CN109940609B - Robot dynamics modeling method based on centrosymmetric static friction model - Google Patents

Robot dynamics modeling method based on centrosymmetric static friction model Download PDF

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CN109940609B
CN109940609B CN201910131871.XA CN201910131871A CN109940609B CN 109940609 B CN109940609 B CN 109940609B CN 201910131871 A CN201910131871 A CN 201910131871A CN 109940609 B CN109940609 B CN 109940609B
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陈教料
王佳才
张立彬
胥芳
沈一丰
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Zhejiang University of Technology ZJUT
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Abstract

A robot dynamics modeling method based on a centrosymmetric static friction model comprises the following steps: step 1: establishing a calculation formula of the inertia moment of the robot joint; step 2: establishing a calculation formula of the friction torque of the robot joint; step 3, obtaining a mathematical expression of the industrial robot dynamic model; step 4, unknown parameter identification is carried out, and the P is obtained by adopting WOA identificationinerAnd the unknown inertial parameter in the friction calculation formula (5) and the unknown friction parameter in the friction calculation formula (5)
Figure DDA0001975651000000012
[+ ‑]And
Figure DDA0001975651000000011
and 5, verifying and obtaining the industrial robot dynamic model. The invention provides a centrosymmetric static friction model for accurately describing the hysteresis effect of joint friction, and compared with other static friction models, the dynamic model of the robot joint can be more accurately established.

Description

Robot dynamics modeling method based on centrosymmetric static friction model
Technical Field
The invention relates to a robot dynamics modeling method, in particular to an industrial robot dynamics modeling method.
Background
The high motion precision and speed can improve the working efficiency of the robot when the robot executes complex tasks. A feedback-based robot controller is difficult to achieve because it relies only on the operating state of the robot and does not take into account the dynamics of the robot. Therefore, establishing an accurate dynamic model of the robot is a key problem for improving the motion accuracy of the industrial robot. In the dynamic modeling process of the industrial robot, friction is one of the key factors limiting the accuracy of the dynamic model of the robot joint. The robot joint friction during high-speed movement can be accurately calculated according to the joint rotating speed by adopting a linear friction model, but when the robot joint moving speed is low, the joint friction and the joint rotating speed have complex nonlinear dynamic characteristics, so that the accurate calculation of the robot joint friction has certain difficulty. At the same time, accurate modeling of robot dynamics is also made difficult.
Disclosure of Invention
The invention provides a robot dynamics modeling method based on a centrosymmetric static friction model, aiming at overcoming the defect that the existing static friction model cannot describe the dynamic friction characteristics of a robot joint so as to realize accurate modeling of the dynamics of an industrial robot.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a robot dynamics modeling method based on a centrosymmetric static friction model comprises the following steps:
step 1: calculation formula for establishing robot joint inertia moment
According to the inertial parameter P of the ith joint of the robotiner,i＝(Ixx,i,Ixy,i,Ixz,i,Iyy,i,Iyz,i,Izz,i,Cx,i,Cy,i,Cz,i,mi) And the Newton Euler recursion formula simplifies the inertia moment of each robot joint into the following form:
Figure GDA0002500273020000011
wherein the ratio of q,
Figure GDA0002500273020000021
position, velocity and acceleration vectors of the joint, respectively; m (q) is a quality matrix of the joints of the industrial robot,
Figure GDA0002500273020000022
the terms Copenforces and centrifugal forces, G (q) the gravity term; i isxx,i，Iyy,,iIzz,iRespectively setting the rotational inertia parameters of the ith mechanical arm relative to the x, y and z axes of a joint coordinate system; i isxy,i，Ixz,,i，Iyz,iThe inertia product of the ith mechanical arm to the corresponding coordinate axis is obtained; cx,i,Cy,i,Cz,iRespectively the x, y, z coordinates of the mass center of the ith mechanical arm, miMass of the ith mechanical arm;
step 2: calculation formula for establishing robot joint friction torque
The form of the robot joint friction torque calculated by adopting the Stribeck friction model is as follows:
Figure GDA0002500273020000023
wherein, taufricFor robot joint friction torque, TcAnd TvCoefficient of viscous friction, T, and coulombs，
Figure GDA0002500273020000024
Respectively representing the static friction coefficient, the Stribeck speed parameter and the shape factor;
the Stribeck model does not describe the different behavior of the joint friction torque in different rotational directions. And because of the application of the sign function sign (·), the joint static friction moment (T) calculated by adopting a Stribeck models) A sudden change at the velocity zero point will occur. To represent coulomb and viscous friction in different rotational directions,
Figure GDA0002500273020000025
and
Figure GDA0002500273020000026
are respectively set as the coulomb and viscous friction coefficients of the positive and negative rotation directions of the joint. And introduces the inverse of the coefficient of static friction (-T)s) Eliminating the influence of the sign function so that the friction torque calculated from the joint rotation speed is continuous at zero point. According to the joint movement speed obtained by sampling
Figure GDA0002500273020000027
And a sampling interval TspBy the formula
Figure GDA0002500273020000028
The corresponding joint acceleration is obtained. In joint acceleration
Figure GDA0002500273020000029
The equation for the continuous friction calculation is as follows:
Figure GDA00025002730200000210
but due to the Stribeck speed parameter
Figure GDA00025002730200000211
And the shape factor () is kept constant before and after the speed reversal, the nonlinear characteristics of the joint friction at the time of forward and reverse rotation are consistent, so that equation (3) does not describe the hysteresis effect of the joint friction sufficiently; introducing two sets of Stribeck velocity parameters and shape factors: (
Figure GDA00025002730200000212
And
Figure GDA00025002730200000213
) The dynamic friction characteristics when the robot joint rotates forward and backward are respectively shown, and the hysteresis effect when the joint accelerates is obtained as follows:
Figure GDA0002500273020000031
retarding by hysteresis effect
Figure GDA0002500273020000032
The phases can be considered as being centrosymmetric to the acceleration motion phases. Thus defining two static coefficients of friction
Figure GDA0002500273020000033
And
Figure GDA0002500273020000034
so as to distinguish the acceleration and deceleration stages of the friction hysteresis effect of the joint. The finally obtained static friction model of the center symmetry of the joint of the industrial robot is as follows:
Figure GDA0002500273020000035
step 3, obtaining a mathematical expression of the industrial robot dynamic model
Calculation formula tau of driving torque of each joint of n-degree-of-freedom industrial roboti＝τiner,i+τfric,i(i is 1-n) is a dynamic model of each joint of the industrial robot, wherein tauinerAnd τfricThe moment of inertia and the moment of friction of the robot joint are respectively expressed as a formula (1) and a formula (5);
step 4 unknown parameter identification
Obtaining P by WOA recognitioninerThe unknown inertial parameter in (1) and the unknown friction parameter in the friction calculation formula (equation (5)))
Figure GDA0002500273020000036
[+ -]And
Figure GDA0002500273020000037
step 5, verifying and obtaining the industrial robot dynamic model
And (4) substituting the kinetic parameters obtained by identification in the step (4) into a joint driving moment calculation formula to obtain the driving moment when the robot moves, comparing the calculated moment with the actual joint moment, if the deviation is within the acceptance range, considering that the established robot kinetic model is reasonable and usable, and returning to the step (4) if the deviation is not within the acceptance range.
The main technical conception of the invention is as follows: and calculating the inertia moment of each joint in the robot dynamics by adopting a Newton Euler recurrence formula. For the friction torque of the industrial robot joint, the dynamic characteristics (particularly the hysteresis effect of friction) of the friction are described by adopting a central symmetry friction model improved by a Stribeck friction model: according to the speed and the acceleration direction of the joint motion, the motion of the robot joint is divided into four states of positive acceleration, positive deceleration, reverse acceleration and reverse deceleration, and different function expressions are adopted to respectively calculate the joint friction in the four motion states. On the basis of the determined robot dynamics mathematical model, unknown parameters in the model are obtained by adopting WOA optimization algorithm identification, and the dynamics modeling of the industrial robot is completed.
And calculating the friction of the robot joints in different motion phases respectively by a piecewise function method, so that the established static friction model can describe the dynamic characteristics of the friction of the robot joints. And unknown parameters in the dynamics model are obtained through an identification method, and the modeling of the robot dynamics is completed.
The invention has the following beneficial effects: the centrosymmetric static friction model is provided for accurately describing the hysteresis effect of joint friction, and compared with other static friction models, the dynamic model of the robot joint can be established more accurately.
Drawings
Fig. 1 is a flow chart of a method of a dynamic model of an industrial robot.
FIG. 2 is a calculated joint friction-velocity curve based on a centrosymmetric stiction model.
FIG. 3 is a flow chart of calculating joint friction based on a centrosymmetric stiction model.
Fig. 4 shows the model verification result.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 4, a robot dynamics modeling method based on a centrosymmetric static friction model calculates the inertia moment of each joint in robot dynamics by using a newton-euler recursion formula. For the friction torque of the industrial robot joint, the dynamic characteristics (particularly the hysteresis effect of friction) of the friction are described by adopting a central symmetry friction model improved by a Stribeck friction model: according to the speed and the acceleration direction of the joint motion, the motion of the robot joint is divided into four states of positive acceleration, positive deceleration, reverse acceleration and reverse deceleration, and different function expressions are adopted to respectively calculate the joint friction in the four motion states. On the basis of the determined robot dynamics mathematical model, unknown parameters in the model are obtained by adopting WOA optimization algorithm identification, and the dynamics modeling of the industrial robot is completed.
The method takes a Mitsubishi 6-degree-of-freedom RV-4F robot as an object, and comprises the following steps:
step 1: calculation formula for establishing robot joint inertia moment
According to the inertial parameter P of the ith joint of the robotiner,i＝(Ixx,i,Ixy,i,Ixz,i,Iyy,i,Iyz,i,Izz,i,Cx,i,Cy,i,Cz,i,mi) And the Newton Euler recurrence formula can simplify the inertia moment of the RV-4F robot joint into the following form:
Figure GDA0002500273020000051
wherein the ratio of q,
Figure GDA0002500273020000052
respectively the position, velocity and acceleration vectors of the joint. M (q) is the quality matrix of the robot joint,
Figure GDA0002500273020000053
the terms Copenforces and centrifugal forces, and G (q) the terms gravity. In the inertial parameter, Ixx,i，Iyy,,iIzz,iRespectively setting the rotational inertia parameters of the ith mechanical arm relative to the x, y and z axes of a joint coordinate system; i isxy,i，Ixz,,i，Iyz,iThe inertia product of the ith mechanical arm to the corresponding coordinate axis is obtained; cx,i,Cy,i,Cz,iRespectively the x, y and z coordinates of the mass center of the ith mechanical arm. m isiIs the mass of the ith robot arm.
Step 2: calculation formula for establishing robot joint friction torque
According to the joint movement speed obtained by sampling
Figure GDA0002500273020000054
And a sampling interval TspBy the formula
Figure GDA0002500273020000055
The corresponding joint acceleration is obtained. And establishing an RV-4FL robot joint central symmetry static friction model as follows:
Figure GDA0002500273020000056
step 3, obtaining a mathematical expression of the industrial robot dynamic model
Calculation formula tau of driving torque of each joint of RV-4F roboti＝τiner,i+τfric,iAnd (i is 1-6) is the dynamic model of each joint of the industrial robot. Wherein tau isinerAnd τfricThe moment of inertia and the moment of friction of the robot joint are respectively.
Step 4 unknown parameter identification
Obtaining P by WOA recognitioninerThe unknown inertia parameter in (1) and the unknown friction parameter in the friction calculation formula
Figure GDA0002500273020000061
[+ -]And
Figure GDA0002500273020000062
partial kinetic parameters obtained by taking the sixth joint of the RV-4F robot as an example are as follows:
Figure GDA0002500273020000063
Figure GDA0002500273020000064
step 5, verifying and obtaining the industrial robot dynamic model
And (4) substituting the kinetic parameters obtained by identification in the step (4) into a joint driving torque calculation formula to obtain the driving torque of the robot during movement, and comparing the driving torque with the actual joint torque. The deviation is within the acceptance range (as shown in fig. 4) and the established robot dynamics model is considered to be reasonably usable.
The foregoing lists merely illustrate specific embodiments of the invention. It is obvious that the invention is not limited to the above embodiments, but that many variations are possible. All modifications which can be derived or suggested directly from the disclosure of the invention by a person skilled in the art are to be considered within the scope of the invention.

Claims (1)

1. A robot dynamics modeling method based on a centrosymmetric static friction model is characterized by comprising the following steps:
step 1: calculation formula for establishing robot joint inertia moment
According to the inertial parameter P of the ith joint of the robotiner,i＝(Ixx,i,Ixy,i,Ixz,i,Iyy,i,Iyz,i,Izz,i,Cx,i,Cy,i,Cz,i,mi) And the Newton Euler recursion formula simplifies the inertia moment of each robot joint into the following form:
Figure FDA0002049471540000011
wherein the ratio of q,
Figure FDA0002049471540000012
position, velocity and acceleration vectors of the joint, respectively; m (q) is a quality matrix of the joints of the industrial robot,
Figure FDA0002049471540000013
the terms Copenforces and centrifugal forces, G (q) the gravity term; i isxx,i，Iyy,,iIzz,iRespectively setting the rotational inertia parameters of the ith mechanical arm relative to the x, y and z axes of a joint coordinate system; i isxy,i，Ixz,,i，Iyz,iIs the product of inertia, C, of the ith arm about the corresponding coordinate axisx,i,Cy,i,Cz,iRespectively the x, y, z coordinates of the mass center of the ith mechanical arm, miMass of the ith mechanical arm;
step 2: calculation formula for establishing robot joint friction torque
The form of the robot joint friction torque calculated by adopting the Stribeck friction model is as follows:
Figure FDA0002049471540000014
wherein, taufricFor robot joint friction torque, TcAnd TvCoefficient of viscous friction, T, and coulombs,
Figure FDA0002049471540000015
Respectively representing the static friction coefficient, the Stribeck speed parameter and the shape factor;
to represent coulomb and viscous friction in different rotational directions,
Figure FDA0002049471540000016
and
Figure FDA0002049471540000017
set as Coulomb and viscous friction coefficient in positive and negative rotation directions of joint, and introduce the opposite number (-T) of static friction coefficients) Eliminating the influence of sign function sign (DEG) makes the friction torque calculated according to the joint rotation speed continuous at the zero point, and obtains the joint motion speed according to the sampling
Figure FDA0002049471540000018
And a sampling interval TspBy the formula
Figure FDA0002049471540000019
Obtaining corresponding joint acceleration, and accelerating movement of the joint
Figure FDA00020494715400000110
The equation for the continuous friction calculation is as follows:
Figure FDA00020494715400000111
introducing two sets of Stribeck velocity parameters and shape factors: (
Figure FDA00020494715400000112
And
Figure FDA00020494715400000113
) The dynamic friction characteristics when the robot joint rotates forward and backward are respectively shown, and the hysteresis effect when the joint accelerates is obtained as follows:
Figure FDA00020494715400000114
retarding by hysteresis effect
Figure FDA00020494715400000115
The phases can be considered as centrosymmetric to the acceleration motion phases, thus defining two static friction coefficients
Figure FDA00020494715400000116
And
Figure FDA00020494715400000117
the acceleration and deceleration stages of the joint friction hysteresis effect are distinguished, and the finally obtained static friction model of the industrial robot joint center symmetry is as follows:
Figure FDA00020494715400000118
step 3, obtaining a mathematical expression of the industrial robot dynamic model
Calculation formula tau of driving torque of each joint of n-degree-of-freedom industrial roboti＝τiner,i+τfric,i(i is 1-n) is a dynamic model of each joint of the industrial robot, wherein tauinerAnd τfricThe moment of inertia and the moment of friction of the robot joint are respectively expressed as a formula (1) and a formula (5);
step 4 unknown parameter identification
Obtaining P by WOA recognitioninerAnd the unknown inertial parameter in the friction calculation formula (5) and the unknown friction parameter in the friction calculation formula (5)
Figure FDA0002049471540000021
[+ -]And
Figure FDA0002049471540000022
step 5, verifying and obtaining the industrial robot dynamic model
And (4) substituting the kinetic parameters obtained by identification in the step (4) into a joint driving moment calculation formula to obtain the driving moment when the robot moves, comparing the calculated moment with the actual joint moment, if the deviation is within the acceptance range, considering that the established robot kinetic model is reasonable and usable, and returning to the step (4) if the deviation is not within the acceptance range.
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