A Kinematic Calibration Method for Industrial Robots Using Autonomous Visual Measurement

Transcription

1 A Kinematic Calibration Method for Indutrial obot Uing Autonomou Viual Meaurement A. Watanabe 1 (3), S. Sakakibara 1, K. Ban 1, M. Yamada 1, G. Shen 1 1 ANUC LD, Yamanahi, Japan Submitted by. Arai (1) Abtract Several new method have been developed to achieve practical accuracy for offline programming of robot and it applicability to the real world. In thi paper, a new kinematic calibration method i propoed to automatically improve abolute poitioning accuracy of robot. Key point of the method include autonomou meaurement and the automatic generation of meauring poe. A new viual feedback motion control method of the robot i propoed to achieve accurate meaurement. An algorithm i alo propoed to improve the condition of meauring poe automatically. he effectivene of the propoed method and algorithm wa invetigated through experiment with actual robot. Keyword: obot Calibration, Viual Meaurement, Poitioning Accuracy 1 INODUCION Offline teaching i now being recognized a a neceity to horten tart-up time of indutrial robot ytem, and to thu, grow indutrial robot application. It i alo well known that, improving abolute poitioning accuracy of a robot, and improving detection accuracy of the location of workpiece in a matter of minute are two very challenging hurdle to putting offline teaching into practical ue. he author have previouly developed workpiece poition detection method uing autonomou viual meaurement in robotic cell [1]. Currently, the improvement of abolute poitioning accuracy of an indutrial robot with erial mechanim by kinematic calibration i being tudied intenively. Variou method of kinematic calibration for an indutrial robot have been reported [2][3]. However, very few calibration method have been experimentally confirmed a practical for ue on the hop floor. Indutrial robot poitioning error oberved on the hop floor include thoe due to varying environmental condition, uch a change in temperature and load, that are difficult to predict prior to robot hipment. In addition, it i impoible to predict error due to platic deformation in robot link reulting from mechanical damage. o decreae thee type of error, a practical kinematic calibration method which cannot only achieve indicated poitioning accuracy but alo be ued eaily and fat without changing the et location of the robot, i required. Conventional method generally ued at the hop floor increae the quantity of meaurement to improve accuracy of calibration. hu, a large amount of time i required to achieve high accuracy. o balance accuracy with time, meauring data, meauring accuracy and an error model mut be comprehenively conidered in determining a meauring device, a etting method for the meauring device and an identification algorithm for the model. It i alo neceary to develop an algorithm for generating meauring poe and an automatic calibration proce for realizing efficient meaurement, to aure that the reult can be tably obtained. In addition to the above, becaue indutrial robot were previouly only ued in playback procee, improving their abolute poitioning accuracy ha been neglected for a long period of time. A a reult of thi awarene, mot reearcher in kinematic calibration focu their obective on machine tool and poitioning device for which abolute poitioning accuracy i given priority over other performance characteritic. In thee circumtance, there i not a practical calibration method which can atify not only indicated poitioning accuracy but alo low cot, hort operating time and narrow working pace. he author have been conducting reearch to develop a practical offline teaching method uing a CCD camera a a meauring device, becaue of the advantage of it wide range of view, high repeatability and low cot. In thi paper, an automatic robot calibration method i propoed a a reult of thi reearch. hi method work with a camera that can be eaily mounted on a robot without etting camera-intrinic parameter. or improving accuracy of calibration and hortening meauring time, an autonomou viual meaurement baed on 3D meauring data, and an algorithm for determining a et of meauring poe are alo propoed. he effectivene of the propoed method wa evaluated with experiment. 2 CAMEA-BASED CALIBAION MEHOD O OBO KINEMAIC PAAMEES 2.1. Autonomou Meaurement Method for Calibration An example of conventional method for moving a robot according to image taken with a camera mounted on the robot utilize viual feedback control [4][5][6]. With thi method, the robot i moved in a way uch that the image captured with the camera will match a predetermined target image. he author have propoed a method for controlling robot poe in a way uch that a predefined point on the target will alway be on a given view line; that i, to be alway captured with a precribed pixel, thereby making it unneceary to calibrate camera-intrinic parameter. Obtaining the 3D poition of the target according to 2D view line information, however, require obtaining the target Annal of the CIP Vol. 55/1/2006

2 poition a the interection of more than one view line a hown in igure 1 (a). If the relative angle made by the view line i mall, thi method till ha a problem in that a target poition error in depth along a view line i affected largely by meaurement error of the camera. If the relative angle i made bigger on the other hand, the robot require larger working pace. o achieve high accuracy with maller working pace in the identification calculation for kinematic calibration, the author propoe herein a meaurement method hown in igure 1 (b). hi method can obtain information about the poition along a view line uing a target ize a well a conventional meaurement data, while uing only a ingle meauring poe. In thi paper, thi method i referred to a the viual touch-up method, ince what i done with thi method amount to making the tip, P V, of a virtual pin touch up the meauring point. he viual touch-up make it poible to prevent the relatively mall angle made by the view line from affecting calibration, thu achieving more meaurement information from the ame number of meauring poe. α (a) Stereo meaurement meauring data (V,H,α) Virtual pin P V (b) Viual touch-up meauring data (V,H,) igure 1: 3D meauring method uing camera. In thi paper, two meaurement are made on a target whoe contour i a perfect circle. he firt i defined a the center of the circular target contour on a camera-taken image which i deignated a, P M, (hereafter called a meauring point). he econd i the long axi (diameter) length of the contour which i referred to a the ize of the target. Camera-intrinic parameter are not identified in thi cae, however, ditortion in the len may affect calculation of the center and the long axi length on the image. Suppreing thi effect require uing a target having an appropriate ize and uing an image plane around the optical axi where the ditortion in the len i le. In thi paper, the center of a CCD image plane i aumed a pixel ued for meaurement, becaue the optical axi of off-the-helf CCD camera generally pae at or around the center of the image plane. rom a geometric relation hown in igure 2, the ize,, of the target image i obtained uing the following expreion: = f d where d i the ditance between the meauring point and the len center in the D direction in the Σ I. In expreion (1), i proportional to the reciprocal number of d, becaue f and are contant. or the ake of calculation, geometrical characteritic data obtained from the target image ued in meaurement for the calibration i repreented with the poition (V,H) of the target meauring point on the image plane and the reciprocal number, inv =1/, of the target ize (hereafter called meauring data). he meaurement reult i repreented with a poe of the robot for which the meauring data matche a deignated value; that i, the (1) target meauring point and the image plane have a deignated relationhip. lange frame Σ Len center ocal length f Image frame Σ I obot frame Σ V D Camera frame Σ C H Meauring ditance d Image center Image plane Image of target Size of image View line Optical axi igure 2: Camera model. Meauring point Size of target he relationhip between the target meauring point and the image plane i intended to match a deignated value. hat i, the interection of the view line paing through the meauring point and the image plane i made to match the center of the image plane, and the target ize on the image plane i made to match a ize 0, correponding to the deignated relationhip, P V0. he coincidence of the meauring data with the deignated value i realized by moving the robot according to an arm tip diplacement value p(dx,dy,dz). he arm tip diplacement value i obtained by meauring the difference e (dv,dh,d inv ) between the meauring data and the deignated value and then making e zero in the relationhip between the poition and ize of the target in the image frame and the poition of the target in the robot frame a hown in igure 3. hi operation i repeated to control the poe of the robot in uch a way that the value e become lower than or equal to (dv,dh) d Image center Σ I Image of Σ it threhold value. p Meauring point ool fixed on robot flange Camera Σ I igure 3: Viual touch-up control. In igure 2, the relationhip among the robot flange frame Σ, the camera frame Σ C and the image frame Σ I i invariable becaue the camera i attached to the tip of the robot arm. he relationhip between the robot flange frame Σ and the robot frame Σ i obtained from information about the current poition of the robot. In thi paper, therefore, the relationhip between the robot frame Σ and the image frame Σ I i repreented uing the poe of the Σ I in the flange frame Σ. he poe of the Σ I in the Σ i obtained a follow: irt, the robot arm tip i hifted by a very mall value ΔX, ΔY, ΔZ in each direction eparately. Change of the meauring data

3 of the meauring point in the Σ I, Δe,X (ΔV X,ΔH X, Δ X,inv ), Δe,X (ΔV X,ΔH X,Δ X,inv ), Δe,Z (ΔV Z,ΔH Z, Δ Z,inv ) are meaured repectively. he Jacobean matrix J i obtained a hown in the following expreion: ΔVX ΔX 0 ΔH X J = ΔX 0 ΔX,inv ΔX ΔV ΔY ΔH ΔY Δ Y Y Y,inv ΔY 0 0 ΔV ΔZ ΔH ΔZ Δ Z,inv ΔZ In the viual touch-up operation, firt, e on the image plane i meaured, and the hift value p of the arm tip i obtained a hown in the following expreion. 1 e Z Z p = J (3) Implementing a control algorithm a hown in igure 4 a robot can be enabled to perform viual touch-up autonomouly. However, the control algorithm hould alo conider uppreing the effect of lot motion in robot reducer including backlah while executing autonomou viual touch-up. Start Meauring e w.r.t. X, Y, Z Calculation of J uing X, Y, Z, e Meauring e in the Σ I Calculation of p= J -1 e p<threhold value? No Moving robot End Ye igure 4: Algorithm of viual touch-up Algorithm for Identifying Kinematic Parameter Error hi paper ue error in n p kinematic parameter p k =[P k,1,p k,2,,p k,np ], the poition p V =[X V,Y V,Z V ] of the virtual pin tip P V in the Σ and the poition p M =[X M,Y M,Z M ] of the meauring point P M in the Σ a identifying parameter p ID =[Δp k,δp V,Δp M ]. Under an ideal condition, the poition p i of the point P V in the Σ at the ith poe of the robot obtained in viual touch-up will match the poition p M of the meauring point P M. However, the error p ID containing kinematic parameter error will yield the following poitional error, e i, between p i and p M : e i = p i p M (4) A een from the geometric relation, p i i a function of p ID to be identified if an angular diplacement in each robot articulation i contant. In thi paper, the Newton-aphon method i ued to determine p ID in uch a way that the error e=(e 1, e 2,,e n ) between the poition of the point P V in the Σ and P M become the lowet for n robot poe obtained in viual touch-up. In the identifying calculation, the differential g i, i obtained for the th identifying parameter p ID, of e i a hown in the following expreion. (2) de e e i i, i g i, = = (5) dpid, ΔPID, where e i, i the poitional error in the ith poe of the robot obtained by giving a very mall error value Δp ID,i to p ID, Index for Evaluating Meauring Poe for Calibration In the identifying calculation decribed in the previou ection, if Δp ID, i very mall, the matrix G, where g =[ g 1,, g 2,,,g n, ] i the th column vector, can be ued to repreent error relationhip in the following linear expreion. e = Gp ID (6) Uing the following peudo invere matrix expreion: 1 ( G G) G G + = (7) p ID i obtained a follow: + pid = G e (8) A een from expreion (8), the error in p ID to be identified i the one magnified under the G + condition, that i, at a magnifying factor of an error, Δe (meaurement error and non-modeled error), included in e. Achieving higher calibration accuracy require uing a le error-prone meaurement method, a complete model, and meauring poe elected to provide favorable reult. Given a predetermined meaurement method, the availability of favorable meauring poe determine the accuracy of calibration. Uing G + enable the calibration to be evaluated in advance becaue it component can be obtained if meauring poe are elected. Several evaluation indexe have been propoed for the coefficient matrix G for calibration [7][8][9]. hi paper ue the condition number baed on abolute value of the component a an evaluation index C G becaue of it imple calculation [7]. ( G G) = G G ( G ) 1 C = Cond G (9) G Where G G = max h (10) h = hi (11) where h i, i the (i,) component of the quare matrix (G G). o handle each component of p ID equally, though whoe component have different unit, G, which ha been normalized uing the following expreion, i ued intead of G. g = g max g (12) ' i where g i, i the (i,) component of G, and g i the th column vector of G Algorithm for Generating and Aduting Meauring Poe Automatically Several method have been propoed which automatically generate candidate of meauring poe and efficiently elect the mot favorable et of poe uing an evaluation index [7][10]. hee method mut calculate the evaluation indice at leat one time for all generated meauring poe acro the entire parametric pace. he calculation period

4 i very extenive. It i well known that larger diplacement in articulation of a robot for meauring poe are effectual to produce better calibration reult. hi paper ue erial link indutrial robot to be calibrated, and propoe a method to generate meauring poe with larger angular diplacement from a limited motion area. he method conequently evaluate the pairing of meauring poe and optimize them baed on the evaluation index. Start Input parameter of meauring poe meauring poe. hen obtain robot poe that have the ame relative location to the meauring point on the target by uing viual touch-up. After the meaurement, the identification algorithm can calculate p ID. 3 EXPEIMEN VEIICAION 3.1. Experiment Condition he following equipment wa ued in the experiment: obot ANUC obot 2000iA165 (a hown in igure 6 and 7) Generation of meauring poe All of meauring poe i realizable? Ye No Adutment of unrealizable poe CCD Camera C G <threhold value? No Exchange parameter of meauring poe Ye 20mm End igure 5: Algorithm for generating poe. 1. Specify parameter for generating initial meauring poe. 2. Generate a candidate et of the initial meauring poe. 3. Check whether the meauring poe in the et are reachable. If all the poe are reachable, kip to Step 5. If any poe i unreachable, go to Step Adutment of the meauring poe: or unreachable meauring poe, adut the rotation angle of all axe including the out-of-range one o that their diplacement from thoe of other meauring poe will become a large a poible to move within the operating range. 5. Evaluation of the pairing of the meauring poe: Complete generating meauring poe if the condition number i lower than predefined threhold value. Otherwie, go to Step Adut the parameter for generating initial meauring poe by predefined value o that the condition number will decreae, and then go back to Step Automatic Calibration Proce A a minimum requirement for autonomou meaurement uing a CCD camera, the operator mut move the camera mounted on the tip of robot arm to a poition where the target can be viewed by the camera, and teach the poition to the robot a the initial meauring poe. o improve eae of operation and reduce total operating time, a 2-tep automatic meauring proce i propoed which doe not require the pecification of initial value for camera mounting and target poition. 1. Inch the robot keeping the target in the view and meaure robot poe around the ingle meauring point uing viual touch-up. hen roughly identify the poition of the camera and the target but with enough accuracy to achieve the next meaurement for kinematic calibration. 2. Determine a et of meauring poe uing the above-mentioned algorithm for generating and aduting L 6 L 5 igure 6: Experimental robot ytem. L 4 X L 3 L 2 L 1 Z igure 7: Mechanim of 2000iA165. End of Arm ool 106 kg pot welding gun (a hown in igure 6). Camera Opteon USB camera (1/3 CCD of pixel). Len f = 12 mm. Stand-off = approximately 350 mm. A cro mark in a circle (a hown in igure 6). Generation of meauring poe Parameter of meauring poe: Initial meauring poe p B = [X B B,YBB,Z B,W B BB,P B, B BB] Meauring poe variation D W, D P, and D In thi paper, roll, pitch and yaw angle are ued to expre the orientation of robot poe (WP). Meauring poe generation: he ith meauring poe i obtained uing the following expreion. L 1 L 2 L 3 L 4 L 5 L 6 [ X, Y, Z, W + i D, P + i D + i D ] p (13) i, 0 = B B B B W W B P P, B where, i W,i P,i =-1,0,1.In thi cae, 27 meauring poe can be generated uing preet parameter for meauring poe. 479mm 1075mm 0mm 1300mm 260mm 0mm Deigned Value of the kinematic parameter

5 Calculating device for generation obot controller 3.2. Error model he error model for the experimental robot i hown in igure 8. Since robot link and drive ytem have been proceed and aembled under trict dimenional control, elatic deformation are aumed a the main caue of abolute poitioning inaccuracie at the tip of the robot arm. By conidering that elatic deformation occur mainly in the reducer mounted on each rotation axi, elatic deformation caued by load are defined a a hift in the zero point on the reducer of each rotation axi. Becaue the relative poition among the tip of robot arm, P V (ip of virtual pin) and P M (meauring point on the target) are ued in identification, zero point error of J 1 and J 6 are dependent on error of p V,0 and p M,0. herefore, independent zero point error of J 2, J 3, J 4, and J 5 axe [Δθ 2,Δθ 3, Δθ 4,Δθ 5 ] are defined a kinematic parameter of robot p k, and error [ΔX V,ΔY V,ΔZ V ] included in p V are defined a fixture parameter of virtual pin P V, error [ΔX M,ΔY M,ΔZ M ] included in p M are defined a fixture parameter of target P M. In thi paper a total of 10 calibration parameter were identified. θ 5 +Δθ 5 X Virtual pin p V,0 Z θ 3 +Δθ 3 J J 5 4 J 6 θ 4 +Δθ 4 X +(ΔX VΤ, ΔY VΤ, ΔZ VΤ ) p M,0 +(ΔX Μ, ΔY Μ, ΔZ Μ ) θ 2 +Δθ 2 Z J 3 J 2 J 1 igure 8: Error model of the meauring ytem Accuracy of viual touch-up epeatability in poition meaurement 1. View line follow-up meaurement: able 1 lit variation in 100 tereo meaurement reult with view line parameter identified in the flange coordinate ytem Σ. he tereo meaurement reult were obtained from three meauring poe of the robot arm tip by rotating it ±15deg about an initial 0deg meaurement poition. In thi evaluation each meaurement poe required about 20 econd to complete, or approximately 60 econd for a complete tereo meaurement. X Y Z 3σ 0.02mm 0.04mm 0.16mm able 1: epeatability of view line follow-up control. 2. Viual touch-up: able 2 lit variation in 100 viual touch-up reult for the ame target with the poe WP of the Σ ince the touch-up value wa changed every time. Each ingle viual touch-up operation required about 20 econd to complete. rom the reult comparion, adding the ize information wa ucceful in improving the repeatability in the D direction. equired meaurement time wa reduced to 1/3 or le of the conventional value while keeping the meaurement error at 3/4. V H D 3σ 0.02mm 0.02mm 0.12mm able 2: epeatability of viual touch-up. Abolute accuracy in poition meaurement he robot poe obtained by viual touch-up and manual touch-up uing an actual pin to a ingle target were alo invetigated by changing the orientation of the Σ. able 3 how the difference Δp between the poe in the Σ obtained by the viual touch-up and the poe in the Σ obtained by the manual touch-up. When the accuracy in the manual touch-up performed with an actual pin (empirically meaured to be about 0.1 mm) i taken into account, it can be conidered that viual touch-up can achieve accuracy equivalent to conventional manual pin touch-up. ΔX ΔY ΔZ Δp (45deg,0,0) 0.2mm 0.1mm -0.1mm Δp (0,45deg,0) -0.1mm -0.1mm -0.1mm Δp (0,0,45deg) -0.2mm -0.1mm 0.1mm 3.4. Calibration eult able 3: Error of viual touch-up. elationhip among variation in identification reult, condition number and meauring method At firt, the initial vale of (D W,D P,D ) wa et a (5deg,5deg,5deg). With preet threhold and earching tep (each 5deg in WP), everal et of meauring poe were determined by uing the propoed algorithm. In thi cae, time required for generating, aduting and evaluating a et of meauring poe i approximately 15ec by uing the robot controller. o evaluate the effectivene of condition number the threhold wa changed everal time and then everal et of meauring poe were obtained. our et were elected randomly for the evaluation. In order to evaluate the relationhip between variation in the identification reult and the condition number, 10 et of meauring data obtained from each et of meauring poe were ued for the identification. ime required for tep 1 of the propoed calibration proce wa approximately 5min, and time required for tep 2 wa approximately 12min. A a part of the identification reult, J 2 zero point error Δθ 2 i hown in igure 8 with repect to the condition number. Δθ 2 [deg] C G igure 9: elationhip between identifying accuracy and condition number(calibration uing viual touch-up).

6 Δθ 2 [deg] C G igure 10: elationhip between identifying accuracy and condition number(calibration uing view line data only). igure 9 how the relationhip in the cae when viual touch-up wa ued. igure 10 how the relationhip in the cae when only 2D data of the view line orientation wa ued in the identification. he figure how that table identification reult can be obtained by uing a et of meauring poe with mall enough condition number. Comparing igure 9 with 10, it i alo confirmed that accuracy of the identification can be improved by uing viual touch-up without increaing the number of meauring poe ued. rom thee reult, it can be concluded that the condition number i an adequate index for evaluating tability of the identification and it i effective to ue viual touch-up in calibration. Poitioning accuracy before and after calibration An evaluation tet wa conducted uing a plate that ha 25 (5x5) target uniformly placed with 100mm pitche on it urface. or the poition of the target on the plate, deigned value were ued. he poition can be aumed to have le than 0.1mm accuracy by machining. he poition of all point were meaured uing viual touch-up after compenating the robot and the meauring ytem with it baed on identified reult. igure 11 how the relationhip between maximum error Δe max in the ditance between arbitrary two point in the ame row or column meaured againt the deigned value d and the condition number a wa evaluated above. Δe max [mm] Without Calibration C G ( : d = 400mm; + : d = 300mm; Δ : d = 200mm; Ο : d = 100mm ) igure 11: elationhip between ditance error and condition number. A hown in igure 11, relatively high poitioning accuracy wa achieved by uing the et of meauring poe with a mall condition number. It i confirmed that the condition number i alo an adequate index for evaluating poitioning accuracy after the calibration. Although it i not perfect to repreent elatic deformation on the robot arm reducer by the contant zero point error, the ditance error Δe max after the calibration uing the et of meauring poe with repect to mallet condition number wa reduced to below 1/2 of the cae without calibration. Conidering the time required for the calibration, the ratio between the error after the calibration and the ditance (1/600 when d =100mm, 1/800 when d =400mm) and achieved poitioning accuracy of the robot (0.5mm when nominal repeatability of the robot i 0.3mm), it can alo be concluded that propoed method are practical. 4 CONCLUSIONS A new automatic kinematic calibration method uing an autonomou meaurement and an algorithm for determining meauring poe baed on the condition number wa propoed and it effectivene wa experimentally invetigated. he concluion are ummarized a follow: 1. In order to improve accuracy of the identification and horten meauring time, a viual touch-up (rather than tereo meaurement) wa propoed. 2. In order to increae efficiency of the meaurement in the calibration, an algorithm wa propoed to determine a et of meauring poe baed on the condition number and working pace of an indutrial robot on the hop floor. 3. Uing the method propoed in 1 and 2, an automatic calibration method wa propoed. 4. he effectivene of the propoed method wa evaluated through experiment with an actual indutrial robot. 5 EEENCES [1] A. Watanabe, S. Sakakibara, K. Ban, M. Yamada and G. Shen, 2005, Autonomou Viual Meaurement for Accurate Setting of Work Piece in obotic Cell, Annal of the CIP, 54/1:13-18 [2] X.L. Zhong and J. M. Lewi, 1995, A new method for autonomou robot calibration, Proc. of IEEE Int. Conf. on obotic and Automation, [3] S. oyama, S. Hatae,. Haga, 1991, Kinematic calibration of SCAA robot with condition number and error map method, Annal of the CIP, 40/1: 9-12 [4] Y. Shirai, H. Inoue, 1973, Guiding a robot by viual feedback in aembling tak, Pattern ecognition, [5] L. E. Wei, A.C. Sanderon, and C.P. Newman, 1987, Dynamic enor-baed control of robot with viual feedback, IEEE J. of obotic and Automation, A-3/5: [6] B. Epiau,. Chaumette, P. ive, 1992, A new approach to viual ervoing in robotic, IEEE ran. on obotic and Automation, A-8/3: [7] Y. akeda, G. Shen, H. unahahi, 2004, A DBB-Baed kinematic Calibration Method for In-Parallel Actuated mechanim Uing a ourier Serie, ran. of the ASME, J. of Mechanical Deign, 126: [8] A. Nahvi, J. M. Hollerbach, 1996, he noie amplification index for optimal poe election in robot calibration, Proc. of IEEE Int. Conf. on obotic and Automation, [9] J.H. Borm, C. H. Menq, 1991, Determination of optimal meaurement configuration for robot calibration baed on obervability meaure, Int. J. of obotic eearch, 10/1:51-63 [10] D. Daney, 2002, Optimal meaurement configuration for Gough platform calibration, Proc. of IEEE Int. Conf. on obotic and Automation,