-speed end, Nm; τ fr is low speed end friction torque, Nm; n represents a reduction ratio; j2 represents low-speed shaft rotational inertia, kg · m 2; q represents the low speed end turn angle, rad; τ r represents the low-speed-end output torque, i.e., the load torque τ load, Nm.
Preferably, in step S1, Km is a motor torque constant, Nm/a; i is the motor current, a.
Preferably, in step S1, ml (q) represents an equivalent rotational inertia term at the load end; cl (q, q-is) represents centripetal and Coriolis force terms at the load end; gl (q) represents a gravity term at the load end, and J ═ n2J1+J2Denotes the equivalent moment of inertia, kg · m 2; tau isf＝τfm+τfrAnd/n represents the equivalent friction torque at the high-speed end, kg · m 2. .
Preferably, in step S2, τ -c and τ + c are coulombic friction torque, Nm; τ -s and τ + s are the maximum static friction moment, Nm; τ -v and τ + v are viscous friction coefficients, Nm; ω -s and ω + s are the Stribeck characteristic velocity, rad/s.
Preferably, in step S4, the speed ranges from [ -62.4, 62.4] rad/S, wherein when the speed ranges from (0, 5.2) rad/S, the step size is 0.52rad/S, when the step size ranges from [5.2, 52 ] rad/S, the step size is 1.04rad/S, and when the step size ranges from [52, 62.4] rad/S, the step size is 5.2 rad/S.
(III) advantageous effects
According to the joint friction modeling method for improving the tracking precision of the robot track, the tracking precision of each joint of the robot is improved, the joint friction is a key factor influencing the dynamic characteristic of the robot, the dynamic characteristic of the robot is analyzed, an accurate robot dynamics model is established, the control precision of the robot is improved, the system is simplified and processed, and the control precision of the system is improved.
Drawings
FIG. 1 is a schematic view of the joint drive mechanism of the present invention;
FIG. 2 is a schematic diagram of the main performance parameters of the robot joint of the present invention;
FIG. 3 is a schematic diagram of a friction model parameter identification result according to the present invention;
FIG. 4 is a graphical illustration of the speed-friction torque fit of the present invention;
FIG. 5 is a block diagram of a control system according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1 to 5, an embodiment of the present invention provides a technical solution: a joint friction modeling method for improving the tracking precision of a robot track comprises the following steps,
s1, joint friction modeling: dividing a speed reducer into a high-speed side and a low-speed side according to the speed, wherein a motor shaft is a high-speed shaft, an output side shaft of a harmonic speed reducer is a low-speed shaft, obtaining a joint transmission chain mechanism through analysis, obtaining a dynamic model of a robot joint through modeling the high-speed shaft and the low-speed shaft respectively, firstly, carrying out high-speed shaft modeling, and obtaining a high-speed shaft dynamic equation according to an input and output torque balance principle
Figure BDA0003324095230000041
Then modeling the low-speed shaft, and obtaining a dynamic equation of the low-speed shaft in the same way as
Figure BDA0003324095230000042
Based on the Lagrangian equation, the load τ r can be expressed as
Figure BDA0003324095230000043
The relationship between the high-speed shaft rotation angle thetam and the low-speed shaft rotation angle q is q ═ thetamAnd/n. The dynamic model of the robot joint can be obtained as
Figure BDA0003324095230000051
S2, modeling joint nonlinear friction: based on the Stribeck model in the static friction model, the joint friction torque can be expressed as,
Figure BDA0003324095230000052
equation of joint friction torque tau f and motor current i
Figure BDA0003324095230000053
When the robot joint is in a no-load and uniform motion state, the electromagnetic torque and the friction torque generated by the robot joint friction modeling and self-adaptive RBF neural network compensation calculation torque control motor are equal, and tau can be obtainedf＝Kmi. Calculating to obtain an equivalent friction torque tau f at a high-speed end, wherein tau f comprises tau fm and tau fr;
s3, identifying friction force model parameters: in order to identify the parameters of the friction model, a parameter identification experiment is carried out on the robot joint, a joint transmission system mainly comprises a brushless servo motor and a harmonic reducer, a motor shaft is directly connected with an input shaft of the reducer, and meanwhile, a rotary encoder is arranged on one side of the joint to measure the rotation angle of the joint;
s4, experimental method: the robot joint is set in an idle state, the output torque of the motor at different speeds is recorded, in MATLAB, data obtained by experiment measurement are utilized, a least square method is used for identifying friction model parameters in the positive direction and the negative direction, and modeling errors are identified and compensated on line.
In a further improvement, in step S1, τ motor represents the electromagnetic torque, Nm, generated by the motor; j1 denotes the moment of inertia of the high speed shaft, kg · m 2; τ fm is high speed end friction torque, Nm; θ m is the high-speed end corner, rad; τ m is the torque output from the high-speed end and the torque input from the low-speed end, Nm; τ fr is low speed end friction torque, Nm; n represents a reduction ratio; j2 represents low-speed shaft rotational inertia, kg · m 2; q represents the low speed end turn angle, rad; τ r represents the low-speed-end output torque, i.e., the load torque τ load, Nm.
In a further improvement, in step S1, Km is a motor torque constant, Nm/a; i is the motor current, a.
In a further improvement, in step S1, ml (q) represents an equivalent rotational inertia term at the load end; cl (q, q-is) represents centripetal and Coriolis force terms at the load end; gl (q) represents a gravity term at the load end, and J ═ n2J1+J2Denotes the equivalent moment of inertia, kg · m 2; tau isf＝τfm+τfrAnd/n represents the equivalent friction torque at the high-speed end, kg · m 2. .
In a further improvement, in step S2, τ -c and τ + c are coulomb friction torque, Nm; τ -s and τ + s are the maximum static friction moment, Nm; τ -v and τ + v are viscous friction coefficients, Nm; ω -s and ω + s are the Stribeck characteristic velocity, rad/s.
Specifically, in step S4, the speed is in the range of [ -62.4, 62.4] rad/S, wherein when the speed is in the range of (0, 5.2) rad/S, the step size is 0.52rad/S, when the step size is [5.2, 52 ] rad/S, the step size is 1.04rad/S, and when the step size is [52, 62.4] rad/S, the step size is 5.2 rad/S.
A calculation torque control method is adopted to design a trajectory tracking controller for a robot joint containing nonlinear friction, and meanwhile, the self-adaptive RBF neural network is combined to perform online observation and compensation on friction model errors and dynamic model parameter errors.
The working principle is as follows: firstly, establishing a continuous joint friction modeling method for overcoming the influence caused by discontinuous friction during reversing; then, fitting a modeling error by introducing a radial basis function neural network, and solving the influence of nonlinear factors in the system; secondly, in order to realize the actual control of the robot, a high-precision encoder is adopted to obtain the position, the speed and the joint torque data of the robot in the actual track tracking process, and the obtained data is filtered and denoised; and finally, in order to verify the effectiveness of the method, a track tracking experiment of the robot joint is designed and completed.
The result shows that compared with the uncompensated condition, the maximum tracking error is greatly reduced based on the average tracking error before and after compensation controlled by the RBFNN, wherein the tracking precision of the robot track after data filtering is improved by 73.46%, and the algorithm can effectively compensate joint friction and other non-linear factors in the system.
The parts of the invention are all universal standard parts or parts known by technicians in the field, the structure and the principle of the parts can be known by technicians through technical manuals or conventional experimental methods, the invention solves the problems that the tracking precision of each joint of the robot cannot be improved, the joint friction is a key factor influencing the dynamic characteristic of the robot, the control precision is low, and the system processing is complex.
While there have been shown and described what are at present considered the fundamental principles and essential features of the invention and its advantages, it will be apparent to those skilled in the art that the invention is not limited to the details of the foregoing exemplary embodiments, but is capable of other specific forms without departing from the spirit or essential characteristics 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 should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (6)

1. A joint friction modeling method for improving the tracking precision of a robot track is characterized by comprising the following steps,
s1, joint friction modeling: dividing a speed reducer into a high-speed side and a low-speed side according to the speed, wherein a motor shaft is a high-speed shaft, an output side shaft of a harmonic speed reducer is a low-speed shaft, obtaining a joint transmission chain mechanism through analysis, obtaining a dynamic model of a robot joint through modeling the high-speed shaft and the low-speed shaft respectively, firstly, carrying out high-speed shaft modeling, and obtaining a high-speed shaft dynamic equation according to an input and output torque balance principle
Figure FDA0003324095220000011
Then modeling the low-speed shaft, and obtaining a dynamic equation of the low-speed shaft in the same way as
Figure FDA0003324095220000012
Based on the Lagrangian equation, the load τ r can be expressed as
Figure FDA0003324095220000013
The relationship between the high-speed shaft rotation angle thetam and the low-speed shaft rotation angle q is q ═ theta mAnd/n. The dynamic model of the robot joint can be obtained as
Figure FDA0003324095220000014
S2, modeling joint nonlinear friction: based on the Stribeck model in the static friction model, the joint friction torque can be expressed as,
Figure FDA0003324095220000015
equation of joint friction torque tau f and motor current i
Figure FDA0003324095220000016
When the robot joint is in a no-load and uniform motion state, the electromagnetic torque and the friction torque generated by the robot joint friction modeling and self-adaptive RBF neural network compensation calculation torque control motor are equal, and the electromagnetic torque and the friction torque can be obtained
Figure FDA0003324095220000017
Calculating to obtain an equivalent friction torque tau f at a high speed end, wherein tau f comprises tau fm and tau fr;
s3, identifying friction force model parameters: in order to identify the parameters of the friction model, a parameter identification experiment is carried out on the robot joint, a joint transmission system mainly comprises a brushless servo motor and a harmonic reducer, a motor shaft is directly connected with an input shaft of the reducer, and meanwhile, a rotary encoder is arranged on one side of the joint to measure the rotation angle of the joint;
s4, experimental method: the robot joint is set in an idle state, the output torque of the motor at different speeds is recorded, in MATLAB, data obtained by experiment measurement are utilized, a least square method is used for identifying friction model parameters in the positive direction and the negative direction, and modeling errors are identified and compensated on line.
2. The joint friction modeling method for improving the tracking accuracy of the robot trajectory according to claim 1, characterized in that: in step S1, τ motor represents an electromagnetic torque, Nm, generated by the motor; j1 denotes the moment of inertia of the high speed shaft, kg · m 2; τ fm is high speed end friction torque, Nm; θ m is the high-speed end corner, rad; τ m is the torque output from the high-speed end and the torque input from the low-speed end, Nm; τ fr is low speed end friction torque, Nm; n represents a reduction ratio; j2 represents low-speed shaft rotational inertia, kg · m 2; q represents the low speed end turn angle, rad; τ r represents the low-speed-end output torque, i.e., the load torque τ load, Nm.
3. The joint friction modeling method for improving the tracking accuracy of the robot trajectory according to claim 1, characterized in that: in step S1, Km is a motor torque constant, Nm/A; i is the motor current, a.
4. The joint friction modeling method for improving the tracking accuracy of the robot trajectory according to claim 1, characterized in that: in step S1, M1(q) represents an equivalent rotational inertia term at the load end; c1(q, q. cndot.) denotes the direction of the load sideThe cardiac and coriolis force terms; g1(q) represents the gravity term at the load end, J ═ n2J1+J2Denotes the equivalent moment of inertia, kg · m 2; tau is f＝τfm+τfrAnd/n represents the equivalent friction torque at the high-speed end, kg · m 2. .
5. The joint friction modeling method for improving the tracking accuracy of the robot trajectory according to claim 1, characterized in that: in step S2, τ -c and τ + c are coulomb friction torque, Nm; τ -s and τ + s are the maximum static friction moment, Nm; τ -v and τ + v are viscous friction coefficients, Nm; ω -s and ω + s are the Stribeck characteristic velocity, rad/s.
6. The joint friction modeling method for improving the tracking accuracy of the robot trajectory according to claim 1, characterized in that: in step S4, the speed value range is [ -62.4, 62.4] rad/S, wherein when the speed value range is (0, 5.2) rad/S, the step size is 0.52rad/S, when the [5.2, 52) rad/S, the step size is 1.04rad/S, and when the [52, 62.4] rad/S, the step size is 5.2 rad/S.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114700939A (en) * 2022-03-04 2022-07-05 华中科技大学 Method and system for observing joint load torque of cooperative robot and storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114700939A (en) * 2022-03-04 2022-07-05 华中科技大学 Method and system for observing joint load torque of cooperative robot and storage medium
CN114700939B (en) * 2022-03-04 2024-02-06 华中科技大学 Collaborative robot joint load torque observation method, system and storage medium

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Application publication date: 20220128