CN105716525B - End effector of robot coordinate system scaling method based on laser tracker - Google Patents

End effector of robot coordinate system scaling method based on laser tracker Download PDF

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CN105716525B
CN105716525B CN201610190887.4A CN201610190887A CN105716525B CN 105716525 B CN105716525 B CN 105716525B CN 201610190887 A CN201610190887 A CN 201610190887A CN 105716525 B CN105716525 B CN 105716525B
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msub
mtd
coordinate system
scaling board
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CN105716525A (en
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李飞飞
王战玺
秦现生
谭小群
王宁
郭欣
王玮
白晶
李靖
张顺琦
刘健
杨奇
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Northwestern Polytechnical University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
    • G01B11/005—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates coordinate measuring machines

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Abstract

The present invention proposes a kind of end effector of robot coordinate system scaling method based on laser tracker, being actually needed according to processing works such as drillings in method, defines tool coordinates system and camera coordinates system；It is instrument by means of laser tracker and homemade scaling board, defines scaling board coordinate system；By calibrate laser tracker coordinate system lower flange coordinate system, tool coordinates system, scaling board coordinate system position auto―control, the position auto―control of scaling board coordinate system under camera coordinates system, to try to achieve the position auto―control that tool coordinates system and camera coordinates are tied up under flange coordinate system, so as to obtain accurate tool coordinates system and camera coordinates system.

Description

End effector of robot coordinate system scaling method based on laser tracker
Technical field
The present invention relates to industrial robot calibration technique field, is a kind of end effector of robot tool coordinates system and phase The scaling method of machine coordinate system.Specially a kind of end effector of robot coordinate system scaling method based on laser tracker.
Background technology
In modern production manufacturing technology, industrial robot is gradually applied in fields such as aircraft, automobiles, and robot is used for The operations such as the drillings of parts, riveting, assembling, and production efficiency can be greatly improved, ensure product quality and its consistency, Shorten production cycle etc., applicable industry robot turns into a kind of new trend of industrial automation.During the manufacturing, industry Robot is moved according to the Program path finished in advance, and after reaching processing stations, workpiece is identified by high-precision industrial camera Co-ordinate system location, the error compensation of the theoretical location of workpiece and physical location is carried out, then the instrument on end effector of robot Moved in workpiece coordinate system, complete the processing tasks of correlation.
During robot motion, it is necessary to establish accurate end effector of robot coordinate system, the main identification position that includes is used Camera coordinates system and processing tool coordinates system.The typical method of Robot calibration ending coordinates system such as XYZ4 points at present Method, suitable for small instruments and tools, contact of the instrument fixing point with reference point is estimated in calibration process, precision is not high；Painted by three-dimensional Figure software, simulate theoretical coordinate system and actually have certain error.For large-sized end effector, it is necessary to using one The new method of kind comes calibration tool coordinate system and camera coordinates system exactly.
The content of the invention
The present invention is in order to solve tool coordinates system and camera coordinates system accurate calibration on industrial robot end effector Problem, by proposing the fast conversion method of a kind of robot relative coordinate system and laser tracker coordinate system, solves robot During practical application, end effector of robot quick and the problem of be accurately positioned.
The essence of end effector coordinate system demarcation is to determine tool coordinates system xtytzt, camera coordinates system xpypzpIn flange Coordinate system xFyFzFUnder position auto―control TFtAnd TFp, the parameter of two position auto―controls is then input to instrument corresponding to robot In Tool1 and camera Tool2 coordinate systems, robot can be with identification, and carries out the operation of correlation.
The technical scheme is that：
A kind of end effector of robot coordinate system scaling method based on laser tracker, it is characterised in that：Bag Include following steps：
Step 1：Laser tracker is placed around in robot, preheats laser tracker, laser tracker establishes acquiescence Laser tracker coordinate system xmymzm；Feeding motor is adjusted to zero-bit, the pressure nose on retraction end effector of robot, will demarcate Plate is fixed in robotic workstation, and adjustment robot makes pressure nose distance calibration plate plane be standard value ltp, and to scaling board Leveling, make the main-shaft axis of end effector of robot perpendicular to scaling board；The camera of end effector of robot can be simultaneously Photographing the laser tracker target ball in 5 holes of plum blossom-shaped distribution on scaling board, and in main shaft knife handle can receive The laser beam of laser tracker；Teaching current point is robot HOME1 points, and robot is all from HOME1 in calibration process afterwards Point sets out, and ensures that laser tracker has fixed reference point during coordinate system is demarcated；
Step 2：Measure flange coordinate system：
Step 2.1：Robot rotates around the 6th axle from HOME1 points, is recorded and rotated with Survey Software in a direction During target ball coordinate, until target ball does not receive the laser beam of laser tracker；Robot returns to HOME1 points, further around the Six axle opposite directions are rotated, and the coordinate of target ball in rotary course is recorded with Survey Software, until target ball does not receive laser tracker Laser beam；6th axle rotational circle and the 6th axle Plane of rotation are gone out according to the target ball coordinate fitting of record；Robot returns to HOME1 Point, rotated in a direction around the 5th axle, the coordinate of target ball in rotary course is recorded with Survey Software, until target ball does not receive The laser beam of laser tracker；Robot returns to HOME1 points, is rotated further around the 5th axle opposite direction, is recorded and rotated with Survey Software During target ball coordinate, until target ball does not receive the laser beam of laser tracker；Gone out according to the target ball coordinate fitting of record 5th axle rotational circle and the 5th axle Plane of rotation；
Step 2.2：The center of circle O of the 5th axle rotational circle is measured using Survey Software5O'clock to the 6th axle Plane of rotation distance D56, and then obtain flange coordinate system xFyFzFOrigin OFTo the distance D of the 6th axle surfaces of revolutionF6For：
DF6=D56-H
Wherein H is the center of circle O of the 5th axle rotational circle5Initial point distance of the point to flange coordinate system；With the 6th axle rotational circle Center of circle O6Centered on, using the normal orientation of the 6th axle surfaces of revolution as offset direction, offset up DF6, obtained point is that flange is sat Mark system xFyFzFOrigin OF(xmF,ymF,zmF)；
Step 2.3：Robot makes robot along flange coordinate system x from HOME1 pointsFyFzFXFDirection is moved, Fitting vectorFurther along the y of flange coordinate systemFDirection is moved, fitting vector6th axle Plane of rotation direction is downward Normal as flange coordinate system xFyFzFZFPositive direction, it is respectively compared zFPositive direction and vectorVectorAngle：
If above-mentioned two angle in the range of 89.95 °~90.05 °, takes vector corresponding to close 90 ° angle to make For accurate direction；If only an angle is in the range of 89.95 °~90.05 °, vector corresponding to the angle is taken as accurate side To；If two angles not in the range of 89.95 °~90.05 °, re-start this step；
Step 2.4：Using zFPlane is set up in the accurate direction that positive direction and step 2.3 determine, and obtains institute Jianping face Normal direction, so as to obtain flange coordinate system yFPositive direction and xFPositive direction；With origin O in laser tracker control softwareF、xFJust Direction, yFPositive direction structure flange coordinate system xFyFzF, it is obtained in laser tracker coordinate system xmymzmUnder position auto―control TmF：
Wherein omFIt is vectorial for unit,
nmF=omF×amF
TransmF=(xmF,ymF,zmF)T
Step 3：Calibration tool coordinate system：
Step 3.1：Robot feeds the feeding straight line of motor from HOME1 points, feeding motor linear motion, fitting, Machine direction is pointed to as tool coordinates system x in directiontytztXtPositive direction；It is motionless that robot is maintained at HOME1 points, uses laser Tracker nominal pressure nose plane, by pressure nose plane along tool coordinates system xtytztXtPositive direction is offset, and offset is pressure Nose length degree ltp, simulate theoretical workpiece planarization, theoretical workpiece planarization and the feeding motorized feed straight-line intersection O being fittedt(xmt, ymt,zmt) it is tool center point；
Step 3.2：By flange coordinate system xFyFzFXFPositive direction projects to tool coordinates system xtytztXtPositive direction is cut On face, tool coordinates system x is obtainedtytztZtPositive direction, further according to the right-hand rule, obtain tool coordinates system xtytztYtIt is square To；With tool coordinates system xtytztTool center point, xtPositive direction, ytPositive direction, ztPositive direction the build tool coordinate system xtytzt, it is obtained in laser tracker coordinate system xmymzmUnder position auto―control Tmt：
omt=nmt×amt
Transmt=(xmt,ymt,zmt)T
Step 4：Build scaling board coordinate system xbybzb, and obtain scaling board coordinate system xbybzbIn laser tracker coordinate system xmymzmUnder position auto―control Tmb：
Step 4.1：Target ball is placed on target seat, target seat is put into five in scaling board holes respectively, is kept Target seat lower surface and scaling board plane are adjacent to, and five holes of measurement are in laser tracker coordinate system xmymzmUnder coordinate value Pmb10 (xmb10,ymb10,zmb10)、Pmb20(xmb20,ymb20,zmb20)、Pmb30(xmb30,ymb30,zmb30)、Pmb40(xmb40,ymb40,zmb40)、 Pmb50(xmb50,ymb50,zmb50)；
Step 4.2：Scaling board is fixed on robot workbench, if the uniformly collection in scaling board plane with target ball Dry not conllinear point, excludes the radius size of target ball, scaling board plane is built under laser tracker coordinate system；Utilize measurement Software projects in five holes of measurement in scaling board plane, and the subpoint for obtaining five holes is respectively Pmb1(xmb1,ymb1, zmb1)、Pmb2(xmb2,ymb2,zmb2)、Pmb3(xmb3,ymb3,zmb3)、Pmb4(xmb4,ymb4,zmb4) and Pmb5(xmb5,ymb5,zmb5)；
Step 4.3：With the projection P of the centre bore in five holesmb1For origin, with Pmb1Point to the projection P in hole 2mb2Direction is Scaling board coordinate system xbybzbXbAxle positive direction, obtaining unit vector is：
With the normal direction of scaling board and vertical calibrating plate is downwards for scaling board coordinate system xbybzbZbAxle positive direction, its unit Vector is：
Scaling board coordinate system x is obtained by the right-hand rulebybzbYbAxle positive direction, its unit vector are：
omb0=amb0×nmb0
Scaling board coordinate system xbybzbIn laser tracker coordinate system xmymzmUnder position auto―control be：
Wherein：
nmb=nmb0
omb=omb0
amb=amb0
Transmb=(xmb1 ymb1 zmb1)T
Step 5：Calibration for cameras coordinate system：
Step 5.1：It is motionless that robot is maintained at HOME1 points, opens the camera of end effector of robot and adjusts camera Focal length, until being clearly apparent in the camera on scaling board in 5 holes of plum blossom-shaped distribution, it is recorded in camera and carries coordinate system xp0Oyp0The coordinate value at lower five holes center, Ppb01(xpb01,ypb01)、Ppb02(xpb02,ypb02)、Ppb03(xpb03,ypb03)、Ppb04 (xpb04,ypb04)、Ppb05(xpb05,ypb05)；
Step 5.2：The coordinate value at five holes center is obtained according to step 4.1, calculate pixel between each two hole away from From lpij：
Wherein i, j=1~5 and i ≠ j, obtains l successivelyp12、lp13、lp14、lp15、lp23、lp24、lp25、lp34、lp35、lp45；
Step 5.3：According to Pmb1(xmb1,ymb1,zmb1)、Pmb2(xmb2,ymb2,zmb2)、Pmb3(xmb3,ymb3,zmb3)、Pmb4 (xmb4,ymb4,zmb4) and Pmb5(xmb5,ymb5,zmb5) actual range L between two holes corresponding to calculatingpij：
Wherein i, j=1~5 and i ≠ j, obtain the actual range L between five holes on scaling boardp12、Lp13、Lp14、Lp15、 Lp23、Lp24、Lp25、Lp34、Lp35、Lp45；Actual each millimeter pixel number N is obtained successivelyij
Obtain corresponding N12、N13、N14、N15、N23、N24、N25、N34、N35、N45Average value N；
Step 5.4：Five holes are obtained on scaling board in camera coordinates system xpypzpUnder coordinate be Ppb1(xpb1,ypb1, zpb1)、Ppb2(xpb2,ypb2,zpb2)、Ppb3(xpb3,ypb3,zpb3)、Ppb4(xpb4,ypb4,zpb4)、Ppb5(xpb5,ypb5,zpb5) be：
zpbi=0
Wherein i=1~5, L0*B0For camera pixel point actual size；
Step 5.5：Coordinate points P of the centre bore under camera coordinates system on scaling board in five holespb1(xpb1,ypb1, zpb1) it is origin,For scaling board coordinate system xbybzbXbAxle positive direction, then build vectorAccording to the right side Hand rule fromPositive direction points to xbThe positive direction of axle, obtain scaling board coordinate system xbybzbZbAxle positive direction, then with xbAxle positive direction and zbAxle positive direction draws y according to the right-hand rulebAxle positive direction, so as to obtain scaling board coordinate system xbybzbIn phase Machine coordinate system xpypzpIn position auto―control Tpb：
Wherein：
opb=apb×npb
Transpb=(xpb1 ypb1 zpb1)T
Step 6：According to obtained laser tracker coordinate system xmymzmUnder, flange coordinate system xFyFzF, tool coordinates system xtytzt, scaling board coordinate system xbybzbPosition auto―control TmF、Tmt、Tmb, and scaling board coordinate system xbybzbIn camera coordinates system xpypzpUnder position auto―control Tpb, using matrix conversion relation, obtain in flange coordinate system xFyFzFUnder, tool coordinates system xtytzt Position auto―control TFtWith camera coordinates system xpypzpPosition auto―control TFp：
TFt=(TmF)-1Tmt
Tmp=Tmb(Tpb)-1
TFp=(TmF)-1Tmb(Tpb)-1
Step 7：By tool coordinates system xtytzt, camera coordinates system xpypzpIn flange coordinate system xFyFzFUnder position auto―control TFtAnd TFpCorresponding parameter be input in tool coordinates system Tool1 and Tool2 parameter list corresponding to robot, define Tool1 be Tool coordinates system xtytzt, Tool2 is camera coordinates system xpypzp, robot identification Tool1 and Tool2 parameter, so as to Work is run in the coordinate system that programming personnel specifies.
Beneficial effect
Being actually needed according to processing works such as drillings of the invention, defines tool coordinates system and camera coordinates system.By means of Laser tracker and homemade scaling board are instrument, define scaling board coordinate system.The method according to the invention, calibrate in laser Tracker coordinate system lower flange coordinate system, tool coordinates system, the position auto―control of scaling board coordinate system, are demarcated under camera coordinates system The position auto―control of plate coordinate system, to try to achieve the position auto―control that tool coordinates system and camera coordinates are tied up under flange coordinate system, so as to Obtain accurate tool coordinates system and camera coordinates system.
Brief description of the drawings
The above-mentioned and/or additional aspect and advantage of the present invention will become in the description from combination accompanying drawings below to embodiment Substantially and it is readily appreciated that, wherein：
Fig. 1 tool coordinates system calibration principle figures；
Fig. 2 laser tracker software SpatialAnalyzer interfaces；
Fig. 3 robot coordinate systems demarcate scene photo；
Fig. 4 flanges coordinate system and tool coordinates system calibration principle figure；
Schematic diagram is demarcated by Fig. 5 ending coordinates system；(origin of tool coordinates system and camera coordinates system is defined on theoretical workpiece In plane)
Fig. 6 camera fields of view；
Fig. 7 scaling boards.
Embodiment
Embodiments of the invention are described below in detail, the example of the embodiment is shown in the drawings, is described with reference to the drawings Embodiment be exemplary, it is intended to for explaining the present invention, and be not considered as limiting the invention.
In the description of the invention, it is to be understood that term " " center ", " longitudinal direction ", " transverse direction ", " length ", " width ", " thickness ", " on ", " under ", "front", "rear", "left", "right", " vertical ", " level ", " top ", " bottom ", " interior ", " outer ", " up time The orientation or position relationship of the instruction such as pin ", " counterclockwise " are based on orientation shown in the drawings or position relationship, are for only for ease of Description is of the invention to be described with simplified, rather than the device or element of instruction or hint meaning must be with specific orientation, Yi Te Fixed azimuth configuration and operation, therefore be not considered as limiting the invention.
The present embodiment is that example is processed in drilling, demarcates concretely comprising the following steps for accurate tool coordinates system and camera coordinates system：
Step 1：According to shown in Fig. 1, laser tracker is placed around in robot, preheats laser tracker, preheated simultaneously, Laser tracker establishes the laser tracker coordinate system x of acquiescencemymzm, feed motor and be adjusted to zero-bit set during drilling, machine Pressure nose on device people's end effector is retracted, and scaling board is fixed on immediately ahead of robot on workbench, and adjustment robot makes it Pressure nose distance calibration plate plane is standard value ltp, and the main-shaft axis in scaling board leveling, guarantee end effector is vertical In scaling board, and enable the camera on end effector to photograph 5 plum blossom holes on scaling board simultaneously, and ensure to be arranged on Laser tracker target ball in main shaft knife handle can receive the laser beam of follower head.Teaching current point is robot HOME1 points, All calibration process robots are all from HOME1 points afterwards, and it is solid to ensure that laser tracker has during coordinate system is demarcated Fixed reference point.In addition, in addition to demarcation feeds motor drive direction, it is impossible to mobile feeding motor, to ensure that target ball and end perform The connected relation of device.
Step 2：The measurement of flange coordinate system.Robot rotates rotating around the 5th axle, the 6th axle, then makes robot at itself Moved respectively by each coordinate direction under flange coordinate system, sample some groups of points using laser tracker, recycle Survey Software Spatial Analyzer, fit flange coordinate system xFyFzF, flange coordinate system is obtained in laser tracker coordinate system xmymzm Under position auto―control TmF。
Step 2.1：Robot rotates around the 6th axle from HOME1, Survey Software is used every 1 ° or so in a direction Spatial Analyzer record the coordinate of target ball, and adjustment target ball continues measurement until target ball does not receive laser beam, robot Rotated after returning HOME1 further around the 6th axle opposite direction, measure the coordinate of target ball, adjustment target ball continues measurement until target ball does not receive Laser beam, robot return HOME1 points.Robot from HOME1 points, rotates around the 5th axle again, ibid gathers some row points, such as Shown in Fig. 2 and Fig. 3.In Survey Software Spatial Analyzer, the 6th axle rotational circle, the 6th axle are fitted with the point of collection Plane, the 5th axle rotational circle, the 5th axle rotation plane are revolved, as shown in Figure 4.
Step 2.2：The center of circle O of the 5th axle rotational circle is tried to achieve using Spatial Analyzer5O'clock to the 6th axle surfaces of revolution Distance D56, and the axle of robot five and six axles are met at a bit, the center of circle O of the 5th axle rotational circle5Origin of the point to flange coordinate system Distance is H.Flange coordinate system x can be tried to achieveFyFzFOrigin OFTo the distance D of the 6th axle surfaces of revolutionF6For：
DF6=D56-H
With the center of circle O of the 6th axle rotational circle6Centered on, using the normal orientation of the 6th axle surfaces of revolution as offset direction, upwards Offset DF6, obtained point is flange coordinate system xFyFzFOrigin OF(xmF,ymF,zmF)。
Step 2.3：Robot makes robot along flange coordinate system x from HOME1 pointsFyFzFXFPositive direction ( Can be along xFNegative direction) it is mobile, gather a point, fitting vector every 50mm or soFurther along the y of flange coordinate systemFIt is square To (also can be along yFNegative direction) mobile, fitting vectorSat the downward normal in the 6th axle Plane of rotation direction as flange Mark system xFyFzFZFPositive direction, it is respectively compared zFPositive direction and vectorVectorAngle：
If above-mentioned two angle in the range of 89.95 °~90.05 °, takes vector corresponding to close 90 ° angle to make For accurate direction；If only an angle is in the range of 89.95 °~90.05 °, vector corresponding to the angle is taken as accurate side To；If two angles not in the range of 89.95 °~90.05 °, re-start this step；
Step 2.4：Using zFPlane is set up in the accurate direction that positive direction and step 2.3 determine, and obtains institute Jianping face Normal direction, so as to obtain flange coordinate system yFPositive direction and xFPositive direction；With origin O in laser tracker control softwareF、xFJust Direction, yFPositive direction structure flange coordinate system xFyFzF, it is obtained in laser tracker coordinate system xmymzmUnder position auto―control TmF：
Wherein omFFor unit vector
nmF=omF×amF
TransmF=(xmF,ymF,zmF)T
Step 3：Calibration tool coordinate system：The moving direction of feeding motor is fitted using laser tracker sampling, also It is main axle cutter axis, as tool coordinates system xtytztXtPositive direction.Demarcation fits theoretical workpiece planarization and tool axis Intersection point as tool coordinates system xtytztOrigin TCP points, during drilling after robot motion in place, TCP points are the positions for treating drilling Put；Then according to flange coordinate system xFyFzFDirection determine tool coordinates system xtytztYtAnd ztDirection, so as to soft in measurement The tool coordinates system x of end effector is obtained in part Spatial AnalyzertytztIn laser tracker coordinate system xmymzmUnder Position auto―control Tmt。
Step 3.1：The feeding motor drive direction of end effector is demarcated, as tool coordinates system xtytztXtPositive direction：Machine Device people is from HOME1 points, and feeding motor linear motion, if being done every 5mm or so collections, the feeding of fitting feeding motor is straight Machine direction is pointed to as tool coordinates system x in line, directiontytztXtPositive direction.
Calibration tool coordinate system xtytztTCP points：It is motionless that robot is maintained at HOME1 points, is demarcated and pressed with laser tracker Power nose plane, by pressure nose plane along tool coordinates system xtytztXtPositive direction is offset, and offset is pressure nose length degree ltp, mould Draw up the feeding motorized feed straight-line intersection O of theoretical workpiece planarization, theoretical workpiece planarization and fittingt(xmt,ymt,zmt) it is instrument Central point；
Step 3.2：Tool coordinates system x is obtained using Survey Software Spatial Analyzer processing datastytzt：By method Blue coordinate system xFyFzFXFPositive direction projects to tool coordinates system xtytztXtOn the section of positive direction, tool coordinates system is obtained xtytztZtPositive direction, further according to the right-hand rule, obtain tool coordinates system xtytztYtPositive direction；With tool coordinates system xtytzt Tool center point, xtPositive direction, ytPositive direction, ztPositive direction the build tool coordinate system xtytzt, it is obtained in laser tracker Coordinate system xmymzmUnder position auto―control Tmt：
omt=nmt×amt
Transmt=(xmt,ymt,zmt)T
Step 4：As shown in fig. 7, five holes on scaling board are measured in laser tracker coordinate using laser tracker It is xmymzmUnder coordinate Pmb10(xmb10,ymb10,zmb10)、Pmb20(xmb20,ymb20,zmb20)、Pmb30(xmb30,ymb30,zmb30)、 Pmb40(xmb40,ymb40,zmb40)、Pmb50(xmb50,ymb50,zmb50), after projecting to scaling board plane, obtain subpoint Pmb1(xmb1, ymb1,zmb1)、Pmb2(xmb2,ymb2,zmb2)、Pmb3(xmb3,ymb3,zmb3)、Pmb4(xmb4,ymb4,zmb4) and Pmb5(xmb5,ymb5, zmb5), then build scaling board coordinate system xbybzb, and obtain scaling board coordinate system xbybzbIn laser tracker coordinate system xmymzm Under position auto―control Tmb：
Step 4.1：The hole on scaling board is measured in laser tracker coordinate system xmymzmUnder coordinate value：Target ball is placed on On target seat, target seat is put into five in scaling board holes respectively, keeps target seat lower surface and scaling board plane patch Tightly, five holes are measured in laser tracker coordinate system xmymzmUnder coordinate value Pmb10(xmb10,ymb10,zmb10)、Pmb20(xmb20, ymb20,zmb20)、Pmb30(xmb30,ymb30,zmb30)、Pmb40(xmb40,ymb40,zmb40)、Pmb50(xmb50,ymb50,zmb50)；
Step 4.2：Scaling board plane is built, and by the coordinate projection in measure five holes to scaling board plane, is obtained Hole position coordinate information in plane：Scaling board is fixed on robot workbench, with target ball in scaling board plane uniformly Several not conllinear points are gathered, exclude the radius size of target ball, scaling board plane is built under laser tracker coordinate system；Profit Five holes of measurement are projected in scaling board plane with Survey Software.During due to target ball measured hole, target seat is not necessarily strict Scaling board is adjacent to, excludes the hole position coordinate after target ball radius size not necessarily on scaling board, so utilizing Survey Software For SpatialAnalyzer by the hole coordinate projection of measurement to scaling board plane, the subpoint for obtaining five holes is respectively Pmb1 (xmb1,ymb1,zmb1)、Pmb2(xmb2,ymb2,zmb2)、Pmb3(xmb3,ymb3,zmb3)、Pmb4(xmb4,ymb4,zmb4) and Pmb5(xmb5, ymb5,zmb5)；
Step 4.3：Scaling board coordinate system x is established using subpoint coordinate valuebybzb.As shown in fig. 6, with five holes The projection P of centre boremb1For origin, with Pmb1Point to the projection P in hole 2mb2Direction is scaling board coordinate system xbybzbXbAxle is square To obtaining unit vector is：
With the normal direction of scaling board and vertical calibrating plate is downwards for scaling board coordinate system xbybzbZbAxle positive direction, its unit Vector is：
Scaling board coordinate system x is obtained by the right-hand rulebybzbYbAxle positive direction, its unit vector are：
omb0=amb0×nmb0
Scaling board coordinate system xbybzbIn laser tracker coordinate system xmymzmUnder position auto―control be：
N in formulamb、omb、ambIt is scaling board coordinate system x respectivelybybzbThree directions in laser tracker coordinate system xmymzmUnder unit vector, TransmbIt is scaling board coordinate system xbybzbPoint of origin Pmb1In laser tracker coordinate system xmymzmUnder Coordinate value transposition：
nmb=nmb0
omb=omb0
amb=amb0
Transmb=(xmb1 ymb1 zmb1)T
Step 5：Calibration for cameras coordinate system：The origin of camera coordinates system is the friendship of image center axis and theoretical workpiece planarization Point, the z of camera coordinates systempPositive direction and tool coordinates system xtytztXtPositive direction is identical, and the x of camera coordinates systempPositive direction And ypPositive direction carries coordinate system x with camera respectivelyp0Oyp0Xp0Direction and yp0Direction is parallel, as shown in Figure 6.In drilling benchmark In detection process, during using camera, the coordinate origin of camera coordinates system is the normal place of datum hole.It is clear by camera Five holes on scaling board are shot, hole is obtained and carries coordinate system x in camerap0Oyp0Under coordinate, be then transformed into camera coordinates It is xpypzpUnder, establish scaling board coordinate system xbybzbIn camera coordinates system xpypzpIn position auto―control Tpb。
Step 5.1：It is motionless that robot is maintained at HOME1 points, opens the camera of end effector of robot and adjusts camera Focal length, until being clearly apparent in the camera on scaling board in 5 holes of plum blossom-shaped distribution, it is recorded in camera and carries coordinate system xp0Oyp0The coordinate value at lower five holes center, Ppb01(xpb01,ypb01)、Ppb02(xpb02,ypb02)、Ppb03(xpb03,ypb03)、Ppb04 (xpb04,ypb04)、Ppb05(xpb05,ypb05)；
Step 5.2：The coordinate value at five holes center is obtained according to step 4.1, calculate pixel between each two hole away from From lpij：
Wherein i, j=1~5 and i ≠ j, obtains l successivelyp12、lp13、lp14、lp15、lp23、lp24、lp25、lp34、lp35、lp45；
Step 5.3：According to Pmb1(xmb1,ymb1,zmb1)、Pmb2(xmb2,ymb2,zmb2)、Pmb3(xmb3,ymb3,zmb3)、Pmb4 (xmb4,ymb4,zmb4) and Pmb5(xmb5,ymb5,zmb5) actual range L between two holes corresponding to calculatingpij：
Wherein i, j=1~5 and i ≠ j, obtain the actual range L between five holes on scaling boardp12、Lp13、Lp14、Lp15、 Lp23、Lp24、Lp25、Lp34、Lp35、Lp45；Actual each millimeter pixel number N is obtained successivelyij
Obtain corresponding N12、N13、N14、N15、N23、N24、N25、N34、N35、N45Average value N；
Step 5.4：It is camera coordinates system x by the pixel coordinate transformation in five holespypzpUnder coordinate, and from two dimension sit Mark expands to three-dimensional coordinate：Camera coordinates system x in Fig. 6pypzpOrigin OpIt is projected in the centre of camera fields of view, calibration process Middle scaling board is fixed on the pressure nose l apart from retracted modetpParallel plane on, then on scaling board five holes in camera coordinates system xpypzpUnder coordinate be Ppb1(xpb1,ypb1,zpb1)、Ppb2(xpb2,ypb2,zpb2)、Ppb3(xpb3,ypb3,zpb3)、Ppb4(xpb4, ypb4,zpb4)、Ppb5(xpb5,ypb5,zpb5), now the coordinate in five holes is in camera coordinates system xpypzpLower physical length unit is sat Mark.Five holes are in camera coordinates system x on scaling boardpypzpUnder coordinate be Ppb1(xpb1,ypb1,zpb1)、Ppb2(xpb2,ypb2, zpb2)、Ppb3(xpb3,ypb3,zpb3)、Ppb4(xpb4,ypb4,zpb4)、Ppb5(xpb5,ypb5,zpb5) be
zpbi=0
Wherein i=1~5, L0*B0For camera pixel point actual size.
Step 5.5：Coordinate points P of the centre bore under camera coordinates system on scaling board in five holespb1(xpb1,ypb1, zpb1) it is origin,For scaling board coordinate system xbybzbXbAxle positive direction, then build vectorAccording to the right hand Rule fromPositive direction points to xbThe positive direction of axle, obtain scaling board coordinate system xbybzbZbAxle positive direction, then with xb Axle positive direction and zbAxle positive direction draws y according to the right-hand rulebAxle positive direction, so as to obtain scaling board coordinate system xbybzbIn camera Coordinate system xpypzpIn position auto―control Tpb：
Wherein：
opb=apb×npb
Transpb=(xpb1 ypb1 zpb1)T
Step 6：According to obtained laser tracker coordinate system xmymzmUnder, flange coordinate system xFyFzF, tool coordinates system xtytzt, scaling board coordinate system xbybzbPosition auto―control TmF、Tmt、Tmb, and scaling board coordinate system xbybzbIn camera coordinates system xpypzpUnder position auto―control Tpb, using matrix conversion relation, obtain in flange coordinate system xFyFzFUnder, tool coordinates system xtytzt Position auto―control TFtWith camera coordinates system xpypzpPosition auto―control TFp。
The position auto―control T tied up to according to flange and tool coordinates under laser tracker coordinate systemmF、Tmt, obtain tool coordinates It is xtytztIn flange coordinate system xFyFzFUnder position auto―control TFt：
TFt=(TmF)-1Tmt
According to the relation T of camera, scaling board coordinate system and laser tracker coordinate systempb、Tmb, obtain camera coordinates system xpypzpIn laser tracker coordinate system xmymzmUnder position auto―control Tmp：
Tmp=Tmb(Tpb)-1
According to position auto―control T of the flange coordinate system under laser tracker coordinate systemmF, obtain camera coordinates system xpypzp Flange coordinate system xFyFzFUnder position auto―control TFp。
TFp=(TmF)-1Tmb(Tpb)-1
Step 7：By tool coordinates system xtytzt, camera coordinates system xpypzpIn flange coordinate system xFyFzFUnder position auto―control TFtAnd TFpCorresponding parameter be input in tool coordinates system Tool1 and Tool2 parameter list corresponding to robot, define Tool1 be Tool coordinates system xtytzt, Tool2 is camera coordinates system xpypzp, robot identification Tool1 and Tool2 parameter, so as to Work is run in the coordinate system that programming personnel specifies.
Although embodiments of the invention have been shown and described above, it is to be understood that above-described embodiment is example Property, it is impossible to limitation of the present invention is interpreted as, one of ordinary skill in the art is not departing from the principle and objective of the present invention In the case of above-described embodiment can be changed within the scope of the invention, change, replace and modification.

Claims (1)

  1. A kind of 1. end effector of robot coordinate system scaling method based on laser tracker, it is characterised in that：Including following Step：
    Step 1：Laser tracker is placed around in robot, preheats laser tracker, laser tracker establishes the laser of acquiescence Tracker coordinate system xmymzm；Feeding motor is adjusted to zero-bit, the pressure nose on retraction end effector of robot, scaling board is consolidated It is scheduled in robotic workstation, adjustment robot makes pressure nose distance calibration plate plane be standard value ltp, and to scaling board leveling, Make the main-shaft axis of end effector of robot perpendicular to scaling board；The camera of end effector of robot can photograph mark simultaneously In 5 holes of plum blossom-shaped distribution on fixed board, and the laser tracker target ball in the main shaft knife handle can receive laser with The laser beam of track instrument；Teaching current point is robot HOME1 points, afterwards in calibration process robot be all from HOME1 points, Ensure that laser tracker has fixed reference point during coordinate system is demarcated；The artificial six axis joints robot of machine；
    Step 2：Measure flange coordinate system：
    Step 2.1：Robot rotates around the 6th axle from HOME1 points, rotary course is recorded with Survey Software in a direction The coordinate of middle target ball, until target ball does not receive the laser beam of laser tracker；Robot returns to HOME1 points, further around the 6th axle Opposite direction is rotated, and the coordinate of target ball in rotary course is recorded with Survey Software, until target ball does not receive swashing for laser tracker Light beam；6th axle rotational circle and the 6th axle Plane of rotation are gone out according to the target ball coordinate fitting of record；Robot returns to HOME1 points, In a direction around the 5th axle rotate, with Survey Software record rotary course in target ball coordinate, until target ball do not receive it is sharp The laser beam of optical tracker system；Robot returns to HOME1 points, is rotated further around the 5th axle opposite direction, is rotated through with Survey Software record The coordinate of target ball in journey, until target ball does not receive the laser beam of laser tracker；Go out according to the target ball coordinate fitting of record Five axle rotational circles and the 5th axle Plane of rotation；
    Step 2.2：The center of circle O of the 5th axle rotational circle is measured using Survey Software5O'clock to the 6th axle Plane of rotation distance D56, enter And obtain flange coordinate system xFyFzFOrigin OFTo the distance D of the 6th axle surfaces of revolutionF6For：
    DF6=D56-H
    Wherein H is the center of circle O of the 5th axle rotational circle5Initial point distance of the point to flange coordinate system；With the center of circle O of the 6th axle rotational circle6 Centered on, using the normal orientation of the 6th axle surfaces of revolution as offset direction, offset up DF6, obtained point is flange coordinate system xFyFzFOrigin OF(xmF,ymF,zmF)；
    Step 2.3：Robot makes robot along flange coordinate system x from HOME1 pointsFyFzFXFDirection move, be fitted to AmountFurther along the y of flange coordinate systemFDirection is moved, fitting vectorBy the normal that the 6th axle Plane of rotation direction is downward As flange coordinate system xFyFzFZFPositive direction, it is respectively compared zFPositive direction and vectorVectorAngle：
    If above-mentioned two angle in the range of 89.95 °~90.05 °, takes vector corresponding to close 90 ° angle as accurate True direction；If only an angle is in the range of 89.95 °~90.05 °, it is accurate direction to take vector corresponding to the angle；If Two angles not in the range of 89.95 °~90.05 °, then re-start this step；
    Step 2.4：Using zFPlane is set up in the accurate direction that positive direction and step 2.3 determine, and obtains the normal direction in institute Jianping face, So as to obtain flange coordinate system yFPositive direction and xFPositive direction；With origin O in laser tracker control softwareF、xFPositive direction, yF Positive direction structure flange coordinate system xFyFzF, it is obtained in laser tracker coordinate system xmymzmUnder position auto―control TmF：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>n</mi> <mrow> <mi>m</mi> <mi>F</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>o</mi> <mrow> <mi>m</mi> <mi>F</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>F</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>Trans</mi> <mrow> <mi>m</mi> <mi>F</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein omFIt is vectorial for unit,
    nmF=omF×amF
    TransmF=(xmF,ymF,zmF)T
    Step 3：Calibration tool coordinate system：
    Step 3.1：Robot is from HOME1 points, feeding motor linear motion, the feeding straight line of fitting feeding motor, direction Machine direction is pointed to as tool coordinates system xtytztXtPositive direction；It is motionless that robot is maintained at HOME1 points, is tracked with laser Instrument nominal pressure nose plane, by pressure nose plane along tool coordinates system xtytztXtPositive direction is offset, and offset is pressure nose length Spend ltp, simulate theoretical workpiece planarization, theoretical workpiece planarization and the feeding motorized feed straight-line intersection O being fittedt(xmt,ymt,zmt) For tool center point；
    Step 3.2：By flange coordinate system xFyFzFXFPositive direction projects to tool coordinates system xtytztXtThe section of positive direction On, obtain tool coordinates system xtytztZtPositive direction, further according to the right-hand rule, obtain tool coordinates system xtytztYtPositive direction； With tool coordinates system xtytztTool center point, xtPositive direction, ytPositive direction, ztPositive direction the build tool coordinate system xtytzt, obtain To it in laser tracker coordinate system xmymzmUnder position auto―control Tmt：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>n</mi> <mrow> <mi>m</mi> <mi>t</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>o</mi> <mrow> <mi>m</mi> <mi>t</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>t</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>Trans</mi> <mrow> <mi>m</mi> <mi>t</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    <mrow> <msub> <mi>n</mi> <mrow> <mi>m</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mover> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mover> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> </mrow> </mfrac> </mrow>
    <mrow> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mover> <msub> <mi>y</mi> <mi>F</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;times;</mo> <mover> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> </mrow> <mrow> <mo>|</mo> <mover> <msub> <mi>y</mi> <mi>F</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> <mo>&amp;times;</mo> <mover> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>&amp;RightArrow;</mo> </mover> <mo>|</mo> </mrow> </mfrac> </mrow>
    omt=nmt×amt
    Transmt=(xmt,ymt,zmt)T
    Step 4：Build scaling board coordinate system xbybzb, and obtain scaling board coordinate system xbybzbIn laser tracker coordinate system xmymzmUnder position auto―control Tmb：
    Step 4.1：Target ball is placed on target seat, target seat is put into five in scaling board holes respectively, keeps target Seat lower surface and scaling board plane are adjacent to, and five holes of measurement are in laser tracker coordinate system xmymzmUnder coordinate value Pmb10(xmb10, ymb10,zmb10)、Pmb20(xmb20,ymb20,zmb20)、Pmb30(xmb30,ymb30,zmb30)、Pmb40(xmb40,ymb40,zmb40)、Pmb50 (xmb50,ymb50,zmb50)；
    Step 4.2：Scaling board is fixed on robot workbench, several are uniformly gathered in scaling board plane with target ball Not conllinear point, the radius size of target ball is excluded, scaling board plane is built under laser tracker coordinate system；Utilize Survey Software Five holes of measurement are projected in scaling board plane, the subpoint for obtaining five holes is respectively Pmb1(xmb1,ymb1,zmb1)、Pmb2 (xmb2,ymb2,zmb2)、Pmb3(xmb3,ymb3,zmb3)、Pmb4(xmb4,ymb4,zmb4) and Pmb5(xmb5,ymb5,zmb5)；
    Step 4.3：With the projection P of the centre bore in five holesmb1For origin, with Pmb1Point to the projection P in hole 2mb2Direction is demarcation Plate coordinate system xbybzbXbAxle positive direction, obtaining unit vector is：
    With the normal direction of scaling board and vertical calibrating plate is downwards for scaling board coordinate system xbybzbZbAxle positive direction, its unit vector For：
    Scaling board coordinate system x is obtained by the right-hand rulebybzbYbAxle positive direction, its unit vector are：
    omb0=amb0×nmb0
    Scaling board coordinate system xbybzbIn laser tracker coordinate system xmymzmUnder position auto―control be：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>n</mi> <mrow> <mi>m</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>o</mi> <mrow> <mi>m</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mi>m</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>Trans</mi> <mrow> <mi>m</mi> <mi>b</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein：
    nmb=nmb0
    omb=omb0
    amb=amb0
    Transmb=(xmb1 ymb1 zmb1)T
    Step 5：Calibration for cameras coordinate system：
    Step 5.1：It is motionless that robot is maintained at HOME1 points, opens the camera of end effector of robot and adjusts camera focus, Until being clearly apparent in the camera on scaling board in 5 holes of plum blossom-shaped distribution, it is recorded in camera and carries coordinate system xp0Oyp0Under The coordinate value at five holes center, Ppb01(xpb01,ypb01)、Ppb02(xpb02,ypb02)、Ppb03(xpb03,ypb03)、Ppb04(xpb04, ypb04)、Ppb05(xpb05,ypb05)；
    Step 5.2：The coordinate value at five holes center is obtained according to step 4.1, calculates the pixel distance between each two hole lpij：
    <mrow> <msub> <mi>l</mi> <mrow> <mi>p</mi> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>p</mi> <mi>b</mi> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>p</mi> <mi>b</mi> <mn>0</mn> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>p</mi> <mi>b</mi> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>p</mi> <mi>b</mi> <mn>0</mn> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow>
    Wherein i, j=1~5 and i ≠ j, obtains l successivelyp12、lp13、lp14、lp15、lp23、lp24、lp25、lp34、lp35、lp45；
    Step 5.3：According to Pmb1(xmb1,ymb1,zmb1)、Pmb2(xmb2,ymb2,zmb2)、Pmb3(xmb3,ymb3,zmb3)、Pmb4(xmb4, ymb4,zmb4) and Pmb5(xmb5,ymb5,zmb5) actual range L between two holes corresponding to calculatingpij：
    <mrow> <msub> <mi>l</mi> <mrow> <mi>p</mi> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>m</mi> <mi>b</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> Wherein i, j=1~5 and i ≠ j, Obtain the actual range L between five holes on scaling boardp12、Lp13、Lp14、Lp15、Lp23、Lp24、Lp25、Lp34、Lp35、Lp45；Successively Obtain actual each millimeter pixel number Nij
    <mrow> <msub> <mi>N</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>l</mi> <mrow> <mi>p</mi> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>L</mi> <mrow> <mi>p</mi> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mfrac> </mrow>
    Obtain corresponding N12、N13、N14、N15、N23、N24、N25、N34、N35、N45Average value N；
    Step 5.4：Five holes are obtained on scaling board in camera coordinates system xpypzpUnder coordinate be Ppb1(xpb1,ypb1,zpb1)、Ppb2 (xpb2,ypb2,zpb2)、Ppb3(xpb3,ypb3,zpb3)、Ppb4(xpb4,ypb4,zpb4)、Ppb5(xpb5,ypb5,zpb5) be：
    <mrow> <msub> <mi>x</mi> <mrow> <mi>p</mi> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mrow> <mi>p</mi> <mi>b</mi> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>L</mi> <mn>0</mn> </msub> <mo>/</mo> <mn>2</mn> </mrow> <mi>N</mi> </mfrac> </mrow>
    <mrow> <msub> <mi>y</mi> <mrow> <mi>p</mi> <mi>b</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mrow> <mi>p</mi> <mi>b</mi> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>B</mi> <mn>0</mn> </msub> <mo>/</mo> <mn>2</mn> </mrow> <mi>N</mi> </mfrac> </mrow>
    zpbi=0
    Wherein i=1~5, L0*B0For camera pixel point actual size；
    Step 5.5：Coordinate points P of the centre bore under camera coordinates system on scaling board in five holespb1(xpb1,ypb1,zpb1) be Origin,For scaling board coordinate system xbybzbXbAxle positive direction, then build vectorAccording to the right-hand rule FromPositive direction points to xbThe positive direction of axle, obtain scaling board coordinate system xbybzbZbAxle positive direction, then with xbAxle is just Direction and zbAxle positive direction draws y according to the right-hand rulebAxle positive direction, so as to obtain scaling board coordinate system xbybzbIn camera coordinates It is xpypzpIn position auto―control Tpb：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>p</mi> <mi>b</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>n</mi> <mrow> <mi>p</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>o</mi> <mrow> <mi>p</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mi>p</mi> <mi>b</mi> </mrow> </msub> </mtd> <mtd> <mrow> <msub> <mi>Trans</mi> <mrow> <mi>p</mi> <mi>b</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    Wherein：
    opb=apb×npb
    Transpb=(xpb1ypb1zpb1)T
    Step 6：According to obtained laser tracker coordinate system xmymzmUnder, flange coordinate system xFyFzF, tool coordinates system xtytzt、 Scaling board coordinate system xbybzbPosition auto―control TmF、Tmt、Tmb, and scaling board coordinate system xbybzbIn camera coordinates system xpypzpUnder Position auto―control Tpb, using matrix conversion relation, obtain in flange coordinate system xFyFzFUnder, tool coordinates system xtytztPosition auto―control TFtWith camera coordinates system xpypzpPosition auto―control TFp：
    TFt=(TmF)-1Tmt
    Tmp=Tmb(Tpb)-1
    TFp=(TmF)-1Tmb(Tpb)-1
    Step 7：By tool coordinates system xtytzt, camera coordinates system xpypzpIn flange coordinate system xFyFzFUnder position auto―control TFtWith TFpCorresponding parameter be input in tool coordinates system Tool1 and Tool2 parameter list corresponding to robot, definition Tool1 is instrument Coordinate system xtytzt, Tool2 is camera coordinates system xpypzp, robot identifies Tool1 and Tool2 parameter, so as to compile Work is run in the coordinate system that Cheng personnel specify.
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