Path Planning of Automated Optical Inspection Machines for PCB Assembly Systems

Transcription

1 96 International Journal Tae-Hyoung of Control, Park, Automation, Hwa-Jung Kim, and Systems, and Nam vol. Kim 4, no., pp , February 2006 Path Planning of Automated Optial Inspetion Mahines for PCB Assembly Systems Tae-Hyoung Park, Hwa-Jung Kim, and Nam Kim Abstrat: We propose a path planning method to improve the produtivity of AOI (automated optial inspetion) mahines in PCB (printed iruit board) assembly lines. The path-planning problem is the optimization problem of finding inspetion lusters and the visiting sequene of ameras to minimize the overall working time. A unified method is newly proposed to determine the inspetion lusters and visiting sequene simultaneously. We apply a hybrid geneti algorithm to solve the highly ompliated optimization problem. Comparative simulation results are presented to verify the usefulness of the proposed method. Keywords: AOI mahine, geneti algorithm, path planning, optimization, PCB assembly.. INTRODUCTION One important proess in eletroni manufaturing today is PCB (printed iruit board) assembly using SMT (surfae mount tehnology). SMT has replaed the older through-hole-tehnology beause it an dramatially inrease the densities of omponent per board. Fig. shows a SMT in-line system for PCB assembly. The AOI (automated optial inspetion) mahine is employed in the SMT in-line systems to perform a sequene of optial inspetions on omponent plaement and soldering. Due to the growth of image proessing tehnology, they have beome very popular in PCB assembly lines. Effiient operation of the AOI mahine is essential for reduing produt ost and therefore inreasing ompetitiveness. In this paper, we propose a method to redue the overall working time of the AOI mahine. The path-planning problem of the AOI mahine is to find the optimal path of a amera suh that the overall working time is minimized. Sine the image aquisition area of the amera is limited by its FO (field-of-view), all omponents and soldering pads in the PCB should be divided into many lusters. The size of eah luster should be within the size of the Manusript reeived February 23, 2005; revised August 2, 2005; aepted Deember 6, Reommended by Editorial Board member Sangdeok Park under the diretion of Editor Keum-Shik Hong. This work was supported by the Regional Researh Centers Program of the Ministry of Eduation & Human Resoure Development in Korea. Tae-Hyoung Park and Nam Kim are with the Shool of Eletrial and Computer Engineering, Chungbuk National University, Cheongju, Chungbuk , Korea ( s: {taehpark, namkim}@hungbuk.a.kr). Hwa-Jung Kim is with the R&D Center, KEC Mehatronis Co., LTD, Kumi, Kyungbook , Korea ( jjakji@korea.om). FO. The amera visits every luster and aquires an image to perform the PCB inspetion. The number of lusters and the moving path of amera have great influene on the total working time. Hene the pathplanning problem is to determine the lusters and visiting sequene minimizing the total working time. This problem is under the ategory of the NP-hard optimization problem, so it is very diffiult to find the optimal solution in a reasonable time. In this paper, we propose a method to find the near-optimal solution of the path-planning problem. Most researhes on AOI mahines have been foused on image proessing [-3]. It is very diffiult to diretly apply the typial lustering algorithms [4,5] to our problem beause our problem is different from the typial lustering problem in the viewpoint of deision variables and optimization riteria. The optimization method for the TSP (traveling salesman problem) [6] an be partly applied to our problem, but it is neessary to develop a new method to solve the whole path-planning problem. We an solve the path-planning problem by dividing the whole problem into two sub-problems: lustering problem and sequening problem. The lustering algorithms are applied to solve the upper stage problem, and then the TSP algorithms are applied to solve the lower stage problem. This hierarhial approah an generate a good solution in a short time, but may generate an ineffiient solution sine the lustering and sequening are not independent. To improve the effiieny of the solution, we newly propose the unified method that solves the lustering problem and sequening problem simultaneously. The hybrid geneti algorithm is applied to solve the optimization problem. We verify the effiieny and usefulness of the proposed method through the

2 Path Planning of Automated Optial Inspetion Mahines for PCB Assembly Systems 97 omparative simulation using a ommerial mahine. 2. PATH PLANNING PROBLEM Fig.. PCB assembly system and AOI mahine. Fig. 2 shows a typial AOI mahine that onsists of a gantry and a amera. The gantry moves in the y- diretion, and the amera moves along the gantry in the x-diretion. These x and y-diretion movements an our onurrently. Sine the FO (field-of-view) of the amera is bounded by its limit, the amera travels over the entire board area to aquire overall images. Fig. 3 depits inspetion windows, FO and amera path of the AOI mahine. The inspetion window is a retangular area to be inspeted by the amera, whih inludes omponent and soldering pad. Several hundreds or thousands of windows are usually loated in one PCB. The FO is the maximum image area that an be aquired by one shot of the amera. The size of the FO is a onstant parameter of the amera, whih is usually about several tens of millimeters. The inspetion luster is a group of inspetion windows that an be aptured by one shot of the amera. So the size of the FO limits that of the inspetion luster. The amera starts from a given initial position, and visits every luster to aquire image data for all inspetion windows. The amera path is the sequene of lusters visited by the amera. The number of inspetion lusters is equal to the number of shots by the amera. Hene if we redue the number of lusters, we an redue the total image aquisition time of the AOI mahine. The overall working time also inludes the amera moving time between lusters. The total moving time is deided by the visiting sequene of the amera. Therefore, inspetion lusters and visiting sequene should be determined to redue the overall working time. The path-planning problem of the AOI mahine is to determine the inspetion lusters and visiting sequene of the amera. Now we formulate the path-planning problem mathematially. Let W be a set of window indexes and C be a set of luster indexes as: W = {, L, m}, () C = {, L, n}, (2) Fig. 2. Struture of AOI mahine. Fig. 3. Inspetion windows, FO and amera path. where n is the number of lusters, whih is a variable to be determined. Define the luster variable {0,} m n as: z w z w =, if window w is a member of luster. 0, otherwise and define the sequene variable x ij = 0, otherwise. x ij {0,} n n as:, if luster j is visited diretly from luster i. Then the path-planning problem is formulated as the following integer- programming problem:

3 98 Tae-Hyoung Park, Hwa-Jung Kim, and Nam Kim s.t. min { nt aq + tij xij } (3) i C j C zw =, w W, (4) C zw, C, (5) ww max min FO, max min FO, X X X C, (6) Y Y Y C, (7) xij =, j C, (8) i C xij =, i C, (9) j C xij S, S C. (0) i S j S In (3), n is the number of lusters related with the luster variable z w. T aq is the image aquisition time for one luster, whih is assumed to be a onstant value. And t ij is the amera moving time between luster i and luster j, whih depends on the luster variable z w. Hene the objetive funtion in (3) is the overall working time, whih is the sum of total image aquisition time and total moving time. Constraint (4) means that every inspetion window should be inluded in an inspetion luster, and onstraint (5) means that every inspetion luster should inlude at least one inspetion window. X min max and X denote the maximum and the minimum x- oordinates of luster, respetively. Also Y max and Y min denote the maximum and the minimum y- oordinates of luster, respetively. Therefore onstraints (6)-(7) mean that the size of luster should be smaller than the size of the FO. Constraints (8)- (9) mean that every luster should be visited exatly one, and onstraint (0) prohibits split yles from the amera path. Hene the amera path should be the Hamiltonian tour for the traveling salesman problem. The path-planning problem is to find the luster variable and the sequene variable suh that the objetive funtion (3) is minimized subjet to the onstraints in (4)-(0). The formulated problem is a nonlinear integer-programming problem with oupled variables. It is known to be very hard to obtain the global solution for the ategory of these problems. Hene we approah the problem by the loal or heuristi method to obtain the near-optimal solution in a reasonable time. 3. HIERARCHICAL METHOD To overome the diffiulties of the path-planning problem, we divide the overall problem into two subproblems hierarhially: lustering problem and sequening problem. The lustering problem is to reate the minimum number of inspetion lusters, and the sequening problem is to find the visiting sequene minimizing the total moving time. The sequening problem an be modeled as a standard traveling salesman problem (TSP). Therefore we an diretly apply the well-known TSP algorithms [6,7] to the sequening problem. The start node and end node are pre-determined at the wait loation of a amera. The ost is the moving time, whih an be alulated by profiles of the x and y gantries. The typial lustering problem [4] is to reate lusters to minimize the sum of distanes between windows and the enter of lusters. The problem does not limit the maximum size of lusters. Also, the number of lusters is usually fixed as a given ondition. However, in our lustering problem, the maximum size of lusters should be bounded by the size of the FO. Furthermore, the number of lusters is not given a ondition but a variable to be minimized. Therefore it is neessary to modify the typial lustering algorithms for our lustering problem. 3.. Single-link lustering The single-link algorithm [4,8] is one of the typial lustering algorithms. It initiates from numerous initial lusters, and merges them together iteratively until the number of lusters reahes a fixed value. This algorithm is very simple to be implemented, and requires low omputational omplexity. However, the performane of the solution highly depends on the distribution of windows beause of loal improvement. To apply the single-link algorithm to our problem, the size of the FO should be onsidered. The modified single-link algorithm is as follows: S. Generate initial lusters by setting eah window as a luster. S2. For eah luster, find the nearest luster that an be merged together. If the size of the new luster is within the FO, merge the two lusters. S3. Repeat S2 until there is no more merging ISODATA lustering The ISODATA (iterative self-organizing data analysis) algorithm [4] is the most popular algorithm for the typial lustering problem. This algorithm was updated from the K-means algorithm [9], whih improves the lustering by moving the enter (mean) of k-lusters. The ISODATA algorithm improves them more effiiently through iterative merging or splitting. Basially this algorithm is also under the ategory of loal improvement method, so the solution depends on the initial lusters. The modified ISODATA algorithm for our lustering problem is as follows: S. Generate initial lusters by dividing the board into retangular grids. The size of eah grid is

4 Path Planning of Automated Optial Inspetion Mahines for PCB Assembly Systems 99 idential with the FO. S2. Delete the luster in whih there is no window. S3. For eah luster, move the enter to inlude more windows. S4. If some windows are not inluded in any lusters, add new lusters for those windows. S5. For eah luster, find the nearest luster that an be merged together. If the size of the new luster is within the FO, merge the two lusters. S6. Repeat S3-S5 until there is no more hange on lusters. 4. UNIFIED METHOD The hierarhial methods find the luster variables and the sequene variables at two different stages. However, it is desirable to find the solution simultaneously beause both variables are oupled to eah other. The proposed method is for the purpose of finding the luster variables and the sequene variables simultaneously. The geneti algorithms have been widely used for omplex optimization problems. These algorithms an allow the solution to get out of the loal problems and approah the global problem [0]. However, onvergene of the solution may take a lot of time, whih depends on the problem size and parameters. Several researhes have been announed for the typial lustering problems [,2] and TSP [3,4]. Fig. 4 shows the flow of the hybrid geneti algorithm proposed to solve our path-planning problem. To apply the geneti algorithm into our problem, we have to newly define the hromosome, fitness funtion, and operators. We define the hromosome of the lustering problem as: w w a * w 2 w 2 b * * w n Initialization Fitness Evaluation Stop? Stop? n Initialization Seletion Fitness Crossover Evaluation Initialization Mutation Fitness Sequening Evaluation Path Initialization Generation Fig. 4. Flow of hybrid geneti algorithm. w nx * (Cluster ) (Cluster2) (Cluster n) y The gene, the element of the hromosome, has the value of window index w W or mark *, where ij w ij denotes the j -th window of the i -th luster and * denotes the end of the luster. The order of lusters in the hromosome is equivalent to the visiting sequene of the amera. Therefore, one hromosome an represent both the lustering and sequening results. 4.. Initialization Eah generation onsists of N hromosomes, where N is the population size. The initial population is generated by random number generation. For eah gene of a hromosome, window index r W is seleted at random. If the size of the luster inluding the seleted window is within the size of the FO, the window index is set to the gene. Otherwise, another window index is seleted randomly until the feasible ondition is satisfied. If a feasible window index is not found, then set mark * to the gene. This initialization step starts from the first bit and moves toward the last bit of the hromosome Fitness evaluation and seletion Let t k be the working time for the k-th hromosome k ( k =, L, N), and t max be the maximum value for all hromosomes in a generation. We define the fitness funtion f k for the k-th hromosome as: f = ( t t ) k max k N i= N. () ( t t ) max The fitness will be 0 for the ase of a maximumtime hromosome, and for the ase of an averagetime hromosome. The value inreases as the working time dereases. The above fitness funtion is used at the seletion stage to perform reprodution of good hromosomes. We adopt the remainder stohasti sampling method [4] to prevent the stohasti sampling error Crossover operator At the rossover stage, two hromosomes (, 2 ) are seleted randomly with rossover probability. Then, the rossover operator hanges the seleted hromosomes to new hromosomes ( ', 2 ' ) by ombining the genes of eah hromosome as: S. Selet a luster from randomly. S2. Searh 2 until all windows of the seleted luster of are disovered. Then, selet the lusters of 2 if they inlude any of the disovered windows. S3. Searh until all windows of the seleted luster of 2 are disovered. Then, selet the lusters of if they inlude any of the disovered windows. S4. Repeat S2-S3 until the seleted windows of both i

5 00 Tae-Hyoung Park, Hwa-Jung Kim, and Nam Kim hromosomes are exatly the same. S5. Exhange the seleted lusters between and 2, and make new hromosomes ' and 2 '. For example, assume that two hromosomes are seleted as: = 2 = In S, we randomly selet an initial luster from as: = 3 * * 3 * * * In S2, lusters are seleted from 2 as: 2 = In S3, lusters are seleted from again as: = Sine the seleted windows of both hromosomes are exatly the same, we go to S5. In S5, the new hromosomes are generated as: ' = 2 ' = 4.4. Mutation operator In the mutation stage, one hromosome is seleted randomly with mutation probability. Then, the mutation operator hanges the seleted hromosome to new hromosome ' by random alteration of genes. The proposed mutation operator is as follows: S. Selet a luster from randomly. S2. Chek whether the windows of the seleted luster an be moved to other lusters. If possible, move them to the feasible lusters and make a new hromosome '. In S2, the size of the luster is heked before moving the window sine the size of the luster should be bounded by the FO. For example, assume that a hromosome is seleted as: = In S, we randomly selet a luster from as: = In S2, all seleted windows 3, 9, 6, 2 are heked to move. If only two windows 6, 2 an be moved, we move them to the feasible lusters as: ' = 3 * * 3 * * * * 8 7 *8 2 4 * 9 * 3 6 * * * *9 * 3 6 * * 3 * * 3 * * * 3 * * 8 7 * * 3 6 * * * 3 * * 9 * * 3 * * * * 0 2 * 3 * * * * 0 2 * 3 6 * * 3 9 * * 0 2 2* 4.5. Sequene operator The sequene operator generates new luster sequenes of the hromosomes whose genes are hanged by rossover operator or mutation operator. This operator is also an unary operator for the hromosome. In the sequene operator, a sequene array is used as auxiliary data. The element of the sequene array is the luster, and the index of the sequene array denotes the visiting sequene of the luster. The proposed sequene operator is as follows: S. Set the first luster of as a urrent luster, and add it to a sequene array. S2. Find the nearest luster from the urrent luster, where the luster should not be an element of the sequene queue. Set the nearest luster as a urrent luster, and add it to the sequene array. S3. Repeat S2-S3 until all lusters are inluded in the sequene array. S4. Selet a pair of lusters from the sequene array, and exhange the sequene if the total moving time is redued. S5. Repeat S4 until all pairs of lusters are seleted from the sequene array. S6. Make a new hromosome ' by reassignment of lusters aording to the order of the sequene array. Assume that rossover operator or mutation operator has hanged the following hromosome. = 3 6 * * 3 9 * * * (Cluster) (Cluster2) (Cluster3) (Cluster4) (Cluster5) The sequene array is generated by S-S3 as: (Cluster ) (Cluster 4) (Cluster 2) (Cluster 5) (Cluster 3) And the sequene array is modified by S4-S5 as: (Cluster 5) (Cluster 3) (Cluster 4) (Cluster ) (Cluster 2) By S6, a new hromosome is generated from the sequene array as: ' = 02 2 * 3 9 * * 3 6 * * While the rossover operator and mutation operator hange both lusters and sequene, the sequene operator hanges sequene only. An initial sequene is generated by the nearest neighbour searh at S-S3, and the sequene is improved by 2-opt heuristis [7] at S4-S5. This method is one of the typial loal searh methods for TSP. The other TSP methods suh as 3-opt heuristis or Lin-Kernighan heuristi an also be applied to the sequene operator, but whih may result in the lower onvergene speed. The rossover operator and mutation operator guarantee the diversity of searh, but the sequene operator helps the fast onvergene by loal improvement. The hybrid geneti algorithm is the

6 Path Planning of Automated Optial Inspetion Mahines for PCB Assembly Systems 0 geneti algorithm that adopts the loal searh to overome the problem of onvergene speed. 5. SIMULATION We used a ommerial AOI mahine (AI-400, Samsung Tehwin Co. LTD) [5] for simulation. The size of the FO was 6(mm) 2(mm), and the image aquisition time for one FO was 0.25 (se). The maximum speed and aeleration of the X and Y gantries were 700 (mm/se) and 0.2 (mm/se 2 ), respetively. All PCBs used in the simulation were ommerial boards with different number of windows. Table shows the number of windows and size of test PCBs used in our simulation. We implemented the proposed algorithms using C++ programming language under MS-Windows XP, and installed them to the off-line programming software of the ommerial mahine. The population size for the geneti algorithm was set at 00. The rossover probability and mutation probability were set at 0.3 and 0.2, respetively. These parameters were determined by experimental ase study. As inreasing the population size, the alulation time was inreased but the optimization performane was improved. Fig. 5 presents onvergene graphs of the proposed geneti algorithm. Aording to variations of rossover probability and mutation probability, the best working time in eah generation was hanged as in Fig. 5(a) and Fig. 5(b). The parameters of the geneti algorithm were seleted suh that the best working time onverged to its minimum value in a short generation. Fig. 6 indiates the results of path planning obtained from different methods. Fig. 6(a) shows a test PCB with 44 inspetion widows. Fig. 6(b)-(d) show inspetion lusters and amera paths generated by different path-planning methods. Fig. 6(b) was obtained from the hierarhial method with single-link lustering (method ). Fig. 6() was obtained from the hierarhial method with the ISODATA lustering (method 2). Fig. 6(d) was obtained from the unified method using the hybrid geneti algorithm (method 3). Method 2 is the ommerial path-planning version of Table. Test PCBs. No. of PCB Id windows PCB size X(mm) x Y(mm) x x x x x x x x 245 working time (se) working time (se) generation (a) Crossover probability (P ) generation (b) Mutation probability (P m ). Fig. 5. Convergene graphs for GA parameters. AI-400. Both the number of lusters and distane of the amera path were redued by method 3, whih resulted in the redution of the overall working time of the AOI mahine. Fig. 7 shows the results of path planning for two PCBs with different distribution of inspetion windows. Both PCBs have the same number of inspetion windows and the same board size while they have different distributions of inspetion windows. Fig. 7(a) and Fig. 7(b) indiate the lusters and sequenes generated for PCBs with sattered inspetion windows and onentrated inspetion windows, respetively. As the inspetion windows are sattered, the number of lusters is inreased to over all inspetion windows and the overall working time of the AOI is also inreased. This simulation shows that the overall working time of the AOI depends on the distribution of inspetion windows as well as on the number of inspetion windows. Table 2 presents omparative results of path planning results for the test PCBs in Table. The working time is the sum of total image aquisition time and total moving time of the amera. This table shows that the working time stritly depends on the number of lusters, so that lustering is more

7 02 Tae-Hyoung Park, Hwa-Jung Kim, and Nam Kim (a) Inspetion windows. (a) PCB with sattered inspetion windows. (lusters: 87, working time: 30. se ) (b) Hierarhial method using single-link lustering. () Hierarhial method using ISOSATA lustering. (b) PCB with onentrated inspetion windows. (lusters: 39, working time: 9.6 se) Fig. 7. Example of path planning for PCBs with different window distributions(pcb size: 244(mm) x 26(mm), inspetion windows: 000). Table 2. Path-planning results: working time. (d) Unified method. Fig. 6. Examples of path planning by different methods. important than sequening in the sense of time optimization. The performane of method 3 is the best among all methods. Table 3 indiates the improvement ratio of method 3 with respet to the other methods. It verifies that the proposed method 3 an improve the performane by about 6 ~ 0%. Table 4 ompares the omputational time of eah method. The algorithms were run at the Pentium-I 3GHz omputer. The omputational time of method 3 is relatively longer than that of other methods. Sine the path planning is performed at an offline omputer, long alulation time an be allowed if it generates better performane. PCB Id. Method Method 2 Method 3 Working No. of lusters time (se) No. of lusters Working time (se) Working No. of time lusters (se) Method : Hierarhial method using single-link lustering Method 2: Hierarhial method using ISODATA lustering Method 3: Unified method

8 Path Planning of Automated Optial Inspetion Mahines for PCB Assembly Systems 03 Table 3. Path-planning results: improvement by Method 3. PCB Id. W.r.t. Method (%) W.r.t. Method 2 (%) Ave Table 4. Path-planning results: omputational time. PCB Id. Method Method 2 Method 3 (se) (se) (se) CONCLUSIONS In this paper, we proposed a path-planning method for AOI mahines. We defined the path-planning problem and formulated it mathematially. By mathematial formulation, we verified that the problem is a nonlinear integer-programming problem with two oupled variables. To obtain the better solution, we tried to find the two deision variables onurrently. The hybrid geneti algorithm was applied to overome the problem of loal improvement and onvergene speed. The hromosome, fitness funtion and operators were newly defined to solve our problem by geneti algorithm. The simulation results show that the proposed algorithm an be implemented and installed suessfully to pratial mahines. Also, it an ontribute to improve the produtivity of the mahine by reduing the number of lusters and the amera moving time. The optimization performane of the proposed method was relatively higher than the other methods. The AOI mahines have beome more popular in the PCB assembly systems, so our results will be useful for inreasing the produtivity of eletroni manufaturing systems. REFERENCES [] T. S. Newman and A. K. Jain, A survey of automated visual inspetion, Computer ision and Image Understanding, vol. 6, no. 2, pp , 995. [2] Y. Hara, N. Akiyama, and K. Karasaki, Automati inspetion system for printed iruit boards, IEEE Trans. on Pattern Analysis and Mahine Intelligene, vol. PAMI-5, no. 6, pp , 983. [3] H. H. Loh and M. S. Lu, Printed iruit board inspetion using image analysis, IEEE Trans. on Industry Appliations, vol. 35, no. 2, pp , 999. [4] A. K. Jain, M. N. Murty, and P. J. Flynn, Data lustering: A review, ACM Computing Surveys, vol. 3, no. 3, pp , 999. [5] B. S. Everitt, S. Landau, and M. Leese, Cluster Analysis, Fourth Edition, Arnold, 200. [6] G. Reinelt, The Traveling Salesman: Computational Solutions for TSP Appliations, Springer-erlag, 994. [7] M. Bellmore and G. Nemhauser, The travelingsalesman problem: A survey, Operation Researh, vol. 6, pp , 968. [8] E. Dahlhaus, "Fast parallel algorithm for the single link heuristis of hierarhial lustering, IEEE Symposium on Parallel and Distributed Proessing, vol., no. 4, pp , 992. [9] T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman, and A. Y. Wu, An effiient k-means lustering algorithm: Analysis and implementation, IEEE Trans. on Pattern Analysis and Mahine Intelligene, vol. 24, pp , [0] Z. Mihalewiz, Geneti Algorithms+Data Strutures=Evolution Programs, Springer-erlag, 996. [] L. Y. Tseng and S. B. Yang, A geneti approah to the automati lustering problem, Pattern Reognition, vol. 34, pp , 200. [2] H. S. Kim and S. B. Cho, An effiient geneti algorithm with less fitness evaluation by lustering, IEEE Trans. on Evolutionary Computation, vol. 2, pp , 200. [3] J. Gu, Effiient loal searh with searh spae smoothing: A ase study of the traveling salesman problem, IEEE Trans. on Systems, Man and Cybernetis, vol. 24, no. 5, pp , 994. [4] R. Baraglia, J. I. Hidalgo, and R. Perego, A hybrid heuristi for the traveling salesman problem, IEEE Trans. on Evolutionary Computation, vol. 5, no. 6, pp , 200. [5] Samsung Tehwin Co., LTD, SMT Inspetion equipment - AI400, om.

9 04 Tae-Hyoung Park, Hwa-Jung Kim, and Nam Kim Tae-Hyoung Park reeived the Ph.D. in Control and Instrumentation Engineering from Seoul National University, Korea in 994. From 994 to 997, he was a Senior Researh Engineer at Samsung Tehwin Co., where he developed the optimization software for PCB assembly systems. Sine 997 he has been a Professor of Control and Instrumentation Engineering at Chungbuk National University. From 2000 to 200, he was a isiting Professor at the University of Toronto, Canada. His researh interests inlude robotis, optimization algorithms, and eletroni manufaturing systems. Nam Kim reeived the Ph.D. degree in Eletronis Engineering from Yonsei University, Korea in 988. Sine 989, he has worked as a Professor in the Dept. of Computer and Communiation Engineering, Chungbuk National University. From 992 to 993, he was a isiting Professor at Stanford University. From 2000 to 200 he was a isiting Professor at Calteh. He is interested in the appliations of holography, diffrative optis, optial interonnetion, and the optial memory system. Hwa-Jung Kim reeived the M.S. degree in Control and Instrumentation Engineering from Chungbuk National University, Korea in He is urrently a Researh Engineer in the Mehatronis Laboratory at KEC Co. His researh interests inlude robotis, optimization algorithms, and mahine vision.