DESIGN OF A HAPTIC DEVICE FOR EXCAVATOR EQUIPPED WITH CRUSHER
|
|
- Samuel Fleming
- 6 years ago
- Views:
Transcription
1 DESIGN OF A HAPTIC DEVICE FOR EXCAVATOR EQUIPPED WITH CRUSHER Kyeong Won Oh, Dongnam Km Korea Unversty, Graduate School 5Ga-1, Anam-Dong, Sungbuk-Gu, Seoul, Korea {locosk, smleast}@korea.ac.kr Jong-Hyup Park Naekyung Engneeng Co., Ltd. 5-1 Sewon buldng, Yangjae-Dong, Seocho-Gu, Seoul, Korea nk2900@empal.com Daehe Hong Korea Unversty, Dvson of Mech. Engneerng 5Ga-1, Anam-Dong, Sungbuk-Gu, Seoul, Korea dhhong@korea.ac.kr Sukhe Hong Naekyung Engneeng Co., Ltd. 5-1 Sewon buldng, Yangjae-Dong, Seocho-Gu, Seoul, Korea hongcon@korea.com ABSTRACT The dsmantlng processes are very dangerous and there have been many studes for utlzng a remote control system to ncrease operator s safety. Ths paper deals wth the remote control problem by developng a novel haptc devce to control an excavator equpped wth the crusher whch s one of the most frequently used attachments. Frstly, the newly desgned haptc devce s descrbed to explore the operablty to the excavator equpped wth the crusher. Not only the excavator body but also ts arm, boom, swng, and crusher are consdered n the desgn. Then, ts workspace s analyzed and the mappng between the haptc devce and the excavator s examned. Also, the performance ndex of haptc devce s used to dscuss the control effcency. Secondly, through the knematcs analyss about arm, boom, and swng motons of the excavator, the poston nformaton of each jont s analyzed n 3-dmensonal space. Lastly, both the haptc devce and the excavator are modeled usng OpenGL program and 3D graphcal smulatons are extensvely performed. The structure of ths new haptc devce s smple and can be easly manufactured. It can be used to operate the excavator wth crusher more convenently and transparently from a remote ste away from the dangerous stes. KEYWORDS Haptc Devce, Excavator, Crusher Attachment, Dsmantlng Process, Remote Control 1. INTRODUCTION Today, there are lots of remodelng and dsmantlng of buldngs to buld new skyscrapers n constructon stes. And to dsmantle the buldng, excavator equpped wth the crusher s the most frequently used. However, n ths case, operators have to rde on the excavator drectly, so they have had a lot of exposure to unexpected danger. 202
2 There have been some current studes about the teleoperaton of excavator to make up for ts defects. Frst, remote control of excavator usng Phantom, whch s commercal haptc, was studed by Frankel [1]. And knematcs analyss and smulaton of constructon devces were conducted by Frmpong [2]. Moreover Hrabayash [3] studed teleoperaton of excavator, whch was operated n underwater. And last, before ths research, a new desgned haptc devce for excavator s moton s proposed by Km [4]. In ths paper, a novel concept of tele-operated haptc devce s proposed, n order to make an offer more safe and effcent control to operator whle n dsmantlng processes. Ths new haptc devce s consdered not only drvng of excavator body but also controllng the basc moton of excavator such as swng, boom, arm and crusher. It has smlartes to exstng joystck of excavator and smple structure. So, operator can use haptc devce easly, even f they control for the frst tme. To explan operaton prncple of the haptc devce, frst of all, knematcs analyss of excavator and haptc devce has to be preceded through ts modelng. And then, connecton between excavator and haptc devce should be dscussed. Sometmes, t s mpossble to control, because of exceedngly generaton of reflecton force. For more effectve operaton, t s mportant that operator takes cognzance of reflecton force whch s exerted on excavator especally crusher. So, a new desgned haptc devce s consdered force feedback. Then, to ncrease performance and capablty of haptc devce, the performance ndex of haptc devce should be analyzed. On ths occason, mappng s based on performance ndex, through analyss of workspace between excavator and haptc devce. Lastly, both the haptc devce and the excavator are modeled usng OpenGL program and 3D graphcal smulatons are extensvely performed. 2. KINEMATICS OF EXCAVATOR EQUIPPED WITH CRUSHER 2.1. Modelng of Excavator In ths paper, the excavator whch has 4 basc motons, swng, boom, arm and bucket, among many knds of backhoes s used. And ths s equpped wth 203 crusher nstead of bucket. Bucket jont has an only 1DOF, rotaton of bucket, orgnally. But, n ths case, t has totally 5DOFs, because cuttng and rotatng moton are ncluded n crusher. Hence, based on ths moton, the coordnate system and moton of each lnk about modeled excavator equpped wth crusher are shown n Fg. 1. There s one more DOF of rotatonal crusher jonts about X e4 n large sze of excavator, however t s not consdered n ths paper. Fgure 1. Modelng of Excavator Equpped wth Crusher Axs of swng jont s represented by Z e1, and the rest of four jont axes, boom, arm, and crusher are also represented n sequence. Rotatonal axes of each lnk are perpendcular at Fg. 1 except for axs of swng Knematcs Analyss of Excavator After ths modelng process, forward and nverse knematcs analyss of excavator has to be studed. When the haptc devces are desgned, especally, nverse knematc s very mportant. When control moton of boom and arm are tred, these postons should be analyzed to understand whole of excavator status. Through, nverse knematcs analyss, the poston of each lnk, boom, arm, and crusher can be acqured. In order to acqure nformaton of poston more easly for operator, poston of crusher jont, arm s tp, s analyzed frst of all [4]. In actualty, for dsmantlng processes, swng moton and moton of crusher do not take part n poston of arm s dstal jont. So, knematcs analyss can be treated 2- dmentonal problem of 2DOFs, boom and arm. Ths can be obtaned by absolute poston of the haptc stylus. Then, usng ths, the poston of each lnk can be obtaned by analyss of nverse knematcs. Followng equatons are nverse knematcs
3 equatons to calculate the angles of boom and arm. ( ) + r ( ) r24 y 1 a2 24 a3 θ e2 = tan + cos r x 2a r (1) a2 a3 r13 θe3 = π + cos (2) a a 2 3 θ e : Rotatonal angle of excavator ( = 1, 2, 3, 4) r jk : Dstance between Z ej and Z ek ( j, k =1, 2, 3, 4) 3. THE NOVEL CONCEPT OF HAPTIC DEVICE 3.1. Desgn Concept and Knematcs A novel haptc devce s smlar to lever of excavator whch s currently used. Fg. 2 shows new desgned haptc devce. Coordnate assgnment s also shown n the fgure wth D-H coordnate system. The haptc devce has 3 rotatonal jonts, 1 prsmatc jont, and buttons for crusher and a sphercal jont for excavator drvng. And the used parameter values are defned, as shown n Table 1. Moton of swng and crusher s drectly connected to three jonts of haptc devce to provde convenence to operator. The swng moton s controlled by θ and moton of the crusher, rotaton and nppng moton are controlled by θ and buttons, drectly. And the h4 poston of arm s dstal jont s controlled by only θ, d of haptc devce and the angle of boom and arm can be calculated by analyss of nverse knematcs. It was ponted out n the prevous chapter. And to calculate the poston vector of endpont of haptc stylus relatve to base frame, transformaton matrx T s used lke followng equaton (3). It s necessary that haptc devce connect wth excavator to control dstal jont of arm. Fgure 2. Haptc Devce wth D-H Coordnates Table 1. D-H Parameters of Haptc Devce cosθ snθ cos sn cos cos α θ α a θ sn cos cos cos sn a snθ θ θ α θ α T = (3) 0 snα cosα d Jont θ h 2 / 2+ α h a h d h π θ π / d And there are 5 actuators, electrcal motors and 5 encoders nsde the haptc devce. The nternal mechansm of haptc devce appears n Fg. 3. The encoders read the angle of each lnk and the actuators offer force feedback to operator actng on excavator. In order to ncrease the effcency of operaton and the protecton of equpment, t s necessary to detect the reflecton forces. 204
4 Fgure 3. Internal Mechansm of Haptc Devce d. Fg. 4 (a) s a pcture of show the moton of θ and d. θ and Fg. 4 (b), (c) Movement of Haptc Devce for Crusher In order to operate more smply, shape and operatng prncple of crusher should be consdered. Fg. 5 s an extended pcture of crusher part of haptc. The nppng moton of crusher can be operated easly by fngers of operator. Whle pushng the buttons, operator makes fngers lke tweezers and takes the moton smlar to crusher. And rotatonal moton of crusher s operated by thumb wheel. The motons of crusher are controlled drectly lke swng. (a) θ (b) θ (c) d Fgure 4. Moton of Haptc Devce 3.2. Moton of Haptc Devce Moton of Excavator Fg. 4 shows the moton of haptc devce to operateθ, θ and d. To provde smple functonal adaptaton, operaton method of haptc devce s desgned qute smlar to excavator. When an actual condton, the swng of excavator s controlled by the rght and left movement of left sde lever. And operaton of boom and arm s controlled by front and rear motons of each sde joystck. So, the swng moton s represented by rght and left moton of haptc, θ, just lke excavator s controller. And operaton s progressed n actual, operator usually control moton of boom and arm at the same tme wth both hands, through movng the lever front and rear. The haptc devce s desgned smlarly. Usng the haptc devce, operator also can control boom and arm at once through the combnaton of θ wth 205 Fgure 5. Crusher Part of Haptc Devce Fgure. 6. Drvng Control Part of Haptc Devce Whle the work s progressed, operator should have a grasp of the problem about reflecton force actng on crusher to mprove effcency. For ths reason, the nsde of haptc devce that has torson sprngs, servo motor [5].
5 If the crusher takes a nppng moton wthout object, an assstant lnk whch s connected wth the servo motor can move up and down as torson sprngs hold ts shape. If the crusher dsmantles some objects, torson sprngs wll be changed by the movement of assstant lnk. Owng to the servo motor pushes up the assstant lnk that depends on the acton of reflecton force upon the crusher. At ths moment, operator can perceve the force that s exerted on crusher by ncreased moment of torson sprng. If there s an outbreak of great force over the lmt, the servo motor wll prevent the assstant lnk from movng and protect the crusher Drvng Control Usng Haptc Devce In ths study, one of the notable features of the new desgned haptc devce s that operator can control each lnk of excavator and drve body usng only one joystck, as shown n Fg. 6. For the drvng excavator, frst, the haptc stylus should be taken down. In ths case, another part of haptc devce holds the ntal poston of thers so as not to operate durng the drvng. The bottom of stylus equpped wth sphercal jont so that t can move freely. And sphercal jont pushes down the drecton button. Whle the drvng of excavator s controlled, the whole of upper body of haptc devce wll move to any drecton relatve to the base frame of haptc devce. And equpped sprngs make the stylus move to ntal poston. There are force-sensors under the button, so that veloctes of both caterpllars are controlled separately by the pressure. 4. WORKSPACE MAPPING AND PERFORMANCE INDEX 4.1. Workspace Analyss of Excavator Workspace of excavator should be analyzed to evaluate the performance ndex of haptc devce. Fg. 7 shows the workspace of excavator by boom and arm from the sde vew wthout swng moton. Parameters are based upon a small sze excavator, SOLAR 015, whch has 1.5 tons of receptve capacty. In the fgure, rotatonal axs of boom s the orgn. When the boom jont moves from -56 to 74 degrees, the cross ponts represent the trajectory ponts of dstal jont of boom. And dot ponts represent jont of arm when the range angle of arm s from 218 to 328 degrees. For the reason mentoned prevous chapter, end-pont of arm, the poston of crusher jont, s controlled ultmately. Now to conclude, ths area can be defned as workspace of excavator Workspace Mappng and Performance Index The dstal jont of arm s controlled by end-pont of haptc stylus. So, workspace of excavator should be covered by workspace of tp of stylus, completely. Fg. 8 shows workspace mappng between excavator and haptc devce. Workspace of haptc devce s concerned about only θ, d, because end-pont of stylus connected wth dstal jont of arm are the most needed. Although there s an angle dfference n workspace analyss, whch t s not concerned, operator can put to rghts t by ntuton durng the dsmantlng process. And performance ndex s defned, as shown n equaton (4). For the better performance ndex, θ, d should be as small as possble on mappng. (1 R) 100 P. I.( A, D, R) = A D and remanng area (4) When the performance ndex s bgger, the more effcent operaton can be advanced. In ths equaton, A s the range of θ, ths value s from 50 to 90 degrees. And D s the range of d, R s the rato of remanng area whch s calculated by AutoCAD. In ths paper, among all plausble cases, three of them whch have the best results were compared, and then, the best performance ndex s decded. Now, n order to adjust dfference dmenson between excavator and haptc, scalng factor s appled and same scalng factor s used, 30. The frst case, the functon s P. I.(82, 0.066, 63.0) and the value of functon s And the second case, P. I.(60, 0.070, 55.5), the performance ndex s evaluated by And then, n the last case, P. I.(57, 0.071, 59.5), s performance ndex. At ths moment, the most effcent operaton wll be progressed. As ths result, workspace of haptc devce can be defned. 206
6 Fgure 7. Workspace of Excavator Fgure 8. Workspace Mappng between Excavator and Haptc Devce Table 2. Smulaton Results Usng OpenGL Program Swng Moton Control of Boom and Arm Nppng Moton Rotaton of Crusher 5. SIMULATION RESULTS Table 2 summarzes smulaton results whch are modelng of excavator equpped wth crusher usng OpenGL program and movements of excavator are shown. One excepton to ths s drvng moton, snce t s not easy to dsplay on fgure. In the smulaton, ths program works n real tme. So mouse s used to control haptc and poston of mouse cursor represents the 2D poston of crusher jont, and thumb wheel s drectly used to control rotaton of crusher. Swng and drvng of excavator s controlled by pushng the arrow key. 6. CONCLUSION In ths paper, the haptc devce s newly desgned to control excavator equpped wth crusher. Knematcs and workspace analyss are conducted and performance ndex s evaluated by workspace mappng. Then, usng OpenGL, graphcal smulaton 207
7 control of excavator s ncluded. As a result, ntutvely convenent haptc devce s desgned. 7. ACKNOWLEDGEMENTS Ths research was supported by a grant (code : 06 Constructon Core B04) from Constructon Core Technology Program funded by Mnstry of Constructon & Transportaton of Korean government and BK21. REFERENCES [1] Frmpong, S.; LI, Y. 2005, Vrtual prototype smulaton of hydraulc shovel knematcs for spatal characterzaton n surface mnng operatons, Internatonal Journal of Surface Mnng, Reclamaton and Envronment Vol. 19, No. 4, pp. 238~250. [2] Frankel, J. G. 2004, Development of a Haptc Backhoe Testbed, A Thess of Master of Scence, School of Mechancal Engneerng Georga Insttute of Technology. [3] Hrabayash, T.; Yamamoto, T. 2006, Experment of Teleoperaton of Underwater Backhoe wth Haptc Informaton, 23 rd Internatonal Symposum on Automaton and Robotcs n Constructon, pp. 36~41. [4] Km, D.; Hong, K.; Oh, D.; Park, J.; Hong, S. 2007, Desgn of Haptc Devce for Dsmantlng Process Usng Excavator, 24 th Internatonal Symposum on Automaton & Robotcs n Constructon, pp. 175~180. [5] Oh, K.; Km, D.; Hong, D.; Park, J. 2007, Desgn of a Haptc Devce for Crusher Attachment of Excavator, Korean Socety for Precson Engneerng 2007 Sprng Conference, pp. 381~
3D vector computer graphics
3D vector computer graphcs Paolo Varagnolo: freelance engneer Padova Aprl 2016 Prvate Practce ----------------------------------- 1. Introducton Vector 3D model representaton n computer graphcs requres
More informationAnalysis on the Workspace of Six-degrees-of-freedom Industrial Robot Based on AutoCAD
Analyss on the Workspace of Sx-degrees-of-freedom Industral Robot Based on AutoCAD Jn-quan L 1, Ru Zhang 1,a, Fang Cu 1, Q Guan 1 and Yang Zhang 1 1 School of Automaton, Bejng Unversty of Posts and Telecommuncatons,
More information3D Virtual Eyeglass Frames Modeling from Multiple Camera Image Data Based on the GFFD Deformation Method
NICOGRAPH Internatonal 2012, pp. 114-119 3D Vrtual Eyeglass Frames Modelng from Multple Camera Image Data Based on the GFFD Deformaton Method Norak Tamura, Somsangouane Sngthemphone and Katsuhro Ktama
More informationProper Choice of Data Used for the Estimation of Datum Transformation Parameters
Proper Choce of Data Used for the Estmaton of Datum Transformaton Parameters Hakan S. KUTOGLU, Turkey Key words: Coordnate systems; transformaton; estmaton, relablty. SUMMARY Advances n technologes and
More informationAnalysis of Continuous Beams in General
Analyss of Contnuous Beams n General Contnuous beams consdered here are prsmatc, rgdly connected to each beam segment and supported at varous ponts along the beam. onts are selected at ponts of support,
More informationON THE DESIGN OF LARGE SCALE REDUNDANT PARALLEL MANIPULATOR. Wu huapeng, Heikki handroos and Juha kilkki
ON THE DESIGN OF LARGE SCALE REDUNDANT PARALLEL MANIPULATOR Wu huapeng, Hekk handroos and Juha klkk Machne Automaton Lab, Lappeenranta Unversty of Technology LPR-5385 Fnland huapeng@lut.f, handroos@lut.f,
More informationA proposal for the motion analysis method of skiing turn by measurement of orientation and gliding trajectory
Avalable onlne at www.scencedrect.com Proceda Engneerng 13 (211) 17 22 5 th Asa-Pacfc Congress on Sports Technology (APCST) A proposal for the moton analyss method of skng turn by measurement of orentaton
More informationThe motion simulation of three-dof parallel manipulator based on VBAI and MATLAB Zhuo Zhen, Chaoying Liu* and Xueling Song
Internatonal Conference on Automaton, Mechancal Control and Computatonal Engneerng (AMCCE 25) he moton smulaton of three-dof parallel manpulator based on VBAI and MALAB Zhuo Zhen, Chaoyng Lu* and Xuelng
More informationReal-time Motion Capture System Using One Video Camera Based on Color and Edge Distribution
Real-tme Moton Capture System Usng One Vdeo Camera Based on Color and Edge Dstrbuton YOSHIAKI AKAZAWA, YOSHIHIRO OKADA, AND KOICHI NIIJIMA Graduate School of Informaton Scence and Electrcal Engneerng,
More informationInverse kinematic Modeling of 3RRR Parallel Robot
ème Congrès Franças de Mécanque Lyon, 4 au 8 Août 5 Inverse knematc Modelng of RRR Parallel Robot Ouafae HAMDOUN, Fatma Zahra BAGHLI, Larb EL BAKKALI Modelng and Smulaton of Mechancal Systems Laboratory,
More informationROBOT KINEMATICS. ME Robotics ME Robotics
ROBOT KINEMATICS Purpose: The purpose of ths chapter s to ntroduce you to robot knematcs, and the concepts related to both open and closed knematcs chans. Forward knematcs s dstngushed from nverse knematcs.
More informationA high precision collaborative vision measurement of gear chamfering profile
Internatonal Conference on Advances n Mechancal Engneerng and Industral Informatcs (AMEII 05) A hgh precson collaboratve vson measurement of gear chamferng profle Conglng Zhou, a, Zengpu Xu, b, Chunmng
More informationR s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes
SPH3UW Unt 7.3 Sphercal Concave Mrrors Page 1 of 1 Notes Physcs Tool box Concave Mrror If the reflectng surface takes place on the nner surface of the sphercal shape so that the centre of the mrror bulges
More informationComplex Numbers. Now we also saw that if a and b were both positive then ab = a b. For a second let s forget that restriction and do the following.
Complex Numbers The last topc n ths secton s not really related to most of what we ve done n ths chapter, although t s somewhat related to the radcals secton as we wll see. We also won t need the materal
More informationPose, Posture, Formation and Contortion in Kinematic Systems
Pose, Posture, Formaton and Contorton n Knematc Systems J. Rooney and T. K. Tanev Department of Desgn and Innovaton, Faculty of Technology, The Open Unversty, Unted Kngdom Abstract. The concepts of pose,
More informationWORKSPACE OPTIMIZATION OF ORIENTATIONAL 3-LEGGED UPS PARALLEL PLATFORMS
Proceedngs of DETC 02 ASME 2002 Desgn Engneerng Techncal Conferences and Computers and Informaton n Engneerng Conference Montreal, Canada, September 29-October 2, 2002 DETC2002/MECH-34366 WORKSPACE OPTIMIZATION
More information2x x l. Module 3: Element Properties Lecture 4: Lagrange and Serendipity Elements
Module 3: Element Propertes Lecture : Lagrange and Serendpty Elements 5 In last lecture note, the nterpolaton functons are derved on the bass of assumed polynomal from Pascal s trangle for the fled varable.
More informationKinematics of pantograph masts
Abstract Spacecraft Mechansms Group, ISRO Satellte Centre, Arport Road, Bangalore 560 07, Emal:bpn@sac.ernet.n Flght Dynamcs Dvson, ISRO Satellte Centre, Arport Road, Bangalore 560 07 Emal:pandyan@sac.ernet.n
More informationThe Research of Ellipse Parameter Fitting Algorithm of Ultrasonic Imaging Logging in the Casing Hole
Appled Mathematcs, 04, 5, 37-3 Publshed Onlne May 04 n ScRes. http://www.scrp.org/journal/am http://dx.do.org/0.436/am.04.584 The Research of Ellpse Parameter Fttng Algorthm of Ultrasonc Imagng Loggng
More informationParallelism for Nested Loops with Non-uniform and Flow Dependences
Parallelsm for Nested Loops wth Non-unform and Flow Dependences Sam-Jn Jeong Dept. of Informaton & Communcaton Engneerng, Cheonan Unversty, 5, Anseo-dong, Cheonan, Chungnam, 330-80, Korea. seong@cheonan.ac.kr
More informationCluster Analysis of Electrical Behavior
Journal of Computer and Communcatons, 205, 3, 88-93 Publshed Onlne May 205 n ScRes. http://www.scrp.org/ournal/cc http://dx.do.org/0.4236/cc.205.350 Cluster Analyss of Electrcal Behavor Ln Lu Ln Lu, School
More informationA Binarization Algorithm specialized on Document Images and Photos
A Bnarzaton Algorthm specalzed on Document mages and Photos Ergna Kavalleratou Dept. of nformaton and Communcaton Systems Engneerng Unversty of the Aegean kavalleratou@aegean.gr Abstract n ths paper, a
More informationResolving Ambiguity in Depth Extraction for Motion Capture using Genetic Algorithm
Resolvng Ambguty n Depth Extracton for Moton Capture usng Genetc Algorthm Yn Yee Wa, Ch Kn Chow, Tong Lee Computer Vson and Image Processng Laboratory Dept. of Electronc Engneerng The Chnese Unversty of
More informationDesign and Implementation of Trainable Robotic Arm
Internatonal Journal of Scence, Engneerng and Technology Research (IJSETR) Desgn and Implementaton of Tranable Robotc Arm Mo Mo Aung 1, Saw Aung Nyen Oo 2 1 Master Canddate, Department of Electronc Engneerng,
More informationPhysics 132 4/24/17. April 24, 2017 Physics 132 Prof. E. F. Redish. Outline
Aprl 24, 2017 Physcs 132 Prof. E. F. Redsh Theme Musc: Justn Tmberlake Mrrors Cartoon: Gary Larson The Far Sde 1 Outlne Images produced by a curved mrror Image equatons for a curved mrror Lght n dense
More informationAccounting for the Use of Different Length Scale Factors in x, y and z Directions
1 Accountng for the Use of Dfferent Length Scale Factors n x, y and z Drectons Taha Soch (taha.soch@kcl.ac.uk) Imagng Scences & Bomedcal Engneerng, Kng s College London, The Rayne Insttute, St Thomas Hosptal,
More informationMathematics 256 a course in differential equations for engineering students
Mathematcs 56 a course n dfferental equatons for engneerng students Chapter 5. More effcent methods of numercal soluton Euler s method s qute neffcent. Because the error s essentally proportonal to the
More informationKinematics Modeling and Analysis of MOTOMAN-HP20 Robot
nd Workshop on Advanced Research and Technolog n Industr Applcatons (WARTIA ) Knematcs Modelng and Analss of MOTOMAN-HP Robot Jou Fe, Chen Huang School of Mechancal Engneerng, Dalan Jaotong Unverst, Dalan,
More informationSLAM Summer School 2006 Practical 2: SLAM using Monocular Vision
SLAM Summer School 2006 Practcal 2: SLAM usng Monocular Vson Javer Cvera, Unversty of Zaragoza Andrew J. Davson, Imperal College London J.M.M Montel, Unversty of Zaragoza. josemar@unzar.es, jcvera@unzar.es,
More informationImprovement of Spatial Resolution Using BlockMatching Based Motion Estimation and Frame. Integration
Improvement of Spatal Resoluton Usng BlockMatchng Based Moton Estmaton and Frame Integraton Danya Suga and Takayuk Hamamoto Graduate School of Engneerng, Tokyo Unversty of Scence, 6-3-1, Nuku, Katsuska-ku,
More informationSix-axis Robot Manipulator Numerical Control Programming and Motion Simulation
2016 Internatonal Conference on Appled Mechancs, Mechancal and Materals Engneerng (AMMME 2016) ISBN: 978-1-60595-409-7 S-as Robot Manpulator Numercal Control Programmng and Moton Smulaton Chen-hua SHE
More informationAn efficient method to build panoramic image mosaics
An effcent method to buld panoramc mage mosacs Pattern Recognton Letters vol. 4 003 Dae-Hyun Km Yong-In Yoon Jong-Soo Cho School of Electrcal Engneerng and Computer Scence Kyungpook Natonal Unv. Abstract
More informationPLANAR PARALLEL 3-RPR MANIPULATOR
PLANAR PARALLEL 3-RPR MANIPULATOR Robert L. Wllams II Atul R. Josh Oho Unversty Athens, O 45701 Proceedngs of the Sxth Conference on Appled Mechansms and Robotcs Cncnnat O, December 12-15, 1999 Contact
More informationReducing Frame Rate for Object Tracking
Reducng Frame Rate for Object Trackng Pavel Korshunov 1 and We Tsang Oo 2 1 Natonal Unversty of Sngapore, Sngapore 11977, pavelkor@comp.nus.edu.sg 2 Natonal Unversty of Sngapore, Sngapore 11977, oowt@comp.nus.edu.sg
More informationParallel manipulator robots design and simulation
Proceedngs of the 5th WSEAS Int. Conf. on System Scence and Smulaton n Engneerng, Tenerfe, Canary Islands, Span, December 16-18, 26 358 Parallel manpulator robots desgn and smulaton SAMIR LAHOUAR SAID
More informationProblem Definitions and Evaluation Criteria for Computational Expensive Optimization
Problem efntons and Evaluaton Crtera for Computatonal Expensve Optmzaton B. Lu 1, Q. Chen and Q. Zhang 3, J. J. Lang 4, P. N. Suganthan, B. Y. Qu 6 1 epartment of Computng, Glyndwr Unversty, UK Faclty
More informationAn Optimal Algorithm for Prufer Codes *
J. Software Engneerng & Applcatons, 2009, 2: 111-115 do:10.4236/jsea.2009.22016 Publshed Onlne July 2009 (www.scrp.org/journal/jsea) An Optmal Algorthm for Prufer Codes * Xaodong Wang 1, 2, Le Wang 3,
More informationPose and Position Estimation of Dozer Blade in 3- dimensional by Integration of IMU with Two RTK GPSs
Pose and Poston Estmaton of Dozer Blade n 3- dmensonal by Integraton of IMU wth Two RTK GPSs D.I. Sun a and S.H. Km b, Y.S. Lee b, S.K. Lee a, C.S. Han c a Mechatroncs Engneerng of Hanyang Unversty of
More informationNUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS
ARPN Journal of Engneerng and Appled Scences 006-017 Asan Research Publshng Network (ARPN). All rghts reserved. NUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS Igor Grgoryev, Svetlana
More informationModeling Concave Globoidal Cam with Swinging Roller Follower: A Case Study
Modelng Concave Globodal Cam wth Swngng Roller Follower: A Case Study Nguyen Van Tuong, and Premysl Pokorny Abstract Ths paper descrbes a computer-aded desgn for desgn of the concave globodal cam wth cylndrcal
More informationLoad Balancing for Hex-Cell Interconnection Network
Int. J. Communcatons, Network and System Scences,,, - Publshed Onlne Aprl n ScRes. http://www.scrp.org/journal/jcns http://dx.do.org/./jcns.. Load Balancng for Hex-Cell Interconnecton Network Saher Manaseer,
More informationBasic Walking Simulations and Gravitational Stability Analysis for a Hexapod Robot Using Matlab
Basc Walkng Smulatons and Gravtatonal Stablty Analyss for a Hexapod Robot Usng Matlab Sorn Mănou-Olaru*, Mrcea Nţulescu ** *Department of Automaton, Electroncs and Mechatroncs, Unversty of Craova, Romana
More informationTHE MAP MATCHING ALGORITHM OF GPS DATA WITH RELATIVELY LONG POLLING TIME INTERVALS
THE MA MATCHING ALGORITHM OF GS DATA WITH RELATIVELY LONG OLLING TIME INTERVALS Jae-seok YANG Graduate Student Graduate School of Engneerng Seoul Natonal Unversty San56-, Shllm-dong, Gwanak-gu, Seoul,
More informationAPPLICATION OF AN AUGMENTED REALITY SYSTEM FOR DISASTER RELIEF
APPLICATION OF AN AUGMENTED REALITY SYSTEM FOR DISASTER RELIEF Johannes Leebmann Insttute of Photogrammetry and Remote Sensng, Unversty of Karlsruhe (TH, Englerstrasse 7, 7618 Karlsruhe, Germany - leebmann@pf.un-karlsruhe.de
More informationComputer models of motion: Iterative calculations
Computer models o moton: Iteratve calculatons OBJECTIVES In ths actvty you wll learn how to: Create 3D box objects Update the poston o an object teratvely (repeatedly) to anmate ts moton Update the momentum
More informationModeling linkages in R using linkr
Modelng lnkages n R usng lnkr Smulatng two- and three-dmensonal lnkage mechansms usng the R package lnkr Input dsplacement 0.0 0.2 0.4 0.6 0.8 1.0 Output dsplacement 0.0 0.2 0.4 0.6 0.8 1 / fma 0.4 0.6
More informationINVERSE DYNAMICS ANALYSIS AND SIMULATION OF A CLASS OF UNDER- CONSTRAINED CABLE-DRIVEN PARALLEL SYSTEM
U.P.B. Sc. Bull., Seres D, Vol. 78, Iss., 6 ISSN 454-58 INVERSE DYNAMICS ANALYSIS AND SIMULATION OF A CLASS OF UNDER- CONSTRAINED CABLE-DRIVEN PARALLEL SYSTEM We LI, Zhgang ZHAO, Guangtan SHI, Jnsong LI
More informationLearning the Kernel Parameters in Kernel Minimum Distance Classifier
Learnng the Kernel Parameters n Kernel Mnmum Dstance Classfer Daoqang Zhang 1,, Songcan Chen and Zh-Hua Zhou 1* 1 Natonal Laboratory for Novel Software Technology Nanjng Unversty, Nanjng 193, Chna Department
More informationWe are IntechOpen, the first native scientific publisher of Open Access books. International authors and editors. Our authors are among the TOP 1%
We are IntechOpen, the frst natve scentfc publsher of Open Access books 3,350 108,000 1.7 M Open access books avalable Internatonal authors and edtors Downloads Our authors are among the 151 Countres delvered
More informationExperiments of a Novel Magnetic Levitation Stage for Wide Area Movements
558 Journal of Electrcal Engneerng & Technology Vol. 7, No., pp. 558~563, 1 http://dx.do.org/1.537/jeet.1.7..558 Experments of a Novel Magnetc Levtaton Stage for Wde Area Movements Jeong-Woo Jeon, MtcaCaraan*,
More informationVISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES
UbCC 2011, Volume 6, 5002981-x manuscrpts OPEN ACCES UbCC Journal ISSN 1992-8424 www.ubcc.org VISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES
More informationComputational Issues in the Planning and Kinematics of Binary Robots Abstract 1. Introduction 2. Workspace Analysis and Optimization
Computatonal Issues n the Plannng and Knematcs of Bnary Robots Matthew D. Lchter, Vvek A. Sujan, and Steven Dubowsky { lchter vasujan dubowsky@mt.edu } Department of Mechancal Engneerng Massachusetts Insttute
More informationVirtual Machine Migration based on Trust Measurement of Computer Node
Appled Mechancs and Materals Onlne: 2014-04-04 ISSN: 1662-7482, Vols. 536-537, pp 678-682 do:10.4028/www.scentfc.net/amm.536-537.678 2014 Trans Tech Publcatons, Swtzerland Vrtual Machne Mgraton based on
More informationLearning-Based Top-N Selection Query Evaluation over Relational Databases
Learnng-Based Top-N Selecton Query Evaluaton over Relatonal Databases Lang Zhu *, Wey Meng ** * School of Mathematcs and Computer Scence, Hebe Unversty, Baodng, Hebe 071002, Chna, zhu@mal.hbu.edu.cn **
More informationMobile Robot Localization and Mapping by Scan Matching using Laser Reflection Intensity of the SOKUIKI Sensor
Moble Robot Localzaton and Mappng by Scan Matchng usng Reflecton Intensty of the SOKUIKI Sensor *HARA Yoshtaka, KAWATA Hrohko, OHYA Akhsa, YUTA Shn ch Intellgent Robot Laboratory Unversty of Tsukuba 1-1-1,
More informationDynamic wetting property investigation of AFM tips in micro/nanoscale
Dynamc wettng property nvestgaton of AFM tps n mcro/nanoscale The wettng propertes of AFM probe tps are of concern n AFM tp related force measurement, fabrcaton, and manpulaton technques, such as dp-pen
More informationFree-Form Tactile Sensor Using 3-Dimensional Shape Capture Sheet
Free-Form Tactle Sensor Usng 3-Dmensonal Shape Capture Sheet Takayuk Hosh and Hroyuk Shnoda The Unversty of Tokyo {star, shno}@alab.t.u-tokyo.ac.p Abstract We are developng a novel sensng devce named 3-dmensonal
More informationVirtual Ergonomic Assessment on Handheld Products based on Virtual Grasping by Digital Hand
07M-50 Vrtual Ergonomc Assessment on Handheld s based on Vrtual Graspng by Dgtal Hand Yu Endo, Satosh Kana and Takesh Kshnam Hokkado Unversty, JAPAN Natsuk Myata, Makko Kouch, Masaak Mochmaru Dgtal Human
More informationSteps for Computing the Dissimilarity, Entropy, Herfindahl-Hirschman and. Accessibility (Gravity with Competition) Indices
Steps for Computng the Dssmlarty, Entropy, Herfndahl-Hrschman and Accessblty (Gravty wth Competton) Indces I. Dssmlarty Index Measurement: The followng formula can be used to measure the evenness between
More informationDETC ANALYSIS OF THREE DEGREE OF FREEDOM 6 6 TENSEGRITY PLATFORM
Proceedngs of 006 DETC: ASME 006 Desgn Engneerng Techncal Conferences and Computers and Informaton n Engneerng Conference September 0-, 006, Phladelpha, Pennsylvana, USA DETC006-990 AAYSIS OF THREE DEGREE
More informationLecture #15 Lecture Notes
Lecture #15 Lecture Notes The ocean water column s very much a 3-D spatal entt and we need to represent that structure n an economcal way to deal wth t n calculatons. We wll dscuss one way to do so, emprcal
More informationQuick error verification of portable coordinate measuring arm
Quck error verfcaton of portable coordnate measurng arm J.F. Ouang, W.L. Lu, X.H. Qu State Ke Laborator of Precson Measurng Technolog and Instruments, Tanjn Unverst, Tanjn 7, Chna Tel.: + 86 [] 7-8-99
More informationRELATIVE ORIENTATION ESTIMATION OF VIDEO STREAMS FROM A SINGLE PAN-TILT-ZOOM CAMERA. Commission I, WG I/5
RELATIVE ORIENTATION ESTIMATION OF VIDEO STREAMS FROM A SINGLE PAN-TILT-ZOOM CAMERA Taeyoon Lee a, *, Taeung Km a, Gunho Sohn b, James Elder a a Department of Geonformatc Engneerng, Inha Unersty, 253 Yonghyun-dong,
More informationA Fast Visual Tracking Algorithm Based on Circle Pixels Matching
A Fast Vsual Trackng Algorthm Based on Crcle Pxels Matchng Zhqang Hou hou_zhq@sohu.com Chongzhao Han czhan@mal.xjtu.edu.cn Ln Zheng Abstract: A fast vsual trackng algorthm based on crcle pxels matchng
More informationA Fast Content-Based Multimedia Retrieval Technique Using Compressed Data
A Fast Content-Based Multmeda Retreval Technque Usng Compressed Data Borko Furht and Pornvt Saksobhavvat NSF Multmeda Laboratory Florda Atlantc Unversty, Boca Raton, Florda 3343 ABSTRACT In ths paper,
More informationDistance Calculation from Single Optical Image
17 Internatonal Conference on Mathematcs, Modellng and Smulaton Technologes and Applcatons (MMSTA 17) ISBN: 978-1-6595-53-8 Dstance Calculaton from Sngle Optcal Image Xao-yng DUAN 1,, Yang-je WEI 1,,*
More informationContent Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers
IOSR Journal of Electroncs and Communcaton Engneerng (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue, Ver. IV (Mar - Apr. 04), PP 0-07 Content Based Image Retreval Usng -D Dscrete Wavelet wth
More informationType-2 Fuzzy Non-uniform Rational B-spline Model with Type-2 Fuzzy Data
Malaysan Journal of Mathematcal Scences 11(S) Aprl : 35 46 (2017) Specal Issue: The 2nd Internatonal Conference and Workshop on Mathematcal Analyss (ICWOMA 2016) MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES
More informationISSN 2409-9392,,, 2017,. 30 backlashes. Ths allows conductng the cuttng process wthout the formaton of technologcal protruson between wres. Dstnctve features of a new cut shapng technology scheme are reflected
More informationMeta-heuristics for Multidimensional Knapsack Problems
2012 4th Internatonal Conference on Computer Research and Development IPCSIT vol.39 (2012) (2012) IACSIT Press, Sngapore Meta-heurstcs for Multdmensonal Knapsack Problems Zhbao Man + Computer Scence Department,
More informationContour Error of the 3-DoF Hydraulic Translational Parallel Manipulator. Ryszard Dindorf 1,a, Piotr Wos 2,b
Advanced Materals Research Vol. 874 (2014) 57-62 Onlne avalable snce 2014/Jan/08 at www.scentfc.net (2014) rans ech Publcatons, Swtzerland do:10.4028/www.scentfc.net/amr.874.57 Contour Error of the 3-DoF
More informationAn Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices
Internatonal Mathematcal Forum, Vol 7, 2012, no 52, 2549-2554 An Applcaton of the Dulmage-Mendelsohn Decomposton to Sparse Null Space Bases of Full Row Rank Matrces Mostafa Khorramzadeh Department of Mathematcal
More informationCompiler Design. Spring Register Allocation. Sample Exercises and Solutions. Prof. Pedro C. Diniz
Compler Desgn Sprng 2014 Regster Allocaton Sample Exercses and Solutons Prof. Pedro C. Dnz USC / Informaton Scences Insttute 4676 Admralty Way, Sute 1001 Marna del Rey, Calforna 90292 pedro@s.edu Regster
More informationLine-based Camera Movement Estimation by Using Parallel Lines in Omnidirectional Video
01 IEEE Internatonal Conference on Robotcs and Automaton RverCentre, Sant Paul, Mnnesota, USA May 14-18, 01 Lne-based Camera Movement Estmaton by Usng Parallel Lnes n Omndrectonal Vdeo Ryosuke kawansh,
More informationHermite Splines in Lie Groups as Products of Geodesics
Hermte Splnes n Le Groups as Products of Geodescs Ethan Eade Updated May 28, 2017 1 Introducton 1.1 Goal Ths document defnes a curve n the Le group G parametrzed by tme and by structural parameters n the
More informationThe Codesign Challenge
ECE 4530 Codesgn Challenge Fall 2007 Hardware/Software Codesgn The Codesgn Challenge Objectves In the codesgn challenge, your task s to accelerate a gven software reference mplementaton as fast as possble.
More informationSensory Redundant Parallel Mobile Mechanism
Sensory Redundant Parallel Moble Mechansm Shraga Shoval and Moshe Shoham* Department of Industral Engneerng & Management, Academc College of Judea and Samara, Arel., *Faculty of Mechancal Engneerng, Technon,
More informationAvailable online at ScienceDirect. Procedia Computer Science 103 (2017 )
Avalable onlne at www.scencedrect.com ScenceDrect Proceda Computer Scence 03 (207 ) 562 568 XIIth Internatonal Symposum «Intellgent Systems», INTELS 6, 5-7 October 206, Moscow, Russa Retral queueng systems
More informationBrave New World Pseudocode Reference
Brave New World Pseudocode Reference Pseudocode s a way to descrbe how to accomplsh tasks usng basc steps lke those a computer mght perform. In ths week s lab, you'll see how a form of pseudocode can be
More informationComputer Animation and Visualisation. Lecture 4. Rigging / Skinning
Computer Anmaton and Vsualsaton Lecture 4. Rggng / Sknnng Taku Komura Overvew Sknnng / Rggng Background knowledge Lnear Blendng How to decde weghts? Example-based Method Anatomcal models Sknnng Assume
More informationXV International PhD Workshop OWD 2013, October Machine Learning for the Efficient Control of a Multi-Wheeled Mobile Robot
XV Internatonal PhD Workshop OWD 203, 9 22 October 203 Machne Learnng for the Effcent Control of a Mult-Wheeled Moble Robot Uladzmr Dzomn, Brest State Techncal Unversty (prof. Vladmr Golovko, Brest State
More informationA MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS
Proceedngs of the Wnter Smulaton Conference M E Kuhl, N M Steger, F B Armstrong, and J A Jones, eds A MOVING MESH APPROACH FOR SIMULATION BUDGET ALLOCATION ON CONTINUOUS DOMAINS Mark W Brantley Chun-Hung
More informationDesign of a Haptic Device for Teleoperation and Virtual Reality Systems
Proceedngs of the 2009 IEEE Internatonal Conference on Systems, Man, and Cybernetcs San Antono, TX, USA - October 2009 Desgn of a Haptc Devce for Teleoperaton and Vrtual Realty Systems Mehmet smet Can
More informationA mathematical programming approach to the analysis, design and scheduling of offshore oilfields
17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 A mathematcal programmng approach to the analyss, desgn and
More information6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour
6.854 Advanced Algorthms Petar Maymounkov Problem Set 11 (November 23, 2005) Wth: Benjamn Rossman, Oren Wemann, and Pouya Kheradpour Problem 1. We reduce vertex cover to MAX-SAT wth weghts, such that the
More informationDesign, Simulation and Implementation of a 3-PUU Parallel Mechanism for a Macro/mini Manipulator
Desgn, Smulaton and Implementaton of a 3-PUU Parallel Mechansm for a Macro/mn Manpulator Zheng Ma, Aun-Neow Poo, Marcelo H. Ang Jr, Geok-Soon Hong, and Feng Huo, Abstract Parallel mechansms have the advantages
More informationStep-3 New Harmony vector, improvised based on the following three mechanisms: (1) random selection, (2) memory consideration, and (3)
Optmal synthess of a Path Generator Lnkage usng Non Conventonal Approach Mr. Monsh P. Wasnk 1, Prof. M. K. Sonpmple 2, Prof. S. K. Undrwade 3 1 M-Tech MED Pryadarshn College of Engneerng, Nagpur 2,3 Mechancal
More informationDesign of Simulation Model on the Battlefield Environment ZHANG Jianli 1,a, ZHANG Lin 2,b *, JI Lijian 1,c, GUO Zhongwei 1,d
Internatonal Conference on Materals Engneerng and Informaton Technology Applcatons (MEITA 2015 Desgn of Smulaton Model on the Battlefeld Envronment ZHANG Janl 1,a, ZHANG Ln 2,b *, JI Ljan 1,c, GUO Zhongwe
More informationGenetic Tuning of Fuzzy Logic Controller for a Flexible-Link Manipulator
Genetc Tunng of Fuzzy Logc Controller for a Flexble-Lnk Manpulator Lnda Zhxa Sh Mohamed B. Traba Department of Mechancal Unversty of Nevada, Las Vegas Department of Mechancal Engneerng Las Vegas, NV 89154-407
More informationREFRACTION. a. To study the refraction of light from plane surfaces. b. To determine the index of refraction for Acrylic and Water.
Purpose Theory REFRACTION a. To study the refracton of lght from plane surfaces. b. To determne the ndex of refracton for Acrylc and Water. When a ray of lght passes from one medum nto another one of dfferent
More informationCalibration of an Articulated Camera System
Calbraton of an Artculated Camera System CHEN Junzhou and Kn Hong WONG Department of Computer Scence and Engneerng The Chnese Unversty of Hong Kong {jzchen, khwong}@cse.cuhk.edu.hk Abstract Multple Camera
More informationInvariant Shape Object Recognition Using B-Spline, Cardinal Spline, and Genetic Algorithm
Proceedngs of the 5th WSEAS Int. Conf. on Sgnal Processng, Robotcs and Automaton, Madrd, Span, February 5-7, 6 (pp4-45) Invarant Shape Obect Recognton Usng B-Splne, Cardnal Splne, and Genetc Algorthm PISIT
More informationEvaluation of an Enhanced Scheme for High-level Nested Network Mobility
IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.15 No.10, October 2015 1 Evaluaton of an Enhanced Scheme for Hgh-level Nested Network Moblty Mohammed Babker Al Mohammed, Asha Hassan.
More informationMachine Learning 9. week
Machne Learnng 9. week Mappng Concept Radal Bass Functons (RBF) RBF Networks 1 Mappng It s probably the best scenaro for the classfcaton of two dataset s to separate them lnearly. As you see n the below
More informationDevelopment of Inverse Dynamic Controller for Industrial robots with HyRoHILS system
June 2-5, KINTEX, Gyeongg-Do, Korea Development of Inverse Dynamc Controller for Industral robots wth HyRoHILS system Je Sung Yeon*, Eu Jn Km**, Sang-Hun Lee**, Jong Hyeon Park*, and Jong-Sung Hur** *
More informationInverse Kinematics (part 2) CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Spring 2016
Inverse Knematcs (part 2) CSE169: Computer Anmaton Instructor: Steve Rotenberg UCSD, Sprng 2016 Forward Knematcs We wll use the vector: Φ... 1 2 M to represent the array of M jont DOF values We wll also
More informationON SOME ENTERTAINING APPLICATIONS OF THE CONCEPT OF SET IN COMPUTER SCIENCE COURSE
Yordzhev K., Kostadnova H. Інформаційні технології в освіті ON SOME ENTERTAINING APPLICATIONS OF THE CONCEPT OF SET IN COMPUTER SCIENCE COURSE Yordzhev K., Kostadnova H. Some aspects of programmng educaton
More informationPositive Semi-definite Programming Localization in Wireless Sensor Networks
Postve Sem-defnte Programmng Localzaton n Wreless Sensor etworks Shengdong Xe 1,, Jn Wang, Aqun Hu 1, Yunl Gu, Jang Xu, 1 School of Informaton Scence and Engneerng, Southeast Unversty, 10096, anjng Computer
More informationTsinghua University at TAC 2009: Summarizing Multi-documents by Information Distance
Tsnghua Unversty at TAC 2009: Summarzng Mult-documents by Informaton Dstance Chong Long, Mnle Huang, Xaoyan Zhu State Key Laboratory of Intellgent Technology and Systems, Tsnghua Natonal Laboratory for
More informationOn Some Entertaining Applications of the Concept of Set in Computer Science Course
On Some Entertanng Applcatons of the Concept of Set n Computer Scence Course Krasmr Yordzhev *, Hrstna Kostadnova ** * Assocate Professor Krasmr Yordzhev, Ph.D., Faculty of Mathematcs and Natural Scences,
More information