CN104535027B - A kind of robot precision's compensation method of variable element error identification - Google Patents
A kind of robot precision's compensation method of variable element error identification Download PDFInfo
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Abstract
The invention discloses a kind of robot precision's compensation method of variable element error identification.Belong to robot inverse calibration technique field.Propose a kind of variable element error model, by the error of the pose point under laser tracker sampling robot different spaces, space according to where expected pose point, if seeking doing closest to the point in the range of the near zone, using the modified Levenberg-Marquardt damping interative least square method Algorithm for Solving corresponding parameter errors of point global convergence solution so that obtain its actual parameter.Pose point should be actually arrived using what the actual parameter and its Inverse Kinematics Solution of the point obtained robot, absolute fix accuracy compensation of the robot in pose point is realized.The present invention is remarkably improved the absolute fix precision of robot, can apply to require robot precision in field high.
Description
Technical field
The present invention relates to a kind of robot precision's compensation method of variable element error identification, belong to robot inverse calibration technique
Field.
Background technology
In recent years, robot technology is subject to domestic and foreign scholars extensive concern.Wherein robot repetitive positioning accuracy and definitely
Positioning precision is the important indicator of robot.The repetitive positioning accuracy of current robot can reach higher level, and absolute fix
Precision is relatively low, and the repetitive positioning accuracy of such as KUKA-KR210 can reach 0.06mm, and absolute fix precision is manufactured, filled
With the influence with the factor such as flexibility, 1-3mm is can only achieve, it is difficult to meet and require that robot precision field higher (such as is being navigated
Empty field, it is desirable to which it is in ± 0.5mm).
Propose to increase 6D sensors in robot end to meet this requirement, Henrik Kihlman and Qu Weiwei etc.
And the method that the closed-loop feedback of robot is realized using laser tracker, substantially increase the absolute fix precision of robot.
But because this method is (laser tracker is worth 100,000 $) with high costs, and the portion poor for processing opening character
Part, is difficult to implement in industry spot.Therefore most of research all concentrates on demarcation and parameter identification aspect.
Document " waits method [J] that is demarcated using laser tracker to robot in Ren Yongjie, Zhu, a state in the Zhou Dynasty after expensive, Yang schoolmates
Mechanical engineering journal, 2007,09:195-200. " is proposed using laser tracker and linear side to improve the precision of robot
Journey least square solution is demarcated to the carrying out of robot.For ABB-IRB2400 industrial robots, machine is determined using laser tracker
The basis coordinates system of device people simultaneously solves the linear equation of each joint motor by three figure method, and then can be in the hope of the company of robot
Bar torsional angle.By the coordinate value of laser tracker robot measurement impact point, and 6 angles of axle of robot are obtained by serial ports
Value sets up calibration equation.By solving this equation, the actual D-H parameters of robot are obtained, and this parameter is applied to amendment system
The kinematics model of system, it is possible to increase the absolute precision of robot.But in actual applications, the method has the following disadvantages：
1) robot is considered as rigid body, does not consider influence of the flexibility to robot；
2) error of parameter item a and d is only considered, and the influence actually to positioning precision is not only by two above parameter
Determine, can more be influenceed by α and θ；
3) result of the test shows that robot is still not satisfactory in calibrated effect.
" Nanjing Aero-Space University, Chengdu Airplane Industry (Group) Corp., Ltd. is a kind of to be used for industrial machine to patent
The three-dimensional grid precision compensation method of people:China, CN201110113246.6 [P] .2011-11-2. " is for the enveloping space
Any point in certain cube grid of interior division, using space lattice divide method, using the method for space interpolation come
Theoretical coordinate to robot is modified, and completes absolute fix accuracy compensation of the robot in the point.The method exists following
It is not enough：
1) determination of step-length needs to carry out substantial amounts of experiment；
2) working space using the mesh generation robot and method with interpolation is processed error, in the method
The consideration of Error weight mainly estimated the error distribution in space, but cannot accurate description its error model, because
The precision that this can be improved is still limited；
The compensation to robot absolute fix precision under different attitudes can not be realized in the method.
The content of the invention
Goal of the invention：In order to overcome the deficiencies in the prior art, the present invention to provide a kind of variable element error identification
Robot precision's compensation method, improves the absolute fix precision of robot.
To achieve the above object, the technical solution adopted by the present invention is：A kind of robot precision of variable element error identification
Compensation method, it is proposed that a kind of variable element error model, by the pose point under laser tracker sampling robot different spaces
Error, the space according to where expected pose point, if seeking doing closest to the point in the range of the near zone, utilize
Modified Levenberg-Marquardt damp the global receipts of the interative least square method Algorithm for Solving corresponding parameter error of point
Hold back solution and then obtain its actual parameter.The reality for obtaining robot using the actual parameter and its Inverse Kinematics Solution of the point should be in place
Appearance point, realizes absolute fix accuracy compensation of the robot in pose point.
Comprise the following steps：
The first step, laser tracker is fixed on ground, and robot base mark system and method are set up using laser tracker
Blue disk coordinate system, while giving random pose point theoretical coordinate Pt；
Second step, using laser tracker according to given random pose point theoretical coordinate PtEnter in robot base mark system
Row sampling, obtains the sample coordinate P of random pose pointa；
3rd step, the structural parameters according to robot set up robot kinematics' model by D-H methods；
4th step, according to given random pose point theoretical coordinate Pt, according to sample coordinate P in second stepa, the 3rd step machine
Robot kinematics' model that each structural parameters and the 3rd step are obtained in people's kinematics model, sets up kinematic error model；
Then interative least square method is damped by Levenberg-Marquardt and solves the kinematic error model, obtain each structure
Parameter error；
5th step, according to expected pose point position, selection most connects with it in the sample coordinate obtained in second step
Several near sampled points, the structural parameters error of the expected pose point are obtained by the 4th step, so as to obtain the expected pose
The corresponding robot actual structure parameters of point；Robot inverse solution is solved according to expected pose simultaneously；
6th step, robot is obtained using the actual structure parameters and the robot inverse solution for solving of the robot for picking out
Position should be actually arrived, absolute fix accuracy compensation of the robot in pose point is realized.
The side of robot base mark system and ring flange coordinate system is measured and sets up in the first step using laser tracker
Method, comprises the following steps：
Step one by one, the spherical reflector SMR of laser tracker is placed in robot base plane, along base plane
A mobile segment distance, the series of points on the segment distance is gathered using the continuous metering system of laser tracker, and utilize laser
Tracker carries the fit Plane instruction of software and offset commands fit a plane, and the plane is robot base plane
Baseplane, wherein offset commands are the offset distance of SMR radiuses；
Step one two, in robot ring flange Plane Installation one SMR, SMR is fixed on the SMR seats, Ran Housuo
The A2 axles of dead robot rotate certain distance to A6 axles around A1 axles, and the section is gathered using the continuous metering system of laser tracker
The series of points of distance, fits A1 and justifies using the fitting circle instruction of software；
Step one three, crosses the vertical line L1 that the circle is made in the A1 centers of circle, makees the intersection point of vertical line L1 and base plane Baseplane, the friendship
Point is the origin O of base coordinate systemB；
Step one four, mechanical zero position is placed in by robot, and SMR is placed in robot ring flange plane, flat along this
Face moves a certain distance, and gathers the series of points of the segment distance using the continuous metering system of laser tracker, and utilize software
Fit Plane instruction and offset commands fit a plane, the plane is the ring flange plane of robot
Frangeplane；
Step First Five-Year Plan, six mounting holes in robotic's dead-center position robot measurement ring flange plane, by this
Six spot projections fit round a C, center of the circle to robot ring flange plane Frangeplane using six subpoints
The as origin O of ring flange coordinate system；
Step one six, the subpoint using two mounting holes in six mounting holes of ring flange plane by robot base is made
Straight line L2, makees the midpoint X of the straight lineF, the midpoint is the point in ring flange coordinate system X-axis；
Step one seven, with OFIt is origin, crosses OFPoint on the vertical line of ring flange plane is the point on Z axis, XFIt is ZX
Point in plane sets up coordinate system, and the coordinate system is ring flange coordinate system；
Step one eight, with OB as origin, the point on vertical line L1 is the point on Z axis, XFFor the point in ZX planes sets up coordinate
System, the coordinate system is robot base mark system.
The method for being set up robot kinematics' model in 3rd step by D-H methods, is comprised the following steps：
Step 3 one, the kinematic relation that the structural parameters according to robot are set up between adjacent two bar of robot；
Step 3 two, introduces rotationally-varying to the kinematic relation between adjacent two bar of robot of foundation in step 3 one
Rot (y, β), eliminate due to be parallel to each other between adjacent two axle or close to it is parallel when the singular problem that produces；
Step 3 three, for the robot that N number of joint is connected, between adjacent two bar of robot in step 3 two
Kinematic relation, obtains the relation between robot end's coordinate system and basis coordinates system.
The method that kinematic error model is set up in the step 4, comprises the following steps：
Step 4 one, according to error, the sample coordinate P of each parameter in the 3rd step robot kinematics' modelaAnd it is theoretical
Coordinate Pt, and then obtain its error position Δ P；
Step 4 two, the kinematic error mould that linearisation after High Order Perturbation obtains Xie Huahou is cast out by error position Δ P
Type.
The determination method of each parameter error, comprises the following steps in the step 4 two：
Step 1), the change according to robot links flexibility is a continuous process, obtain the angle that is turned over to joint with
Apply moment conditions on its axis；
Step 2), by step 1) change that draws the parameter error caused by connecting rod flexibility is also a continuous process,
Obtain the parameter error caused by connecting rod flexibility, and the parameter error that this is caused by connecting rod flexibility is it is determined that the appearance of robot
It is transformed into the working space of robot under conditions of state, obtains the parameter error caused by connecting rod flexibility；
Step 3), according to robot a certain determination pose, what its error parameter was to determine within a certain period of time, this
Corner in pose one joint space of correspondence, and in certain limit near this corner, error parameter with determine pose
Error parameter is very close to obtaining：
E=| | Δ x1-Δx2||<ξ works as Δ θ → 0；
Wherein, Δ x1Each parameter error i.e. under joint rotation angle 1, Δ x2I.e. in the joint rotation angle with pose 1 closely
Each parameter error at 2, Δ θ is the changing value of the joint rotation angle under state 1 and state 2, and E is Δ x1With Δ x2Difference
Norm；
Step 4), by step 3) in obtain the norm of difference by it is determined that being transformed into the base of robot under conditions of attitude
Coordinate system：
E=| | Δ x1-Δx2||<ξ is as (Δ x, Δ y, Δ z) → 0.
Preferably, the number of the sampled point closest to the expected pose of each expected pose corresponding selection is 9.
Preferably, interative least square method is damped by Levenberg-Marquardt in the 4th step and solves parameter
Error, tries to achieve the global convergence solution under the position and posture, and the solution is parameter error.
Interative least square method is damped by Levenberg-Marquardt in the step 4 and solves kinematic error mould
The method of type, comprises the following steps：
Step a, the concrete structure and its theoretical structural parameters according to robot are to Jacobian matrix and other specification
Initialized, ε >=0, α1>m>0,0≤p0≤p1≤p2<1, k=1；Calculate Jacobian matrix J (x during kth time iterationk)；
Step b, parameter error matrix is solved using damped least square method：
Δxk=-{ [J (xk)]TJ(xk)+λkI}-1[J(xk)]TΔP(xk)
Wherein k represents iterations, Δ xkThe change value of parameter error, x when representing kth time iterationkRepresent kth time iteration
Parameter error, λkRepresent damping factor during kth time iteration；
Step c, actual slippage Ared when calculating kth time iterationkWith estimate slippage PredkRatio rk：
Aredk=| | Δ Pk||2-||ΔP(xk+Δxk)||2；
Predk=| | Δ Pk||2-||ΔPk+JkΔxk||2；
Order：
Update iterative parameter：
K=k+1；
WhenOr iterations meet 1000 times when, circulation terminates, and obtains parameter error and then obtains reality
Parameter.
A kind of robot precision's compensation method of variable element error identification that the present invention is provided, compared to existing technology, has
Following beneficial effect：
1) kinematic error model is variable element error identification model, and the model considers robot inaccuracy distribution
It is uneven, the realistic model of robot is similar to, so that for variable element identification provides theoretical foundation.It is right therefore, it is possible to solve
Robot repetitive positioning accuracy is high and the low problem of absolute fix precision,
2) different parameter errors are asked in the space according to where expected pose point, and the parameter error is closer to the pose point
Actual parameter error.
3) this method can greatly improve the absolute fix precision of robot after, so that the application of robot is more wide
It is general.
4) modified Levenberg-Marquardt damping interative least square methods are employed, each pose shape can be tried to achieve
Global convergence solution under state, so as to improve stated accuracy.
Brief description of the drawings
Fig. 1 is working space variable element error identification schematic diagram.
Fig. 2 is using the result of the inventive method.
Specific embodiment
The present invention is further described below in conjunction with the accompanying drawings.
A kind of robot precision's compensation method of variable element error identification, as shown in figure 1, comprising the following steps：
The first step, laser tracker is fixed on ground, and robot base mark system and method are set up using laser tracker
Blue disk coordinate system：
1) the spherical reflector SMR of laser tracker is placed in robot base plane, one is moved along base plane
Segment distance, the series of points on the segment distance is gathered using the continuous metering system of laser tracker, and utilization carries software
Fit Plane is instructed and offset commands (offset distance is SMR radiuses) fit a plane, and the plane is robot base and puts down
Face Baseplane；
2) in robot ring flange Plane Installation one SMR, SMR is fixed on the SMR seats, then locked robot
A2 axles to A6 axles, rotate certain distance around A1 axles, gather the one of the segment distance using the continuous metering system of laser tracker
Point, fits A1 and justifies using the fitting circle instruction of software；
3) the vertical line L1 that the circle is made in the A1 centers of circle is crossed, makees the intersection point of vertical line L1 and base plane Baseplane, the intersection point is pedestal
Mark the origin O of systemB；
4) robot is placed in mechanical zero position, SMR is placed in robot ring flange plane, along the planar movement one
Set a distance, the series of points of the segment distance is gathered using the continuous metering system of laser tracker, and flat using the fitting of software
Face instructs and offset commands fit a plane, and the plane is the ring flange plane Frangeplane of robot；
5) six mounting holes in robotic's dead-center position robot measurement ring flange plane, six points are thrown
Shadow fits a round C to robot ring flange plane Frangeplane using six subpoints, and center of the circle is flange
The origin O of disk coordinate systemF；
6) straight line L2 is made using the subpoint of two mounting holes in six mounting holes of ring flange plane by robot base,
Make the midpoint X of the straight lineF, the midpoint is the point in ring flange coordinate system X-axis；
7) with OFIt is origin, crosses OFPoint on the vertical line of ring flange plane is the point on Z axis, XFFor in ZX planes
Point set up coordinate system, the coordinate system be ring flange coordinate system；
8) with OB as origin, the point on vertical line L1 is the point on Z axis, XFFor the point in ZX planes sets up coordinate system, the seat
Mark system is robot base mark system.
Second step, is sampled using laser tracker to the random pose point in robot base mark system, obtains random
The sample coordinate P of pose pointa；
3rd step, the structural parameters according to robot set up robot kinematics' model by D-H methods：Including following step
Suddenly：
Step 3 one, the kinematic relation that the structural parameters according to robot are set up between adjacent two bar of robot.It is adjacent
Kinematic relation between two bars is：
In above formula, c represents that cos, s represent sin, aiIt is length of connecting rod, αi-1It is joint torsional angle, diIt is connecting rod offset distance, θiFor
Joint rotation angle.
Step 3 two, introduces rotationally-varying to the kinematic relation between adjacent two bar of robot of foundation in step 3 one
Rot (y, β), eliminate due to be parallel to each other between adjacent two axle or close to it is parallel when the singular problem that produces；
β in above formulaiRepresent the anglec of rotation of robot the i-th bar coordinate system around y.
Step 3 three, for the robot that N number of joint is connected, between adjacent two bar of robot in step 3 two
Kinematic relation, obtains the relation between robot end's coordinate system and basis coordinates system：
In above formulaThe connecting rod homogeneous transformation from pedestal mark to end is represented,ArriveRepresent the company of adjacent two connecting rod
Bar homogeneous transformation.
Step 3 four, according to the relation between robot end's coordinate system and basis coordinates system, obtains robot end's flange
The theoretical coordinate P of disk center's point：
P=F (a, d, α, θ, β)
Wherein, P represents the theoretical coordinate of robot ring flange center point, (a, d, α, θ, β) represent from robot links 1 to
The structural parameters of n；Wherein, a is length of connecting rod, and d is connecting rod offset distance, and α is joint torsional angle, and θ is joint rotation angle, and β represents i bar coordinates
It is the anglec of rotation around y.
4th step, gives random pose point theoretical coordinate P firstt, according to sample coordinate P in second stepa, the 3rd step machine
Robot kinematics' model that each structural parameters and the 3rd step are obtained in people's kinematics model, sets up kinematic error model；
Then interative least square method is damped by Levenberg-Marquardt and solves the kinematic error model, obtain each structure
Parameter error：
Step 4 one, according to error, the sample coordinate P of each parameter in the 3rd step robot kinematics' modelaAnd it is theoretical
Coordinate Pt, and then obtain its error position Δ P；
Because in kinematics model established above there is error in each parameter, therefore robot end's ring flange center point
Physical location (sample coordinate) PaCan be expressed as：
Pa=F (a+ Δs a, d+ Δ d, α+Δ α, θ+Δ θ, β+Δ β)；
Δ P=Pa-Pt；
PtIt is theoretical position.Step 4 two, linearisation obtains Xie Huahou's after error position Δ P is cast out into High Order Perturbation
Kinematic error model：
M depends on the points of sampling.
Because robot is in joint space, its parameter error corresponds to certain because of the flexible uneven distribution of connecting rod
The joint rotation angle of individual determination, do not consider temperature, robot with the abrasion etc. of time account for factor of the overall error less than 3% with chance error
Poor influence, parameter error is a relative value for determining.And with the change of robot pose, due to the change of connecting rod flexibility
Change is a continuous process, it was found that flexible joint can be reduced into linear torsion spring model, then the angle that joint turns over
Apply torque direct proportionality on its axis：
Δ θ=Cθτ；
In above formula, Δ θ is the flexible deflection angle for being loaded or mechanical arm deadweight causes joint flexibility deformation to produce, single
Position is radian.CθIt is softness factor, τ is the equivalent moment being applied on flexible joint axis.Therefore, caused by connecting rod flexibility
The change of parameter error is also a continuous process.Therefore can be represented with below equation：
(Δ a, Δ d, Δ α, Δ θ, Δ β)=f (θ1,θ2…,θn)；
In view of θ1,θ2…,θnThere is coupling in each joint, it is difficult to error model is set up in joint space, while also not straight enough
See, therefore can be it is determined that in the working space for being transformed into robot under conditions of the attitude of robot, then above formula can be converted
For：
(Δ a, Δ d, Δ α, Δ θ, Δ β)=g (x, y, z)；
Because above functional relation is complex, it is difficult to it is determined that, and pose of the robot in a certain determination is considered, its mistake
(temperature-resistant, wear extent is constant) is to determine difference parameter within a certain period of time.In this pose one joint space of correspondence
Corner, and in certain limit near this corner, error parameter with determine the error parameter of pose very close to：
E=| | Δ x1-Δx2||<ξ works as Δ θ → 0；
Δ x in above formula1Each parameter error i.e. under joint rotation angle 1, Δ x2Turn in the joint with pose 1 closely
Each parameter error at angle 2, Δ θ is the changing value of the joint rotation angle under state 1 and state 2.E is Δ x1With Δ x2Difference
Norm.Above formula represent when Δ θ level off to 0 when, the ξ that close to 0 can be found>0 makes E<ξ.By it is determined that attitude
Under the conditions of be transformed into the working space of robot, then：
E=| | Δ x1-Δx2||<ξ is as (Δ x, Δ y, Δ z) → 0；
Above formula represented under the working space of robot, when its change in location (Δ x, Δ y, Δ z) level off to 0 when, total energy
Find a ξ>0 makes E<ξ.
Derived based on more than, can be according to the position selection where expected pose point with its immediate 9 sampled point (altogether
25 unknown numbers are, it is necessary at least 25 prescription journeys, therefore 9 points of selection) as shown in figure 1, being clicked through to expected pose using 9 points
Row envelope, so as to solve the corresponding parameter error of point.
Interative least square method is damped by Levenberg-Marquardt in 4th step and solves parameter error, asked
The global convergence solution under the position and posture is obtained, the solution is parameter error.
Interative least square method is damped by Levenberg-Marquardt in the step 4 and solves kinematic error mould
The method of type, comprises the following steps：Concrete structure according to robot and its theoretical structural parameters to Jacobian matrix and
Other specification is initialized：
ε≥0,α1>m>0,0≤p0≤p1≤p2<Each iteration of 1, k=1, LM algorithm mainly includes five parts：
1) Jacobian matrix J (x during kth time iteration are calculatedk)；
2) parameter error matrix is solved using damped least square method：
Δxk=-{ [J (xk)]TJ(xk)+λkI}-1[J(xk)]TΔP(xk)
K represents iterations, Δ x in above formulakThe change value of parameter error, x when representing kth time iterationkRepresent kth time repeatedly
The parameter error in generation, λkRepresent damping factor during kth time iteration.It is determined according to following formula：
3) actual slippage Ared when calculating kth time iterationkWith estimate slippage PredkRatio rkThen：
Aredk=| | Δ Pk||2-||ΔP(xk+Δxk)||2；
Predk=| | Δ Pk||2-||ΔPk+JkΔxk||2；
Order：
Update iterative parameter：
K=k+1；
WhenOr iterations meet 1000 times when, circulation terminates, and obtains parameter error and then obtains reality
Parameter.
5th step, according to expected pose point position, selection most connects with it in the sample coordinate obtained in second step
Several near sampled points, the parameter error of the expected pose point are obtained by the 4th step, so as to obtain the expected pose point pair
The robot actual parameter answered, (asks the inverse solution of simple narration to solve while solving robot inverse solution according to expected pose herein
Method), solve robot inverse solution and use numerical method, the main equation using in step 3 three will be knownIt is updated to equation
In, and the element one-to-one corresponding in the equation of matrix can be obtained into inverse solution；
6th step, robot reality is obtained using the actual parameter and the robot inverse solution for solving of the robot for picking out
Position should be arrived, absolute fix accuracy compensation of the robot in pose point is realized.
According to the error for identifying, it is possible to use it for carrying out the error prediction of robot end and compensating.
According to expected pose point, Inverse Kinematics Solution is asked for, obtain theoretical θ1,θ2…,θn, in the kinematics model after substitution amendment,
Try to achieve actual pose point.
In above formula, PcThe pose point after compensation is represented,Represent using the structural parameters x after compensationciObtain from bar
The homogeneous connecting rod conversion of i-1 to bar i.
Specific implementation step of the invention is illustrated by taking KUKA-KR210 industrial robots as an example below：
Step one：Kinematics model is set up using D-H methods, it is specific as follows shown：
The connecting rod transformation parameter table of table 1
Step 2：Kinematic error model is set up, single expected pose point there are 9 sampled points, then its kinematic error mould
Type is shown below：
Step 3：By laser tracker coordinate system and robot basis coordinates system unification, and set up ring flange coordinate system；
Step 4：The working space random point for generating is sampled using laser tracker, the working environment temperature of experiment
It is constant room temperature to spend, and have chosen demarcation space of the robot 600mm × 600mm × 600mm working regions as robot, this examination
189 stochastical sampling points are generated in testing；
Step 5：Iteration goes out the point in being selected 9 points near the point to be updated to LM algorithms according to robot expected pose
Corresponding parameter error, and then obtain its actual parameter；
Step 6：Obtaining robot using the Inverse Kinematics Solution and actual parameter of the position and posture should actually arrive pose.This
Experiment have chosen 64 random points, be verified, the result is as shown in Figure 2：
In sum, a kind of variable element error model proposed by the present invention, it is different by laser tracker sampling robot
The error of the pose point under space, closest in the range of the near zone being somebody's turn to do is sought in the space according to where expected pose point
If that puts does, using modified Levenberg-Marquardt damping interative least square method Algorithm for Solving, the point is corresponding
The global convergence solution of parameter error and then obtain its actual parameter.Machine is obtained using the actual parameter and its Inverse Kinematics Solution of the point
Device people's should actually arrive pose point, realize absolute fix accuracy compensation of the robot in pose point.The present invention is remarkably improved machine
The absolute fix precision of device people, can apply to require robot precision in field high.
The above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art
For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should
It is considered as protection scope of the present invention.
Claims (6)
1. a kind of robot precision's compensation method of variable element error identification, it is characterised in that comprise the following steps：
The first step, laser tracker is fixed on ground, and robot base mark system and ring flange are set up using laser tracker
Coordinate system, while giving random pose point theoretical coordinate Pt；
Second step, using laser tracker according to given random pose point theoretical coordinate PtAdopted in robot base mark system
Sample, obtains the sample coordinate P of random pose pointa；
3rd step, the structural parameters according to robot set up robot kinematics' model by D-H methods；
4th step, according to given random pose point theoretical coordinate Pt, according to sample coordinate P in second stepa, the 3rd step robot fortune
Robot kinematics' model that each structural parameters and the 3rd step are obtained in dynamic model, sets up kinematic error model；Then
Interative least square method is damped by Levenberg-Marquardt and solves the kinematic error model, obtain each structural parameters
Error；
The method that kinematic error model is set up in the step 4, comprises the following steps：
Step 4 one, according to error, the sample coordinate P of each parameter in the 3rd step robot kinematics' modelaAnd theoretical coordinate
Pt, and then obtain its error position Δ P；
Step 4 two, the kinematic error model that linearisation after High Order Perturbation obtains Xie Huahou is cast out by error position Δ P；
The determination method of each parameter error, comprises the following steps in the step 4 two：
Step 1), the change according to robot links flexibility is a continuous process, obtains the angle and applying turned over to joint
Moment conditions on its axis；
Step 2), by step 1) change that draws the parameter error caused by connecting rod flexibility is also a continuous process, obtain
The parameter error caused by connecting rod flexibility, and parameter error that this is caused by connecting rod flexibility is it is determined that the attitude of robot
Under the conditions of be transformed into the working space of robot, obtain the parameter error caused by connecting rod flexibility；
Step 3), according to robot a certain determination pose, what its error parameter was to determine within a certain period of time, this pose
Corner in one joint space of correspondence, and in certain limit near this corner, error parameter and the error for determining pose
Parameter is very close to obtaining：
E=| | Δ x1-Δx2||<ξ works as Δ θ → 0；
Wherein, Δ x1Each parameter error i.e. under joint rotation angle 1, Δ x2I.e. with the joint rotation angle 2 closely of pose 1 at
Each parameter error, Δ θ is the changing value of the joint rotation angle under state 1 and state 2, and E is Δ x1With Δ x2Difference model
Number；
Step 4), by step 3) in obtain the norm of difference by it is determined that being transformed into the pedestal mark of robot under conditions of attitude
System：
E=| | Δ x1-Δx2||<ξ is as (Δ x, Δ y, Δ z) → 0；
5th step, selects immediate with it according to expected pose point position, in the sample coordinate obtained in second step
Several sampled points, the structural parameters error of the expected pose point is obtained by the 4th step, so as to obtain the expected pose point pair
The robot actual structure parameters answered；Robot inverse solution is solved according to expected pose simultaneously；
6th step, robot reality is obtained using the actual structure parameters and the robot inverse solution for solving of the robot for picking out
Position should be arrived, absolute fix accuracy compensation of the robot in pose point is realized.
2. robot precision's compensation method of variable element error identification according to claim 1, it is characterised in that：Described
The method for being measured using laser tracker in one step and setting up robot base mark system and ring flange coordinate system, including following step
Suddenly：
Step one by one, the spherical reflector SMR of laser tracker is placed in robot base plane, is moved along base plane
One segment distance, the series of points on the segment distance is gathered using the continuous metering system of laser tracker, and using laser tracking
Instrument carries the fit Plane instruction of software and offset commands fit a plane, and the plane is robot base plane
Baseplane, wherein offset commands are the offset distance of SMR radiuses；
Step one two, in robot ring flange Plane Installation one SMR, SMR is fixed on the SMR seats, then locked machine
The A2 axles of device people rotate certain distance to A6 axles around A1 axles, and the segment distance is gathered using the continuous metering system of laser tracker
Series of points, using software fitting circle instruction fit A1 justify；
Step one three, crosses the vertical line L1 that the circle is made in the A1 centers of circle, makees the intersection point of vertical line L1 and base plane Baseplane, and the intersection point is
The origin O of base coordinate systemB；
Step one four, mechanical zero position is placed in by robot, and SMR is placed in robot ring flange plane, is moved along the plane
Dynamic certain distance, the series of points of the segment distance is gathered using the continuous metering system of laser tracker, and using the plan of software
Close plane instruction and offset commands fit a plane, the plane is the ring flange plane Frangeplane of robot；
Step First Five-Year Plan, six mounting holes in robotic's dead-center position robot measurement ring flange plane, by this six
Spot projection fits a round C to robot ring flange plane Frangeplane using six subpoints, and center of the circle is
The origin O of ring flange coordinate system；
Step one six, the subpoint using two mounting holes in six mounting holes of ring flange plane by robot base makees straight line
L2, makees the midpoint X of the straight lineF, the midpoint is the point in ring flange coordinate system X-axis；
Step one seven, with OFIt is origin, crosses OFPoint on the vertical line of ring flange plane is the point on Z axis, XFIt is ZX planes
On point set up coordinate system, the coordinate system be ring flange coordinate system；
Step one eight, with OB as origin, the point on vertical line L1 is the point on Z axis, XFFor the point in ZX planes sets up coordinate system, should
Coordinate system is robot base mark system.
3. robot precision's compensation method of variable element error identification according to claim 1, it is characterised in that：Described
The method for being set up robot kinematics' model in three steps by D-H methods, is comprised the following steps：
Step 3 one, the kinematic relation that the structural parameters according to robot are set up between adjacent two bar of robot；
Step 3 two, rotationally-varying Rot is introduced to the kinematic relation between adjacent two bar of robot of foundation in step 3 one
(y, β), eliminate due to be parallel to each other between adjacent two axle or close to it is parallel when the singular problem that produces；
Step 3 three, for the robot that N number of joint is connected, the motion between adjacent two bar of robot in step 3 two
Relation, obtains the relation between robot end's coordinate system and basis coordinates system.
4. robot precision's compensation method of variable element error identification according to claim 1, it is characterised in that：Each phase
The number for hoping the sampled point closest to the expected pose of pose corresponding selection is 9.
5. robot precision's compensation method of variable element error identification according to claim 1, it is characterised in that：Described
Interative least square method is damped by Levenberg-Marquardt in four steps and solves parameter error, tried to achieve under the position and posture
Global convergence solution, the solution is parameter error.
6. robot precision's compensation method of variable element error identification according to claim 1, it is characterised in that：The step
The method that interative least square method solves kinematic error model is damped by Levenberg-Marquardt in rapid four, including
Following steps：
Step a, concrete structure and its theoretical structural parameters according to robot are carried out to Jacobian matrix and other specification
Initialization, ε >=0, α1>m>0,0≤p0≤p1≤p2<1, k=1；Calculate Jacobian matrix J (x during kth time iterationk)；
Step b, parameter error matrix is solved using damped least square method：
Δxk=-{ [J (xk)]TJ(xk)+λkI}-1[J(xk)]TΔP(xk)
Wherein k represents iterations, Δ xkThe change value of parameter error, x when representing kth time iterationkRepresent the ginseng of kth time iteration
Number error, λkRepresent damping factor during kth time iteration；
Step c, actual slippage Ared when calculating kth time iterationkWith estimate slippage PredkRatio rk：
Aredk=| | Δ Pk||2-||ΔP(xk+Δxk)||2；
Predk=| | Δ Pk||2-||ΔPk+JkΔxk||2；
Order：
Update iterative parameter：
K=k+1；
WhenOr iterations meet 1000 times when, circulation terminates, and obtains parameter error and then obtains actual parameter.
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