CN112775935B - Parallel robot calibration method based on terminal error detection information subset - Google Patents

Parallel robot calibration method based on terminal error detection information subset Download PDF

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CN112775935B
CN112775935B CN202011467216.0A CN202011467216A CN112775935B CN 112775935 B CN112775935 B CN 112775935B CN 202011467216 A CN202011467216 A CN 202011467216A CN 112775935 B CN112775935 B CN 112775935B
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parallel robot
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detection information
matrix
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CN112775935A (en
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张铁
马广才
曹亚超
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South China University of Technology SCUT
Zhongshan Institute of Modern Industrial Technology of South China University of Technology
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Zhongshan Institute of Modern Industrial Technology of South China University of Technology
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    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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Abstract

The invention discloses a parallel robot calibration method based on a terminal error detection information subset. The method comprises the following steps: establishing a parallel robot kinematic model based on a D-H method; establishing an error model of the parallel robot based on a matrix method; simplifying a parallel robot error model based on a least parameter linear combination theorem; establishing a parallel robot error identification model based on the tail end error detection information subset; measuring the actual pose of the tail end of the parallel robot, and obtaining the pose error of the tail end of the parallel robot by making a difference with the theoretical pose; and compensating the tail end error of the parallel robot based on the structural error identification result of the parallel robot. The parallel robot calibration method based on the terminal error detection information subset has the advantages of simplicity, practicality, high efficiency and quickness, is suitable for parallel robots with 6 degrees of freedom and few degrees of freedom, and has certain reference significance for the precision calibration of other mechanisms.

Description

Parallel robot calibration method based on terminal error detection information subset
Technical Field
The invention relates to a calibration method, in particular to a parallel robot calibration method based on a terminal error detection information subset.
Background
The precision calibration is an effective means for improving the motion precision of the tail end of the parallel robot, however, the existing calibration method mostly needs to measure a complete set of six-dimensional pose errors of the tail end, and the calibration process is complicated.
The tail end error detection information complete set is formed by six-dimensional pose errors of the tail end of the robot at a measuring point, and the tail end error detection information subset is a part of the tail end error detection information complete set. In most cases, the attitude error at the end of the measuring mechanism is extremely difficult and inefficient because commercial instruments that do not precisely measure the three-dimensional attitude of the spatial rigid body are available. Therefore, many scholars attempt to use a subset of the mechanism end 6-dimensional pose errors to achieve error parameter identification, and thus kinematic calibration.
In the prior art, the literature entitled "a 6-degree-of-freedom parallel configuration equipment kinematics calibration technique based on minimum subset detection information of end errors" (fifth marine and overseas youth design and manufacturing science conference.0.) proposes a kinematics calibration method based on minimum error subset detection information, which can simplify the work of error measurement, but does not propose how to solve the identifiability problem of structural errors. The document entitled "step kinematics calibration of planar three-degree-of-freedom parallel machine tools" (china (edition E: technical science), 2009(01):67-75.) proposes to perform QR decomposition on an identification matrix, and proposes a linear combination theorem with the least parameter error by using an upper triangular square matrix R after decomposition, wherein the theorem ensures the identifiability of structural parameters but the tail end error required to be measured is still large.
Therefore, in view of the above technical problems, it is necessary to provide a calibration method for parallel robots based on a subset of end error detection information.
Disclosure of Invention
The invention mainly aims to provide a parallel robot calibration method based on a tail end error detection information subset, which can overcome the defects of the prior art, can accurately, quickly and reliably identify structural errors on the basis of a kinematic error model of a parallel robot, and achieves the purpose of improving calibration precision and efficiency.
The purpose of the invention is realized by at least one of the following technical solutions.
A parallel robot calibration method based on an end error detection information subset comprises the following steps:
s1, establishing a parallel robot kinematics model based on a D-H method;
s2, establishing a parallel robot error model based on a matrix method;
s3, simplifying the error model of the parallel robot based on the least parameter linear combination theorem;
s4, establishing a parallel robot error identification model based on the tail end error detection information subset;
s5, measuring the actual pose of the tail end of the parallel robot, and obtaining the pose error of the tail end of the parallel robot by making a difference with the theoretical pose;
and S6, compensating the end error of the parallel robot based on the parallel robot structure error identification result.
Further, in step S1, the parallel robot includes a moving platform and a static platformThe device comprises a platform and I branched chains, wherein each branched chain is provided with N connecting rods, and a movable platform and a static platform are connected together through each branched chain; respectively establishing a moving coordinate system O-XYZ and a static coordinate system O-XYZ on the moving platform and the static platform of the parallel robot according to a right-hand rule, establishing a connecting rod coordinate system on each connecting rod of the ith branched chain based on a D-H method, wherein I is 1,2,3, …, I, and defining a homogeneous transformation matrix from the j-1 connecting rod coordinate system of the ith branched chain to the j connecting rod coordinate system as TijJ is 1,2,3, …, N, as follows:
Figure BDA0002834794780000021
wherein s represents sin, c represents cos, ai(j-1)Represents the length of the connecting rod between the joint axis j-1 and the joint axis j in the branch chain i, dijIs the link offset, α, on the joint axis j in the branch ii(j-1)Denotes the link angle between link j-1 and link j in branch i, θijDenotes ai(j-1)Extension line of (a)ijWhile rotating the resulting joint angle about joint axis j.
Further, the kinematic model of the movable platform of the parallel robot relative to the static platform is as follows:
P＝Ti1Ti2Ti3...TiN；
wherein P is a pose matrix of the moving coordinate system O-XYZ relative to the static coordinate system O-XYZ.
Further, in step S2, the two sides of the kinematic model are differentiated to obtain:
Figure BDA0002834794780000022
wherein, Delta is a differential motion matrix of the moving coordinate system relative to the static coordinate system, DeltaijIs a differential motion matrix of the ith branched chain jth connecting rod coordinate system relative to the jth connecting rod coordinate system of the (j-1) th connecting rod;
the differential rotation and differential movement of the ith branched chain j-1 link coordinate system relative to the jth link coordinate system are respectively assumed to be deltaij＝(δxij,δyij,δzij)TAnd dij＝(dxij,dyij,dzij)TThe differential rotation and differential movement of the parallel robot dynamic coordinate system relative to the static coordinate system are respectively delta (delta x, delta y, delta z)TAnd d ═ d (dx, dy, dz)TThen the error matrix at the ith branch and jth link coordinate system can be expressed as:
Figure BDA0002834794780000031
analyzing error sources existing in the parallel robot, converting error variables caused by the error sources into differential rotation and differential movement, and substituting the differential rotation and the differential movement into deltaijThen, the error model of the ith branch chain is:
Figure BDA0002834794780000032
wherein A isijCan be expressed as:
Aij＝Ti1Ti2…Tij；
separating error caused by error source from error model, and expressing the error as delta E in the form of L-dimensional differential error vectoriAnd L is the number of error variables caused by error sources, the error model of the ith branch chain of the parallel robot can be rewritten as follows:
Δ＝[dT,δT]T＝Ji·ΔEi；
wherein, JiThe error Jacobian matrix of the ith branch.
Further, in step S3, the jacobian matrix J is corrected for the erroriPerforming QR decomposition to obtain an upper triangular matrix R, then:
(1) when 0 row exists in the upper triangular matrix R, the parameter corresponding to the 0 row cannot be identified;
(2) when the upper triangular matrix R has the proportional columns, all the parameters corresponding to the proportional columns are combined into one parameter to be identified;
(3) when linear correlation columns exist in the upper triangular matrix R, combining parameters corresponding to all the linear correlation columns into M parameters to be identified, wherein M is the column number of the maximum linear correlation group forming the linear correlation columns;
(4)ΔEithe number of identifiable parameters after simplification is the rank of the upper triangular matrix R.
Further, after simplification, the error model of the ith branch becomes:
Δ＝[dT,δT]T＝Ji'·ΔEi'；
wherein, J'iAs an error Jacobian matrix JiSimplified matrix, Δ E'iFor the differential error vector Δ E to be identifiediAnd (5) simplifying the vector.
Further, step S4 is specifically as follows:
selecting n position measurement points in the theoretical motion space of the parallel robot, wherein n is more than or equal to K, and K is delta E'iIf the number of the parameters to be identified is greater than the number of the parameters to be identified, n groups of three-dimensional attitude errors and n groups of three-dimensional position errors can be obtained at most through the position measuring points, one group of the n groups of three-dimensional attitude errors is selected at will, and n-1 groups of the n groups of three-dimensional position errors are selected at will to form a terminal pose error detection information subset, so that an error model of the ith branch chain can be rewritten as follows:
[δ(0),d(1),d(2),...,d(n-1)]T＝Ji”·ΔEi'；
wherein, delta(0)Is a selected set of attitude errors, d(t)Is the selected t-th set of position errors, t 1,2,3, …, n-1; j'iAn error Jacobian matrix matched with the end error detection information subset is obtained by substituting n position measurement points into Ji' obtaining.
Further, based on the least square method, the error identification model of the ith branch chain of the parallel robot is as follows:
ΔE'i＝(Ji”T·Ji”)-1·Ji”T·[δ(0),d(1),d(2),...,d(n-1)]T。
further, step S5 is specifically as follows:
in a reference coordinate system OJThe posture and position of the UVW measurement moving platform coordinate system o-xyz at the zero point are respectivelyoRJAndoPJthen the transformation matrix from the slave platform zero coordinate system to the reference coordinate system is:
Figure BDA0002834794780000041
similarly, the transformation matrix from the reference coordinate system to the coordinate system of the movable platform at the measuring point is as follows:
Figure BDA0002834794780000042
wherein,JRCandJPCrespectively the attitude and position of the moving platform coordinate system measured in the reference coordinate system at the measuring point; then, the actual pose of the movable platform at any theoretical measuring point relative to the zero point is as follows:
oTC＝oTJ JTC；
and moving the movable platform to a theoretical position of any measuring point, further obtaining an actual pose of the movable platform relative to a zero point, and obtaining a pose error of the tail end of the parallel robot by subtracting the actual pose from the theoretical pose.
Further, step S6 is specifically as follows:
structural error Delta E obtained by identificationiSubstituting the error model to obtain the error of the movable platform at any theoretical position p (x, y, z, rx, ry, rz) as follows:
Figure BDA0002834794780000051
the practical end pose obtained by compensating the end pose of the parallel robot is as follows:
Figure BDA0002834794780000052
compared with the prior art, the invention has the beneficial effects that:
the parallel robot calibration method based on the tail end error detection information subset has the advantages of simplicity, high efficiency, practicality and quickness, is suitable for parallel robots with 6 degrees of freedom and few degrees of freedom, has obvious effect of improving motion precision after calibration, and has certain reference significance for the research of calibration methods of other types of mechanisms.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a specific flow of the parallel robot calibration method based on the end error detection information subset according to the present invention.
FIG. 2 is a schematic diagram of a 3-CRU parallel robot mechanism used in the embodiment of the present invention and a coordinate system diagram of a D-H kinematic model established by taking a first branched chain as an example.
FIG. 3 is a schematic diagram of measuring the pose of the end of a parallel robot based on a laser tracker.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not a whole embodiment. 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.
Example (b):
a calibration method for parallel robots based on a subset of end error detection information, as shown in fig. 1, includes the following steps:
s1, establishing a parallel robot kinematics model based on a D-H method;
in this embodiment, the 3-CRU parallel robot includes a movable platform, a stationary platform, and 3 CRU branched chains arranged in a central symmetry manner, where C, R, and U represent a cylinder pair, a revolute pair, and a hooke joint, respectively. Each branched chain is connected with the static platform at one end through a cylindrical pair, and is connected with the movable platform at the other end through a Hooke hinge. Establishing a kinematic model of the 3-CRU parallel robot based on a D-H method, taking a branched chain 1 as an example, embedding a connecting rod coordinate system into each connecting rod mechanism of the 3-CRU parallel robot according to a certain rule, thereby establishing each connecting rod coordinate system of the branched chain 1, and establishing a connecting rod coordinate system of a branched chain 2 and a branched chain 3 in the same way as shown in figure 2; respectively establishing a moving coordinate system O-XYZ and a static coordinate system O-XYZ on the moving platform and the static platform of the parallel robot according to a right-hand rule, establishing a connecting rod coordinate system on each connecting rod of the ith branched chain based on a D-H method, wherein i is 1,2,3, …,3, and defining a homogeneous transformation matrix from the j-1 connecting rod coordinate system of the ith branched chain to the j connecting rod coordinate system as TijJ is 1,2,3, …,5, as follows:
Figure BDA0002834794780000061
wherein s represents sin, c represents cos, ai(j-1)Represents the length of the connecting rod between the joint axis j-1 and the joint axis j in the branch chain i, dijIs the link offset, α, on the joint axis j in the branch ii(j-1)Denotes the link angle between link j-1 and link j in branch i, θijDenotes ai(j-1)Extension line of (a)ijWhile rotating the resulting joint angle about joint axis j.
Then the kinematic model of the moving platform of the 3-CRU parallel robot relative to the static platform is:
P＝Ti1Ti2Ti3...Ti5。
wherein P is a pose matrix of the moving coordinate system O-XYZ relative to the static coordinate system O-XYZ.
S2, establishing a parallel robot error model based on a matrix method;
and (3) differentiating two sides of the kinematic model respectively to obtain:
Figure BDA0002834794780000071
wherein, Delta is a differential motion matrix of the moving coordinate system relative to the static coordinate system, DeltaijIs a differential motion matrix of the ith branched chain jth connecting rod coordinate system relative to the jth connecting rod coordinate system of the (j-1) th connecting rod;
the differential rotation and differential movement of the ith branched chain j-1 link coordinate system relative to the jth link coordinate system are respectively assumed to be deltaij＝(δxij,δyij,δzij)TAnd dij＝(dxij,dyij,dzij)TThe differential rotation and differential movement of the parallel robot dynamic coordinate system relative to the static coordinate system are respectively delta (delta x, delta y, delta z)TAnd d ═ d (dx, dy, dz)TThen the error matrix at the ith branch and jth link coordinate system can be expressed as:
Figure BDA0002834794780000072
separating error caused by error source from error model, and expressing the error as delta E in the form of L-dimensional differential error vectoriAnd L is the number of error variables caused by error sources, the error model of the ith branch chain of the 3-CRU parallel robot can be rewritten as follows:
Figure BDA0002834794780000073
wherein A isijCan be expressed as:
Aij＝Ti1Ti2…Tij；
the differential rotation and differential movement are separated from the error model and expressed as Δ E in the form of a differential error vectoriThen, the error model of the ith branch of the 3-CRU parallel robot can be rewritten as:
Δ＝[d,δ]T＝Ji·ΔEi；
wherein, JiThe error Jacobian matrix of the ith branch.
S3, simplifying an error model of the 3-CRU parallel robot based on the least parameter linear combination theorem, which is specifically as follows:
to error Jacobian matrix JiPerforming QR decomposition to obtain an upper triangular matrix R, then:
(1) when 0 row exists in the upper triangular matrix R, the parameter corresponding to the 0 row cannot be identified;
(2) when the upper triangular matrix R has the proportional columns, all the parameters corresponding to the proportional columns are combined into one parameter to be identified;
(3) when linear correlation columns exist in the upper triangular matrix R, combining parameters corresponding to all the linear correlation columns into M parameters to be identified, wherein M is the column number of the maximum linear correlation group forming the linear correlation columns;
(4)ΔEithe number of identifiable parameters after simplification is the rank of the upper triangular matrix R.
After simplification, the error model of the ith branched chain becomes:
Δ＝[d,δ]T＝Ji'·ΔEi'；
wherein, J'iAs an error Jacobian matrix JiSimplified matrix, Δ E'iIs a differential error vector Delta EiAnd (5) simplifying the vector.
S4, establishing a 3-CRU parallel robot error identification model based on the terminal error detection information subset, which is as follows:
selecting n position measurement points in the theoretical motion space of the 3-CRU parallel robot, wherein n is more than or equal to K, and K is delta Ei' number of parameters to be identified, then by these measurementsAt most, n groups of three-dimensional attitude errors and n groups of three-dimensional position errors can be obtained through points, one group is arbitrarily selected from the n groups of three-dimensional attitude errors, and n-1 groups are arbitrarily selected from the n groups of three-dimensional position errors to jointly form a terminal pose error detection information subset, so that an error model of the ith branch chain can be written as follows:
Ji”·ΔEi'＝[δ(0),d(1),d(2),...,d(n-1)]T；
wherein, delta(0)Is a selected set of attitude errors, d(t)Is the selected t-th set of position errors, t 1,2,3, …, n-1; j'iIs an error Jacobian matrix matched with the tail end error detection information subset, and substitutes n measuring point positions into Ji' obtaining.
Based on a least square method, the error identification model of the ith branched chain of the 3-CRU parallel robot is as follows:
ΔE'i＝(Ji”T·Ji”)-1·Ji”T·[δ(0),d(1),d(2),...,d(n-1)]T。
s5, measuring the actual pose of the tail end of the 3-CRU parallel robot, and obtaining the error of the pose of the tail end of the 3-CRU parallel robot by making a difference with the theoretical pose, wherein the error is as follows:
as shown in fig. 3, in the laser tracker coordinate system OJThe posture and position of the UVW measurement moving platform coordinate system o-xyz at the zero point are respectivelyoRJAndoPJthen the transformation matrix from the zero coordinate system of the driven platform to the coordinate system of the laser tracker is:
Figure BDA0002834794780000091
similarly, the transformation matrix from the laser tracker coordinate system to the coordinate system of the movable platform at the measuring point is as follows:
Figure BDA0002834794780000092
wherein,JRCandJPCrespectively the attitude and the position of a moving platform coordinate system measured in a laser tracker coordinate system at a measuring point; then, the actual pose of the movable platform at any theoretical measuring point relative to the zero point is as follows:
oTC＝oTJ JTC；
and moving the movable platform to a theoretical position of any measuring point, further obtaining an actual pose of the movable platform relative to a zero point, and obtaining a pose error of the tail end of the parallel robot by subtracting the actual pose from the theoretical pose.
S6, compensating the robot end error based on the identification result of the structure error of the 3-CRU parallel robot, which is as follows:
structural error Delta E obtained by identificationiSubstituting the error model to obtain the error of the movable platform at any theoretical position p (x, y, z, rx, ry, rz) as follows:
Figure BDA0002834794780000093
the practical end pose obtained by compensating the end pose of the 3-CRU parallel robot is as follows:
Figure BDA0002834794780000094
the calibration method is based on the tail end error detection information subset, the set only comprises a group of tail end attitude errors of the parallel robots, and the calibration process can be simpler and more efficient by considering the difficulty of attitude error measurement.
After the error model is established, the calibration method firstly simplifies the structural error to be identified based on the least parameter linear combination theorem, so that the identifiability of the structural error is effectively ensured, and the calibration method is reliable and stable.
The processing process of the experimental data of the calibration method is simple, the experimental data is substituted into a formula to obtain a multivariate linear equation set, and the test result can be quickly obtained by applying MATLAB and other mathematical analysis software.
In conclusion, the parallel robot calibration method based on the terminal error detection information subset has the advantages of simplicity, high efficiency, practicability and quickness, is suitable for parallel robots with 6 degrees of freedom and few degrees of freedom, and has certain reference significance for precision calibration of other mechanisms.
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 as designed.
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 (10)

1. A parallel robot calibration method based on a terminal error detection information subset is characterized by comprising the following steps:
s1, establishing a parallel robot kinematics model based on a D-H method;
s2, establishing a parallel robot error model based on a matrix method;
s3, simplifying the error model of the parallel robot based on the least parameter linear combination theorem;
s4, establishing a parallel robot error identification model based on the tail end error detection information subset;
s5, measuring the actual pose of the tail end of the parallel robot, and obtaining the pose error of the tail end of the parallel robot by making a difference with the theoretical pose;
and S6, compensating the end error of the parallel robot based on the parallel robot structure error identification result.
2. The calibration method of the parallel robot based on the terminal error detection information subset as claimed in claim 1, wherein in step S1, the parallel robot comprises a movable platform, a static platform and I branched chains, each branched chain has N connecting rods, the movable platform and the static platform are connected together through each branched chain; respectively establishing a moving coordinate system O-XYZ and a static coordinate system O-XYZ on the moving platform and the static platform of the parallel robot according to a right-hand rule, establishing a connecting rod coordinate system on each connecting rod of the ith branched chain based on a D-H method, wherein I is 1,2,3, …, I, and defining a homogeneous transformation matrix from the j-1 connecting rod coordinate system of the ith branched chain to the j connecting rod coordinate system as TijJ is 1,2,3, …, N, as follows:
Figure FDA0003418843800000011
wherein s represents sin, c represents cos, ai(j-1)Represents the length of the connecting rod between the joint axis j-1 and the joint axis j in the branch chain i, dijIs the link offset, α, on the joint axis j in the branch ii(j-1)Denotes the link angle between link j-1 and link j in branch i, θijDenotes ai(j-1)Extension line of (a)ijWhile rotating the resulting joint angle about joint axis j.
3. The method for calibrating the parallel robot based on the tail end error detection information subset as claimed in claim 2, wherein the kinematic model of the movable platform of the parallel robot relative to the static platform is as follows:
P＝Ti1Ti2Ti3...TiN；
wherein P is a pose matrix of the moving coordinate system O-XYZ relative to the static coordinate system O-XYZ.
4. The method for calibrating parallel robots based on the end error detection information subset as claimed in claim 3, wherein in step S2, the two sides of the kinematic model are differentiated respectively to obtain:
Figure FDA0003418843800000021
wherein, Delta is a differential motion matrix of the moving coordinate system relative to the static coordinate system, DeltaijIs a differential motion matrix of the ith branched chain jth connecting rod coordinate system relative to the jth connecting rod coordinate system of the (j-1) th connecting rod;
the differential rotation and differential movement of the ith branched chain j-1 link coordinate system relative to the jth link coordinate system are respectively assumed to be deltaij＝(δxij,δyij,δzij)TAnd dij＝(dxij,dyij,dzij)TThe differential rotation and differential movement of the parallel robot dynamic coordinate system relative to the static coordinate system are respectively delta (delta x, delta y, delta z)TAnd d ═ d (dx, dy, dz)TThen the error matrix at the ith branch and jth link coordinate system can be expressed as:
Figure FDA0003418843800000022
analyzing error sources existing in the parallel robot, converting error variables caused by the error sources into differential rotation and differential movement, and substituting the differential rotation and the differential movement into deltaijThen, the error model of the ith branch chain is:
Figure FDA0003418843800000023
wherein A isijCan be expressed as:
Aij＝Ti1Ti2…Tij；
separating error caused by error source from error model, and expressing the error as delta E in the form of L-dimensional differential error vectoriAnd L is the number of error variables caused by error sources, the error model of the ith branch chain of the parallel robot can be rewritten as follows:
Δ＝[dΤ,δΤ]Τ＝Ji·ΔEi；
wherein, JiThe error Jacobian matrix of the ith branch.
5. The method for calibrating parallel robots based on the end error detection information subset as claimed in claim 4, wherein in step S3, the Jacobian matrix J is applied to the erroriPerforming QR decomposition to obtain an upper triangular matrix R, then:
(1) when 0 row exists in the upper triangular matrix R, the parameter corresponding to the 0 row cannot be identified;
(2) when the upper triangular matrix R has the proportional columns, all the parameters corresponding to the proportional columns are combined into one parameter to be identified;
(3) when linear correlation columns exist in the upper triangular matrix R, combining parameters corresponding to all the linear correlation columns into M parameters to be identified, wherein M is the column number of the maximum linear correlation group forming the linear correlation columns;
(4)ΔEithe number of identifiable parameters after simplification is the rank of the upper triangular matrix R.
6. The method for calibrating the parallel robot based on the terminal error detection information subset as claimed in claim 5, wherein the error model of the i-th branch chain after simplification is changed into:
Δ＝[dΤ,δΤ]Τ＝Ji'·ΔEi'；
wherein, J'iAs an error Jacobian matrix JiSimplified matrix, Δ E'iFor the differential error vector Δ E to be identifiediAnd (5) simplifying the vector.
7. The method for calibrating the parallel robot based on the end error detection information subset according to claim 6, wherein the step S4 is as follows:
selecting n position measurement points in the theoretical motion space of the parallel robot, wherein n is more than or equal to K, and K is delta E'iIf the number of the parameters to be identified is greater than the number of the parameters to be identified, n groups of three-dimensional attitude errors and n groups of three-dimensional position errors can be obtained at most through the position measuring points, one group of the n groups of three-dimensional attitude errors is selected at will, and n-1 groups of the n groups of three-dimensional position errors are selected at will to form a terminal pose error detection information subset, so that an error model of the ith branch chain can be rewritten as follows:
[δ(0),d(1),d(2),...,d(n-1)]Τ＝Ji”·ΔEi'；
wherein, delta(0)Is a selected set of attitude errors, d(t)Is the selected t-th set of position errors, t 1,2,3, …, n-1; j ″)iAn error Jacobian matrix matching the end error detection information subset by substituting n position measurement points into J'iAnd (4) obtaining the product.
8. The calibration method of the parallel robot based on the terminal error detection information subset as claimed in claim 7, wherein based on the least square method, the error identification model of the ith branch chain of the parallel robot is:
ΔE′i＝(J″i Τ·J″i)-1·J″i Τ·[δ(0),d(1),d(2),...,d(n-1)]Τ。
9. the method for calibrating the parallel robot based on the end error detection information subset according to claim 8, wherein the step S5 is as follows:
in a reference coordinate system OJThe posture and position of the UVW measurement moving platform coordinate system o-xyz at the zero point are respectivelyoRJAndoPJthen is drivenThe transformation matrix from the platform zero coordinate system to the reference coordinate system is:
Figure FDA0003418843800000041
similarly, the transformation matrix from the reference coordinate system to the coordinate system of the movable platform at the measuring point is as follows:
Figure FDA0003418843800000042
wherein,JRCandJPCrespectively the attitude and position of the moving platform coordinate system measured in the reference coordinate system at the measuring point; then, the actual pose of the movable platform at any theoretical measuring point relative to the zero point is as follows:
oTC＝oTJ JTC；
and moving the movable platform to a theoretical position of any measuring point, further obtaining an actual pose of the movable platform relative to a zero point, and obtaining a pose error of the tail end of the parallel robot by subtracting the actual pose from the theoretical pose.
10. The method for calibrating the parallel robot based on the end error detection information subset according to any one of claims 1 to 9, wherein the step S6 is as follows:
identifying the obtained structure error delta E'iSubstituting the error model to obtain the error of the movable platform at any theoretical position p (x, y, z, rx, ry, rz) as follows:
Figure FDA0003418843800000043
the practical end pose obtained by compensating the end pose of the parallel robot is as follows:
Figure FDA0003418843800000044
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108015808A (en) * 2017-12-07 2018-05-11 天津大学 A kind of Kinematic Calibration method of series-parallel robot
CN110900610A (en) * 2019-12-11 2020-03-24 哈尔滨工业大学 Industrial robot calibration method based on LM algorithm and particle filter algorithm optimization

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20050038563A1 (en) * 2003-08-16 2005-02-17 Abdul Rauf Device and method for kinematic calibration of robots
JP4464318B2 (en) * 2005-05-16 2010-05-19 オークマ株式会社 Calibration method for parallel mechanism machine
CZ302911B6 (en) * 2007-10-31 2012-01-18 Cvut V Praze Device for a body's spherical motion control
CN106813638B (en) * 2017-03-15 2018-05-18 吉林大学 A kind of 3RPS parallel robots geometric parameter discrimination method
CN107116537A (en) * 2017-06-15 2017-09-01 燕山大学 A kind of constant Jacobi parallel institution of branch containing five degree of freedom
CN107627299B (en) * 2017-09-12 2019-10-25 中国科学技术大学 A kind of kinematic parameter errors scaling method of rope driving parallel robot
CN110815206B (en) * 2018-08-14 2022-11-29 中国科学院沈阳自动化研究所 Kinematics calibration method for Stewart parallel robot
CN110977940B (en) * 2019-11-28 2021-04-23 清华大学 Geometric error modeling method and device for parallel-series robot

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108015808A (en) * 2017-12-07 2018-05-11 天津大学 A kind of Kinematic Calibration method of series-parallel robot
CN110900610A (en) * 2019-12-11 2020-03-24 哈尔滨工业大学 Industrial robot calibration method based on LM algorithm and particle filter algorithm optimization

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