CN104408299B - Robot location's error compensating method based on distance identification redundancy kinematics parameters - Google Patents
Robot location's error compensating method based on distance identification redundancy kinematics parameters Download PDFInfo
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Abstract
The invention discloses a kind of robot location's error compensating methods based on distance identification redundancy kinematics parameters to pass through the nuisance parameter in first rejecting kinematics parameters, determine robot recognizes kinematics parameters, then parameter error computation model is calculated, and it is compensated for the parameter error, it is avoided that the problem of encountering singular matrix, effectively reduce calculation amount, improve accuracy, and compensation effect is significant, the standard deviation for greatly reducing the range error of robot greatly improves robot localization precision.The present invention is based on robot location's error compensating methods of distance identification redundancy kinematics parameters can be widely applied in robot research field.
Description
Technical field
The present invention relates to a kind of robot location's error compensating methods, more particularly to a kind of distance identification redundancy that is based on to move
Learn robot location's error compensating method of parameter.
Background technique
The repeatable accuracy of industrial robot is generally all very high, and usually within 0.1mm, the robot of early stage mostly uses teaching
Therefore programming only needs repeatable accuracy height to be able to satisfy industrial requirement.But with the application range further expansion of robot, machine
Device people's off-line programing is also more and more common, and positioning accuracy is very low, is unable to satisfy the required precision of off-line programing.It measures simultaneously
The coordinate transform between measuring system coordinate system and robot coordinate system is necessarily referred to when the absolute positional accuracy of robot, this transformation
Matrix is difficult accurately to measure, and the measurement accuracy for eventually leading to entire measuring system reduces, therefore IS09283:1998 standard, uses
Range error carries out accuracy detection specifically for the robot of off-line programing.Zhou Xuecai is according to space any two points in existing literature
Coordinate under different orthogonal coordinate system is different, but its distance be it is identical, introduce distance carry out exterior syndrome robot coordinate
Transformation between system is measured using the method that range error detects；Zhang Tie obtains MDH for DH model modification using Hayati
Model introduces the micro component rotated around y-axis, meanwhile, and eliminate the micro component of respective link distance；Cai Hegao etc. is utilized and is repaired
Positive D-H Mo Xing has derived the relationship between the practical geometric parameter of robot and tool position and attitude error；King's first-class is using amendment
D-H parameter model establish the Model of locating error of robot relative positional accuracy.
Robot precision is detected by range error method, and robot coordinate system and measurement coordinate can be reduced
System converts and increased error, but research distance model uses the analysis method of geometry above, needs craftsmenship stronger；And
And the kinematic parameter errors in whole joints are compensated, the error parameter matrix used in solution procedure can generate singular value,
Solving singular value, justice can lose the partial information of kinematics parameters in the process.
Summary of the invention
In order to solve the above-mentioned technical problem, the object of the present invention is to provide one kind to be avoided that occurring singular value, reduces and calculates
Robot location's error compensating method based on distance identification redundancy kinematics parameters of error.
The technical scheme adopted by the invention is that:
Robot location's error compensating method based on distance identification redundancy kinematics parameters, comprising the following steps:
A, robot kinematics' model is established, base of the end effector coordinate system relative to robot of robot is obtained
Mark the transformation matrix of coordinates of system；
B, robot kinematics' parameter error selection analysis is carried out to transformation matrix of coordinates to calculate, obtain each joint of robot
Recognize kinematics parameters；
C, kinematics parameters are recognized according to each joint of robot, compensation pseudo inverse matrix and joint of robot is calculated
Error parameter model；
D, according to end effector of robot instruction distance, laser tracker measurement obtain actual range, can recognize
Kinematics parameters, compensation pseudo inverse matrix and joint of robot error parameter model, are calculated parameter error computation model；
E, control robot is repeatedly moved, and is detected the instruction distance of the end effector of robot moved every time and is swashed
The actual range that optical tracker system measurement obtains；
F, according to parameter error computation model, the instruction of the end effector of robot moved every time that detection is obtained away from
Least square method is used from the actual range obtained with laser tracker measurement, obtains robot kinematics' parameter error；
G, according to robot kinematics' parameter error, new robot kinematics' parameter is calculated, robot is mended
It repays.
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
It improves, robot kinematics' parameter error selection analysis is carried out to transformation matrix of coordinates in the step B and is calculated, specifically:
QR decomposition is carried out to transformation matrix of coordinates.
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
It improves, the step C includes:
C1, kinematics parameters are recognized according to each joint of robot, to corresponding kinematics parameters on any one joint
Differential is carried out, the change in location matrix for corresponding to the joint is obtained；
C2, according to the change in location matrix in the corresponding joint, show that the articular kinesiology parameter error is mapped to robot
Basis coordinates caused by location error；
C3, it the articular kinesiology parameter error is mapped to location error caused by the basis coordinates of robot transforms to machine
Device people's end effector coordinate, obtains the differential error transformation matrix of end effector of robot；
C4, it is mapped to according to the differential error transformation matrix and articular kinesiology parameter error of end effector of robot
Location error caused by the basis coordinates of robot obtains compensation pseudo inverse matrix and joint of robot error parameter model.
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
Improve, robot kinematics' model uses MDH kinematics model, the end effector coordinate system of the robot relative to
The transformation matrix of coordinates of the basis coordinates system of robot is indicated by MDH kinematics model parameter.
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
It improves, parameter error computation model in the step D are as follows:
Wherein, δ k expression parameter error,Indicate that the laser tracker measurement of j and j+1 two o'clock obtains it is practical away from
From,Indicate the instruction distance of the end effector of robot of j and j+1 two o'clock, HjAnd Hj+1Respectively indicate j and j+1 two o'clock
Compensation pseudo inverse matrix.
The beneficial effects of the present invention are:
The present invention is based on robot location's error compensating methods of distance identification redundancy kinematics parameters by first rejecting fortune
The dynamic nuisance parameter learned in parameter determines the kinematics parameters that recognize of robot, and compensates for the parameter, is avoided that
The problem of encountering singular matrix effectively reduces calculation amount, improves accuracy, and compensation effect is significant, greatly reduces robot
Range error standard deviation, greatly improve robot localization precision.
Detailed description of the invention
Specific embodiments of the present invention will be further explained with reference to the accompanying drawing:
Fig. 1 is the step of the present invention is based on robot location's error compensating methods of distance identification redundancy kinematics parameters stream
Cheng Tu；
Fig. 2 is that the present invention is based on robot location's error compensating method step C of distance identification redundancy kinematics parameters
Flow chart of steps.
Specific embodiment
With reference to Fig. 1-Fig. 2, the present invention is based on robot location's error compensating method of distance identification redundancy kinematics parameters,
The following steps are included:
A, robot kinematics' model is established, base of the end effector coordinate system relative to robot of robot is obtained
Mark the transformation matrix of coordinates of system；
B, robot kinematics' parameter error selection analysis is carried out to transformation matrix of coordinates to calculate, obtain each joint of robot
Recognize kinematics parameters；
C, kinematics parameters are recognized according to each joint of robot, compensation pseudo inverse matrix and joint of robot is calculated
Error parameter model；
D, according to end effector of robot instruction distance, laser tracker measurement obtain actual range, can recognize
Kinematics parameters, compensation pseudo inverse matrix and joint of robot error parameter model, are calculated parameter error computation model；
E, control robot is repeatedly moved, and is detected the instruction distance of the end effector of robot moved every time and is swashed
The actual range that optical tracker system measurement obtains；
F, according to parameter error computation model, the instruction of the end effector of robot moved every time that detection is obtained away from
Least square method is used from the actual range obtained with laser tracker measurement, obtains robot kinematics' parameter error；
G, according to robot kinematics' parameter error, new robot kinematics' parameter is calculated, robot is mended
It repays.
Wherein, { 0 } indicates the basis coordinates system of robot, and { 1 }~{ 5 } indicate the coordinate system of joint of robot, and { 6 } indicate machine
The end effector coordinate system of device people, { M } indicate external measurement coordinate system, that is, laser tracker measurement coordinate system.0TeExpression machine
Transformation matrix of coordinates between the basis coordinates system of device people and the coordinate system of end effector of robot,
MT6=MT0·0T6
Then for:
0T6=(MT0)-1·MT6=A1A2A3A4A5A6
Basis coordinates for full rotation robot are overlapped with the first axial coordinate of robot, i.e., { 0 } coordinate system is machine
First joint coordinate system of human body's coordinate system.A1... ..., A6For the homogeneous coordinates of simple joint, using range error identification side
Method, the error and end effector error of the basis coordinates system of robot are unrelated.
Kinematics model generallys use the expression of D-H parameter, the transformation matrix between adjacent two connecting rod are as follows:
But the joint shaft parallel for two, the error that lesser error can cause end effector very big, and DH mould
Type cannot describe the minor change between parallel joint shaft.MDH kinematics model has modified DH model, introduces torsional angle βiIt indicates
Rotation angle of each joint coordinate system relative to Y-axis, the transformation matrix A in jointiBecomeIt is indicated are as follows:
Therein to write a Chinese character in simplified form: c indicates that cos, s indicate sin.
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
It improves, robot kinematics' parameter error selection analysis is carried out to transformation matrix of coordinates in the step B and is calculated, specifically:
QR decomposition is carried out to transformation matrix of coordinates.
It is calculated according to robot kinematics' parameter error selection analysis, QR decomposition is carried out to transformation matrix of coordinates, obtains this
Each joint of robot recognizes kinematics parameters in invention, and cognizable parameter is further reduced can identified parameters to 21.
The cognizable kinematics parameters table of robot is as follows in the present invention:
Table 1
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
It improves, the step C includes:
C1, kinematics parameters are recognized according to each joint of robot, to corresponding kinematics parameters on any one joint
Differential is carried out, the change in location matrix for corresponding to the joint is obtained；
C2, according to the change in location matrix in the corresponding joint, show that the articular kinesiology parameter error is mapped to robot
Basis coordinates caused by location error；
C3, it the articular kinesiology parameter error is mapped to location error caused by the basis coordinates of robot transforms to machine
Device people's end effector coordinate, obtains the differential error transformation matrix of end effector of robot；
C4, it is mapped to according to the differential error transformation matrix and articular kinesiology parameter error of end effector of robot
Location error caused by the basis coordinates of robot obtains compensation pseudo inverse matrix and joint of robot error parameter model.
If the position of end effector of robot is x=g (k), k is the total movement parameter of robot, k=[θ1 a1
d1 α1 β1…θi ai di αi βi … θn an dn αn βn]
The differential relationship of change in location and kinematics parameters for the generation in each joint are as follows:
Wherein,Indicate physical location.
Carrying out differential for the kinematics parameters on the joint to any one joint of robot can obtain:
Then ΔiAre as follows: Δi=(Ai)-1δAi
4 × 4 matrixes0T6Preceding 3 × 3 submatrix indicate end effector posture, εiIndicate that end effector position is missed
Difference.
Location error caused by any one basis coordinates of joint parameter error map to robot of robot is ei:
kiFor any articular kinesiology parameter: when the joint i is parallel with the joint i+l, ki=[θi aidi αi βi]T, joint i
Kinematic parameter errors be δ ki=[δ θi δai δdi δαi δβi]T；The k when joint i is not parallel with the joint i+li=[θi ai
di αi]T, kinematic parameter errors are δ ki=[δ θi δai δdiδαi]T。GiFor robot inaccuracy coefficient matrix.
The error e generated for any one jointi, it is the error generated relative to robot basis coordinates, and actually survey
Amount is end effector, it is therefore desirable to by these error transforms to end effector of robot coordinate, be introducednUiFor robot
Coordinate conversion matrix of the joint i-l to robot end:
JiThe error transform of differential transform by any joint i-l to end effector is to end effector of robot, JiFor
The differential error of robot end converts, and the solution of Ji is correspondingnUiIn each vector.
X indicates end effector of robot to robot basis coordinates system position x=[px,py,pz], δ x be robot for
Measure the error of resulting robot location and robot instruction position.
Then joint of robot error parameter model are as follows:
Wherein, H indicates supplement pseudo inverse matrix.
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
Improve, robot kinematics' model uses MDH kinematics model, the end effector coordinate system of the robot relative to
The transformation matrix of coordinates of the basis coordinates system of robot is indicated by MDH kinematics model parameter.
As the further of robot location's error compensating method based on distance identification redundancy kinematics parameters
It improves, parameter error computation model in the step D are as follows:
Wherein, δ k expression parameter error,Indicate that the laser tracker measurement of j and j+1 two o'clock obtains it is practical away from
From,Indicate the instruction distance of the end effector of robot of j and j+1 two o'clock, HjAnd Hj+1Respectively indicate j and j+1 two o'clock
Compensation pseudo inverse matrix.
The position of robot any two points j and j+1 are as follows:
xj=f (kj) and xk=f (kj+1)
Coordinate resulting for robot instruction isWithMeasuring resulting coordinate for measuring instrument isWith
For the distance of the two o'clock coordinate of robot arbitrary motion are as follows: xj,j+1=xj-xj+1
Then two o'clock instructs distance are as follows:
Then two o'clock actual range are as follows:
Due to δ xj=Hjδ k, δ xj+1=Hj+1δ k,
Robot any point measures gained and instructs the error between resulting are as follows:
The actual range of j and j+1 two o'clock are as follows:
Using square being expressed as actual range:
Ignore quadratic term, obtain:
Therefore, parameter error computation model is obtained are as follows:
Then least square method is used, by repeated detection as a result, multiple range errors of formation, show that robot transports
It is dynamic to learn parameter errorThen basisNew kinematics parameters are calculated, robot is compensated.
The kinematics parameters table obtained after robot compensation is as follows:
Table 2
It is to be illustrated to preferable implementation of the invention, but the invention is not limited to the implementation above
Example, those skilled in the art can also make various equivalent variations on the premise of without prejudice to spirit of the invention or replace
It changes, these equivalent deformations or replacement are all included in the scope defined by the claims of the present application.
Claims (3)
1. robot location's error compensating method based on distance identification redundancy kinematics parameters, it is characterised in that: including following
Step:
A, robot kinematics' model is established, basis coordinates system of the end effector coordinate system relative to robot of robot is obtained
Transformation matrix of coordinates；
B, transformation matrix of coordinates is decomposed by QR and carries out the calculating of robot kinematics' parameter error selection analysis, obtain robot
Each joint recognizes kinematics parameters；
C, kinematics parameters are recognized according to each joint of robot, compensation pseudo inverse matrix and joint of robot error is calculated
Parameter model；
D, according to end effector of robot instruction distance, laser tracker measurement obtain actual range, movement can be recognized
Parameter, compensation pseudo inverse matrix and joint of robot error parameter model are learned, parameter error computation model is calculated；
E, control robot is repeatedly moved, the instruction distance of end effector of robot that detection moves every time and laser with
The actual range that track instrument measurement obtains；
F, according to parameter error computation model, the instruction distance for the end effector of robot moved every time that detection is obtained and
The actual range that laser tracker measurement obtains uses least square method, obtains robot kinematics' parameter error；
G, according to robot kinematics' parameter error, new robot kinematics' parameter is calculated, robot is compensated；
Parameter error computation model in the step D are as follows:
Wherein, δ k expression parameter error,Indicate the actual range that the laser tracker measurement of j and j+1 two o'clock obtains,Indicate the instruction distance of the end effector of robot of j and j+1 two o'clock, HjAnd Hj+1Respectively indicate the benefit of j and j+1 two o'clock
Repay pseudo inverse matrix.
2. robot location's error compensating method according to claim 1 based on distance identification redundancy kinematics parameters,
It is characterized by: the step C includes:
C1, kinematics parameters are recognized according to each joint of robot, kinematics parameters corresponding on any one joint is carried out
Differential obtains the change in location matrix for corresponding to the joint；
C2, according to the change in location matrix in the corresponding joint, show that the articular kinesiology parameter error is mapped to the base of robot
Location error caused by coordinate；
C3, it the articular kinesiology parameter error is mapped to location error caused by the basis coordinates of robot transforms to robot
End effector coordinate obtains the differential error transformation matrix of end effector of robot；
C4, machine is mapped to according to the differential error transformation matrix and articular kinesiology parameter error of end effector of robot
Location error caused by the basis coordinates of people obtains compensation pseudo inverse matrix and joint of robot error parameter model.
3. robot location's error compensating method according to claim 1 based on distance identification redundancy kinematics parameters,
It is characterized by: robot kinematics' model uses MDH kinematics model, the end effector coordinate system of the robot
The transformation matrix of coordinates of basis coordinates system relative to robot is indicated by MDH kinematics model parameter.
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| CN106737855B (en) * | 2016-08-22 | 2019-07-02 | 南京理工大学 | A kind of robot precision's compensation method of comprehensive position and attitude error model and rigidity compensation |
| CN106584464B (en) * | 2016-12-31 | 2019-11-12 | 重庆大学 | The dummy vehicle transmission chain error compensation method of decoupling mechanism in a kind of captive trajectory testing |
| CN107175660B (en) * | 2017-05-08 | 2019-11-29 | 同济大学 | A kind of six-freedom degree robot kinematics scaling method based on monocular vision |
| CN107443382B (en) * | 2017-09-12 | 2020-09-22 | 清华大学 | Industrial robot structure parameter error identification and compensation method |
| CN108638060B (en) * | 2018-05-03 | 2021-09-28 | 大连理工大学 | Method for analyzing and rejecting redundant parameters in multi-degree-of-freedom machine ginseng number calibration |
| CN108818540B (en) * | 2018-08-28 | 2021-12-10 | 珠海格力智能装备有限公司 | Method and apparatus for compensating parameter, processor and storage medium |
| CN110181509A (en) * | 2019-05-14 | 2019-08-30 | 浙江树人学院（浙江树人大学） | A kind of industrial robot motion control method based on error compensation |
| CN111055273B (en) * | 2019-05-16 | 2022-10-11 | 广西大学 | Two-step error compensation method for robot |
| CN112880555B (en) * | 2021-01-06 | 2022-03-22 | 浙江吉利控股集团有限公司 | Calibration method and system of coordinate system |
| CN114083534B (en) * | 2021-11-11 | 2023-05-23 | 浙江大学 | Mechanical arm kinematics MDH parameter calibration method based on self-adaptive gradient descent |
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