Contours Planning and Visual Servo Control of XXY Positioning System Using NURBS Interpolation Approach

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1 Inventon Journal of Research Technology n Engneerng & Management (IJRTEM) ISSN: olume 1 Issue 4 ǁ June ǁ PP Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach Syuan-Y Chen 1, Yu-Hsuan La 2, Han-Tng Lu 3 1,2,3 Department of Electrcal Engneerng, Natonal Tawan Normal Unversty, Tawan, R.O.C ABSTRACT : Ths study ams to develop contours plannng and vsual servo control technologes for a XXY postonng stage for tracng the two-dmensonal contours precsely. Frst, the two-dmensonal contours are planned by usng the non-unform ratonal bass splne (NURBS) nterpolaton approach. Subsequently, the vsual servo control mechansm, whch nvolves fve steps mage processng procedures, s further desgned to perform the closed-loop moton control for hgh-precson postonng performance. Durng the control process, the postonng error s montored onlne. If the postonng error s larger than the pre-defned threshold, a compensaton control wll be executed mmedately to compensate the naccurate motons. In addton, a frendly human-machne nterface (HMI), whch can show the movement of the stage n real-tme, s developed. Fnally, the expermental results demonstrated the favorable postonng performance of the XXY postonng system for tracng the two-dmensonal contours. Keywords: Image processng, NURBS, postonng control, XXY postonng stage. 1. Introducton Hgh-precson XXY postonng stage s compettve on the maret due to ts smaller dmensons, larger weght-carryng capacty, and faster postonng speed comparng wth the tradtonal XYθ stage [1]. Therefore, t has attracted ncreasng attentons sgnfcantly for wde engneerng, ndustral, scentfc and bomedcal applcatons [2]. Because the postonng performance plays an mportant role on the process of manufacturng, many advanced control technologes have been developed for the postonng and auto-algnment of the XXY postonng stage [2]-[5]. On the other hand, because vson system s able to recognze the mages just le human s eyes, t has been adopted popularly to mprove the accuracy of the system and avod the defect from manual operatons effectvely [2], [5]. In ths study, the trajectory plannng and vsual servo control technologes for the XXY postonng stage are developed usng NURBS nterpolaton approach [6]. The expermental results due to varous two-dmensonal contours show the stable and hgh-precson postonng performance. 2. XXY Postonng System The XXY postonng system s composed of a XXY postonng stage (AF-XXY-NR1-175-R28, Chuan Yan Ltd.), a CMOS camera (Lu375c, Lumenera), three drvers (EXD2020MB) and a personal computer (PC)-based control core as shown n Fg. 1. In the system, the XXY postonng stage uses X 1, X 2 and Y axes step motors wth couplng, ball screw, screw mount, crossed ball bearng, and slde unt to carry out ±5mm avalable dsplacement and ±1.5 o avalable angle of the moton as shown n Fg. 2. When the moton of the X 1 and X 2 axes motors are moved for the same dsplacements synchronously, the stage wll be moved n X-drecton. Moreover, when only the moton of Y-axs motor s moved, the stage wll be moved n Y-drecton. Furthermore, f the moton of the X 1 and X 2 axes motors are moved for the dfferent dsplacements, the stage wll be rotated n clocwse or counter-clocwse drectons. Obvously, XXY stage provdes varous moton modes to meet the requrements of the dverse ndustral applcatons. The PC ncludes one stepper moton control card (PCI-8144, Adln) wth 2.4MHz pulse output rate s used to realze the control algorthm for controllng the three axes motors smultaneously. Thus, the stage can be controlled to trac the reference contours precsely. On the other hand, the mage processng algorthm, reference contours plannng, and vsual servo mechansm are realzed n the PC va sual Basc.NET language. Moreover, the adopted camera s wth 3 mllon pxels and 2048*1536 resoluton. Through the Ethernet nterface, the camera can feedbac the practcal stage poston nformaton to the PC n real-tme. In addton, the HMI, on whch the users can easly desgn the path of the postonng stage, s also developed and wll be ntroduced later. olume 1 Issue 4 June

2 Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach son Servo System CMOS Camera Lu375C Drve Sgnals Step Motor Drver EXD2020MB Y-axs Ethernet Drve and Control System X 2 -axs X 1 -axs HMI and NURBS Interpolaton Software PCI Bus AF-XXY-NR1-175-R28 XXY Postonng Stage Control Sgnals Termnal Board DIN-68S-01 Fg. 1 Structure of XXY postonng system. 68-pn Cable ACL axs Moton Control Board PCI-8144 X-drecton Wor stage Free-axs Y-drecton Y-axs Y-axs motor X 1 -axs X 1 -axs motor X 2 -axs Base X 2 -axs motor Fg. 2 XXY postonng stage. 3. Trajectory Plannng Usng NURBS Approach The two-dmensonal contours are produced usng NURBS curve nterpolator n ths study. The NURBS nterpolator can create free-form curves easly by manpulatng the values of control ponts, weght and not vectors. The mathematcal formulaton of NURBS curve s descrbed as follows [6]: and C( p) R, n 0 n 0, n, 0 W,, n 0 R, where s the control ponts; s the correspondng weghts of ; n+1 s the number of control ponts; s the order of the NURBS curve; Z, (p) s the th order B-splne bass functon; R, (p) s the ratonal bass functon. The recursve formulae for computng Z, (p) can be found as (1) (2) olume 1 Issue 4 June

3 Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach 1 for p p p 1,1( p ) 0 otherwse (3) p p p p, 1( p) 1, 1( ) p p p p (4) 1 1 where P=[p,, p + ] represents the not vector. Theoretcally, by manpulatng the values of control ponts, weghts, and nots, the NURBS can produce arbtrary reference contour. Wth the NURBS, the users could set up the curved path nstead of the straght lne. Tradtonally, the curved path s made up of the short straght lne. It s hard to generate the command about the curved path. In addton, there s the unavodable error between the real path and the path we set. Another problem of the tradtonal way s that the platform need to stop or accelerate n the process of move. Therefore, the platform ddn t move smoothly. In ths study, we can mprove the dsadvantage of tradtonal way. The use of the NURBS could let the path of the platform more flexble and changeable. By usng the NURBS nterpolaton approach, the new curve s totally dfferent from the orgnal curve as shown n Fg. 3 when the control pont 2 s moved to the new 2. In addton, the curve becomes sharper f the weght of the correspondng control pont s ncreased as shown n Fg. 3. Obvously, the shape of the contours can be determned va the desgns of the control ponts and ther weghts. Change the locaton of the control pont Regulate the weght of control pont Fg. 3 Illustratons of NURBS nterpolaton approach. 4. Image processng Algorthm The object of the mage processng s to obtan the poston and angle nformaton of the stage from the mage captured by the camera. After calculatng the dfference between the practcal poston and demand contour, the control core wll calculate the approprate control sgnals for controllng the stage poston accurately. The flowchart of the mage processng, whch nclude fve steps majorly, s shown n Fg.4. In the mage processng algorthm, the bnarzaton s frstly used to transform the grayscale pcture nto blac and whte colors. If the pxel s grayscale s hgher than the predefned threshold, t s transferred nto blac color. Otherwse, t s transferred nto whte color. Subsequently, the dlaton and eroson methods of morphologcal operaton are adopted to flter the structure of the mage. Moreover, to fnd the poston of the stage accurately, a Canny edge detecton method s utlzed to fnd the edge, whch means the most amount of change about the mage s grayscale, of the mage. The Canny edge detecton performs convolutoon for the four drectons of the bnary mage. They are horzontal, vertcal and two dagonals drectons. Thus, the gradent wth drecton nformatons of the mage s grayscal can be obtaned. After convoluton, two thresholds are set to contruct a band pass flter for flterng the mage. Afterward, a bnary mage wth clear edge can be obtaned. Furthermore, the best crcle method, whch was developed n [1], s further used to fnd accurate poston of the stage. Fnally, labelng procedure mars the pxels whch connect wth others the same label. Because dsconnected pxels are labelled wth dfferent labels, one can get clear edge of cross target. Thereafter, the target s angle can be calculated va the rectangle surround method. Image Image Image Bnarzaton Morphologcal Bnarzaton Operatons Canny Edge Detecton Best Crcle Method Labelng Fg. 4 Image processng flowchart. olume 1 Issue 4 June

4 Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach 5. sual Servo Control Method Frst, the user can desgn the NURBS curve through the HMI. Subsequently, the software developed n the PC wll transfer the NURBS contour to the three axes moton commands and then control the XXY postonng stage to trac the contour va the drvers. Durng the control process, the camera wll montor the stage poston meanwhle the control core wll regulate the speed and poston control sgnals mmedately for compensatng the postonng error. All the process can be montored onlne va the HMI. The man procedures are lsted as follows: (1) Get coordnate and angle nformaton of the target on the stage: The CMOS camera s used to capture the algnment target s mage frstly. Then, the mage processng algorthm s utlzed to derve the target s coordnate (x 1, y 1 ) and angle. These data are defned as the practcal stage poston. (2) Intal poston algnment: Calculate the dsplacement and angle dfferences between practcal stage poston and predefned ntal poston. Control the stage to the predefned ntal poston by the developed reset functon. (3) NURBS trajectory plannng: Desgn the NURBS trajectory by adjustng the control ponts and correspondng weghts on the HMI. Then use ts prevew functon to prevew the contour. (4) Moton control: Transferrng the contour nformaton to three axs moton commands. Whle the stage s movng, feedbac the stage poston by the vsual servo system and calculate the postonng errors, whch are horzontal error e x, vertcal error e y and average error e a, by the PC as shown n Eq. (5). e a e 2 x e 2 y (5) Postonng error compensaton: If the average error e a s hgher than the predefned threshold, the control core wll regulate the speed and poston control sgnals mmedately for postonng error reducton. By the above steps, the hgh-precson postonng performance can be acheved. 6. Expermental Results 6.1 Software development In ths study, sual Basc.NET wth the Emgu C lbrary was utlzed to develop the software of the XXY postonng system. The control object of ths study s to realze the hgh-precson contour tracng by usng the NURBS nterpolaton approach. There s two ways for changng the contour demand whch are change the locaton of control pont and regulate the weght of each control pont as shown n Fg.3. The users could set up the contour va the HMI drectly. In addton, the users could montor the moton of the stage onlne. 6.2 The developed HMI The developed HMI of ths study s shown n Fg.5. The functon of each bloc s ntroduced n the followng: (1) Inputs for the control ponts coordnates and weghts: The user can type the coordnates and correspondng weghts of the seven control ponts arbtrarly. For example, the coordnates and correspondng weghts of the control ponts for a bow contour are shown n Eq. (8) and Eq. (9), respectvely. (2) Preset contours: The HMI provdes fve preset contours for the users whch are arrow, bow, heart, crcle, and tc. The user can choose one of them for further modfcaton and prevew them below. As shown n Fg. 5, a bow contour s chosen and prevewed. (3) Prevew of the contour: After clcng the NURBS button, the user can prevew the desgned contour on ths wndow. (4) X and Y axes commands of contour: After clcng the NURBS button, ths wndow wll show the requred dsplacement commands of the X and Y axes, respectvely. Thereafter, these control commands wll be sent for the drvers va the moton control board. (5) Functon buttons: Reset: Reset the poston and angle of the stage; NURBS: Plan the contour usng NURBS nterpolaton approach and determne the X and Y axes commands of the contour; Draw: Detect the poston of the stage by usng the camera and draw t on the HMI; Wor: The stage starts to trac the contour; Stop: The stage stops movng mmedately; Clear: Clean the exstent contour and the user can plan a new contour nstead. (6) Real-tme montorng wndow: The moton of the stage wll be shown on ths wndow so that the user can observe t at the same tme. (7) Center of postonng stage: The CMOS camera feedbac the poston of stage. The system deal wth t to determne the coordnate of center. (8) The status of stage and postonng error: Ths wndow shows the status of the stage such as stop and worng. Moreover, ths wndow also shows the postonng errors whch nclude the nstantaneous postonng error and average postonng error. (9) X and Y axes postons: Through the camera, the system turns the coordnate of center nto X-axs poston and Y-axs poston. (10) Performance measure: The system calculates the postonng error va the Eq. (5) and shows the performance measure on ths wndow. (5) olume 1 Issue 4 June

5 Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach (1) (2) (6) (4) Y (8) (9) (7) (3) X (10) (5) Fg. 5 The developed HMI. 6.3 Trajectory plannng In ths study, three two-dmensonal reference contours were demonstrated for the vsual servo control based XXY postonng system. The order of the NURBS curve, not vector, control ponts and weghts of the bow contour are gven as follows: 6 (6) P p, p, p, p, p, p, p, p, p, p ] [0, 0, 0, 0.25, 0.5, 0.5, 0.75,1,1,1] (7) [ [ 0, 1, 2, 3, 4, 5, 6 ] 0,0),( 2, [ 0, 1, 2, 3, 4, 5, 6] [( 2),( 2,2),(0,0),(2, 2),(2,2),(0,0)] (8) [1, 2.5, 2.5,1, 2.5, 2.5,1] (9) The order of the NURBS curve, the not vector, control ponts and weghts of the heart contour are gven as follows: 6 (10) P p, p, p, p, p, p, p, p, p, p ] [0, 0, 0, 0.25, 0.5, 0.5, 0.75,1,1,1] (11) [ [ 0, 1, 2, 3, 4, 5, 6 ] [( 0,0),( 3,2),( [ 0, 1, 2, 3, 4, 5, 6] 2,5),(0,3.6),(2,5),(3,2),(0,0)] (12) [1,1,1,1,1,1,1] (13) The order of the NURBS curve, the not vector, control ponts and weghts of the crcle contour are gven as follows: 6 (14) P p, p, p, p, p, p, p, p, p, p ] [0, 0, 0, 0.25, 0.5, 0.5, 0.75,1,1,1] (15) [ [ 0, 1, 2, 3, 4, 5, 6 ] [ 0, 1, 2, 3, 4, 5, 6] [( 0,0),(0,2),(4,2),(4,0),(4, 2),(0, 2),(0,0)] (16) [1, 0.5, 0.5,1, 0.5, 0.5,1] (17) By usng the parameters as shown n Eq. (6)-(9), Eq. (10)-(13), and Eq. (14)-(17), the desgned bow, heart, and crcle contours were shown n Fg. 6, Fg. 7, and Fg. 8, respectvely. olume 1 Issue 4 June

6 Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach (C) Fg. 6 Desgned bow contour. X-axs command, Y-axs command, (c) Two-dmentonal bow contour. (C) Fg. 7 Desgned heart contour. X-axs command, Y-axs command, (c) Two-dmentonal heart contour. (C) Fg. 8 Desgned crcle contour. X-axs command, Y-axs command, (c) Two-dmentonal crcle contour. 6.4 Expermental result The practcal expermental setup of the XXY postonng system s shown n Fg. 9.The postonng responses due to bow, heart, and crcle contours of the XXY postonng system are shown n Fg. 10, Fg. 11, and Fg. 12, respectvely. From the expermental results, the favorable accuracy and valdty of vsual servo control for the XXY postonng system can be clearly observed. Moreover, the performance measures of the proposed vsual servo control for tracng the bow, heart, and crcle contours are shown n Table 1. The average postonng errors can be controlled wthn 90µm. Thus, the valdtes and performances of the proposed trajectory plannng and vsual servo control for the XXY postonng system usng NURBS nterpolaton approach can be verfed obvously. olume 1 Issue 4 June

7 Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach Camera Step Motor Drver HMI and NURBS Interpolaton Software Termnal Board XXY Postonng Stage Fg. 9 Practcal expermental setup of the XXY postonng system. Fg. 10 Postonng performance due to bow contour. Postonng response, Postonng error. Fg. 11 Postonng performance due to heart contour. Postonng response, Postonng error. Fg. 12 Postonng performance due to crcle contour. Postonng response, Postonng error. Table 1 Performance measures. Control Ponts Complete Tme (sec) Average Error (µm) Bow Shape Heart Shape Round Shape Conclusons In ths study, the contours plannng and vsual servo control technologes for a XXY postonng stage are developed successfully. Accordng to the developed HMI, the users can control the stage for tracng the two-dmensonal contours very easly and olume 1 Issue 4 June

8 Contours Plannng and sual Servo Control of XXY Postonng System Usng NURBS Interpolaton Approach arbtrarly. Wth the CMOS camera, the proposed compensaton control mechansm performs precse postonng performances. The expermental results due to varous contours plannng and tracng demonstrated the favorable performances for the XXY postonng system. REFERENCES [1] C.Y. Nan, S.F. Chuang, Y.S. Tarng. (2006) A new algorthm for a three-axs auto-algnment system usng vson nspecton, Journal of Materals Processng Technology, 171. pp [2] H.W. Lee, C.H. Lu. (2013) son servo moton control and error analyss of a coplanar XXY stage for mage algnment moton, Mathematcal Problems n Engneerng, vol. 2013, artcle ID , 12 pages. [3] A. Yu, I.A. Bonev, P. Zsombor-Murray. (2008) Geometrc approach to the accuracy analyss of a class of 3-DOF planar parallel robots, Mechansm and Machne Theory, 43. pp [4] A. Joubar, M. Slaman, I.A. Bonev. (2012) A novel XY-Theta precson table and a geometrc procedure for ts nematc calbraton, Robotcs and Computer-Integrated Manufacturng, 28, pp [5] H.M. Chen, T.E. Lee, J.P. Su, C.L. Ln. (2014) Realzaton of an mage-based XXY postonng platform control, 2014 Internatonal Symposum on Computer, Consumer and Control. [6] F.J. Ln, S.Y. Chen, P.H. Chou, P.H. Sheh. (2009) Interval type-2 fuzzy neural networ control for X-Y-Theta moton control stage usng lnear ultrasonc motors, Neurocomputng, 72, pp olume 1 Issue 4 June