base detection research of drilling robot system by using

Research ArticleBase Detection Research of Drilling Robot System byUsing Visual Inspection

Zhanxi Wang 12 Jing Bai1 Xiaoyu Zhang1 Xiansheng Qin1

Xiaoqun Tan1 and Yali Zhao2

1School of Mechanical Engineering Northwestern Polytechnical University Xirsquoan 710072 China2Xinlian College Henan Normal University Zhengzhou 451400 China

Correspondence should be addressed to Zhanxi Wang zxwangnwpueducn

Received 8 November 2017 Revised 11 December 2017 Accepted 21 December 2017 Published 31 January 2018

Academic Editor L Fortuna

Copyright copy 2018 Zhanxi Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper expounds the principle and method of calibration and base detection by using the visual measurement system fordetection and correction of installation error between workpiece and the robot drilling system This includes the use of CognexInsight 5403 high precision industrial camera a light source and theKEYENCEcoaxial IL-300 laser displacement sensorThe three-base holes method and two-base holes method are proposed to analyze the transfer relation between the basic coordinate systemof the actual hole drilling robot and the basic coordinate system of the theoretical hole drilling robot The corresponding visioncoordinates calibration and the base detection experiments are examined and the data indicate that the result of base detection isclose to the correct value

1 Introduction

Industrial robotic applications are becoming widely used inthe aviation sector [1] because of lower investment increas-ing automation table working performance and good acces-sibility From the beginning of twenty-first Century Amer-ican GEMCOR EI (ElectroimPact) Italian COMAU andGerman BROETJE-Automation have been committed to thedesign and development of drilling robot systems and theirdrilling robot system production has been used in aircraftmanufacturing enterprises such as the F-16 F-22 verticalwall F-35 aircraft wing panel and A380 wing panel [2ndash4]S H Bi developed a drilling robot system which uses anindustrial camera to establish the relationship between theworkpiece and the robot coordinate system [5] During thedrilling process of the movable robot the moving devicelocks floatingly when the drilling equipment is in the workingposition then the robot will arrive at the designated locationfollowing the programmed workpiece coordinate system [6]Due to errors caused by the orientation of the motion deviceor the installation of the workpiece differences in the relativelocation of the workpiece and the robot drilling system will

occur which will result in the offset of the actual arrivalposition [4 7]

To simplify this problem working pieces are assumed tobe in a theoretical position and all installation errors canbe concentrated on the robot coordinate system [8 9] Thefundamental theory of base detection can be illustrated firstby the actual position being checked through measuring thedatum holes on the workpiece when the drilling robot systemarrives at the designated location and second as the matrixbetween the theoretical robot coordinate system and theactual robot coordinate system being deduced to a generallycorrect position of the holes involved in programming

2 Calibration of Base Detection System

In this paper we have developed a drilling end effector systemand installed it on a Kuka KR-500 robot as the experimentplatform as shown in Figure 1

The calibration of the visual coordinate system is com-posed of two parts the position calibration and the directioncalibration [10 11] Position calibration is used to obtain the2D coordinates of the robot Tool Center Point (TCP) in the

HindawiJournal of RoboticsVolume 2018 Article ID 8767531 9 pageshttpsdoiorg10115520188767531

2 Journal of Robotics

Frame structureIntegrated electric control unit

drilling unit

Pressing unitLaser displacement

sensors

RobotFlange

Integrated pneumatic signal unit

Visual system

XRZRYR

O

Figure 1 The specific structure of drilling end effector and robot system

Spindle center hole

2

45

3

1

109 plusmn 002

185 plusmn 002

d15 = d14 = d13 = d12 = 10 plusmn 001 mm

(a)

Optical Axis

Spindle center hole

Pressure nose

(b)

Figure 2 Visual system calibration plate

visual coordinate system and the readings of the four laserdisplacement sensors where the distance between pressurenose tip and the workpiece surface is 45mm

Direction calibration is used to obtain the rotation anglebetween the visual coordinate system and the tool coordinatesystem around the 119883-axis of tool coordinate system andthe laser emission direction of laser displacement sensor[12 13] Because the vision coordinate system is fixed onbase detection system the calibration of the visual coordinatesystem described is consistent with the calibration of basedetection system

21 Position Calibration A special calibration board has beendesigned for position calibration where several holes arefinished with certain relative positions

As shown in Figure 2 the standard cutter mounted onthe spindle is sheathed in the upper right hole of calibrationplate This hole is referred to as the spindle center hole Theremaining five holes in the calibration plate can be capturedby adjusting the focal length of camera According to therelative positions of the spindle center hole and the remainingholes (Figure 2(a)) the coordinates of the spindle center holecan be calculated in visual coordinates

According to the image of spindle center hole takenby industrial cameras the position in default coordinatesystem can be calculated by the contour detection and imagesegmentation algorithm [14 15] as illustrated in Figure 3

The coordinate of spindle center hole in visual coordinatesystem is given by

[119889119909119889119910] =9978889978889978881198741198751 + 99788899788899788899788811987511198754

|11987511198754| ∙ 1198971 +99788899788899788899788811987511198752|11987511198752| ∙ 1198972 (1)

where 9978889978889978881198741198751 is the vector from 119874 to 1198751 99788899788899788899788811987511198754 is vector from1198751 to 1198754 99788899788899788899788811987511198752 is the vector from 1198752 to 1198751 1198971 is the verticaldistance from TCP to 119874 and 1198972 is the radial distance fromTCP to 119874

As shown in Figure 3 (119889119909 119889119910) can be obtained bysubstituting 1198971 = 185mm and 1198972 = 109mm into (1)

The laser displacement sensor should be installed on theright position to ensure that the laser is projected near thereference hole Manual teaching robot is used to keep thefront end of the pressure nose at a certain distance (program-ming safety height) from the workpiece surface The readingof the laser displacement sensor 1199041199110 is recorded as the zeroposition of the laser displacement sensor by this time

22 Direction Calibration The direction calibration of thevision coordinate system is mainly to obtain the direction ofthe optical axis of the industrial camera and laser displace-ment sensor Calibrationmethod is demonstrated in Figure 4

The calibration plate is fixed to the test bench and thecoordinates of the hole 119875 on the calibration board in the

Journal of Robotics 3

P1

P2

P3

P4P5

Spindlecenter hole

X

Y

O

(TCP)

d15

d13d12

d14

l2

l1(dx dy)

Figure 3 Position of spindle center hole (TCP)

O

TCP

L

minusyt

P(x0 y0)

yxt

xv

yt

Figure 4 Direction calibration of industrial camera

camera coordinate system (1199090 1199100) are recorded Then theindustrial robot is moved a certain distance of 119871 along theminus119884 direction of tool coordinate system and set while thecalibration plate is remeasured with the industrial camera Ifboth the119883- and 119884-axes of the visual coordinate system are inaccordance with the +119884 direction and the minus119883 direction of thetool coordinate system then the119883 coordinate value of hole 119875will increase 119871 while the 119884 coordinates remain unchanged

If there is a certain angle 120579 between the +119883-axis of visualcoordinate system and +119884-axis of tool coordinate system(positive for clockwise negative for counterclockwise) thecoordinates of remeasured hole 119860 will be replaced with (1199090 +119871 times cos(120579) 1199100 minus 119871 times sin(120579)) Then angle 120579 can be calculatedby the coordinate values (119909 119910) obtained from the actualmeasurements

To calibrate the direction of laser displacement sensor aseries of planes that have a certain distance paralleled to thepressure foot plane should be measured so that the planeangle between laser and pressure foot plane 120579119911 can be easilyobtained according to the distance between two adjacentplanes and the reading of the laser displacement sensor asshown in Figure 5

120579119911 = arcsin(119889119904 ) (2)

3 Base Detection Theory

Twomethods are used for base detection in this paper includ-ing three-base holes detection and two-base holes detection

Three-base holes detection is based on both their actual andtheoretical locations to analyze the transfer relation betweenbasic coordinate system of the actual hole drilling robot andthe basic coordinate system of the theoretical hole drillingrobot

On account of the actual and theoretical position ofone base hole the actual position actual normal theoreticalposition and theoretical normal of the other base hole thetwo-base hole detection can be used to calculate the transferrelation

As shown in Figure 6 the theoretical coordinates of three-base holes 1198751 1198752 and 1198753 in robot base coordinate system aregiven by

1198751 = [[[[[

119875111990911987511199101198751119911

]]]]]

1198752 = [[[[[

119875211990911987521199101198752119911

]]]]]

1198753 = [[[[[

119875311990911987531199101198753119911

]]]]]

(3)


ds

Laser

Laser displacementsensor

z

Figure 5 Direction calibration of laser displacement sensor

WorkpieceBase holes

Theoretical position

Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

T1

T2Zo

YoOo

Tco

YcXo

Xc

Oc

Zc

Figure 6 Base detection theorem of three-base holes

Due to the error of workpiece installation and drillingrobot orientation the actual coordinates of three datumholescan be described as

1198751199001 = [[[[

119875101584011199091198751015840111991011987510158401119911

]]]]

1198751199002 = [[[[

119875101584021199091198751015840211991011987510158402119911

]]]]

1198751199003 = [[[[

119875101584031199091198751015840311991011987510158403119911

]]]]

(4)

31 Three-Base Hole Theorem Direct calculation and leastsquare matching are used to serve three-base hole theorem

Direct Calculation Coordinate system 1198751-119883119884119885 is establishedby taking 1198751 for origin the direction of 99788899788899788811987511198752 for 119883-axis andthe normal plane that contains 1198751 1198752 and 1198753 as the119885-axis (asshown in Figure 6) Theoretically the transfer matrix fromthe robot-based coordinate to coordinate 1198751-119883119884119885 is

1198791 = [1198991 1199001 1198861 11990110 0 0 1 ] (5)

The transfer matrix from the actual robot-based coordi-nate 119874119888-119883119888119884119888119885119888 to actual workpiece coordinate is written as

1198792 = [1198992 1199002 1198862 11990120 0 0 1 ] (6)

where

1199011 = 997888rarr11987511198991 =

997888rarr1198752 minus 997888rarr1198751100381610038161003816100381610038161003816997888rarr1198752 minus 997888rarr1198751100381610038161003816100381610038161003816


WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

Zo

Yo

OoTco

YcXo

Xc

Oc

Zc

Figure 7 Base detection theorem of two-base holes

Table 1 Industrial camerarsquos raw data of position calibration

1198751 1198752 1198753 1198754 1198755(8725 5945) (43725 3445) (11205 15825) (6235 10285) (130725 842)

1198861 = (997888rarr1198752 minus 997888rarr1198751) times (997888rarr1198753 minus 997888rarr1198751)100381610038161003816100381610038161003816997888rarr1198752 minus 997888rarr1198751100381610038161003816100381610038161003816 ∙100381610038161003816100381610038161003816(997888rarr1198753 minus 997888rarr1198751)

1003816100381610038161003816100381610038161199001 = 1198861 times 1198991

(7)

We can obtain 1198792 by substituting 1198751119900 by 1198751 1198752119900 by 1198752 and1198753119900 by 1198753119879119888119900 ∙ 1198792 = 1198791

119879119888119900 = 1198791 ∙ 119879minus12 (8)

The least square solution of transformationmatrix can becalculated according to 1198751 1198752 1198753 and 11987501 11987502 11987503 [14 15]32 Two-Base Hole Theorem As shown in Figure 7 two-base point detection is used to obtain the transfer matrix byknowing the actual position of point 1198751199001 the actual normaldirection 1198601199001 1198611199001 theoretical position 1198751 theoretical normaldirection 1198601 1198611 actual position 1198751199002 and theoretical positionof another point 1198752

The principle is shown in Figure 7The workpiece coordinate system is established by the

method shown in Figure 7 where 1198751 is the origin thedirection of 99788899788899788811987511198752 is represented by the 119884-axis the normalvector of the plane that contains 1198751 1198752 1198753 is the 119883-axisand the 119885-axis is determined by the right hand rule The

definitions of 1198791 and 1198792 are those as demonstrated in (5) and(6)

1199011 = 997888rarr11987511198991 = [sin1198611 cos1198621 minus sin1198621 cos1198611 cos1198621]119879

1199001 =997888rarr1198752 minus 997888rarr1198751100381610038161003816100381610038161003816997888rarr1198752 minus 997888rarr1198751

1003816100381610038161003816100381610038161198861 = 1198991 times 1199001

(9)

where 1198611 1198621 are Euler angle of 119885119884119883 that can be detected innormal direction


119879119888119900 = 1198791 ∙ 119879minus12 (10)

4 Base Detection Experiment

41 Calibration Experiment of the Base Detection SystemFirst the position calibration of the industrial camera andthe laser displacement sensor is carried out According to theinstallationmethod of the calibration plate shown in Figure 2the image collected by Insight Explorer software is shownin Figure 8 Coordinates in the default camera coordinatesystem (units pixels) are shown in Table 1

The relation between the pixels and the distance (1mm= 5011 pixel) is obtained by using the distance between thefive calibration holes 11988915 11988914 11988913 11988912 = 10 plusmn 001mm


Table 2 Base holersquos coordinate in camera coordinate system

1198751 1198752 1198753 1198754 1198755(14468 minus01098) (minus72392 50988) (6396 minus88157) (minus35223 05513) (101229 48294)

P2

P1

P3

P4

P5

xy

Figure 8 Image of calibration plate


After moving the default camera coordinate system to thecentral point of view the coordinates of the calibration holein the camera coordinate system are obtained and shown inTable 2

According to (1) the coordinate of the spindle hole in thevisual coordinate system (unit mm) is given as (minus18658381061815)

Figure 9 illustrates the direction calibration of the indus-trial camera The calibration board is adjusted to the normallevel after it is fixed to the test fixture in two different posi-tions making sure that the robot tool axis is perpendicularto the test fixture Then the coordinates of 1198751 1198752 and 1198753 aremeasured in the default camera coordinate (pixels) as shownin Table 3

When the calibration plate is placed in position 1 thecoordinate system in the robot base coordinates is (135451minus262283149466 minus9008 minus055 minus157) and when in position2 the tool coordinate position in the robot base coordinatesystem is (154586 minus266515 146193 minus894 03 minus156) whenthe drilling robotmoves a certain distance in the +119909 directionof the tool coordinate system the coordinates of holes 1198751

1198752 and 1198753 (pixel) are remeasured The results are shown inTable 4

After moving the tool coordinate in the robot basecoordinate system is (135468 minus262278 149915 minus9007minus055 minus157) in position 1 and (153436 minus266526 146224minus894 03 minus156) in position 2

According to the relative position of the calibration holes1198751 1198752 and 1198753 on the calibration board the correspondingrelationship between pixels and the distance can be obtained

1mm= 47741 pixel in position 1 and 1mm= 502792 pixelin position 2

It can be seen from Table 5 that when the movingdistances of robot are 4493mm and 115047mm the errorbetween the actual value and the theoretical value is less than006mm and the rotation angle of the tool coordinate systemin 119885 direction can be neglected

The calibration method of laser displacement sensoris used to make the end effector tool perpendicular tothe calibration plate with the normal adjustment functionReadings of sensors in 119885 direction are shown in Table 6 withdifferent height gauge added onto the calibration plate


Table 3 Data before direction calibration

1198751 1198752 1198753Position 1 (94725 70025) (47025 68675) (959 22475)Position 2 (135075 87825) (84775 86625) (13655 3755)

Table 4 Data after direction calibration


Table 5 The difference of coordinates before and after moving

1198751 1198752 1198753 Displacement of robotPosition 1 (00524 45087) (00576 45191) (00471 4493) +119883 4493mmPosition 2 (minus115320 minus00596) (minus115221 minus00498) (minus115420 minus00543) +119884 115047mm

Table 6 Readings of sensors in 119885 direction

Height of gauge (mm) 0 20 30 40 50 60 70Readings of sensors in 119885 direction (mm) minus604 minus812 minus916 minus102 minus1124 minus1228 minus1332

Table 7 Values before changing coordinate system

Coordinate of industrial camera Value of laser displacement SensorGesture of robot(119883 119884 119885 119860 119861 119862)119883mm 119884mm 119885mm 119860∘ 119861∘ 119862∘

1198751 (8555 5735) minus365 (18509 minus260933 168950 minus89990026 00259)



Table 8 Coordinates of base holes in robot coordinate system before changing coordinate system

1198751 1198752 1198753119883 183894 21373 18364119884 minus260807 minus260831 minus260834119885 169007 168994 166008

The plane angle of the laser displacement sensor andpressure foot is given as arcsin(10104)

The sensor reading is 1198781199110 = minus348mm where the heightbetween the front face of pressure nose and calibration plate119889 = 45mm

42 Base Detection Experiment of Robot Drilling System Thisstudy has determined that the three-point detection theoremis best suited to verify the correctness of the benchmarkdetection principle The experiment field is shown in Fig-ure 10The calibration board is fixed on the test fixture and inorder to reduce the coordinate acquisition errors the normaladjustment function is used to control the verticality of tool

and calibration plate under 01 degrees before industrial thecamera takes images

The drilling robot is taught manually to make the indus-trial camera lens center aligned to the base hole then the lasertracker is used to verify whether the end effector spindle isperpendicular to the calibration plate The three holes on thecalibration board are measured and the coordinates of thecorresponding cameras and the laser displacement sensorsrecorded (unit pixel) The readings in the robot teachingdevice (unit mm) are shown in Table 7

The manual work piece coordinate system is set to [12minus5 minus12 minus03 minus005 minus001] the robot pose is controlled torepeat positioning to the gesture in Table 8 (in work piece


Drillingrobot

Calibrationplate

End effector

system

Figure 10 Base detection experiment of robot drilling system

Table 9 Values after changing coordinate system

Actual value Coordinate of industrial camera Value of laser displacement sensor1198751 (62075 39675) minus3911198752 (63775 3965) minus3921198753 (64825 40675) minus390

Table 10 Coordinates of base holes in robot coordinate system after changing coordinate system


coodinates) and the board holes are recalibrated to achievethe pixel coordinates shown in Table 9

The three coordinates of 1198751 1198752 and 1198753 are converted tothe robot base coordinate system and the coordinates of threepoints are obtained as shown in Table 10

According to the three-base hole detection princi-ple compensation matrix is given as [1370174 minus699429minus12833 minus036 minus008 minus00188] by using direct methodand the compensation matrix is given as [12064 minus69798minus12064 minus036082 minus002936 minus001886] by using least squarematching method

By comparison it can be seen that both two methodscan find accurate solutions but the least square matchingmethod is closer to the true value This proves that the detec-tion principle is feasible Deviation caused by the robotrsquos posi-tioning error and various conversion errors can be reduced byrobot positioning accuracy compensation

5 Conclusion

Improving the positioning accuracy of the drilling robotis significant in improving the quality hole drilling Thedeviation of the relative position between the workpiece andthe robot will affect the positioning accuracy of the drillingholes In order to identify the actual relative position of theworkpiece and the robot the base detection should be donebefore robot drilling preparation This study has discussedcalibration using the base detection system and the basedetection technology principle and then we designed thecalibration experiment and base detection experiment to

verify base detection methods The data indicate that theresult of base detection is close to the correct value and thatthe principle is feasible

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is partially supported by the National Natu-ral Science Foundation of China (Grant no 51505380)Shaanxi Science and Technology Innovation Project (Grantnos 2016KTZDGY06-01 2016KTZDGY4-12) and the ldquo111Projectrdquo of China (Grant no B13044)

References

[1] A Olabi R Bearee O Gibaru and M Damak ldquoFeedrate plan-ning for machining with industrial six-axis robotsrdquo ControlEngineering Practice vol 18 no 5 pp 471ndash482 2010

[2] J Atkinson J Hartmann S Jones and P Gleeson ldquoRoboticdrilling system for 737 aileronrdquo in Proceedings of the SAE 2007AeroTech Congress and Exhibition pp 1ndash3821 SAE TechnicalPapers Los Angeles Calif USA 2007

[3] R DeVlieg and E Feikert ldquoOne-up assembly with robotsrdquoTraining 2008 p 09-30 2013

[4] R Devlieg K Sitton E Feikert and J Inman ldquoONCE (ONe-sided Cell End effector) robotic drilling systemrdquo SAE TechnicalPapers 2002


[5] S Bi and J Liang ldquoRobotic drilling system for titanium struc-turesrdquo The International Journal of Advanced ManufacturingTechnology vol 54 no 5-8 pp 767ndash774 2011

[6] Y Gao D Wu Y Dong X Ma and K Chen ldquoThe methodof aiming towards the normal direction for robotic drillingrdquoInternational Journal of Precision Engineering and Manufactur-ing vol 18 no 6 pp 787ndash794 2017

[7] H Chen T Fuhlbrigge S Choi J Wang and X Li ldquoPracticalindustrial robot zero offset calibrationrdquo in Proceedings of the 4thIEEE Conference on Automation Science and Engineering pp516ndash521 Washington DC USA August 2008

[8] A Nubiola and I A Bonev ldquoAbsolute calibration of an ABBIRB 1600 robot using a laser trackerrdquo Robotics and Computer-Integrated Manufacturing vol 29 no 1 pp 236ndash245 2013

[9] J Wang H Zhang and T Fuhlbrigge ldquoImproving machiningaccuracy with robot deformation compensationrdquo in Proceedingsof the 2009 IEEERSJ International Conference on IntelligentRobots and Systems IROS 2009 pp 3826ndash3831 usa October2009

[10] S Garnier K Subrin and K Waiyagan ldquoModelling of RoboticDrillingrdquo in Proceedings of the 16th CIRP Conference on Mod-elling of Machining Operations CIRP CMMO 2017 pp 416ndash421France June 2017

[11] B Mei W Zhu K Yuan and Y Ke ldquoRobot base frame calibra-tion with a 2D vision system for mobile robotic drillingrdquo TheInternational Journal of Advanced Manufacturing Technologyvol 80 no 9-12 pp 1903ndash1917 2015

[12] A Frommknecht J Kuehnle I Effenberger and S PidanldquoMulti-sensor measurement system for robotic drillingrdquo Robo-tics and Computer-Integrated Manufacturing vol 47 pp 4ndash102017

[13] Y Liu Z Shi P Yuan D ChenM Lin and Z Li ldquoA visual posi-tioning and measurement system for robotic drillingrdquo in Pro-ceedings of the 14th IEEE International Workshop on AdvancedMotion Control AMC 2016 pp 461ndash466 New Zealand April2016

[14] P ArbelaezMMaire C Fowlkes and JMalik ldquoContour detec-tion and hierarchical image segmentationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 33 no 5 pp898ndash916 2011

[15] P Arena A Basile M Bucolo and L Fortuna ldquoAn objectoriented segmentation on analog cnn chiprdquo IEEE Transactionson Circuits and Systems I FundamentalTheory andApplicationsvol 50 no 7 pp 837ndash846 2003

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Frame structureIntegrated electric control unit

drilling unit

Pressing unitLaser displacement

sensors

RobotFlange

Integrated pneumatic signal unit

Visual system

XRZRYR

O

Figure 1 The specific structure of drilling end effector and robot system

Spindle center hole

2

45

3

1

109 plusmn 002

185 plusmn 002

d15 = d14 = d13 = d12 = 10 plusmn 001 mm

(a)

Optical Axis

Spindle center hole

Pressure nose

(b)

Figure 2 Visual system calibration plate

visual coordinate system and the readings of the four laserdisplacement sensors where the distance between pressurenose tip and the workpiece surface is 45mm

Direction calibration is used to obtain the rotation anglebetween the visual coordinate system and the tool coordinatesystem around the 119883-axis of tool coordinate system andthe laser emission direction of laser displacement sensor[12 13] Because the vision coordinate system is fixed onbase detection system the calibration of the visual coordinatesystem described is consistent with the calibration of basedetection system

21 Position Calibration A special calibration board has beendesigned for position calibration where several holes arefinished with certain relative positions

As shown in Figure 2 the standard cutter mounted onthe spindle is sheathed in the upper right hole of calibrationplate This hole is referred to as the spindle center hole Theremaining five holes in the calibration plate can be capturedby adjusting the focal length of camera According to therelative positions of the spindle center hole and the remainingholes (Figure 2(a)) the coordinates of the spindle center holecan be calculated in visual coordinates

According to the image of spindle center hole takenby industrial cameras the position in default coordinatesystem can be calculated by the contour detection and imagesegmentation algorithm [14 15] as illustrated in Figure 3

The coordinate of spindle center hole in visual coordinatesystem is given by

[119889119909119889119910] =9978889978889978881198741198751 + 99788899788899788899788811987511198754

|11987511198754| ∙ 1198971 +99788899788899788899788811987511198752|11987511198752| ∙ 1198972 (1)

where 9978889978889978881198741198751 is the vector from 119874 to 1198751 99788899788899788899788811987511198754 is vector from1198751 to 1198754 99788899788899788899788811987511198752 is the vector from 1198752 to 1198751 1198971 is the verticaldistance from TCP to 119874 and 1198972 is the radial distance fromTCP to 119874

As shown in Figure 3 (119889119909 119889119910) can be obtained bysubstituting 1198971 = 185mm and 1198972 = 109mm into (1)

The laser displacement sensor should be installed on theright position to ensure that the laser is projected near thereference hole Manual teaching robot is used to keep thefront end of the pressure nose at a certain distance (program-ming safety height) from the workpiece surface The readingof the laser displacement sensor 1199041199110 is recorded as the zeroposition of the laser displacement sensor by this time

22 Direction Calibration The direction calibration of thevision coordinate system is mainly to obtain the direction ofthe optical axis of the industrial camera and laser displace-ment sensor Calibrationmethod is demonstrated in Figure 4

The calibration plate is fixed to the test bench and thecoordinates of the hole 119875 on the calibration board in the


P1

P2

P3

P4P5

Spindlecenter hole

X

Y

O

(TCP)

d15

d13d12

d14

l2

l1(dx dy)


O

TCP

L

minusyt

P(x0 y0)

yxt

xv

yt





120579119911 = arcsin(119889119904 ) (2)






1198751 = [[[[[

119875111990911987511199101198751119911

]]]]]

1198752 = [[[[[

119875211990911987521199101198752119911

]]]]]

1198753 = [[[[[

119875311990911987531199101198753119911

]]]]]

(3)


ds

Laser


z


WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

T1

T2Zo

YoOo

Tco

YcXo

Xc

Oc

Zc



1198751199001 = [[[[

119875101584011199091198751015840111991011987510158401119911

]]]]

1198751199002 = [[[[

119875101584021199091198751015840211991011987510158402119911

]]]]

1198751199003 = [[[[

119875101584031199091198751015840311991011987510158403119911

]]]]

(4)



1198791 = [1198991 1199001 1198861 11990110 0 0 1 ] (5)


1198792 = [1198992 1199002 1198862 11990120 0 0 1 ] (6)

where

1199011 = 997888rarr11987511198991 =



WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

Zo

Yo

OoTco

YcXo

Xc

Oc

Zc



1198751 1198752 1198753 1198754 1198755(8725 5945) (43725 3445) (11205 15825) (6235 10285) (130725 842)


1003816100381610038161003816100381610038161199001 = 1198861 times 1198991

(7)


119879119888119900 = 1198791 ∙ 119879minus12 (8)







1003816100381610038161003816100381610038161198861 = 1198991 times 1199001

(9)



119879119888119900 = 1198791 ∙ 119879minus12 (10)







P2

P1

P3

P4

P5

xy




































Drillingrobot

Calibrationplate

End effector

system










5 Conclusion





Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



P1

P2

P3

P4P5

Spindlecenter hole

X

Y

O

(TCP)

d15

d13d12

d14

l2

l1(dx dy)


O

TCP

L

minusyt

P(x0 y0)

yxt

xv

yt





120579119911 = arcsin(119889119904 ) (2)






1198751 = [[[[[

119875111990911987511199101198751119911

]]]]]

1198752 = [[[[[

119875211990911987521199101198752119911

]]]]]

1198753 = [[[[[

119875311990911987531199101198753119911

]]]]]

(3)


ds

Laser


z


WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

T1

T2Zo

YoOo

Tco

YcXo

Xc

Oc

Zc



1198751199001 = [[[[

119875101584011199091198751015840111991011987510158401119911

]]]]

1198751199002 = [[[[

119875101584021199091198751015840211991011987510158402119911

]]]]

1198751199003 = [[[[

119875101584031199091198751015840311991011987510158403119911

]]]]

(4)



1198791 = [1198991 1199001 1198861 11990110 0 0 1 ] (5)


1198792 = [1198992 1199002 1198862 11990120 0 0 1 ] (6)

where

1199011 = 997888rarr11987511198991 =



WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

Zo

Yo

OoTco

YcXo

Xc

Oc

Zc



1198751 1198752 1198753 1198754 1198755(8725 5945) (43725 3445) (11205 15825) (6235 10285) (130725 842)


1003816100381610038161003816100381610038161199001 = 1198861 times 1198991

(7)


119879119888119900 = 1198791 ∙ 119879minus12 (8)







1003816100381610038161003816100381610038161198861 = 1198991 times 1199001

(9)



119879119888119900 = 1198791 ∙ 119879minus12 (10)







P2

P1

P3

P4

P5

xy




































Drillingrobot

Calibrationplate

End effector

system










5 Conclusion





Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



ds

Laser


z


WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

T1

T2Zo

YoOo

Tco

YcXo

Xc

Oc

Zc



1198751199001 = [[[[

119875101584011199091198751015840111991011987510158401119911

]]]]

1198751199002 = [[[[

119875101584021199091198751015840211991011987510158402119911

]]]]

1198751199003 = [[[[

119875101584031199091198751015840311991011987510158403119911

]]]]

(4)



1198791 = [1198991 1199001 1198861 11990110 0 0 1 ] (5)


1198792 = [1198992 1199002 1198862 11990120 0 0 1 ] (6)

where

1199011 = 997888rarr11987511198991 =



WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

Zo

Yo

OoTco

YcXo

Xc

Oc

Zc



1198751 1198752 1198753 1198754 1198755(8725 5945) (43725 3445) (11205 15825) (6235 10285) (130725 842)


1003816100381610038161003816100381610038161199001 = 1198861 times 1198991

(7)


119879119888119900 = 1198791 ∙ 119879minus12 (8)







1003816100381610038161003816100381610038161198861 = 1198991 times 1199001

(9)



119879119888119900 = 1198791 ∙ 119879minus12 (10)







P2

P1

P3

P4

P5

xy




































Drillingrobot

Calibrationplate

End effector

system










5 Conclusion





Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



WorkpieceBase holes


Actual position

P3

P2

xwp

ztyt

xt

zwp

P1

ywp

Zo

Yo

OoTco

YcXo

Xc

Oc

Zc



1198751 1198752 1198753 1198754 1198755(8725 5945) (43725 3445) (11205 15825) (6235 10285) (130725 842)


1003816100381610038161003816100381610038161199001 = 1198861 times 1198991

(7)


119879119888119900 = 1198791 ∙ 119879minus12 (8)







1003816100381610038161003816100381610038161198861 = 1198991 times 1199001

(9)



119879119888119900 = 1198791 ∙ 119879minus12 (10)







P2

P1

P3

P4

P5

xy




































Drillingrobot

Calibrationplate

End effector

system










5 Conclusion





Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





P2

P1

P3

P4

P5

xy




































Drillingrobot

Calibrationplate

End effector

system










5 Conclusion





Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

























Drillingrobot

Calibrationplate

End effector

system










5 Conclusion





Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


base detection research of drilling robot system by using

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