CN105773622B - A kind of industrial robot absolute precision calibration method based on IEKF - Google Patents
A kind of industrial robot absolute precision calibration method based on IEKF Download PDFInfo
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- CN105773622B CN105773622B CN201610297771.0A CN201610297771A CN105773622B CN 105773622 B CN105773622 B CN 105773622B CN 201610297771 A CN201610297771 A CN 201610297771A CN 105773622 B CN105773622 B CN 105773622B
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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
- B25J9/1679—Programme controls characterised by the tasks executed
- B25J9/1692—Calibration of manipulator
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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
Abstract
The invention discloses a kind of industrial robot absolute precision calibration method based on IEKF, it is characterized in that: by establishing parameter error model, data sampling is carried out to robot end position in cartesian space using laser tracking system, to obtain the location error under different coordinates；Parameter vector to be identified is constructed using the kinematics model of geometric parameter nominal value building robot, and in conjunction with Vector product, to obtain parameter Jacobian matrix；The parameter error in parameter error model is recognized using IEKF algorithm, by iterative calculation, to obtain the parameter error of robot.Finally geometric parameter nominal value is modified using parameter error, completes the Kinematic Calibration of industrial robot, realizes the absolute precision calibration of robot.Robot absolute precision calibration method provided by the invention based on IEKF is suitable for any series connection revolute robot and any selective compliance assembly robot arm.
Description
Technical field
The present invention relates to Robot calibration technical fields, and more particularly to one kind, based on IEKF, (iteration spreading kalman is filtered
Wave) industrial robot absolute precision calibration method.
Background technique
The high-end high performance industrial robot of manufacturing industry urgent need, this be also improve entire manufacture system productivity,
The important link for reducing production cost, improving product quality.The positioning accuracy of robot is reflect robot comprehensive performance one
A important indicator mainly includes repetitive positioning accuracy and absolute fix precision.Currently, the repetitive positioning accuracy ratio of industrial robot
It is higher, and its absolute fix precision is lower, it is difficult to meet the production requirement of high-precision industry spot.
The position error of robot is to be broadly divided into geometric error and non-geometric mistake as caused by many factors collective effect
Difference.Wherein, with the geometry such as the error of the manufacture of each connecting rod of robot, assembly and installation, reference frame and actual coordinates because
Element accounts for the 80% of overall error.Therefore, industrial robot needs to carry out Kinematic Calibration to it using calibration technique before use,
The parameter error for picking out robot is modified geometric parameter nominal value, thus to the absolute fix precision of robot into
Row calibration.
Traditional robot localization precision calibration can be divided into: compensate based on neural network penalty method, based on interpolation thought
Method, differential error penalty method, joint space penalty method.It compensates to be divided into again according to modeling pattern and has modelling by mechanism and Experimental modeling
Two major classes.Differential error penalty method and joint space penalty method are a kind of modes compensated according to the Kinematics Law of robot,
Belonging to has modelling by mechanism.And neural network penalty method and interpolation thought penalty method are research Robot Object Models, and estimate its input
With the modeling method of output, belong to Experimental modeling, also known as method of black box.
Experimental Modeling mainly carries out data sampling in robot localization precision aspect with gridding sampled point, then sharp
With neural network model, or similarity relationship is established, or other errors in space is modeled using interpolating method,
Certain compensation effect can be reached.But current problems faced is the step-length of space lattice since the difference of robot needs in this respect
A large amount of time determination is carried out, without theory support, and the data sampled need to be solidificated in the control system of robot
In, and data volume is very big, so that this method practical application value is little.Mechanism modeling method is according to robot kinematics
Then error compensation is modified geometric parameter nominal value by regular identified parameters error.Domestic and foreign scholars propose at present
Linear least squares method method, LM-LS (Levenberg-Marquardt least square) discrimination method, EKF (spreading kalman filter
Wave) discrimination method etc., least square method is easy first to enter singularity problem in use, and scholar proposes for this situation
LM-LS algorithm.Some scholars propose EKF method to make up and use precision when linear least squares method low and identification process
The problems such as time-consuming, but EKF passes through Taylor series expansion and ignores higher order term and linearize to nonlinear system model, this nothing
Method can introduce truncated error with avoiding, and cause the precision recognized to robot parameter error still poor.
Summary of the invention
It is low object of the present invention is to be directed to industrial robot absolute fix precision, propose a kind of industrial robot based on IEKF
Absolute precision calibration method.
To achieve the goals above, the present invention is achieved through the following technical solutions:
Step 1: establishing robot kinematics' model；
Step 2: establishing robot parameter error model；
Step 3: carrying out data sampling in robot cartesian space；
Step 4: constructing parameter vector using Vector product, the parameter Jacobian matrix J under different data sampling is calculatedj,
J=1,2 ... k, k are data sampling number；
Step 5: the parameter error in parameter error model is recognized using IEKF algorithm, by iterating to calculate, when
When meeting some requirements, the parameter error Δ s that is picked out；
Step 6: the parameter error picked out is modified geometric parameter nominal value, the absolute essence of robot is realized
Degree calibration.
According to above technical solution, may be implemented it is below the utility model has the advantages that
(1) the industrial robot absolute precision calibration method of the invention based on IEKF is suitable for any series connection joint type machine
Device people and any selective compliance assembly robot arm, method universal strong；
(2) parameter error model of the present invention considers all geometric parameters of robot body, after identification
Parameter error is compensated into robot geometric parameter nominal value, can be effectively to robot precision closer to realistic model
Realize calibration；
(3) it is recognized due to being directed to parameter error, the valid data after identification are seldom, data will not be brought to store
Problem；
(4) present invention constitutes identification algorithm using IEKF and distinguishes compared to least square method and modified least square method
It is fast to know speed, precision is high；Compared to EKF algorithm, reduce the linearized stability of nonlinear filtering, preferably approaches machine ginseng
Several time of days, improves identification precision.
Detailed description of the invention
Robot cartesian space data sampling schematic diagram Fig. 1 of the invention；
Concrete operations process Fig. 2 of the invention.
Specific embodiment
For the object, technical solutions and advantages of the present invention etc. are more clearly understood, with reference to embodiments, and referring to attached
Figure, the present invention is described in more detail.
A kind of industrial robot absolute precision calibration method based on IEKF, operational flowchart is as shown in Fig. 2, the method
The following steps are included:
Step 1: establishing robot kinematics' model, comprising the following steps:
Step (1) constructs robot kinematics' model using D-H rule.
Kinematic relation in D-H rule, between adjacent two bar are as follows:
It is the movement of connecting rod i and connecting rod i-1 in formulaRelationship, aiFor length of connecting rod, diFor connecting rod offset distance, αiTo close
Save torsional angle, θiFor joint rotation angle.
Step (2), each homogeneous transform matrix is successively defined asThen from the pedestal of robot to
Total transformation between robot end's tool coordinates system are as follows:
Wherein nn、on、anFor the direction vector of robot end, gnFor the position of robot end, n is joint of robot
Number, such as the robot of a six degree of freedom, corresponds to 6 homogeneous transform matrix.
Step (3), according to homogeneous transform matrix, the theoretical coordinate P of available robot endt。
Pt=F (a, d, α, θ) (3)
Step 2: establishing robot parameter error model, comprising the following steps:
Step (1), due to the presence of parameter error, the actual coordinate P of robot endm, PmFor measurement gained.
Pm=F (a, d, α, θ, Δ s)=F (a+ Δ a, d+ Δ d, α+Δ α, θ+Δ θ) (4)
Wherein, Δ s is made of Δ a, Δ d, Δ α, Δ θ, is parameter error existing for robot.
Step (2) calculates the difference Δ P of physical location and theoretical position.
Linearization process is carried out to formula (5)
Wherein, Δ s is the parameter error of robot, Δ s=[Δ a1 Δd1 Δα1 Δθ1…Δan Δdn Δαn Δ
θn]T, J is a parameter Jacobian matrix related with Δ P and Δ s,
N is joint of robot number.General J can be calculated by Vector product and be obtained, and the column vector of J is calculated by following formula:
Jai=[ni], JDi=[ai], Jαi=[ni×gi], Jθi=[ai×gi] (7)
Wherein, ni、oi、aiIt is the direction vector of i-th of connecting rod, is about i-th connecting rod relative to end effector
Position.
Step 3: carrying out data sampling in robot cartesian space, comprising the following steps:
The transformational relation between robot cartesian coordinate system and laser tracking system coordinate system is initially set up before measurement, this
Assume to have had built up coordinate transformation relation in embodiment.
In the cartesian space of robot as far as possible uniformly choose k coordinate points, make robot from dead-center position with
Machine posture reaches theory j point coordinate PT, j, and the joint rotation angle θ of corresponding record robot demonstratorj, use laser tracking system
Measurement conversion obtains the practical j point coordinate P of robotM, j, j=1,2 ... k.
Step 4: calculating the parameter Jacobian matrix J under different coordinatesj, j=1,2 ... k, JjFor the matrix of 3 × m, m is
Number of parameters to be identified.
In real process, the direction in each joint of robot measurement is difficult, the general side calculated using Vector product
Formula obtains.
It is corresponding to calculate in j-th point of theoretical cartesian coordinate, it successively calculates in the process, can calculate at this time pair
The n answeredI, j、oI, j、qI, j、gI, j, each joint is calculated in the formula provided according to step 2Finally construct parameter Jacobian matrix Jj。
Wherein, n is joint of robot number, i=1,2 ... n, j=1,2 ... k.
Step 5: being recognized using IEKF algorithm to the parameter error in parameter error model, the ginseng picked out
Number error delta s, Δ s are the matrix of m × 1, and m is number of parameters to be identified.
IEKF algorithm is the parameter error Δ s for determining robot, and IEKF algorithm is used for robot geometric parameter
In error identification, steps are as follows.
Step (1) calculates the observation vector Z of jth pointj:
Zj=Δ Pj=PM, j-PT, jJ=1,2 ... k (9)
Wherein, ZjFor 3 × 1 matrix.
Step (2), initiation parameter error
Wherein,For the matrix of m × 1, m is number of parameters to be identified；I=1, j=1, i are iteration count, i=
1,2 ... w, w are maximum number of iterations；J is data sampling point, j=1,2 ... k；
Step (3), state one-step prediction:
Wherein,For the state estimation of the sampled point j-1 of i-th iteration；For the sampled point j of i-th iteration
Status predication.
Step (4) predicts error covariance matrix:
Wherein,For the error covariance matrix estimation of the sampled point j-1 of i-th iteration；For adopting for i-th iteration
The error covariance matrix of sampling point j is predicted, is the matrix of m × m, and m is number of parameters to be identified.Q is the variance intensity of process noise W
Battle array is obtained by carrying out mathematical statistics to process signal, in industrial robot, generally takes empirical value Q=10-4Im×m, m be to
The number of parameters of identification.
Step (5) updates filtering gain matrix:
Wherein,It is the matrix of m × 3 for the filtering gain matrix of the sampled point j-1 of i-th iteration, m is to be identified
Number of parameters.R is the variance intensity battle array of observation noise V, and the measurement accuracy according to laser tracking system obtains, and is 3 × 3 square
Battle array.
Step (6) updates state estimation:
Wherein,To observe new breath, It is newly ceased for state, For the state estimation of the sampled point j of i-th iteration.
This method and the difference of EKF identification algorithm are, using the state-updating mode of IEKF using the new breath of observation
It newly ceases and is updated with state, and EKF identification algorithm is updated using observation vector, therefore can using IEKF identification algorithm
So that the error of parameter Estimation further decreases.
Step (7), estimation error variance battle array:
Step (8) updates observation vector
Wherein,For theoretical correction position,For observation vector.
Step (9) updates the number of iterations i or j.If all sampled datas are used in both, i is incremented by, and j is from k to 1；Otherwise,
Use next sampled data.
Repeat step (3) to (9).It enablesIf dmin> d, then dmin=d,Otherwise,Wherein dminFor minimum average B configuration error.When continuous h iteration is not all updated, iteration stopping, then it is assumed that ginseng
Number error amount has restrained stabilization, obtains optimal parameter error Δ s at this time, general h takes 4.
Step 6: the parameter error picked out is modified geometric parameter nominal value, the absolute essence of robot is realized
Degree calibration.The parameter error picked out is Δ s, sg=sn+ Δ s, snFor robot geometric parameter nominal value, sgIt is several for robot
What parameter true value.
Claims (1)
1. a kind of industrial robot absolute precision calibration method based on iterative extended Kalman filter, specifically includes following
Step:
Step 1: establishing robot kinematics' model；
Step 2: establishing robot parameter error model；
Step 3: carrying out data sampling in robot cartesian space；
Step 4: constructing parameter vector using Vector product, the parameter Jacobian matrix J under different data sampling is calculatedj, j=1,
2 ... k, k are data sampling number；
Step 5: being recognized using iterative extended Kalman filter algorithm to the parameter error in parameter error model, pass through
Iterative calculation, when certain conditions are met, the parameter error △ s picked out, comprising the following steps:
(1), the observation vector Z of jth point is calculatedj:
Zj=△ Pj=Pm,j-Pt,jJ=1,2 ... k (1)
Wherein, ZjFor 3 × 1 matrix；Pm,jFor the actual coordinate of robot end's j point；Pt,jFor the theory of robot end's j point
Coordinate；△PjFor the difference of the practical j point of robot end's j point and theory j point position；
(2), initiation parameter error
Wherein,For the matrix of m × 1, m is number of parameters to be identified；I=1, j=1, i are iteration count, i=1,
2 ... w, w are maximum number of iterations；J is data sampling point, j=1,2 ... k；
(3), state one-step prediction:
Wherein,For the state estimation of the sampled point j-1 of i-th iteration；For the shape of the sampled point j of i-th iteration
State prediction；
(4), error covariance matrix is predicted:
Wherein,For the error covariance matrix estimation of the sampled point j-1 of i-th iteration；For the sampled point j of i-th iteration
Error covariance matrix prediction, be m × m matrix, m be number of parameters to be identified；Q is the variance intensity battle array of process noise W, is led to
It crosses and process signal progress mathematical statistics is obtained, in industrial robot, take empirical value Q=10-4Im×m, m is ginseng to be identified
Several numbers；
(5), filtering gain matrix are updated:
Wherein,It is the matrix of m × 3 for the filtering gain matrix of the sampled point j-1 of i-th iteration, m is parameter to be identified
Number；R is the variance intensity battle array of observation noise V, and the measurement accuracy according to laser tracking system obtains, and is 3 × 3 matrix；
(6), state estimation is updated:
Wherein,To observe new breath, It is newly ceased for state, For
The state estimation of the sampled point j of i-th iteration；
(7), estimation error variance battle array:
(8), observation vector is updated
Wherein,For theoretical correction position,For observation vector；
(9), the number of iterations i or j are updated, if all sampled datas are used in both, i is incremented by, and j is from k to 1；Otherwise, use is next
A sampled data；
Step (3) to (9) are repeated, are enabledIf dmin> d, then dmin=d,Otherwise,Wherein dminFor minimum average B configuration error, when continuous h iteration is not all updated, iteration stopping, then it is assumed that ginseng
Number error amount has restrained stabilization, obtains optimal parameter error △ s, h at this time and takes 4；
Step 6: the parameter error picked out is △ s,
Geometric parameter nominal value is modified: sg=sn+ △ s,
Wherein, snFor robot geometric parameter nominal value, sgFor robot geometric parameter true value.
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| CN106777656B (en) * | 2016-12-09 | 2020-04-14 | 江南大学 | Industrial robot absolute accuracy calibration method based on PMPSD |
| CN107457785B (en) * | 2017-09-26 | 2020-08-18 | 南京航空航天大学 | Robot position compensation method based on joint feedback |
| CN109159112B (en) * | 2018-07-09 | 2022-03-29 | 天津大学 | Robot motion parameter estimation method based on unscented Kalman filtering |
| CN109093376B (en) * | 2018-08-17 | 2020-04-03 | 清华大学 | Multi-axis hole automatic alignment method based on laser tracker |
| CN109176531A (en) * | 2018-10-26 | 2019-01-11 | 北京无线电测量研究所 | A kind of tandem type robot kinematics calibration method and system |
| CN109799701B (en) * | 2018-12-29 | 2022-04-29 | 南京埃斯顿机器人工程有限公司 | Industrial robot vibration suppression method |
| CN110053051B (en) * | 2019-04-30 | 2020-08-21 | 杭州亿恒科技有限公司 | Industrial series robot joint stiffness coefficient identification method |
| CN112223277B (en) * | 2020-09-01 | 2022-03-22 | 南京梅森自动化科技有限公司 | Multi-axis robot offline programming method |
| US20220402131A1 (en) * | 2021-06-09 | 2022-12-22 | eBots Inc. | System and method for error correction and compensation for 3d eye-to-hand coordinaton |
| CN114734440B (en) * | 2022-04-15 | 2023-09-05 | 同济大学 | Precise calibration method for kinematic parameters of hybrid double-arm transfer robot |
| CN117124336B (en) * | 2023-10-26 | 2023-12-22 | 佛山科学技术学院 | Two-step absolute positioning error compensation method and system for serial robots |
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| CN104535027B (en) * | 2014-12-18 | 2017-06-13 | 南京航空航天大学 | A kind of robot precision's compensation method of variable element error identification |
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