CN108445765A - A kind of scaling method of aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket - Google Patents
A kind of scaling method of aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket Download PDFInfo
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Abstract
A kind of scaling method of aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket, can be used for the calibration of industrial parallel robot.For object pose, each active moving sets desired displacement amount is found out using inverse kinematic under nominal structure parameter；By each active moving sets desired displacement amount driving active moving sets movement found out；After movement stops, being measured using laser tracker and specify point coordinates on bracket, fit bracket attained pose；Bracket attained pose is compared with object pose, determines calibration front rack position and attitude error；Using space vector chain method, the error model between bracket position and attitude error and structural failure, active moving sets displacement is established, structural failure identification is carried out using least square method；Bracket nominal structure parameter is modified, carries out inverse kinematic again, determination will reach each active moving sets displacement when object pose.The method of the present invention is simple, and identification precision is high, has yesterday in the kinematic accuracy for improving bracket, can meet the requirement of bracket posture adjustment precision to the maximum extent.
Description
Technical field
The present invention relates to a kind of mechanical positioning methods, especially a kind of complex surface bores the technology of riveter positioning, specifically
Say it is a kind of scaling method of the aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket based on locator.
Background technology
Aircraft components area is big, and processing difficulties, efficiency is low by the way of hand assembled, and precision is difficult to ensure, greatly
Ground affects the service life and safety coefficient of aircraft.In order to solve above-mentioned problem, Automated assembly is widely used in countries in the world
Technology carries out the assembly of large aircrafts component such as aircraft target ship and devises a plurality of types of automatic assembly systems.
Nanjing Aero-Space University requires according to work pieces process, devises planer-type automatic Drilling/Riveting system, configured with novel
Locator class parallel connection posture adjustment bracket with adjustment posture and position functions is used for aircraft automatic Drilling/Riveting operation：Gantry system is set
It is low around x-axis rotation axis kinematic accuracy in respect of x, y, z to one-movement-freedom-degree and around x-axis rotational freedom, in order to ensure automatic Drilling/Riveting
Around x-axis rotation precision, bracket design has around x-axis rotational freedom system；Gantry system does not design around y-axis rotational freedom, is
Realize that rack system is designed with around y-axis rotational freedom around y-axis posture adjustment；In order to realize that bracket is rotatably mounted around x-axis, y-axis
Degree, each locator are designed with z to one-movement-freedom-degree.The parallel connection posture adjustment bracket is made of four locater (such as Fig. 2)：1st
Locator is only designed with z to active moving sets, and the 2nd locator is designed with x to, z to active moving sets, and the 3rd, the 4th locator
It is designed with three direction prismatic pair of x, y, z, wherein z is to for active moving sets, and x, y are to be servo-actuated prismatic pair；Each locator and bracket
Between pass through typed ball bearing pair SiConnection；Bracket posture adjusting system structure is shown in Fig. 3, Xi、Yi、ZiExpression sliding pair, i=1,2,3,4, it indicates
Locator is numbered.During bracket use, there is a problem of posture adjustment inaccuracy, in order to solve this problem, is demarcated,
Calibration schematic diagram is shown in Fig. 1, Om-XmYmZmFor laser tracker coordinate system, Ob-XbYbZbFor bracket global coordinate system, Ot-XtYtZtSupport
Frame local coordinate system.
Many scholars have carried out a large amount of research in terms of reducing parallel institution complete machine position and attitude error, but for by locator
The correlative study of class parallel institution position and attitude error and structural failure is less.The existing phase about locator class parallel connection posture adjustment bracket
Research is closed, is had the following disadvantages：1) whole constraint equations are not included in error model, lead to built error model None- identified list
The locator active moving sets angular error of a main driving, for this parallel connection posture adjustment bracket, if built using having mode
Mould, it is impossible to use error model identification major part active moving sets angular error；2) transposition of matrix is used to be multiplied by original matrix
Mode composed structure error term coefficient matrix identification structure error, the error term coefficient matrix be singular matrix, using canonical
Change method eliminates matrix singularity, and error term coefficient can be caused to change, reduce structural failure identification precision.
Invention content
The purpose of the present invention is for the not high problem of existing bracket posture adjustment positioning accuracy, invention is a kind of based on locator
The scaling method of aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket.
The technical scheme is that：
A kind of scaling method of aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket is tied it is characterized in that being directed to object pose in name
Each active moving sets desired displacement amount is found out using inverse kinematic under structure parameter；By each active moving sets desired displacement found out
Amount driving active moving sets movement；After movement stops, being measured using laser tracker and specify point coordinates on bracket, fit bracket
Attained pose；Bracket attained pose is compared with object pose, determines calibration front rack position and attitude error；Using space vector
Chain method establishes the error model between bracket position and attitude error and structural failure, active moving sets displacement, using least square method
Carry out structural failure identification；Bracket nominal structure parameter is modified, carries out inverse kinematic again, determination will reach target
Each active moving sets displacement when pose.
The specific steps are：
(1) it is measured using laser tracker before calibration and specifies point coordinates on bracket, fit bracket attained pose A, for
Object pose B is found out using inverse kinematic by each active moving sets ideal bits of pose A to pose B under nominal structure parameter
Shifting amount；
(2) active movement secondary motion is driven by each active moving sets ideal movements amount found out, is surveyed using laser tracker
It measures and specifies point coordinates on bracket, fit bracket attained pose C；
(3) bracket attained pose C is compared with object pose B, determines calibration front rack position and attitude error；
(4) space vector chain method is used, is established between bracket position and attitude error and structural failure, active moving sets displacement
Error model carries out structural failure identification using least square method；
(5) bracket nominal structure parameter is modified, carries out inverse kinematic again, determination will reach object pose B
When each active moving sets displacement.
The beneficial effects of the invention are as follows：
The present invention establishes the error model suitable for novel automatic drilling riveting parallel connection posture adjustment bracket, and whole constraint equations are received
Enter error model, improve error identification precision, can identify the locator active moving sets angular error of single main driving；Simultaneously
Identification structure error ensure that error identification under the premise of not changing structural failure term coefficient by the way of matrix dimensionality reduction
Precision.
Built error model is combined with subsidiary, realizes the calibration of posture adjustment bracket in parallel：Error identification result is aobvious
Show, identification precision of the present invention is better than having discrimination method；Error compensation the results show that movement of bracket precision has is obviously improved,
It disclosure satisfy that aircraft assembles the requirement to bracket posture adjustment precision.
Description of the drawings
Fig. 1 is that laser tracker demarcates schematic diagram.
Fig. 2 is locator structure schematic diagram.
Fig. 3 is carrier structure schematic diagram.
Fig. 4 is bracket vector chain schematic diagram.
Fig. 5 is bracket vector chain detail drawing.
Fig. 6 is identification precision schematic diagram of the present invention.
Fig. 7 is that forefathers have discrimination method identification precision schematic diagram.
Specific implementation mode
The present invention is further illustrated with reference to the accompanying drawings and detailed description.
As shown in figs. 1-7.
A kind of scaling method of aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket, the specific steps are：
(1) it is measured using laser tracker before calibration and specifies point coordinates on bracket, fit bracket attained pose A, for
Object pose B is found out using inverse kinematic by each active moving sets ideal bits of pose A to pose B under nominal structure parameter
Shifting amount；
(2) active movement secondary motion is driven by each active moving sets ideal movements amount found out, is surveyed using laser tracker
It measures and specifies point coordinates on bracket, fit bracket attained pose C；
(3) bracket attained pose C is compared with object pose B, determines calibration front rack position and attitude error；
(4) space vector chain method is used, is established between bracket position and attitude error and structural failure, active moving sets displacement
Error model carries out structural failure identification using least square method；
(5) bracket nominal structure parameter is modified, carries out inverse kinematic again, determination will reach object pose B
When each active moving sets displacement.
Details are as follows：
When movement of bracket instead solves, 1~4 reference frame origin of locator is located at X1=0, X2=0, X3=0, X4
At=0, i.e. O1、O2、O3、O4At point, 1~4 reference frame of locator is E=relative to the posture changing matrix of basis coordinates system
diag(1,1,1).Basis coordinates system initial point is ObPoint, basis coordinates system x-axis direction are parallel to ideal sliding pair X4, by S2It is directed toward S1, base
Coordinate system y-axis is parallel to ideal sliding pair Y4, by S1It is directed toward S4, basis coordinates system z-axis is parallel to ideal sliding pair Z4, direction is by ObRefer to
To S1.Carrier center point is P relative to the vector of basis coordinates system initial point, and flexural pivot center is relative to bracket reference frame origin
Vector isLocator reference frame origin is λ with respect to the vector of basis coordinates system initial pointi；S1、S2、S3、S4Respectively locator
1~4 corresponding flexural pivot center；SiWith OiBetween include each prismatic pair of locator, i=1,2,3,4, for locator number；ObWith O1
It overlaps.
Definition：(1) " position error " is quoted from " 21 geometric errors ", when referring to movement secondary motion, actual motion distance
With the difference of target move distance；(2) " site error " is error of the point relative to coordinate system in x, y, z direction, such as flexural pivot
Site error, carrier center point site error relative to basis coordinates system of the central point relative to bracket coordinate origin；(3)
" active moving sets angular error " refers to the angular error between active movement pair actual direction vector and ideal orientation vector.
Each locator corresponds to a movement branched chain, by taking branch 3 as an example, establishes related basis coordinates system, locator with reference to seat
Mark system, flexural pivot center, bracket coordinate system closed loop space vector chain, bracket vector chain establishes mode such as Fig. 4, Fig. 5, locator 1,
2,4 corresponding closed loop space vector chain method for building up are similar.
Flexural pivot central point SiRelative to basis coordinates system initial point ObVector be：
SiOb=E (li1·ei1+li2·ei2+li3·ei3)+λi (1)
It is assumed that bracket pose_adjuster is in a certain pose in working space, space vector chain Fa Ke get is utilized：
Wherein, ei1=(1,0,0)T, ei3=(0,0,1)T, ei3=(0,0,1)T, i-th of locator x, y, z is indicated respectively
Direction unit vector, i indicate locator number；It is assumed that carrier center point OtCoordinate is (xp,yp,zp)T, then carrier center point OtPhase
For basis coordinates system initial point ObVectorial P=(xp,yp,zp)T；Posture changing for bracket coordinate system relative to basis coordinates system
Matrix, c represent cos, are behalf sin：
Wherein, α is bracket around axis OtXtThe angle of rotation, β are bracket around axis OtYtThe angle of rotation, γ are bracket around axis
OtZtThe angle of rotation, the positive and negative of α, β, γ meet right-hand rule；li1、li2、li3I-th of locator x, y, z direction is indicated respectively
Amount of exercise, i=1,2,3,4, then the as ideal inverse resolution model of the drive volume of each active moving sets can be expressed as under object pose：
Wherein,It is z to active moving sets elemental height.
It is analysis object with branch 1, establishes bracket position and attitude error, ideal active moving sets drive volume, structural failure, name
The relation equation of structural parameters：Branch 1 is single driving branch, and driving direction is the directions z, according to space vector chain principle：
Carrying out differential to formula (5) both ends can obtain：
Wherein, δ e13Indicate the directions the z active moving sets angular error of locator 1：
Wherein,For differential operator, subtracts unit matrix for differential spin matrix and get；δθ13x、δθ13y、δθ13zIt indicates respectively
The angular error of the directions the z active moving sets of locator 1 and ideal x, y, z axis, radian value.δ P indicate carrier center point relative to
The site error of basis coordinates system, δ P=(δ xp,δyp,δzp)T；Indicate bracket coordinate system relative to basis coordinates system spin matrix
Differential：Wherein, δ α, δ β, δ γ indicate that bracket is sat respectively
Attitude error of the mark system relative to basis coordinates system, radian value；δl13Indicate the directions the z position error of locator 1, δ l21、δl23、
δl33、δl43It defines similar；Indicate site error of the corresponding flexural pivot centers locator i relative to bracket coordinate origin,δλiLocator basis coordinates system initial point initial position is indicated relative to basis coordinates system initial point site error,
δλi=(δ λix,δλiy,δλiz)T；I=1,2,3,4。
2 corresponding constraint equation of branch establishes mode and branch 1 is identical；Branch 3,4 is single driving branch, main driving side
To for the directions z, x, y are to servo-actuated, according to space vector chain principle：
Carrying out differential to formula (7) both ends can obtain：
Wherein, δ li1、δli2To be servo-actuated prismatic pair position error；δei1、δei2To be servo-actuated prismatic pair angular error；It does not examine
Consider and be servo-actuated prismatic pair position error, servo-actuated prismatic pair angular error, then formula (8) can be reduced to：
Wherein, i numbers for locator, i=3, and 4；Remaining variables definition can refer to above in formula (9).
Gained equation (such as 1 corresponding equation (6) of branch) includes three constraints after the corresponding vector chain differential of each branch
Each branch constraint equation of equation is all included in error model by equation, then successively after vector chain differential gained equation two
It is multiplied by vector in sideConstraint equation is detached.It is multiplied by so that equation (6) both sides are same
VectorFor：
Wherein：
δe21、δe23、δe33、δe43Linearized fashion is similar.1 × 1 rank matrix is represented using 0,0 represents 1 × 3 rank matrix, whole
Following equation can be obtained after reason：
Tl·δl+Te·δe-Tλ·δλ=Tpθ·δpθ (10)
Wherein,
Wherein, TlFor 12 × 5 rank matrixes, δlFor 5 × 1 ranks
Matrix, TeFor 12 × 15 rank matrixes, δeFor 15 × 1 rank matrixes, TλFor 12 × 21 rank matrixes, δλFor 21 × 1 rank matrixes, TpθIt is 12
× 6 rank matrixes, δpθFor 6 × 1 rank matrixes.Formula (10) is arranged to obtain：
Wherein, [Tl Te -Tλ] it is 12 × 41 rank matrixes, [δl δe δλ]TFor 41 × 1 rank matrixes.Formula (11) can letter
It turns to：
Tiδ=(Tpθ·δpθ)i (12)
Due to δ e13、δe21、δe23、δe33、δe43Include respectively two unknown quantitys, therefore formula (12) includes 41-5=36
Unknown quantity, single pose are capable of providing 12 algebraic equations in relation to unknown quantity, therefore, to recognize all 36 position and attitude errors,
In the case of matrix T row vectors, column vector linear independence, need to measure 3 groups or more position and attitude error data composition overall errors
Model：
Wherein, n is pose group number, then formula (13) can be abbreviated as：
T δ=M (14)
But the T matrixes in formula (14), containing multiple 0 vector row, conditional number is big, sensitive to measurement error, directly using public
T matrixes in formula (14) carry out structural failure identification, and identification effect is poor, it is therefore desirable to structural failure identification analysis is carried out, to T
Matrix carries out dimension-reduction treatment.
When structural failure recognizes, the structural failure item that coefficient is zero has no influence, linearly related structure to bracket pose
Error needs to carry out whole identification, it is therefore desirable to carry out dimension-reduction treatment to coefficient matrix, use x1、x2…x36Counter structure misses respectively
Poor item δ l13、δl21…δλ4z, the correspondence such as table 1 of x and error term.
1 x, table and error term correspondence
From formula (14)：
1) matrix T the 8th row, the 9th row, the 14th row, the 17th row, the 20th be classified as 0 vector row and corresponding unknown number be 0, because
This, can directly reject related column composition matrix T ' in coefficient matrix T.It can be surveyed by laser tracker by practical measure
Measure bracket only z to movement posture adjustment during each locator prismatic pair specified point change in location into row matrix T the 8th row, the 14th row,
The indirect solution of 17th row, the 20th row counter structure error；The corresponding structural failure of the 9th row can be by bracket around S in matrix T1S4Rotation
Turn, the x of the measurement and positioning device 2 specified point spatial position change on shifting axle calculates indirectly.
2) due to the row of matrix T ' the 2nd, the 22nd linear correlation, the 3rd row, the 24th linear correlation, the 4th row, the 30th alignment
Property related, the 5th row, the 36th linear correlation, without loss of generality, in the case of the row of arbitrary row the 2nd, the 22nd row, then：
1×(x2+x22)+f(x1,x3…x36)=Δii
Wherein, ΔiiIt is multiplied by error term (i.e. (T for the global error term coefficient during bracket certain posture adjustmentpθ·δpθ)iIn
Certain row), f (x1,x3…x36) it is removal structural failure x2、x22Afterwards, remaining structural failure is to ΔiiInfluence.Linear correlation row pair
The structural failure item answered can not be recognized individually, can only pick out combined influence of the structural failure item to bracket global error item.Together
Reason can solve lower list in equation (18) as single entirety：x3+x24；x4+x30；x5+x36.Therefore, it enables：
Q2=x2+x22；Q3=x3+x24；Q4=x4+x30；Q5=x5+x36
Corresponding coefficient matrix T ' is arranged, and can obtain the error transformation matrix T " that columns is 32, it is therefore desirable to the knot of identification
Structure error parameter is transformed to x1、Q2、Q3、Q4、Q5、x6、x7、x8、x9、x10、x11、x12、x13、x14、x15、x16、x17、x18、x19、x20、
x21、x23、x25、x26、x27、x28、x29、x31、x32、x33、x34、x35, then formula (14) can be deformed into：
T " δ=M (15)
T matrixes in formula (14) have carried out dimension-reduction treatment, by the conditional number of matrix T by 1021It is reduced to 103Rank, drop
Low sensibility of the matrix T to measurement error.Error term can be recognized all in the formula (15) obtained by dimension-reduction treatment, can be
Using the left sides square M except " or matrix (T ") is multiplied by formula (15) both sides to matrix T in matlabTCoefficient matrix is become into nonsingular square
Invert after battle array and solve δ, by this section 1) it is found that x2、x3、x4、x5It can measure and calculate indirectly, then x22、x24、x30、x36It can ask.Extremely
This, can pick out all structural failures of posture adjustment bracket in parallel.
The error of error model identification can only be passed through： The error for measuring identification can only be crossed：δl21、δl23、δl33、δl43；Only may be used
Error term as obtained by calculating indirectly：δλ2x、δλ2z、δλ3z、δλ4z；By error model and the error recognized can be measured：δ
l13、δθ13y、δθ13x、δθ21z、δθ21y、δθ23y、δθ23x、δθ33y、δθ33x、δθ43y、δθ43x。
Compared to the modeling pattern that whole constraint equations are included in error model, whole constraint equations error model is not included in
Modeling pattern structural failure identification precision it is low.One group of structural failure is given at random, is chosen given value and is differed larger with identifier
Error term analyzed, the structural failure that the present invention picks out and given value difference maximum value are 0.1mm, are better than existing identification
The structural failure that method picks out and given value difference maximum value 1.13mm, such as Fig. 6 and Fig. 7.
Pose_adjuster actual structure parameters are modified, for object pose, on the basis of corrected structural parameters
Inverse kinematic is carried out again, sees equation group (16), is inputted and is gone out for object pose, nominal structure parameter, error model identification
Structural failure exports as the revised amount of exercise of each axis, calculates and considers structural failure δerror2When each active moving sets drive volume
With servo-actuated prismatic pair amount of exercise.
Wherein, i numbers for locator；li3aIndicate the practical drive volume of the directions z active moving sets of locator i, l21aIt indicates
The practical drive volume in the directions x of locator 2；ei3aIndicate i-th of the directions locator z active moving sets actual direction vector；e21aTable
Show the directions the x active moving sets actual direction vector of locator 2；Indicate that flexural pivot central point is real relative to bracket coordinate origin
Border vector；λiaIndicate locator coordinate origin relative to the practical vector of basis coordinates system initial point；I=1,2,3,4.
For the bracket position and attitude error for solving after compensating, equation group (17) is on the basis of each branch ideal normal solution vector chain (2)
On, the element to being related to structural failure is corrected, input each axis amount of exercise solved for revised inverse kinematic,
Actual structure parameters export as calibrated mechanism attained pose P θ2, with ideal pose P θ0It compares, finds calibrated position
Appearance error substantially reduces, and meets homework precision requirement.
Part that the present invention does not relate to is same as the prior art or can be realized by using the prior art.
Claims (3)
1. a kind of scaling method of aircraft automatic Drilling/Riveting parallel connection posture adjustment bracket, it is characterized in that object pose is directed to, in nominal structure
Each active moving sets desired displacement amount is found out using inverse kinematic under parameter；By each active moving sets desired displacement amount found out
Drive active moving sets movement；It after movement stops, being measured using laser tracker and specifies point coordinates on bracket, fit bracket reality
Border pose；Bracket attained pose is compared with object pose, determines calibration front rack position and attitude error；Using space vector chain
Method establishes the error model between bracket position and attitude error and structural failure, active moving sets displacement, using least square method into
Row structural failure recognizes；Bracket nominal structure parameter is modified, carries out inverse kinematic again, determination will reach target position
Each active moving sets displacement when appearance.
2. according to the method described in claim 1, it is characterized in that, measuring specified point on bracket using laser tracker before calibration
Coordinate fits bracket attained poseA, remaining specific demarcating steps is：
（1）For object poseB, found out by pose using inverse kinematic under nominal structure parameterATo poseBIt is each actively to move
Dynamic assistant manager thinks displacement；
（2）By find out each active moving sets desired displacement amount driving active moving sets movement, movement stop after, using laser with
Track instrument, which measures, specifies point coordinates on bracket, fit bracket attained poseC；
（3）By bracket attained poseCWith object poseBIt is compared, determines calibration front rack position and attitude error；
（4）Using space vector chain method, the error between bracket position and attitude error and structural failure, active moving sets displacement is established
Model carries out structural failure identification using least square method；
（5）Bracket nominal structure parameter is modified, carries out inverse kinematic again, determination will reach object poseBWhen
Each active moving sets displacement.
3. method according to claim 1 or 2, which is characterized in that when error model models, whole constraint equations are included in
Error model improves error identification precision, so as to identify the locator active moving sets angular error of single main driving；Accidentally
When difference identification, the identification structure error by the way of matrix dimensionality reduction ensures to miss under the premise of not changing structural failure term coefficient
Poor identification precision.
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| CN110181514A (en) * | 2019-06-06 | 2019-08-30 | 塞伯睿机器人技术（长沙）有限公司 | The robotic arm alignment device of robot |
| CN110181514B (en) * | 2019-06-06 | 2021-12-21 | 塞伯睿机器人技术（长沙）有限公司 | Mechanical arm calibration device of robot |
| CN110456827A (en) * | 2019-07-31 | 2019-11-15 | 南京理工大学 | A kind of large-scale workpiece packing case digitlization docking system and method |
| CN110456827B (en) * | 2019-07-31 | 2022-09-27 | 南京理工大学 | Large-sized workpiece packaging box digital butt joint system and method |
| CN110849267A (en) * | 2019-12-02 | 2020-02-28 | 南京航空航天大学 | Method for positioning and converting coordinate system on product by mobile automatic system based on local reference hole |
| CN110849267B (en) * | 2019-12-02 | 2021-02-26 | 南京航空航天大学 | Method for positioning and converting coordinate system on product by mobile automatic system based on local reference hole |
| CN112298600A (en) * | 2020-09-18 | 2021-02-02 | 成都飞机工业（集团）有限责任公司 | Multi-axis full-active attitude adjusting method and device for large airplane component with rotating center of gravity |
| CN112298600B (en) * | 2020-09-18 | 2022-05-06 | 成都飞机工业（集团）有限责任公司 | Multi-axis full-active attitude adjusting method and device for large airplane component with rotating center of gravity |
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