Real-time State Estimation and Fault Detection for Controlling Atomic Force Microscope Based Nano Manipualtion

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1 Proceedings of he 17h World Congress The Inernaional Federaion of Auomaic Conrol Real-ime Sae Esimaion and Faul Deecion for Conrolling Aomic Force Microscoe Based Nano Maniualion Lianqing Liu,, Ning Xi Yilun Luo Jiangbo Zhang Guangyong Li Yuechao Wang Roboics Laboraory, Chinese Academy of Sciences, Shenyang, Liaoning Province, 1116 China De.of Elecrical and Comuer Engineering, Michigan Sae Universiy, Eas Lansing, MI, USA De.of Elecrical and Comuer Engineering, Universiy of Pisburgh, Pisburgh, PA, 1621 USA Graduae school of Chinese Academy of Sciences, Beijing 11, China Absrac: The main roblem of Aomic Force Microscoe (AFM) based nanomaniulaion is helackofreal-ime visualfeedback. Alhoughhemodelbasedvisualfeedbackcanarlysolve his roblem, he incorrec dislay caused by he uncerainies in he nano-environmen ofen leads o a failed nanomaniulaion. In his aer, a general sraegy wih hree-level srucure is roosed o overcome his roblem. Wih his hree-level sraegy, he incorrec dislay can be no only real-ime deeced, bu also on-line correced. The difficuly o imlemen his sraegy is hahere is noconinuouswayodescribe andmodel hesysem since boh discree and coninuous commands are involved. A Peri-ne based mehod is roosed o organize his sraegy such ha ask scheduling, which usually deals wih discree evens, as well as ask lanning, which usually deals wih coninuous evens can be reaed in a unified framework. This Peri-ne organized sraegy rovides general insrucions o AFM based maniulaion for dislaying a visual feedback which can be as close as ossible o he rue environmen. The exerimenalresuls resenedin heaer demonsrae headvanage of heroosed sraegy. I also shows he increased efficiency of he AFM based nanomaniulaion. 1. INTRODUCTION Aomic Force Microscoe (AFM) (Binning (1986)) has been roved o be a owerful ool o characerize he roughness, grainsize orfeauresofsurfaceinaomic scale. AyicalAFMconsiss ofanexremely sharimouned or inegraed on he end of a iny canilever which is driven by a mechanical scanner over he samle surface o be observed. The variaion of he surface heigh varies he force acing on he i and herefore varies he bending of hecanilever. Thisbendingcanbe measured wih alaser so refleced from he o of he canilever ino an array of hoodiodes. The surface informaion can be obained by he elecronic conrol device based on he measured bending signal. Inaddiionocharacerize samle surfaces, heexremely shar AFM i can also be used as an end effecor o modify he samle surface. Researchers use AFM o changehe samle surface hroughnanolihograhy (Schaefer (199), Wang (199)) and nanomaniulaion (Kim (1992), Luhi (1994), Junno (199), Sark (1998)) aking advanage of is high resoluion and high alignmen accuracy. Since AFM collecs image daa by feeling raher han looking, he maniulaion rocess can no be moniored in real- This work was suored in ar by he Naional Science Foundaion under grans CMMI-113, and IIS ime due o he slow scanning seed. The oeraion resul has o be verified by a new image scan afer each se of maniulaion, which ofen akes several minues. Obviously, his scan-design-maniulaion-scan cycle is very ime-consuming and inefficien. To enhance he efficiency of AFM based maniulaion, some virual realiy based mehods have been develoed. A 3-D virual realiy visual feedback is buil from he saic AFM image in Sii (1998) and Guhold (2). Alhough a virual realiy can dislay a saic virual environmen and a dynamic i osiion, i does no dislay he environmen changes during maniulaion. The oeraor is sill blind because he environmen changes are no udaed in real ime. To solve his roblem, an augmened realiy sysem has been develoed in Li (23). Wih his mehod, a movie-like visual feedback is rovided, he oeraor can maniulae nano-objecs underheassisance of force and visual feedbacks. Bu his kind of real-ime visual dislay is sill no he real maniulaion resul, bu he calculaed real-ime changes of he rue environmen from he objecs behavior models. Due o he comlexiies and uncerainies of he nano-world, such as surface ension, Van der Waals force, caillary force and so on, i is imossible o accuraely describe he objec s behavior wih a mahmaical model. Thus here is mismach beween he model based visual dislay and he real environmen. As a resul, he false visual feedback leads o a failed maniulaion. Alhough /8/$2. 28 IFAC /2876--KR

2 17h IFAC World Congress (IFAC'8) hemismachcanbe deeced hroughforce feedbackechnology ( Li (23), Zhang (26)), anew AFMimage scan is sill needed o verify and correc he error. From above discussion we can see, here is no available mehod ha can rovidea real-ime visual feedback whichcan maches he rue environmen very well during maniulaion. Logic Daa (Discree) Tasks Task Classfied unified model or framework which could describe boh discree and coninuous evens ogeher. Here Peri ne is used o organize his sraegy. Through adoing Peri ne, ask classify, dynamicmodeldesign, sae esimaion, faul deecion, and hardware execuion can be handled in a unified framework. The exerimenal resuls resened in he aer demonsrae he advanage of he roosed sraegy, which also shows he increased efficiency of he AFM based nanomaniulaion. 2. METHOD FOR FAULT DETECTION AND CORRECTION Numerical Daa (Coninuous) Dynamic Model Design Sae Esimaion and Faul Deecion Acions Planning The funcions of he hree levels have o be well imlemened o ge an reliable visual feedback. How o classify maniulaion asks has been resened in Li (2). The funcions of he hird level can be well erformed by he commercial AFM sysem. So in his secion, we mainly address he imlemenaion of he second level, such as he dynamical model design, he develomen of Kalman filer and he rajecory lanning of local scan. Time-based Execuion AFM Conroller AFM Work Saion Fig. 1. A sraegy wih hree-level srucure for deecion and real-ime correcion of fauly visual feedback in AFM based nanomaniulaion. A sraegy based on real-ime faul deecion and correcion rovides a feasible way o overcome his roblem. This sraegy can be mainly divided ino hree levels as shown in Fig. 1. The firs level is o classify he asks based on he shae of he objec. Some logical variables are generaed in his level o reresen differen maniulaion objecs such as aricle, rod, wire and so on. The second level is in charge of sae esimaion and faul deecion. A kalman filer is develoed in his level o rovide a sae esimaion and judge wheher here is a fauly dislay, based on which he desired AFM acions are lanned. For examle, if no faul is deeced, he maniulaion will be coninued, else he maniulaion is susended and he i s rajecory is designed o ake an AFM scan and ge he rue maniulaion resul. The coninuous commands are generaed and sen o he low level conrollers which drives he AFM i. The final level is ime-based execuion, afer receiving he moion commands, AFM conroller drives he AFM i following he lanned rajecory. In his level, he acion of maniulaion or scanning is erformed. Through hese hree levels, he fauly dislay can be deeced and correced on-line. Onehingneeds o be furher addressed is he scan rocess. Since only ar of he surface area is modified during maniulaion, he whole image scan is no necessary, and local scan is enough o ge he rue maniulaion resul. Since local scan only needs ake several lines scan, i can be finished in a very shor ime, and a movie-like visual feedback maching he rue environmen can be rovided in real-ime, which grealy faciliaes he AFM based nanomaniulaion. One major difficuly o design such a sraegy is ha here is no a 2.1 Sysem Dynamic Model The objec s dynamic model is a rerequisie for faul deecion by using Kalman filering echniques. To make our oin clearer, a ask of maniulaing nano-aricles will be used o exlain his sraegy. The sraegy can be exanded o maniulae oher yes objecs by adoing corresonding dynamic models. To simly he analysis, he moion of he i and objecs is decomosed ino horizonal moion and verical moion along he fas scan direcion and slow scan direcion resecively. The dynamic model of he nano-aricle in horizonal direcion during maniulaion can be exressed as: ẍ + kẋ = λf x (1) Here x is he relaive dislacemen o he sar ushing oin in horizonal direcion, F x is he corresonding force measured from he AFM i, k is he daming coefficien of he dynamic sysem, λ is he roorional gain for adjusing he force. k and λ can be obained hrough exerimens. A similar equaion can be wrien for he verical direcion. The sae sace reresenaion of he nano-aricle in horizonal direcion is: { ẋ = vx v x = λf x kv x (2) Here x,v x are dislacemen and velociy of he aricle in horizonal direcion resecively. The corresonding discree-ime equaionsinhorizonalandvericaldirecion wih a samling eriod T are: { Xk+1 = AX k + BU k Z k = CX k (3) Where X(k) = [x(k),y(k),ẋ k,ẏ k ] T, U k = [,,fk x,fy k ]T, here fk x and fy k is he ineracion force in horizonal and verical direcion resecively. Z k is he saes measuremen from he visual dislay, he observaion marixes C is a 4 4 uni marix, sae ransiion marix A and conrol inu marix B are given as: 8264

3 17h IFAC World Congress (IFAC'8) 1 1 k (1 e kt ) 1 A = 1 k (1 e kt ) e kt e kt λ k (T 1 k + 1 k e kt ) λ B = k (T 1 k + 1 k e kt ) λ k (1 e kt ) λ k (1 e kt )) 2.2 Kalman Filer Based Sae Esimaion and Faul Deecion Wih he objec s dynamic model, i is now ossible o es wheher he visual dislay agrees wih he real-ime changes in he nano environmen or no by using Kalman filer echnology. An esimaion X k/k 1 and an associaed covariance marix P k/k are calculaed in each se. The innovaion e k is calculaed as: e k = Y k CX k/k 1 (4) Here Y k is he sae informaion from he visual dislay. In he ideal case, wihou error he innovaion e k from he Kalman filer should be Gaussian and whie, is associaed covariance R e = e k e T k kees a value near o zero. When he visual dislay does no agree wih he esimaion, he innovaion e k will no be Gaussian nor whie, and is associaed covariance R e will have an abru increase. R e is calculaed as: R e = E[(Y k CX k/k 1 )(Y k CX k/k 1 ) T ] () Subsiuing Y k = CX k + V k ino () (here V k is he measuremennoise wihhe covariancer andindeenden of X k ). Equaion () can be rewrien as: R e = P k/k + R (6) R e can be direcly used o judge wheher here is a inaccurae dislay or no by seing a hreshold on i, bu he erformance of his measure is less of robusness and a false alarm signal is frequenly riggered. One of he robus measures is Mahalanobis disance. The Mahalanobis disance of R e is calculaed as: M = e T R 1 e e (7) A hreshold on M is se o give an alarm signal when a faul haens. When he visual dislay loses mach wih he real environmen, M will have an abru increase and overshoo he hreshold. Then an alarm signal will be riggered o reor he error o he sysem. 2.3 Trajecory Planning of Local Scan Once i is deeced ha he visual dislay does no mach he real-ime changes in he nano environmen, a local scan is needed o ge he real maniulaion resul. To minimize he local scan ime, he scan aern should firs scan he area wih he highes robabiliy ha he objec P1 O e V Q2 Q 1 Fig. 2. Local scan aern for geing he real osiion of nano-aricles O r O P2 9 L 2 L L Fig. 3. Perine modelforhesraegy of sae esimaion and faul deecion. can be found. Since Kalman filer can give an oimal esimaion of he osiion, he esimaed osiion should have he highes robabiliy ha he objec locaed. Thus his osiion should be scanned firs. The scan aern is designed as shown in Fig. 2. The solid circle O reresens he aricle osiion in he visual dislay inerface. The doed circle O e reresens he esimaed osiion from he Kalman filer. In an ideal case, he aricle s real osiion should be same wih he esimaed osiion from Kalman filer. Due o he environmen noise or he dynamic modeling error, he real osiion of he aricle may no be a oin O e. The scan aern will firs go along line L, which asses hrough he dislayed cener O and esimaed cener O e. If he aricle was no found, hen he scanning line moves u and down along he direcion erendicular o Line L alernaively by a disance of 3/2R unil he aricle is found. Once he aricle is found, he scanning line forms wo inersecion oins wih he boundary of he aricle, P 1 and P 2. Anoher line V, which goes hrough he midoin beween P 1 and P 2 and is erendicular o he revious scanning line, is scanned o ge he acual cener O r of he aricle. The las scan line has wo inersecion oins wih he boundary of he aricle, Q 1 and Q 2. The final acual cener of he nanoaricle O r, is locaed a he midoin beween Q 1 and Q 2. The lengh of he scanning line L is deermined by he maximum disance OO e and he radius of he aricle such ha L OO e + 2R. The visual dislay is udaed immediaely afer he acual osiion is obained

4 17h IFAC World Congress (IFAC'8) Table 1. The meaning of i and i Place Meaning Trans Meaning Ready for maniulaion If objec is maniulaed 1 1 Real-ime 2 changed dislay Lengh, widh 2 idenify Ge objec informaion 3 If L/R > 1 3 Lengh=L, 4 Widh=R 4 If 1.< L/R <1 Wire If L/R < 1. 6 Rod Wire model seleced 6 7 Paricle Rod model seleced 7 Model ready for Paricle model 8 8 visual dislay Model ready for 9 Kalman filer Ineracion force 1 informaion Behavior saes 11 in visual dislay Ge he residual 12 value No faul in dislay 13 Alarm signal riggered Ready for local scan True maniulaion resul seleced Model based calculaion 9 Udae visual PETRI NET MODEL dislay Residual calculaion If Residual< δ If Residual> δ Ready for local 14 scan Local scan erformed 1 Udae visual 16 dislay From above discussions we can see his sraegy should erform he following acions during maniulaion, such as ask classifying, sae esimaion, faul deecion, rajecory lanning, hardware real-ime execuion and so on. Obviously, boh discree and coninuously evens are involved in his sraegy. There is no a coninuous mehod ha can analyze and describe his hybrid sysem. As shown Fig. 3, a Peri ne is used here o organize his sraegy in an unified frame. This grah consiss of wo kinds of nodes: laces and ransiions, where arcs are eiher fromalace oaransiionorvice versa. Places reresen condiions and sysem sae, such as being Ready for maniulaion or Model Ready for visual dislay. Transiions reresen evens and acions, such as Model based calculaion or Udae visual dislay. Tokens, which are reresened by dos in laces, corresond o signals owing in he sysem and heir collecion reflecs he sae of he sysem. All he arc weighs in his eri ne are 1 s. The meaning of he laces i and he ransacions i (i=1,2,...16) is exlained in Table 1. The iniial sae of he eri ne has wo okens in 1 and 2 resecively, which means he sysem is ready for maniulaion. The oken will be fired under he ransiion rule of he eri ne. Afer maniulaion sars, 1 is firs fired when an objec is maniulaed by he AFM i. The oograhy informaion of he objec is acquired in 3. A he same ime, he real-ime ineracion force is obained and recorded in 1. Through firing 2, he lengh L and widh R is calculaed and reserved a 4. Based on he raio beween L and R, he curren maniulaion ask is classified ino one of he hree maniulaions: wire, rod and aricle (Li (2)). To ge he unique model of he objec hrough Peri ne, a new kind of arc called inhibior arc is inroduced o Fig. 3 (Peerson (1981)). An inhibior arc connecs a lace o a ransiion and is reresened by a dashed line erminaing wih a small circle insead of an arrowhead a he ransiion, like he arc from 6 o 6 in Fig. 3. The inhibior arc disables he ransiion when he inu lace has a oken and enables he ransiion when he inu lace has no oken. No okens are moved hrough an inhibior arc when he ransiion fires. By his way, he ransiions of 6, 7, 8 each ime only one of hem can be fired, so hecorresondingmodelforcurrenmaniulaion ask is unique and deermined. Then he okens are moved o 8 and 9. Afer 9 is fired, he objec s behavior saes in visual dislay is calculaed and reserved in 11. Each inu lace of ransacion 11 has a oken now, which saisfied he firing qualificaion of 11 and he residual beween he esimaed saes by he Kalman filer and saes in he visual dislay is calculaed. Afer he oken is moved o lace 12, 12 is fired if he residual value is less han he hreshold δ, oherwise 13 is fired o generae an alarm signal o rigger he local scan. Before local scan is erformed, he oken is removed firs from 14 and added o 1 o swich he AFM work mode from maniulaion mode o image mode. Then local scan is erformed, and he rue maniulaion resul is obained. Finally he visual dislay is correced by he rue maniulaion resul. By he okens flowing in he Peri ne, he reques for ime sequence andsynchronizaionof hesraegy are saisfied. The various maniulaion ask can be handled in a unified framework, which makes he sraegy more flexible o he general roblems. The Peri ne also gives faciliy o add new funcion o he sraegy for more comlex alicaion in fuure. 4. IMPLEMENTATION AND EXPERIMENTAL RESULTS The exerimens were erformed in ambien condiion. The exerimenal sysem mainly consiss of a NanoScoe IV Aomic Force Microscoe (Vecco Inc., Sana Barbara, CA) and some eriheral devices including an oical microscoe, a haic device (SensAble Technologies Inc., Woburn, MA ), wo Mulifuncion Daa Acquisiion (DAQ) cards NI PCI-636E and NI PCI-6733 (Naional Insrumens), and hree comuers. 4.1 Imlemenaion of Kalman Filer Based Faul Deecion As shown in Fig. 4a, one laex aricle wih a diameer of 3nm was ushed along he arrow direcion. The dislacemen as a funcion of ime is shown in Fig. a. The solid curve reresens he dislacemen in he visual dislay, he dashed curve is he esimaion dislacemen from he Kalman filer. The ineracion force during maniulaion is shown in Fig. b. Before =4.9s, he esimaion dislacemen from he Kalman filer agreed wih he dislacemen in he visual dislay. The Mahalanobis disance ke a nearzero value. Dueoheuncerainies andcomlexiies of nano-environmen, a = 4.9s, he i slied aside he round aricle. As shown in Fig. b, he ineracion force 8266

5 17h IFAC World Congress (IFAC'8) A B Firs scan line Second scan line.8.6 (a) (b) Y axis (µm).4.2 Fig. 4. Maniulaing laex aricles (diameer 3nm) on olycarbonae surface wih oeraion range of 11.µm. (a) Pushing a aricle along he arrow direcion; (b) Maniulaion resul in he visual dislay. The righ icure is he zoom in image of he recangle area in b. Area A reresens herue osiion whichis online obained by local scan. The area B reresens he fauly dislay osiion. Dislacemen (µm) Force (µn) Faul Pos Mea Pos Kal Time (sec) (a) 1. Force Measuremen Time (sec) (b) 2 Faul 2 Threshold Time (sec) (c) Fig.. Kalman filer based error deecion. (a) Posiion dislayed in he visual feedback and osiion esimaed from Kalman filer; (b) The real-ime ineracion force; (c) The Mahalanobis disance. suddenly droed o zero. Bu in he visual dislay inerface, he aricle sill ke moving wih he AFM i, he residualbeween he esimaed behaviorandhe behavior in he visual dislay would have a significanly increase. Then as shown in Fig. c, he residual s Mahalanobis disance increased raidly and exceeded he hreshold. A inaccurae dislay was deeced and an alarm signal was riggered. 4.2 Imlemenaion of Local Scan Based Faul Correcion Afer he alarm signal was riggered, local scan was erformed o on-line ge he aricle s real osiion. The scanning aern for relocaing nano-aricle is shown in Fig. 6a. The oograhy informaion of he scanning lines is shown in Fig. 6b. From he oograhy informaion, he acual osiion of he nano-aricle can be idenified as described in Secion 2.3. Afer he acual osiion is Z Heigh (nm) X axis (µm) (a) Y axis (µm) 4.8 (b) Firs scan line Second scan line 6. X axis (µm) Fig. 6. Scan aern and he scan resul. a) The local scan aern for nano-aricle; b) The oograhy informaion along he scanning lines. obained, he visual dislay is udaed wih he real maniulaionresul. Fig. 4b shows heosiion error beween hevisualdislayandherealenvironmen. The solid area A shows he real aricle osiion from he local scan. The inden area B reresens he aricle locaion in he visual dislay. The osiion difference beween A and B shows ha he visual dislay loses mach wih he rue environmen, i also verifies ha he osiion error can be deeced by he Kalman filer efficienly and correcly. Wih he sae esimaion and faul deecion, he reliabiliy of AFM based nanomaniulaion is grealy enhanced, he inaccurae dislay no only can be real-ime deeced, bu also can be on-line correced. Coninuous maniulaion can be done wihou any new AFM image scan in beween. Fig. 7 shows he exerimenal resul o form a riangle aern by maniulaing he nano-aricles. Fig. 7a shows some laex aricle deosied on olycarbonae surface. Fig. 7b shows he image of he real-ime dislayinerface. Fig. 7c shows he real maniulaionresuls obained from a new AFM image scan afer finishing he maniulaion ask. Since he fauly dislay was onlinedeeced andcorreced duringmaniulaion, hefinal maniulaion resul in visual dislay inerface erfecly maches he real AFM image. The whole maniulaion rocess were finished coninuously, which roved he significanlyincreased efficiency ofafmbased nanoassembly.. CONCLUSION Due o he uncerainies and comlexiies of nanoenvironmen, he model based visual feedback can no describe he objec s behavior accuraely, which will lead

6 17h IFAC World Congress (IFAC'8) (a) (b) (c) Fig. 7. Maniulaing laex aricles (diameer 3nm) on olycarbonae surface wih oeraion range of 1µm. (a) Image of laex aricles on olycarbonae surface before maniulaion (b) he real-ime dislay on visual feedback inerface afer he final oeraion. (c) A new AFM scan image afer maniulaion o a fauly dislay and a failed maniulaion. In his aer, a sraegy is roosed o overcome his roblem by faul deecion and correcion. Since boh discree and coninuous commands is involved during imlemenaion, Peri ne is adoed o model and organize his sraegy. The exerimenal resuls shows ha under he assisance of he roosed mehod, he inaccurae dislay can no only be real-ime deeced, bu also be on-line correced wihou inerruing maniulaion. Hence, he efficiency and effeciveness of AFM based nanomaniulaion has been significanly imroved. This sraegy also rovides general insrucions o develo new mehods and new echnologies o faciliae AFM based nanomaniulaion in he fuure. M. Sii and H. Hashimoo. Tele-nanoroboics using aomic force microscoe. In Proc. IEEE In. Conf. Inelligen Robos and Sysems, , M. Guhold, M. R. Falvo, W. G. Mahews, S. washburn S. Paulson, and D. A. Erie. Conrolled maniulaion of molecular samles wih he naomaniulaor. IEEE/ASME Transacions on Mecharonics, : , June 2. G. Li, N. Xi, M. Yu, and W. Fung. Develomen of augmened realiy sysem for AFM-based nanomaniulaion. IEEE/ASME Transacions on Mecharonics, 9:38-36, 24. J. Zhang, N. Xi, G. Li, H. Y. Chan, and U. C. Wejinya, Adaable End Effecor for Aomic Force Microscoy Based Nanomaniulaion. IEEE Transacions on Nanoechnology, : , 26. G. Li, N. Xi, H. Chen, C. Pomeroy,and M. Prokos, Videolized aomic force microscoy for ineracive nanomaniulaion and nanoassembly. IEEE Transacions on Nanoechnology, 4:6-61, 2. P. M. Frank, Faul diagnosis in dynamic sysems using analyical and knowledge-based redundancy : A survey and some new resuls. Auomaica 26:49-474, 199. J. L. Peerson, Peri Ne Theory and he Modeling of Sysems. Englewood Cliffss, NJ:Preice-Hall,Inc., ACKNOWLEDGEMENTS The auhors would like o hank Dr. Chanmin Su of Veeco Insrumen Inc. for his echnical advice and hel during he rocess of his research. REFERENCES G. Binning, C. F. Quae, and C. Gerber. Aomic force microscoe. Physical Review Leers, 6:93-933, D. M. Schaefer, R. Reifenberger, A. Pail, and R. P. Andres. Fabricaion of wo-dimensional arrays of nanomeer-size clusers wih he aomic force microscoe. Alied Physics Leers, 66: , 199. D. Wang, L. Tsau, e al. Nanofabricaion of hin chromium film deosied on Si(1) surfaces by i induced anodizaion in aomic force microscoy. Alied Physics Leers, 67: , 199. Y. Kim and C. M. Lieber. Machining oxide hin films wih an aomic force microscoe: aern and objecive formaion on he nanomeer scale. Science,27:37-377, R. Luhi, E. Meyer, H. Haefke, L. Howald, W. Gumannsbauer, and H.-J. Gunherod. Sled-ye moion on he nanomeer scale: Deerminaion of dissiaion and cohesive energies of c6. Science, 266: , T. Junno, K. Deer, L. Monelius and L. Samuelson. Conrolled maniulaion of nanoaricles wih an aomic force microscoe. Alied Physics Leers, 66: , 199 R. W. Sark, S. Thalhammer, J.Wienberg, and W. M. Heckl, The AFM as a ool for chromosomal dissecionhe influence of hysical arameer. Alied Physics A, 66:79-84,