GEOMETRIC REVERSE ENGINEERING USING A LASER PROFILE SCANNER MOUNTED ON AN INDUSTRIAL ROBOT

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1 6th Iteratioal DAAAM Baltic Coferece INDUSTRIAL ENGINEERING April 2008, Talli, Estoia GEOMETRIC REVERSE ENGINEERING USING A LASER PROFILE SCANNER MOUNTED ON AN INDUSTRIAL ROBOT Rahayem, M.; Kjellader, J.A.P, & Larsso, S. Abstract: Laser scaers i combiatio with accurate orietatio devices are ofte used i Geometric Reverse Egieerig (GRE) to measure poit data. The idustrial robot as a device for orietatio has relatively low accuracy but the advatage of beig umerically cotrolled, fast, ad flexible ad it is therefore of iterest to ivestigate if it ca be used i this applicatio. We have built a measurig system based o a laser profile scaer mouted o a idustrial robot. I this paper we preset results from practical tests based o poit data. We also show how data from laser profiles ca be used to icrease accuracy i some cases. Fially we propose a ew method for plae segmetatio usig laser profiles. Keywords: Geometric Reverse egieerig, 3D measuremet systems, laser scaig, segmetatio, regio growig. 1. INTRODUCTION Geometric Reverse Egieerig (GRE) is cocered with the problem of creatig CAD-models of real objects by fittig 3D poit data measured from their surfaces. A itroductio to GRE which is ofte referred to is a paper by Varady [ 1 ]. See also [ 2 ] ad [ 3 ]. Measuremet systems for this purpose are ofte based o laser rage fiders i combiatio with mechaical devices for orietatio. For idustrial applicatios it is preferable that the orietig device is possible to cotrol umerically, so that poit clouds ca be created without huma iteractio. This leads to the idea of usig a idustrial robot as the orietig device. Figure 1: The measurig system To test this idea we have desiged ad built a measurig system based o a profile scaer ad a idustrial robot ABB IRB140 with a turtable see figure 1. To itegrate the two systems ad cotrol the movemet of the scaer, we use Varko, a ope source CAD system; see [ 4 ] ad [ 5 ].With a measuremet system of this kid, a poit o the surface of a object is: P = P + N d (1) r r * Where Pr the curret 3D positio of the robot tool cetre is N r is the directio of the laser rage fider ad d is the distace from P r to the surface of the object. Idustrial robots are usually less accurate tha laser rage fiders ad 3D poit data calculated accordig to (1) will thus be limited i accuracy by the robot. If a

2 profile scaer is used however, some GRE operatios ca be performed without ivolvig the orietatio of the robot. A profile scaer creates a profile o the surface of a object with a lie laser ad uses a camera to capture the image of the profile. 2D image processig is the applied to idetify the pixels i the image that represet the profile ad a calibratio table is fially used to map pixels to a 2D coordiate system. See figure 2. Figure 2: From pixels to profiles A plae surface i 3D space will appear as a straight lie i the 2D profile ad this property ca be used to measure distaces withi the camera picture with relatively high accuracy sice the orietatio of the robot is ot ivolved. GRE of 3D surfaces is ot possible without ivolvig the orietatio of the robot but we believe that if the iformatio i the 2D profiles is used wisely we ca still achieve a accuracy which is better tha the accuracy of the robot. To illustrate this we will first ivestigate traditioal GRE of plaar surfaces based o 3D poit clouds calculated usig (1). We will the preset the result from a experimet where the radius of a cylider is established usig iformatio from a 2D profile oly. This experimet shows that 2D profiles ca be used to measure distaces withi a sigle camera picture without loss of accuracy. We will fially propose a alterative to traditioal segmetatio of plaes based o 2D profiles istead of 3D poit data. 2. GRE BASED ON POINT CLOUDS A well established method for GRE of plaar surfaces is to start with a uordered set of 3D poits ad sort them spatially so that they ca be coected ito a triagular mesh, see [ 6 ], [ 7 ], [ 8 ] ad [ 9 ]. The triagulatio algorithm we use is described i [ 4 ]. Next, segmetatio is used to idetify regios of coplaar triagles. Fially, plaes are fitted to the segmeted regios. See [ 6 ] ad [ 10 ] for surveys of segmetatio methods. A segmetatio method that is well suited for GRE of plaar surfaces is regio growig. A seed triagle is first idetified ad adjacet triagles are the added to form a plaar regio. I [ 11 ], Sacchi et al. propose a method to idetify seeds based o scalar curvature values computed for each triagle usig iformatio from surroudig triagles. We have implemeted this method ad added a growig criterio based o the directio of ormal vectors. The resultig GRE algorithm icludes the followig steps: 1. Joi eighborig poits ito a triagular mesh. This is relatively easy sice the poits from the profile scaer are ordered sequetially withi each profile ad profiles are ordered sequetially i the directio the robot is movig. 2. Calculate scalar curvature estimates for all triagles usig the Sacchi algorithm. A itermediate step i the algorithm is the calculatio of approximate ormal vectors ad these are saved to be used i step 3 below. 3. Use the triagle with lowest curvature as a seed ad add coected triagles to the regio as log as their ormal vectors are reasoably parallel with the ormal of the seed. A coe agle is used as a threshold for the ormal deviatio; see [ 2 ] ad [ 12 ]. 4. Whe o more triagles ca be added to the curret regio, search the remaiig triagles for the oe with the lowest curvature ad start the growig procedure agai with a

3 ew regio util all triagles have bee processed. 5. For each segmeted regio, fit a plae usig Priciple Compoets Aalysis, see [ 13 ]. The behavior of the algorithm depeds o three parameters that eed to be set for each object i order to avoid too may regios to be idetified (over segmetatio) or too few (uder segmetatio). 1. Maximum seed curvature value, Kseed. A value too high will cotribute to over segmetatio; a value too low will cotribute to uder segmetatio. 2. Miimum umber of triagles i a regio, t mi. A value too high may result i uder segmetatio while a value too low may cause over segmetatio. 3. Maximum ormal deviatio (coe agle), Ndev. Icreasig this parameter will icrease the umber of plaes that are added to a regio. A value too high may result i a regio that is bigger tha the actual plae while a value too low may exclude so may plaes that the miimum umber of triagles i a regio is ot reached. Figure 3: The measured object Figure 3 shows a object that has bee used by Varady [ 14 ] ad others [ 11 ], [ 10 ] ad [ 2 ] as a referece. We have maufactured a copy of this object usig a Objet Ede 250 high accuracy rapid prototypig machie ad the measured the object usig our system based o the robot ad profile scaer. After a few iitial tests, we processed the measured data usig Kseed =0.015, t = mi 55 ad Ndev = 3 degrees. Figure 4: Segmeted object The result is show i figure 4. Black triagles are the seeds ad grey areas are the correspodig regios. The umber of poits was ad all 6 plaar regios were correctly idetified. Processig time o a 1.2 GHz AMD Athlo was 56 secods from start of segmetatio util all 6 plaes were fitted. The segmetatio code is writte i MBS laguage, a iterpreted high level laguage for geometric modelig icluded i the Varko CAD system [ 5 ]. Traslatig the code to C/C++ would reduce the processig time cosiderably. For each of the plaes we computed the error i vertical positio E v by comparig the positio of a poit o the plae i the cetre of the regio with its true value measured usig a Mitutoyo CMM. We have also computed the error i ormal directio E as the agle betwee

4 the fitted plae ormal ad the true ormal. The positioal accuracy of a plae seems to be close to 0.5 mm ad the accuracy of the ormal approximately 0.1 degrees. This is also the accuracy you would expect from the robot. The relatively high accuracy of the profile scaer does ot ifluece the results. Although it is a atural choice, we have ot see the combiatio of seeds calculated usig the Sacchi algorithm ad the regio growig based o ormal deviatios published earlier. It is our impressio that it performs well ad should be ivestigated more i depth. 3. GRE BASED ON PROFILES I [ 15 ] we show that a accuracy of 0.05 mm or better is possible whe fittig lies to laser profiles. We also show how itersectig lies from the same camera picture ca be used to measure distaces with high accuracy. I a ew series of experimets we have ivestigated the accuracy i measurig the radius of a circle. We measured a object with cylidrical shape ad took pictures with the scaer head orthogoal with the cylider axis. The cylider will the appear as a circular arc i the sca widow. We used a steel cylider with R = mm measured with a Mitutoyo micrometer (0-25mm / 0.001mm) ad the experimet was repeated 100 times with D icreasig i steps of 1 mm thus coverig the sca widow. To make it possible to distiguish betwee systematic ad radom errors each of the 100 steps was repeated =10 times, ad i each of these the scaer head was moved 0.05 mm i a directio colliear with the cylider axis to filter out the effect of dust, varyig pait thickess or similar effects. The total umber of pictures aalyzed is thus For each distace D we made a LSM fit of a circle to each of the pictures ad calculated the systematic ad radom errors usig Esq. s. (2) ad (3). The result was plotted i figure 5 ad 6. E E s r = R i= 1 R i abs( Ri + Es ) R i= = 1 E s ad radius errors. R ad (2) (3) Er are the systematic ad radom R i are the true ad measured radius ad the umber of profiles for each D. The imum size of the radom error is less tha 0.02 mm for reasoable values of D. Figure 5: Systematic error i radius Figure 6: Radom error i radius

5 4. A COMBINED METHOD Traditioal plae fittig as described i sectio 2 does ot require more iformatio from the measurig system tha 3D coordiates. If we have access to laser profiles however, it should be possible to adopt a alterative strategy. As show i [ 15 ], lie fittig based o profiles ca be doe with relatively high accuracy. A object with oe or more plaar surfaces will give rise to profiles with oe or more straight lie segmets. We believe that well kow segmetatio methods as described i [ 16 ], [ 17 ] ad [ 18 ] ca be used to fid these lies, still with relatively high accuracy. As the robot moves alog a sca path each profile created will be associated with a specific 3D orietatio, see figure 7. We kow each orietatio but oly with the relatively low accuracy of the robot. Figure 7: No parallel sca profiles It is reasoable to believe that the relative error betwee two cosecutive orietatios alog a sca path is smaller tha the overall absolute accuracy of the robot. It should therefore be possible to ivestigate if lie segmets from two cosecutive profiles belog to the same plae with a accuracy that is better tha the overall accuracy of the robot. Two lies i the same plae idicate that a plae actually exists. Groupig all segmeted lies ito plaar regios will create segmetatio similar to the oe described i sectio 2 based o regios growig. 5. CONCLUSION The idustrial robot with a laser profile scaer is a iterestig alterative i applicatios where high speed ad flexibility combied with low cost is importat. Plae segmetatio based o 3D data requires poits to be triagulated ad ormal or curvature for each triagle to be estimated usig approximatio. If the accuracy of the measurig system is high relative to the size of the smallest plae we wat to fit these approximatios are acceptable. The accuracy of a idustrial robot used as a 3D poit measuremet system is relatively low, but if the GRE software has access to camera data, we have show that fittig of lies ad calculatio of distaces withi the same camera picture ca be doe with higher accuracy. We believe that this possibility ca be used to icrease the overall accuracy of the system also for plae segmetatio. If 2D laser profiles are segmeted ito lies ad lies from adjacet profiles are used for plae segmetatio i a similar way as ormal s or curvatures are used i regio growig we believe that the result will be better. This is due to the fact that lies fitted from 2D profiles are more accurate tha ormal s or curvatures approximated from triagular meshes. 6. REFERENCES 1. T. Varady, R. R. Marti, J. Cox, Reverse egieerig of geometric models a itroductio, computer-aided desig,1997, 29, J. Hoschek, U. Dietz, W. Wilke, A geometric cocept of reverse egieerig of shape: approximatio ad feature lies, Proc. of the iteratioal coferece o Math. Methods for curves ad surfaces II Lillehammer, Vaderbilt Uiversity, Nashville, TN, USA, 1998, pp G. Fari, J. Hoschek, M. S. Kim, Hadbook of Computer Aided Geometric Desig, Elsevier, Amsterdam, 2002.

6 4. S. Larsso, J. Kjellader, Motio cotrol ad data capturig for laser scaig with a idustrial robot, Robotics ad Autoomous Systems, 2006, 54, URL: 6. H.Woo, E. Kag, S. Wag, K. H. Lee, A ew segmetatio method for poit cloud data, Iteratioal Joural of machie Tools & Maufacture, 2002, H.-C. Kim, S.-M. Hur, S.-H. Lee, Segmetatio of the measured poit data i reverse egieerig, The Iteratioal Joural of Advaced Maufacturig Techology, 2002, 20, S.-M. H. D.-Y. Y. Seok-Hee Lee, Ho- Cha Kim, Stl file geeratio from measured poit data by segmetatio ad Delauay triagulatio, computer-aided desig, 2002, 34, C. Kuo, H.-T. Yau, a Delauay based regio-growig approach to surface recostructio from uorgaized poits, computer-aided desig, 2005, 37, S. Petitjea, a survey of methods for recoverig quadrics i triagle meshes, ACM Comp. Surveys 2, 2002, 34, R. Sacchi, J. Poliakoff, P. Thomas, Curvature estimatio for segmetatio of triagulated surfaces, Proc. of IEEE coferece o 3-D Digital imagig ad Modelig,1999, G. V. T. Rabbai, F. A. va de heuvel, segmetatio of poit clouds usig smoothess costrait, Proc. of Commissio V Symposium Image Egieerig ad Visio Metrology, 2006, XXXVI, part E. Legyel, Mathematics for 3D Game programmig ad Computer Graphics, Massachusetts, P. B. R. Marti, T. Varady, Algorithms for reverse egieerig boudary represetatio models, computer-aided desig, 2001, M. Rahayem, J. Kjellader, S. Larsso, Accuracy aalysis of a 3d measuremet system based o a laser profile scaer mouted o a idustrial robot with a turtable, Proc. of ETFA 12 th IEEE coferece o Emergig Techologies ad Factory Automatio, 2007, pp S. Horowitz, T. Pavlidis, Picture segmetatio by a directed split-ad merge procedure, Proc. of the Secod Iteratioal Joit Coferece o Patter Recogitio, 1974, pp B. Parvi, G. Medioi, Segmetatio of rage images ito plaar surfaces by split ad merge, CVPR86, 1986, pp X. Jiag, H. Buke, Fast segmetatio of rage images ito plaar regios by sca lie groupig, Mach. Visio Appl. 7, 1994, 2, DATA ABOUT AUTHORS Mohamed Rahayem, B.Sc. Electrical Egieerig, PhD studet Dept. of Techology, Örebro Uiversity SE Örebro mohamed.rahayem@tech.oru.se Fax: Phoe: Joha Kjellader, PhD, Seior lecturer Dept. of Techology, Örebro Uiversity SE Örebro joha.kjellader@tech.oru.se Fax: Phoe: Söre Larsso, PhD, Lecturer Dept. of Techology, Örebro Uiversity SE Örebro sore.larsso@tech.oru.se Fax: Phoe: