CN107443382B - Industrial robot structure parameter error identification and compensation method - Google Patents

Industrial robot structure parameter error identification and compensation method Download PDF

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CN107443382B
CN107443382B CN201710818562.0A CN201710818562A CN107443382B CN 107443382 B CN107443382 B CN 107443382B CN 201710818562 A CN201710818562 A CN 201710818562A CN 107443382 B CN107443382 B CN 107443382B
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industrial robot
parameter
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CN107443382A (en
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谢福贵
刘辛军
梅斌
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Tsinghua University
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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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1638—Programme controls characterised by the control loop compensation for arm bending/inertia, pay load weight/inertia
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis

Abstract

The invention discloses an industrial robot structure parameter error identification and compensation method, which comprises the following steps: determining a structure parameter error which can be compensated according to a numerical control system of an industrial robot; establishing an error model based on a DH method, forcibly zeroing the uncompensable structure parameter errors in the error model, and then constructing an error identification equation; selecting an identification pose, controlling the industrial robot to move according to the identification pose, and recording the position data of the joint corner and the tail end of the industrial robot; calculating an error identification equation according to the joint corner and the tail end position data, and solving the error identification equation to obtain a structural parameter error; and modifying corresponding structural parameters in a numerical control system of the industrial robot according to the structural parameter errors so as to compensate the structural parameter errors. The invention has the following advantages: can discern and compensate industrial robot's reduction ratio error, coupling parameter error and DH parameter error, compensate to above-mentioned error and can reach higher positioning accuracy.

Description

Industrial robot structure parameter error identification and compensation method
Technical Field
The invention relates to the technical field of industrial robots, in particular to an industrial robot structure parameter error identification and compensation method.
Background
With the development of subjects such as mechanical manufacturing, electronic engineering, automatic control and the like, research aiming at the technical field of industrial robots is continuously and deeply carried out. Currently, industrial robots play a role in many industries such as aerospace, machine manufacturing, biomedicine, food packaging and the like, and are widely applied to welding, carrying, spraying, assembling and the like. In some emerging fields, such as full-automatic factories, human-machine cooperation, full-automatic machining systems realized by matching robots with machine tools, and the like, industrial robots play an important role to promote social and economic development.
Teaching is an important working mode of an industrial robot, and automatic operation can be realized in subsequent work by controlling the industrial robot to reach each preset position and recording the preset position, so that the industrial robot reaches each preset position within a specified time to work. Industrial robots generally have a high precision of repeated positioning, i.e. the values of the encoders of the motors when recorded in one position can be controlled to reach the recorded values and return to the recorded position when recorded in another position, thereby achieving a high precision of repeated positioning. At present, some tasks to be processed by an industrial robot are gradually complicated, for example, a camera acquires object position information to control the robot to grab, and the tasks require the robot to have higher positioning precision. However, the positioning accuracy of the industrial robot is generally low, that is, the active control robot end reaches a certain position in space, and the actual reaching position has a certain error from the target position.
The main cause of the positioning error is structural parameter error of the industrial robot, including dh (denavit hartenberg) parameter error, reduction ratio error, coupling parameter error and the like. Generally, a DH method is used for modeling an industrial robot, and the relation of adjacent connecting rod coordinate systems is described by four parameters, namely a joint corner, a joint distance, a connecting rod length and a connecting rod torsion angle. The DH parameters, if erroneous, are inaccurate for the kinematic model, resulting in positioning errors.
In each joint of the industrial robot, a speed reducer is used to connect a motor and a connecting rod, so that the rotating angle of the connecting rod is the rotating angle of the motor divided by a reduction ratio. In some mechanical configurations of industrial robots, the fifth joint and the sixth joint are coupled, that is, when the fifth joint rotates, the sixth joint moves with a certain angle of rotation even if no rotation command is given to the sixth joint. The coupling parameter may be used to describe this condition, defined as the angle the sixth joint rotates with divided by the angle the fifth joint rotates. In some robot control systems, the coupling parameter may control the rotation of the sixth joint to compensate for the coupled motion. If there is an error in the coupling parameters, the coupled motion cannot be exactly compensated, causing an error in the positioning. Also, in some robot control systems, in order to increase the calculation speed, some of the DH parameter values are fixed, and only some of the DH parameter values are modifiable. In this case, if all DH parameter errors are identified by calibration, but only a part of them is compensated, the positioning accuracy of the industrial robot will be improved to some extent, but there is still room for improvement.
Disclosure of Invention
The present invention is directed to solving at least one of the above problems.
Therefore, the invention aims to provide an industrial robot structure parameter error identification and compensation method which can improve the positioning accuracy of the industrial robot.
In order to achieve the above object, an embodiment of the present invention discloses an industrial robot structure parameter error identification and compensation method, which includes the following steps: s1: determining a structure parameter error which can be compensated according to a numerical control system of an industrial robot; s2: establishing an error model based on a DH method, namely a mapping relation between the structure parameter error of the industrial robot and the tail end position error, forcibly zeroing the uncompensated structure parameter error in the error model, and then establishing an error identification equation; s3: selecting an identification pose, controlling the industrial robot to move according to the identification pose, and acquiring joint corner and end position data of the industrial robot; s4: calculating an error identification equation according to the joint corner and the tail end position data, and solving the error identification equation to obtain a structural parameter error; s5: and modifying corresponding structural parameters in a numerical control system of the industrial robot according to the structural parameter errors so as to compensate the structural parameter errors.
Further, the structure parameter errors that can be compensated include DH parameter errors, reduction ratio errors, and coupling parameter errors.
Further, the industrial robot has two joints parallel and adjacent to each other, the first coordinate axes of the link coordinate systems corresponding to the two joints parallel and adjacent to each other are parallel, and the joint distance parameter is replaced with a rotation angle around the second coordinate axis of the previous link coordinate system among the 4 DH parameters.
Further, the step of selecting the identification pose comprises: controlling designated joints of the industrial robot to respectively and independently rotate; and selecting other poses according to the anti-interference indexes.
Further, the anti-interference index is a geometric mean of singular values of the identification matrix.
Further, the measuring instrument is a laser tracker or a measuring arm.
Further, the error identification equation is solved using a least squares method.
According to the method for identifying and compensating the structural parameter errors of the industrial robot, the structural parameter errors which can be identified and compensated comprise DH parameter errors, speed reduction ratio errors and coupling parameter errors, the uncompensable structural parameter errors are forcibly set to be zero in an error model according to a numerical control system, and other structural parameter errors are identified and compensated. The method carries out error identification according to the setting of the robot numerical control system, and can achieve higher positioning accuracy compared with a method of directly identifying all DH parameter errors and only compensating part of the DH parameter errors.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of an industrial robot structural parameter error identification and compensation method of the present invention;
fig. 2 is a schematic structural view of an industrial robot according to an embodiment of the present invention;
fig. 3 is a schematic diagram of each link coordinate system of a six-degree-of-freedom industrial robot established using a DH method according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a TCP (Tool Center Point) trajectory of a single joint rotation according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used only for convenience in describing the present invention and for simplicity in description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
These and other aspects of embodiments of the invention will be apparent with reference to the following description and attached drawings. In the description and drawings, particular embodiments of the invention have been disclosed in detail as being indicative of some of the ways in which the principles of the embodiments of the invention may be practiced, but it is understood that the scope of the embodiments of the invention is not limited correspondingly. On the contrary, the embodiments of the invention include all changes, modifications and equivalents coming within the spirit and terms of the claims appended hereto.
The invention is described below with reference to the accompanying drawings.
Fig. 1 is a flow chart of an industrial robot structure parameter error identification and compensation method according to an embodiment of the invention. As shown in fig. 1, the method for identifying and compensating the structural parameter error of the industrial robot according to the embodiment of the present invention includes the following steps:
s1: and determining the structure parameter error which can be compensated according to the numerical control system of the industrial robot.
In one embodiment of the invention, the structure parameter errors that can be compensated include DH parameter errors, reduction ratio errors, and coupling parameter errors.
In one embodiment of the invention, the industrial robot has two mutually parallel and adjacent joints, the first coordinate axes of the link coordinate systems corresponding to the mutually parallel and adjacent joints are parallel, and the rotation angle around the second coordinate axis of the previous link coordinate system is used in place of the joint distance parameter in the corresponding 4 DH parameters.
S2: an error model is established based on a DH method, namely a mapping relation between the structure parameter error of the industrial robot and the tail end position error, the uncompensated structure parameter error is forced to be zero in the error model, and then an error identification equation is established.
S3: and selecting an identification pose, controlling the industrial robot to move according to the identification pose, and acquiring joint corner and end position data of the industrial robot by using a measuring instrument.
In one embodiment of the present invention, the step of selecting the identification pose includes: controlling each joint of the industrial robot to rotate independently; and selecting other poses according to the anti-interference indexes.
Further, the anti-interference index is a geometric mean of singular values of the identification matrix.
In one embodiment of the invention, the measuring instrument is a laser tracker or a measuring arm.
S4: and calculating an error identification equation according to the joint corner and the tail end position data, and solving the error identification equation by using a least square method to obtain the structural parameter error.
S5: and modifying corresponding structural parameters in a numerical control system of the industrial robot according to the structural parameter errors so as to compensate the structural parameter errors.
In order that those skilled in the art will further understand the present invention, the following examples are given for illustration and description.
[ EXAMPLES one ]
According to the method for identifying and compensating the structural parameter errors of the industrial robot, the structural parameter errors can be identified step by step, each joint of the industrial robot is a revolute pair or a revolute pair, and in the embodiment, the industrial robot with six degrees of freedom shown in fig. 2 is provided and comprises six revolute joints and one operating tool. As shown in fig. 2, the rotation axes of the rotary joint 21, the rotary joint 24 and the rotary joint 26 are in a plane and pass through the common vertex of the two triangles, the rotation axes bisect the two triangles respectively, and the rotation axes of the rotary joint 22, the rotary joint 23 and the rotary joint 25 are in a direction perpendicular to the plane.
As shown in fig. 3, an i-1 link coordinate system is established at an i-th joint of the industrial robot, and z is established along a rotation axis directioni-1And the shaft is fixedly connected with the connecting rod. X of ith link coordinate systemiThe axes being oriented simultaneously perpendicular to zi-1Axis and ziA shaft. Four DH parameters and connecting rod length a are arranged between two adjacent connecting rod coordinate systemsiIs zi-1Axis and ziDistance between shafts, link torsion angle αiIs zi-1Axis and ziThe included angle of the axes; distance d between jointsiIs xi-1Axis and xiThe distance between the axes; angle of rotation theta of jointiIs xi-1Axis and xiAngle between axes, thetai＝θ0,i+θi *，θ0,iIs the joint angle theta between two adjacent connecting rod coordinate systems when the robot is in a zero position statei *Is the angle the joint actually rotates from the zero position, the coordinates use the right hand coordinate system, link torsion angle αiIn the positive direction of (1) is xiEstablishing an axis positive direction and a right-hand spiral criterion; angle of rotation theta of jointiIn the positive direction of (1) in ziPositive axial direction and right-hand spiral criteria are established. Between adjacent link coordinate systems, transformation can be achieved by translation and rotation, along zi-1Axial translation diRotation of thetai(ii) a Then along xiAxial translation aiα rotationiThe transformation from the i-1 link coordinate system to the i link coordinate system can be realized. So that the position of the terminal tcp (tool Center point) under the robot base coordinate system can be obtained. In the industrial robot, the rotation axis of the revolute joint 22 and the rotation axis of the revolute joint 23 are parallel to each other, and the rotation axis y is used2Angle of rotation β of shaft2Replacement joint distance parameter d2。
The homogeneous transformation matrix of the coordinate systems of two adjacent connecting rods is
Figure BDA0001405710360000051
Figure BDA0001405710360000052
Wherein S represents a trigonometric function Sin and C represents a trigonometric function Cos.
The method for identifying and compensating the errors of the structural parameters of the industrial robot comprises the following steps:
s1: according to the numerical control system of the robot, the structure parameter errors capable of being compensated are determined, the structure parameter errors capable of being compensated in the embodiment comprise reduction ratio errors of six motors, coupling parameter errors between a fifth joint and a sixth joint, and a in DH parameters1,a2,a3,a6，d1,d3,d4,d6And theta0,iI is 1,2 … 6.
S2: and establishing an error model on the basis of a DH method, namely establishing a mapping relation between the structure parameter error of the industrial robot and the end position error. Firstly, only the effect of DH parameter error is considered, and the DH parameter error (theta) between adjacent connecting rod coordinate systems of each jointi,di,ai,αi) I is 1,3,4,5,6, and θ2,β2,a2,α2Resulting in an error vector of
qi＝(ai,diSαi+aiθiCαi,diCαi-aiθiSαi,αi,θiSαi,θiCαi)T,i＝1,3,4,5,6
q2＝(a2+a2θ2Sα2Sβ2,a2θ2Cα2,-a2θ2Sα2Cβ2+a2Sβ2,
α2Cβ2-θ2Cα2Sβ2,β2+θ2Sα2,θ2Cα2Cβ2+α2Sβ2)
The error vector in the 0 th connecting rod coordinate system is expressed as
Figure BDA0001405710360000061
Wherein the content of the first and second substances,
Figure BDA0001405710360000062
R0,iis T0,iUpper left corner 3 x 3 rotation matrix, p0,iIs T0,iThe first three elements of the fourth column, representing a translation vector, p0,iX is p0,iIs used to generate the inverse symmetric matrix. Wherein, T0,iRepresenting a transformation matrix, T, from the 0 th link coordinate system to the i-th link coordinate system0,i＝T0,1T1,2...Ti-1,i。
Let gi＝[θi,di,ai,αi]TAnd i is 1,3,4,5 and 6, and is a DH parameter error vector. Then q can be obtainedi＝Gigi，i＝1,3,4,5,6，
Wherein the coefficient matrix
Figure BDA0001405710360000063
DH error vector g for second joint2＝[θ2,β2,a2,α2]THaving q of2＝G2g2，
Wherein the coefficient matrix
Figure BDA0001405710360000064
The merging into a matrix form is:
Figure BDA0001405710360000071
deviation of actual position and ideal position of TCP at tail end of robotDifference is p ═ LqIWherein the matrix
Figure BDA0001405710360000072
[x,y,z]T＝p0,6And is the coordinate of the TCP in the 0 th link coordinate system. Therefore, a mapping equation of each joint error to the terminal position error can be established,
hg ═ p, wherein
Figure BDA0001405710360000073
The error mapping matrix H ═ L [ J ═ L [ J ] ]0,1G1J0,2G2J0,3G3J0,4G4J0,5G5J0,6G6]
When one joint of the industrial robot is independently rotated in consideration of the reduction ratio error effect, as shown in fig. 4, PjAnd Pj+1Two points on the TCP track, radius is the radius of the arc, the corresponding actual rotation angle of the joint
Figure BDA0001405710360000074
The reduction ratio error parameter of the corresponding joint is
Figure BDA0001405710360000075
θn *Is the nominal rotation angle of the joint in the numerical control system. By calculating the reduction ratio error parameter, the actual reduction ratio can be obtained
Figure BDA0001405710360000076
Wherein r isn,iIs the nominal reduction ratio in the numerical control system.
Taking into account the effect of errors in the coupling parameter, coupling parameter ccoupMay be defined as the ratio c of the fifth joint rotation angle to the resulting sixth joint rotation anglecoupθ* 5,nominalcredu,5+θ* 6,nominalcredu,6＝θ* 6,actualWherein, theta* 5,nominalAnd theta* 6,nominalNominal angles of rotation, c, of the fifth and sixth joints, respectivelyredu,5And credu,6Is a reduction ratio error parameter of the fifth joint and the sixth joint. Theta* 6,actualIs the actual angle of rotation of the sixth joint. The coupling parameters can be found by solving for H 'g ═ p'. Wherein, H ═ L [ J4,5G5J4,6G6J4,6Gcoup]，g'＝[g5 T,g6 T,ccoup]TAnd p' is the error of the position of the lower end of the 4 th link coordinate system.
Gcoup＝[0 θ5 *a6Cα6-θ5 *a6Sα60 θ5 *Sα6θ5 *Cα6]T
And forcibly zeroing the uncompensated structure parameter error in the model, namely removing the element in g and the column of a corresponding mapping matrix H for an error mapping equation Hg & ltp & gt, and constructing an error identification equation Dw & ltp & gt, wherein D is an identification matrix and is related to the robot nominal structure parameter and the joint variable, w is a structure parameter error vector, and p is the robot tail end positioning error.
S3: the anti-interference index is set as the root mean square of the singular value of the identification matrix, and the identification pose is selected according to the anti-interference index, wherein the number of the poses is greater than 1/3 of the number of the compensated DH parameters, and can be selected as 14 in the embodiment. The position of the end is set to be measured using a laser tracker, and a target ball is installed at the end of the robot as a TCP point. Firstly, enabling the six joints to rotate independently, recording nominal rotation angle values in a numerical control system and TCP position information obtained through measurement, controlling the robot to move to a corresponding pose, and recording joint corner and end position data;
s4: from the method of calculating the reduction ratio error in S2 and the data in S3, the actual reduction ratio is calculated. Using the data of the first joint rotation, fitting a plane according to a least square method, wherein the normal vector of the plane is the unit vector of the z axis of the 0 th connecting rod coordinate system in laser trackingIn the sub-instrument representation, denoted as zL. Fitting the plane and circle by using the data of the second joint rotation according to the least square method, and recording the circle center position as pLThe expression is that the origin of the 0 th connecting rod coordinate system is under the coordinate system of the laser tracker, the plane normal vector is the expression of the x-axis unit vector of the 0 th connecting rod coordinate system under the coordinate system of the laser tracker and is recorded as xL. Calculation from the right-hand coordinate System
Figure BDA0001405710360000081
I.e. the representation of the y-axis unit vector of the 0 th link coordinate system in the laser tracker coordinate system. Composed matrix
Figure BDA0001405710360000082
A transformation matrix representing the coordinates of the point from the 0 th link coordinate system to the laser tracker coordinate system. Then TLB＝TBL -1And a transformation matrix for expressing the coordinates of the points from the coordinate system of the laser tracker to the coordinate system of the 0 th connecting rod can convert the coordinate data of the position points measured by the laser tracker into the coordinate system of the 0 th connecting rod of the robot for expressing.
The actual reduction ratio is calculated from the data of the individual rotations of the six joints. And calculating the coupling parameters according to the data of the independent rotation of the fifth joint and the independent rotation of the sixth joint.
The nominal rotation angle value in the numerical control system recorded in S3 is converted into an actual rotation angle value based on the actual reduction ratio and the coupling parameter.
Substituting the identification pose data selected by the anti-interference index into an error identification equation, and solving the error identification equation by using a least square method to obtain a DH parameter error. And if the DH parameter error is larger, the current error needs to be superposed on the nominal value to be used as a new nominal DH parameter value, and an error identification equation is established and solved. The iteration is repeated until the calculated DH error vector modulo length is very small, which may be set to less than 0.0000000001.
S5: and modifying corresponding structural parameters in a numerical control system of the robot, and compensating the identified structural parameter errors.
[ example two ]
The method for identifying and compensating the structural parameter errors of the industrial robot can synchronously identify the structural parameter errors, each joint of the industrial robot is a revolute pair or a revolute pair, and in the embodiment, the industrial robot with six degrees of freedom shown in fig. 2 is provided and comprises six revolute joints and one operating tool. In the state shown in the figure, the rotation axes of the rotary joint 21, the rotary joint 24 and the rotary joint 26 are in a plane and pass through the common vertex of the two triangles, the rotation axes bisect the two triangles respectively, and the rotation axes of the rotary joint 22, the rotary joint 23 and the rotary joint 25 are in a direction perpendicular to the plane.
As shown in fig. 3, an i-1 link coordinate system is established at an i-th joint of the industrial robot, and z is established along a rotation axis directioni-1And the shaft is fixedly connected with the connecting rod. X of ith link coordinate systemiThe axes being oriented simultaneously perpendicular to zi-1Axis and ziA shaft. Four DH parameters and connecting rod length a are arranged between two adjacent connecting rod coordinate systemsiIs zi-1Axis and ziDistance between shafts, link torsion angle αiIs zi-1Axis and ziThe included angle of the axes; distance d between jointsiIs xi-1Axis and xiThe distance between the axes; angle of rotation theta of jointiIs xi-1Axis and xiAngle between axes, thetai＝θ0,i+θi *，θ0,iIs the joint angle theta between two adjacent connecting rod coordinate systems when the robot is in a zero position statei *Is the angle the joint actually rotates from the zero position, the coordinates use the right hand coordinate system, link torsion angle αiIn the positive direction of (1) is xiEstablishing an axis positive direction and a right-hand spiral criterion; angle of rotation theta of jointiIn the positive direction of (1) in ziPositive axial direction and right-hand spiral criteria are established. Between adjacent link coordinate systems, transformation can be achieved by translation and rotation, along zi-1Axial translation diRotation of thetai(ii) a Then along xiAxial translation aiα rotationiThe transformation from the i-1 link coordinate system to the i link coordinate system can be realized. Thereby can obtainThe position of the terminal TCP (tool Center point) under the robot base coordinate system in the industrial robot, the rotating shaft of the rotating joint 22 and the rotating shaft of the rotating joint 23 are parallel, and the rotating angle β around the y-axis is used in the corresponding 4 DH parameters between the two link coordinate systems2Replacement joint distance parameter d2。
The homogeneous transformation matrix of the coordinate systems of two adjacent connecting rods is
Figure BDA0001405710360000091
Figure BDA0001405710360000101
Figure BDA0001405710360000102
Wherein S represents a trigonometric function Sin and C represents a trigonometric function Cos.
The method for identifying and compensating the errors of the structural parameters of the industrial robot comprises the following steps:
s1: according to the numerical control system of the robot, the structure parameter errors capable of being compensated are determined, the structure parameter errors capable of being compensated in the embodiment comprise reduction ratio errors of six motors, coupling parameter errors between a fifth joint and a sixth joint, and a in DH parameters1,a2,a3,a6，d1,d3,d4,d6And theta0,iI is 1,2 … 6.
S2: and establishing an error model on the basis of a DH method, namely establishing a mapping relation between the structure parameter error of the industrial robot and the end position error. Firstly, only the effect of DH parameter error is considered, and the DH parameter error (theta) between adjacent connecting rod coordinate systems of each jointi,di,ai,αi) I is 1,3,4,5,6, and θ2,β2,a2,α2Resulting in an error vector of
qi＝(ai,diSαi+aiθiCαi,diCαi-aiθiSαi,αi,θiSαi,θiCαi)T,i＝1,3,4,5,6
q2＝(a2+a2θ2Sα2Sβ2,a2θ2Cα2,-a2θ2Sα2Cβ2+a2Sβ2,
α2Cβ2-θ2Cα2Sβ2,β2+θ2Sα2,θ2Cα2Cβ2+α2Sβ2)
The error vector in the 0 th connecting rod coordinate system is expressed as
Figure BDA0001405710360000103
Wherein the content of the first and second substances,
Figure BDA0001405710360000104
R0,iis T0,iUpper left corner 3 x 3 rotation matrix, p0,iIs T0,iThe first three elements of the fourth column, representing a translation vector, p0,iX is p0,iIs used to generate the inverse symmetric matrix. Wherein, T0,iRepresenting a transformation matrix, T, from the 0 th link coordinate system to the i-th link coordinate system0,i＝T0,1T1,2...Ti-1,i。
Let gi'＝[θi,di,ai,αi]TAnd i is 1,3,4,5 and 6, and is a DH parameter error vector. Then q can be obtainedi＝Gi'gi'，i＝1,3,4,5,6，
Wherein the coefficient matrix
Figure BDA0001405710360000111
DH parameter error vector g for second joint2'＝[θ2,β2,a2,α2]THaving q of2＝G2'g2'，
Wherein the coefficient matrix
Figure BDA0001405710360000112
Taking into account the effect of the reduction ratio error, θiCan be decomposed into zero error theta0,iAnd the sum of errors caused by the reduction ratio, i.e. thetai＝θ0,i+cr,i·θi *Wherein thetai *Is the angle of rotation of the joint, cr,iIs a reduction ratio error parameter. The actual reduction ratio r is compared with the nominal reduction ratio r in the current numerical control systemnThe relationship is r ═ rn(cr,i+1)。
Taking into account the effect of coupling parameter errors, the coupling parameter ccoupCan be defined as the ratio c of the fifth axis rotation angle to the resulting sixth axis rotation anglecoupθ* 5,nominalcredu,5+θ* 6,nominalcredu,6＝θ* 6,actualWherein, theta* 5,nominalAnd theta* 6,nominalIs the nominal angle of rotation of the fifth joint and the sixth joint, credu,5And credu,6Is a reduction ratio error parameter of the fifth joint and the sixth joint. Theta* 6,actualIs the actual angle of rotation of the sixth joint.
Thus, under the combined effect of the DH parameter error, the reduction ratio error and the coupling parameter error, the error vectors and the coefficient matrix are
gi＝[cr,i,θi,di,ai,αi]Ti＝1,3,4,5
Figure BDA0001405710360000113
g2＝[cr,2,θ2,β2,a2,α2]T
Figure BDA0001405710360000121
g6＝[ccoup,cr,i,θ6,d6,a6,α6]T
Figure BDA0001405710360000122
Are combined into a matrix form
Figure BDA0001405710360000123
The deviation p of the actual position of the TCP at the end of the robot from the ideal position is LqIWherein the matrix
Figure BDA0001405710360000124
[x,y,z]T＝p0,6And is the coordinate of the TCP in the 0 th link coordinate system. Thus, a mapping equation Hg ═ p of each joint error to the terminal position error can be established,
wherein
Figure BDA0001405710360000125
The error mapping matrix H ═ L [ J ═ L [ J ] ]0,1G1J0,2G2J0,3G3J0,4G4J0,5G5J0,6G6]
And forcibly zeroing the uncompensated structure parameter error in the model, namely removing the element in g and the column of a corresponding mapping matrix H for an error mapping equation Hg & ltp & gt, and constructing an error identification equation Dw & ltp & gt, wherein D is an identification matrix and is related to the robot nominal structure parameter and the joint variable, w is a structure parameter error vector, and p is the robot tail end positioning error.
S3: the anti-interference index is set to be the root mean square of the singular values of the identification matrix, and the identification pose is selected according to the anti-interference index, wherein the number of the poses is greater than 1/3 of the number of the structure parameters capable of being compensated, and the number of the poses is selected to be 20 in the embodiment. The position of the end is set to be measured using a laser tracker, and a target ball is installed at the end of the robot as a TCP point. The first two joints are made to rotate independently, nominal rotation angle values in the numerical control system and TCP position information obtained through measurement are recorded, then the robot is controlled to move to the selected corresponding pose, and joint rotation angle and end position data are recorded.
S4: fitting a plane according to a least square method by using data of the rotation of the first joint, wherein a normal vector of the plane is represented by a unit vector of a z axis of a 0 th connecting rod coordinate system under a laser tracker and is recorded as zL. Fitting the plane and circle by using the data of the second joint rotation according to the least square method, and recording the circle center position as pLThe expression is that the origin of the 0 th connecting rod coordinate system is under the coordinate system of the laser tracker, the plane normal vector is the expression of the x-axis unit vector of the 0 th connecting rod coordinate system under the coordinate system of the laser tracker and is recorded as xL. Calculating y from the right hand coordinate systemL＝zL×xLI.e. the representation of the y-axis unit vector of the 0 th link coordinate system in the laser tracker coordinate system. Composed matrix
Figure BDA0001405710360000131
A transformation matrix representing the coordinates of the point from the 0 th link coordinate system to the laser tracker coordinate system. Then TLB＝TBL -1And a transformation matrix for expressing the coordinates of the points from the coordinate system of the laser tracker to the coordinate system of the 0 th connecting rod can convert the coordinate data of the position points measured by the laser tracker into the coordinate system of the 0 th connecting rod of the robot for expressing.
And substituting the pose data obtained by measurement into an error identification equation, and solving the error identification equation by using a least square method to obtain the structural parameter error. If the error of the structural parameter is large, the current error needs to be superposed on the nominal value to be used as a new nominal structural parameter value, and an error identification equation is established and solved. The iteration is repeated until the modular length of the calculated structure parameter error vector is very small, and the modular length can be set to be less than 0.0000000001.
S5: and modifying corresponding structural parameters in a numerical control system of the robot, and compensating the identified structural parameter errors.
According to the method for identifying and compensating the structural parameter errors of the industrial robot, the structural parameter errors which can be identified and compensated comprise DH parameter errors, speed reduction ratio errors and coupling parameter errors, the uncompensable structural parameter errors are forcibly set to be zero in an error model according to a numerical control system, and other structural parameter errors are identified and compensated. The method carries out error identification according to the setting of the robot numerical control system, and can achieve higher positioning accuracy compared with a method of directly identifying all DH parameter errors and only compensating part of the DH parameter errors.
In addition, other configurations and functions of the method for identifying and compensating the structural parameter error of the industrial robot according to the embodiment of the present invention are known to those skilled in the art, and are not described in detail for reducing redundancy.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (6)

1. An industrial robot structure parameter error identification and compensation method is characterized by comprising the following steps:
s1: determining a structure parameter error which can be compensated according to a numerical control system of an industrial robot;
wherein the structure parameter errors which can be compensated comprise DH parameter errors, reduction ratio errors and coupling parameter errors;
s2: establishing an error model based on a DH method, namely a mapping relation between the structure parameter error of the industrial robot and the tail end position error, forcibly zeroing the uncompensated structure parameter error in the error model, and then establishing an error identification equation;
s3: selecting an identification pose, controlling the industrial robot to move according to the identification pose, and acquiring joint corner and end position data of the industrial robot;
s4: calculating an error identification equation according to the joint corner and the tail end position data, and solving the error identification equation to obtain a structural parameter error;
s5: and modifying corresponding structural parameters in a numerical control system of the industrial robot according to the structural parameter errors so as to compensate the structural parameter errors.
2. The method for identifying and compensating for errors in structural parameters of an industrial robot according to claim 1, wherein the industrial robot has two joints parallel and adjacent to each other, the first coordinate axes of the link coordinate systems corresponding to the two joints parallel and adjacent to each other are parallel, and the rotation angle around the second coordinate axis of the previous link coordinate system is used instead of the joint distance parameter in the corresponding 4 DH parameters.
3. The industrial robot structural parameter error identification and compensation method according to claim 1, wherein the step of selecting an identification pose comprises:
controlling designated joints of the industrial robot to respectively and independently rotate;
and selecting other poses according to the anti-interference indexes.
4. The method according to claim 3, wherein the interference rejection indicator is a geometric mean of singular values of an identification matrix.
5. Method for identification and compensation of errors in structural parameters of an industrial robot according to claim 1, characterised in that the data of the end position of the industrial robot is acquired using a laser tracker or a measuring arm.
6. The industrial robot structural parameter error identification and compensation method according to claim 1, characterized in that the error identification equation is solved using an iterative method or a least squares method.
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