CN108656116A - Serial manipulator kinematic calibration method based on dimensionality reduction MCPC models - Google Patents
Serial manipulator kinematic calibration method based on dimensionality reduction MCPC models Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
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Abstract
The invention discloses a kind of serial manipulator kinematic calibration methods based on dimensionality reduction MCPC models, including step：(1) kinematics model based on dimensionality reduction MCPC models is established；(2) kinematic error model based on dimensionality reduction MCPC models is established；(3) kinematic calibration based on the LM algorithms using trusted zones skill.The present invention can carry out dimensionality reduction to kinematic error model, to achieve the purpose that simplified operation, under the basis for having established error model, the calibration to Mechanical transmission test parameter be completed, to improve the kinematic accuracy of mechanical arm.
Description
Technical field
The invention belongs to calibration technique field more particularly to a kind of serial manipulator kinematics based on dimensionality reduction MCPC models
Parameter calibration method.
Background technology
It is influenced by process and assemble equal error, the actual motion parameter of serial manipulator exists with nominal kinematics parameters
Error leads to the reduction of serial manipulator end positioning accuracy, to greatly limit the work that robot is engaged in high-accuracy processing.
Therefore, there is important meaning to carry out calibration to the kinematics parameters of serial manipulator using suitable joint parameter scaling method
Justice.
The scaling method of robot kinematics' parameter can be divided into kinematic calibration method and non-model based on model
Kinematic calibration method.The key step of kinematic calibration method based on model include modeling, measure, calibration and
Error compensation.For the staking-out work of robot kinematics' parameter, corresponding research work has been carried out in domestic and international professional person
Make.Most common robot kinematics' model is D-H Mo Xing, is to be proposed by Denavit and Hartenbe in nineteen fifty-five, still
Due to there is singular problem when this model model parameter can be made to demarcate when handling adjacent parallel joint modeling problem,
Hayati at parallel axes by introducing the rotation angle β around y-axis, it is proposed that MDH models.Stone is on the basis of standard D-H Mo Xing
On, it is proposed that the S models of six parameters, Zhuang and Schroer etc. propose CPC models and MCPC models.
When choosing kinematics model, MCPC models the serial manipulator of various different structures can be carried out modeling and
Unusual sexual behaviour can be evaded, but since the kinematics parameters that its construction modeling introduces are excessive, carry out kinematic error modeling
Process it is relatively complicated, be unfavorable for the staking-out work in later stage.
After the completion of Mechanical transmission test parameter calibration, it is also important research work that error compensation is carried out to it.At present most
Common parameter identification method is least square method, this method iterative process is simple, convergence rate is very fast, without consider disturbance because
Element, but this method calculation amount is relatively large.Levemberg-Marquardt methods be to least square method modified hydrothermal process,
The fast convergence rate of this method, strong robustness, but memory required when its operation is larger.Other algorithms also have the karr extended
Graceful filtering algorithm, genetic algorithm, simulated annealing etc..
Invention content
Goal of the invention：In view of the above problems, the present invention proposes a kind of serial manipulator movement based on dimensionality reduction MCPC models
Learn parameter calibration method.
Technical solution：To achieve the purpose of the present invention, the technical solution adopted in the present invention is：One kind being based on dimensionality reduction MCPC
The serial manipulator kinematic calibration method of model, including step：
(1) kinematics model based on dimensionality reduction MCPC models is established；
(2) kinematic error model based on dimensionality reduction MCPC models is established；
(3) kinematic calibration based on the LM algorithms using trusted zones skill.
Further, the step (1) specifically includes：
(1.1) each link rod coordinate system of serial manipulator is begun setting up from inertial coodinate system；
(1.2) derive intermediate connecting rod coordinate system between transformation matrix and tail end connecting rod coordinate system to tool coordinates system transformation
Matrix；
(1.3) transformation matrix from inertial coodinate system to tool coordinates system, i.e. kinematics model are derived.
Further, the step (2) is specifically, judge the variation of each articular kinesiology parameter caused by the pose of end
Error influences situation；It influences to reject in situation data from error and influences smaller kinematics parameters, derive and be based on dimensionality reduction MCPC moulds
The kinematic error model of type.
Further, the step (2) specifically includes：
(2.1) intermediate connecting rod parameter error model is derived：
(2.2) tail end connecting rod parameter error model is derived：
(2.3) it according to the position and attitude error of intermediate connecting rod and tail end connecting rod, establishes mechanical arm tail end position and attitude error and is sat in tool
Expression Δ under mark systemE：
ΔE=JE·Ω
Wherein, JEFor the mapping matrix of mechanical arm tail end position and attitude error and kinematic parameter errors, Ω is manipulator motion
Learn parameter error vector.
Further, the derivation of intermediate connecting rod parameter error model：
(a) intermediate connecting rod transformation matrix differential dTiLinear forms；
Wherein, Δ αi,Δβi,Δxi,ΔyiFor the parameter error of connecting rod i；
(b) according to the choice situation of the kinematics parameters of the intermediate connecting rod of dimensionality reduction MCPC models, each link parameters pair are solved
The position and attitude error matrix T answeredα,Tβ,Tx,Ty；
(c) position and attitude error matrix delta Ts of the link rod coordinate system i+1 relative to link rod coordinate system i is solvedi；
(d) site error ds of the link rod coordinate system i+1 relative to link rod coordinate system i is solvediWith attitude error δi。
Further, the derivation of tail end connecting rod parameter error model：
(a) tail end connecting rod transformation matrix differential dTnLinear forms：
Wherein, Δ αn,Δβn,Δxn,Δyn,Δγn,ΔznFor the parameter error of tail end connecting rod；
(b) according to the choice situation of the kinematics parameters of the tail end connecting rod of dimensionality reduction MCPC models, each link parameters pair are solved
The position and attitude error matrix T answeredα,Tβ,Tx,Ty,Tγ,Tz；
(c) the position and attitude error matrix delta T of tail end connecting rod parameter is solvedn；
(d) the site error d of tail end connecting rod coordinate system is solvednWith attitude error δn。
Further, the step (3) specifically includes：
(3.1) machinery of sampling arm actual end pose vector solves corresponding nominal end pose according to kinematics model
Vector, end position and attitude error are the difference of the two；
(3.2) multi-group data is acquired, machinery is solved using using the Levenberg-Marquardt methods of trusted zones skill
Arm kinematic parameter errors vector Ω；
Wherein,αkIt is modified using trusted zones；
(3.3) limited number of time iteration is carried out according to LM algorithms, until kinematics parameters meet required precision.
Advantageous effect：The present invention can carry out dimensionality reduction to kinematic error model, to achieve the purpose that simplified operation,
It has established under the basis of error model, the calibration to Mechanical transmission test parameter has been completed, to improve the kinematic accuracy of mechanical arm.
Description of the drawings
Fig. 1 is the design cycle block diagram of the present invention；
Fig. 2 is S-R-S seven freedom manipulator model figures；
Fig. 3 is that building for each joint of S-R-S seven freedom mechanical arms is situation map；
Fig. 4 is the kinematics parameters figure of S-R-S seven freedom mechanical arms；
Fig. 5 is influence distribution map of the joint 1-4 kinematics parameters to end pose；
Fig. 6 is influence distribution map of the joint 5-7 kinematics parameters to end pose；
Fig. 7 is end pose experimental data acquisition scheme figure.
Specific implementation mode
Technical scheme of the present invention is further described with reference to the accompanying drawings and examples.
Position is extracted from posture information using MATLAB calculating machine arms end posture information by multigroup input angle
It sets and forms nominal end pose vector T with attitude vectorsN；Practical shape is read by high precision measuring instrument such as laser tracker
Posture information under state forms actual end pose vector TA；Mechanical arm tail end position and attitude error and kinematic parameter errors reflect
Penetrate matrix JEThen obtained by kinematic error model to solve；It is transported finally by based on the LM algorithms of trusted zones skill to calculate
The dynamic error condition for learning parameter, to complete the staking-out work for Mechanical transmission test parameter.
As shown in Figure 1, the serial manipulator kinematic calibration method based on dimensionality reduction MCPC models of the present invention, including
Step：
(1) Kinematic Model based on dimensionality reduction MCPC models is carried out；
(1.1) it is rule according to building for MCPC models, each connecting rod that serial manipulator is begun setting up from inertial coodinate system is sat
Mark system；
(1.2) according to the link rod coordinate system of foundation, the transformation matrix between intermediate connecting rod coordinate system and tail end connecting rod are obtained
Transformation matrix of the coordinate system to tool coordinates system；
MCPC models utilize 4 parameter alphas, β, x, y to describe the transformation relation between inner link coordinate system, it follows that in
Between between link rod coordinate system transformation matrix be：
Ti=QiRot(c,αi)Rot(y,βi)Trans(xi,yi, 0) and i=0,1,2 ..., n-1
Wherein
Two parameter γ are added in the transformation of tail end connecting rod coordinate system to tool coordinates systemn,zn, respectively represented tool
The angle that coordinate system is rotated around tail end connecting rod coordinate system z-axis and the distance along z-axis translation, to show that tail end connecting rod coordinate system arrives
The transformation matrix of tool coordinates system is：
Tn=QnRot(x,αn)Rot(y,βn)Rot(z,γn)Trans(xn,yn,zn)
Wherein,Homogeneous transform matrix corresponding around A axis rotation θ angles is represented, It represents along X, Y, Z axis translates x, the corresponding homogeneous transform matrix of y, z.
As shown in Fig. 2, for the S-R-S type seven freedom manipulator model figures established, the 1 of mechanical arm, 3,5,7 four joints
Rotary shaft is perpendicular to the earth；The rotary shaft in 2,4,6 joints is then parallel to the earth.Fig. 3 is each joint of S-R-S seven freedom mechanical arms
To build be situation map, build herein be in the case of obtain initial motion parameter；Fig. 4 is the movement of S-R-S seven freedom mechanical arms
The mechanical arm name end posture information under different input angle can be extrapolated by original motion parameter by learning Parameter Map.
(1.3) transformation matrix from inertial coodinate system to tool coordinates system, i.e. Mechanical transmission test model are derived；
T=T0·T1…Tn-1Tn
(1.4) according to the initial motion for the serial manipulator established model, each pass is judged by monte carlo method
Save the variation of kinematics parameters influences situation to the error caused by the pose of end；
(1.5) it influences to reject in situation data from error and influences smaller kinematics parameters, to seek based on dimensionality reduction
The kinematic error model of MCPC models；
As shown in Figure 5 and Figure 6, the parameter in joint 1 all retains, and the parameter alfa2 in joint 2 is rejected, and the parameter in joint 3 is complete
Portion retains, and the parameter alfa4 in joint 4 is rejected, and the parameter in joint 5 all retains, and the parameter alfa6 in joint 6, x6, y6 are rejected, closed
The parameter alfa7, beta7, y7 of section 7, gamma7 rejectings.
The foundation of kinematic error model is carried out by the parameter that the above results are retained.
(2) kinematic error model based on dimensionality reduction MCPC models is established：
(2.1) intermediate connecting rod transformation matrix differential dTiWith link parameters αi,βi,xi,yiError it is related, by dTiWrite as line
Property form；
Wherein, Δ αi,Δβi,Δxi,ΔyiFor the parameter error of connecting rod i.
(2.2) it is asked according to the choice situation of the intermediate connecting rod kinematics parameters of dimensionality reduction MCPC models by above-mentioned linear forms
Solve the corresponding position and attitude error matrix T of each link parametersα,Tβ,Tx,Ty；
Wherein, Ti NNominal transformation matrixs of the link rod coordinate system i+1 relative to i is indicated, according to the foundation stream of kinematics model
Journey, can be in the hope of：
Wherein, c βi,sβiRepresent cos (βi) and sin (βi)。
For joint 1,3,5, four position and attitude error matrix Tα,Tβ,Tx,TyIt will solve, for joint 2,4, TαWithout asking
Solution, for joint 6, it is only necessary to solve Tβ。
(2.3) according to transformation matrix differential dTiExpression-form, solve link rod coordinate system i+1 relative to link rod coordinate system i
Position and attitude error matrix delta Ti；
The differential expression-form in different joints is different, for joint 1,3,5：
dTi=Ti N(TαΔαi+TβΔβi+TxΔxi+TyΔyi)
δTi=(TαΔαi+TβΔβi+TxΔxi+TyΔyi)
The differential expression-form in different joints is different, for joint 2,4：
dTi=Ti N(TβΔβi+TxΔxi+TyΔyi)
δTi=(TβΔβi+TxΔxi+TyΔyi)
The differential expression-form in different joints is different, for joint 6：
dTi=Ti N·TβΔβi
δTi=TβΔβi
(2.4) according to position and attitude error matrix delta TiSolve site error ds of the link rod coordinate system i+1 relative to link rod coordinate system ii
With attitude error δi；
For joint 1,3,5, above-mentioned result of calculation is substituted into δ Ti, can obtain：
According to above formula, link rod coordinate system i+1 can be expressed as relative to the site error and attitude error of i：
At this point, enabling
For joint 2,4, attitude error can be derived by identical calculation and be expressed as：
At this point, enabling
For joint 6, can obtain：
At this point, enabling
It then can be by the site error d between intermediate connecting rodiWith attitude error δiAbbreviation is following formula：
So far the derivation of intermediate connecting rod parameter error model is completed.
(2.5) tail end connecting rod transformation matrix differential dTnBy introducing parameter γn,zn, by dTnWrite as linear forms；
Wherein, Δ αn,Δβn,Δxn,Δyn,Δγn,ΔznFor the parameter error of tail end connecting rod.
(2.6) by above-mentioned linear forms, according to the choice situation of the kinematics parameters of the tail end connecting rod of dimensionality reduction MCPC models,
Solve the corresponding position and attitude error matrix T of each link parametersα,Tβ,Tx,Ty,Tγ,Tz；
Since tail end connecting rod only considers parameter x7, z7, so only needing to solve position and attitude error matrix Tx,Tz。
(2.7) according to transformation matrix differential dTnExpression-form, solve tail end connecting rod parameter position and attitude error matrix delta Tn；
(2.8) according to position and attitude error matrix delta TnSolve the site error d of tail end connecting rod coordinate systemnWith attitude error δn；
It is similar with the calculating step of step 2.1 to 2.4, calculate the site error d of tail end connecting rod coordinate systemnIt is missed with posture
Poor δn：
δn=[0,0,0]T
It enables
It then can be by the site error d of tail end connecting rodnWith attitude error δnAbbreviation is the following formula：
So far the derivation of tail end connecting rod parameter error model is completed.
(2.9) it according to the position and attitude error of intermediate connecting rod and tail end connecting rod, establishes mechanical arm tail end position and attitude error and is sat in tool
Expression Δ under mark systemE：
ΔE=JE·Ω
Wherein, JEFor the mapping matrix of mechanical arm tail end position and attitude error and kinematic parameter errors, Ω is manipulator motion
Learn parameter error vector.
By the derivation situation of intermediate connecting rod parameter error model and tail end connecting rod parameter error model, derive from inertial coordinate
The case where being to tool coordinates system, i.e. Mechanical transmission test error model.If dT is to be sat from robot inertial coodinate system to end
The matrix differential transformation of mark system, can derive：
It enables：
In above formula, ni,oi,aiRepresent spin matrix RiIn three column vectors, piPosition vector is represented, further will
DT carries out abbreviation：
It, can further abbreviation according to above formula：
To sum up, the position and attitude error vector that can obtain robot is：
Above formula arrange：
Wherein, Δ is enabledE=[Δ αT,ΔβT,ΔxT,ΔyT,Δγn,Δzn]T, ΔERepresent robot kinematics' parameter
Error vector, wherein Δ α, Δ β, Δ x, Δ y can indicate as follows：
Δ α=[Δ α0,Δα1…Δαn]T
Δ β=[Δ β0,Δβ1…Δβn]T
Δ x=[Δ x0,Δx1…Δxn]T
Δ y=[Δ y0,Δy1…Δyn]T
It is enabled in above formula
Wherein, A1,A2,A3,A4,A5,A6For the matrix of 3 × (n+1), wherein each column vector is represented sequentially asIt is corresponding with above formula successively.
In summary it derives, robot kinematics' error model can be reduced to following forms：
ΔE=JE·Ω
(3) based on the LM algorithms progress kinematic calibration using trusted zones skill；
(3.1) laser tracker machinery of sampling arm actual end pose vector is used, is solved according to kinematics model corresponding
Nominal end pose vector, end position and attitude error be both difference；
As shown in fig. 7, being end pose experimental data acquisition scheme figure, by inputting multigroup joint angles, to measure end
Attained pose data are held, while calculating the nominal pose data that current angular is exported, the difference of the two is ΔE。
(3.2) acquisition multi-group data ensures to solve reliability, using the Levenberg- using trusted zones skill
Marquardt methods solve Mechanical transmission test parameter error vector Ω；
Wherein,αkIt is modified using trusted zones.
(3.3) limited number of time iteration is carried out according to LM algorithms, until kinematics parameters meet required precision；
The present invention chooses under the premise of establishing the kinematics model and kinematic error model based on MCPC models
LM algorithms carry out compensation campaign parameter error, improve end movement precision.
Specific implementation step is as follows：
(a) initial MCPC kinematics parameters, enable：
K=1, ε=10-7,p0=0.25, p1=0.5, p2=0.75, α1=0.01, m=0.001
If (b)Then stop calculating, and solves：
(c) for ΔE, defined function E (x)=| | Δ E | |2, calculate：
AreΩk=| | Δ Ek||2-||E(xk+Ωk)||2
(d) it enables：
K=k+1 is enabled, is gone to step (b), by the iteration of limited number of time, to ensureReach to mechanical arm
The calibration of kinematics parameters.
Claims (7)
1. a kind of serial manipulator kinematic calibration method based on dimensionality reduction MCPC models, it is characterised in that：Including step：
(1) kinematics model based on dimensionality reduction MCPC models is established；
(2) kinematic error model based on dimensionality reduction MCPC models is established；
(3) kinematic calibration based on the LM algorithms using trusted zones skill.
2. the serial manipulator kinematic calibration method according to claim 1 based on dimensionality reduction MCPC models, special
Sign is：The step (1) specifically includes：
(1.1) each link rod coordinate system of serial manipulator is begun setting up from inertial coodinate system；
(1.2) derive intermediate connecting rod coordinate system between transformation matrix and tail end connecting rod coordinate system to tool coordinates system transformation square
Battle array；
(1.3) transformation matrix from inertial coodinate system to tool coordinates system, i.e. kinematics model are derived.
3. the serial manipulator kinematic calibration method according to claim 1 based on dimensionality reduction MCPC models, special
Sign is：The step (2) is specifically, judge that variation error caused by the pose of end of each articular kinesiology parameter influences feelings
Condition；It influences to reject in situation data from error and influences smaller kinematics parameters, derive the kinematics based on dimensionality reduction MCPC models
Error model.
4. the serial manipulator kinematic calibration method according to claim 3 based on dimensionality reduction MCPC models, special
Sign is：The step (2) specifically includes：
(2.1) intermediate connecting rod parameter error model is derived：
(2.2) tail end connecting rod parameter error model is derived：
(2.3) according to the position and attitude error of intermediate connecting rod and tail end connecting rod, mechanical arm tail end position and attitude error is established in tool coordinates system
Under expression ΔE：
ΔE=JE·Ω
Wherein, JEFor the mapping matrix of mechanical arm tail end position and attitude error and kinematic parameter errors, Ω is Mechanical transmission test parameter
Error vector.
5. the serial manipulator kinematic calibration method according to claim 4 based on dimensionality reduction MCPC models, special
Sign is：The derivation of intermediate connecting rod parameter error model：
(a) intermediate connecting rod transformation matrix differential dTiLinear forms；
Wherein, Δ αi,Δβi,Δxi,ΔyiFor the parameter error of connecting rod i；
(b) according to the choice situation of the kinematics parameters of the intermediate connecting rod of dimensionality reduction MCPC models, it is corresponding that each link parameters are solved
Position and attitude error matrix Tα,Tβ,Tx,Ty；
(c) position and attitude error matrix delta Ts of the link rod coordinate system i+1 relative to link rod coordinate system i is solvedi；
(d) site error ds of the link rod coordinate system i+1 relative to link rod coordinate system i is solvediWith attitude error δi。
6. the serial manipulator kinematic calibration method according to claim 4 based on dimensionality reduction MCPC models, special
Sign is：The derivation of tail end connecting rod parameter error model：
(a) tail end connecting rod transformation matrix differential dTnLinear forms：
Wherein, Δ αn,Δβn,Δxn,Δyn,Δγn,ΔznFor the parameter error of tail end connecting rod；
(b) according to the choice situation of the kinematics parameters of the tail end connecting rod of dimensionality reduction MCPC models, it is corresponding that each link parameters are solved
Position and attitude error matrix Tα,Tβ,Tx,Ty,Tγ,Tz；
(c) the position and attitude error matrix delta T of tail end connecting rod parameter is solvedn；
(d) the site error d of tail end connecting rod coordinate system is solvednWith attitude error δn。
7. the serial manipulator kinematic calibration method according to claim 1 based on dimensionality reduction MCPC models, special
Sign is：The step (3) specifically includes：
(3.1) machinery of sampling arm actual end pose vector solves corresponding nominal end pose vector according to kinematics model,
End position and attitude error is the difference of the two；
(3.2) multi-group data is acquired, solving mechanical arm using the Levenberg-Marquardt methods using trusted zones skill transports
It is dynamic to learn parameter error vector Ω；
Wherein,αkIt is modified using trusted zones；
(3.3) limited number of time iteration is carried out according to LM algorithms, until kinematics parameters meet required precision.
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