Pose, Posture, Formation and Contortion in Kinematic Systems

Size: px
Start display at page:

Download "Pose, Posture, Formation and Contortion in Kinematic Systems"

Transcription

1 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, posture, formaton and contorton are defned for seral, parallel and hybrd knematc systems. Workspace and jontspace structure s examned n terms of these concepts. The nter-relatonshps of pose, posture, formaton and contorton are explored for a range of robot workspace and jontspace types. Introducton Robot manpulators (seral, parallel and hybrd) have two spaces assocated wth them. Usually the workspace s consdered to be the physcal space n whch the robot s embedded and through whch t executes movement. At each nstant each lnk of the robot occupes a poston and orentaton n the workspace. Smlarly the jontspace s usually consdered to be the more abstract space defned by the (drven) jont varables. At each nstant the values of the (drven) jont varables determne the state of the robot n the jontspace. Earler work n ths feld used concepts, such as closure and assembly confguraton, derved from the dsplacement analyss of sngle loop knematc lnkages and ther assocated seral systems [Rooney and Duffy, 97]. More recently there has been consderable nterest n parallel systems [Hunt and Prmrose, 993; Gosseln and Merlet, 994; Duffy, 996; Merlet,996; Tanev, 998], but most work to date has focussed on ether the workspace or the jontspace but not usually on both. Sometmes defntons and concepts assocated wth both spaces have been somewhat mprecse, or confused, or even occasonally contradctory. Ths stuaton s unsatsfactory especally when the mappng between the spaces s to be nvestgated. One am of ths paper s to establsh some termnology and defntons that are generc and consstent, so that they may be appled wth common justfcaton to seral, parallel and hybrd knematc systems. Pose, Formaton and Workspace In a knematc system, one way to locate a rgd lnk n space requres the specfcaton of a poston and an orentaton wth respect to some (global) coordnate frame that s consdered to be fxed. The pose of the lnk s defned to be the combnaton of ts poston and orentaton and as the lnk moves t traces out a sequence of poses. A typcal knematc system conssts of several nterconnected lnks wth each lnk havng ts own pose at each nstant. The confguraton of the complete system s therefore specfed by a set of poses (one for each lnk) that change wth tme as the system moves. However, attenton s usually focussed on the end-effector (for seral systems) or the movng platform (for parallel systems), and hence on the pose of just one lnk.

2 The workspace of a robot s often defned n terms of the 'reach' of the system, specfed by ts partcular geometrcal parameters. Usually the prmary defnton mplctly nvolves the orentaton of the end-effector, snce the orentaton, sze and shape of the latter determne the maxmum and mnmum reaches of the robot. The workspace of a D (3D) system s then seen as a twodmensonal (three-dmensonal) Eucldean space. However, n a D knematc system the pose of a lnk nvolves three varables (two for poston and one for orentaton of the lnk), and so t should be represented by a pont n a threedmensonal workspace. Moreover, ths s not a Eucldean space snce the orentaton varable s cyclc wth perod π and dstances between pars of ponts n ths space are not Pythagorean. Smlarly, n a 3D knematc system the pose of a lnk nvolves sx varables (three for poston and three for orentaton of the lnk), and so t should be represented by a pont n a sxdmensonal workspace. Agan, ths s not a Eucldean space snce the orentaton varables are cyclc wth perod π or π and dstances between pars of ponts n ths space are not Pythagorean. These consderatons lead to the followng generc defntons: The workspace of a robot knematc system s the space defned by all those varables requred to specfy the poston and orentaton of the end-effector or movng platform wth respect to a global fxed frame. Ths general defnton of workspace refers to the type of robot knematc system (such as seral 3R manpulator arm, or parallel 3-RPR platform) rather than to a partcular system wth partcular geometry. The workspace of any specfc robot geometry s then a subset of the general workspace wth varous geometrcal lmts mposed by the szes and shapes of the lnks etc.; The pose of a lnk s the combnaton of ts poston and orentaton specfed wth respect to a global fxed frame. It s just a pont n the workspace; A formaton s defned to be a collecton of related poses for one of the lnks, such as the end-effector or movng platform. It s a subset of the workspace and the workspace s thereby parttoned nto separate formatons. 3 Posture, Contorton and Jontspace An alternatve way to locate a rgd lnk n space s to specfy some of ts relatve spatal relatons wth respect to (local) coordnate frames attached to other lnks. For a knematc system the jont varables determne the relatve spatal relatons between adjacent connected lnks. The posture of any lnk s defned to be the combnaton of (drven) jont varables that locate the lnk n space [Rooney and Earl, 983], and as the lnk moves t passes through a sequence of postures. Thus both the pose and the posture of a lnk locate t n space. A typcal knematc system conssts of several nterconnected lnks, wth each lnk havng ts own posture at each nstant. The confguraton of the complete system s therefore specfed by a set of postures (one for each lnk) that change wth tme as the system moves. However, attenton s usually focussed on the end-effector (for seral systems) or the movng platform (for parallel systems), and hence on the posture of just one lnk. These consderatons lead to the followng generc defntons: The jontspace of a robot knematc system s the space defned by all those (drven) jont varables requred to specfy the poston and orentaton of the end-effector or

3 movng platform. Ths general defnton of jontspace refers to the type of robot knematc system (such as seral 3R manpulator arm, or parallel 3-RPR platform) rather than to a partcular system wth partcular geometry. The jontspace of any specfc robot geometry s then a subset of the general jontspace wth varous lmts mposed by the ranges of moton of the jonts etc.; The posture of a lnk s the combnaton of jont varable values specfyng ts poston and orentaton wth respect to local frames at the drven jonts. It s just a pont n the jontspace; A contorton s defned to be a collecton of related postures for one of the lnks, such as the end-effector or movng platform. It s a subset of the jontspace and the jontspace s thereby parttoned nto separate contortons. 4 Seral, Parallel and Hybrd Knematc Systems The number of (drven jont) varables requred for the posture of an end-effector or movng platform lnk s the same as the number of (poston and orentaton) varables requred for the pose of the lnk. As any lnk moves through a sequence of poses t also moves through a correspondng sequence of postures. However, n general t s possble at each nstant for each pose to correspond to more than one posture and conversely for each posture to correspond to more than one pose (Fgure ). Jontspace Workspace Posture Pose Contorton Formaton Fgure. Mappng between the jont space and the workspace. Typcally, seral knematc systems have several postures assocated wth a gven pose, but they always have just one pose assocated wth any gven posture. For example n 3D a general geometry 6R robot manpulator arm may have up to sxteen possble postures for a gven pose [Duffy and Crane, 980; Raghavan and Roth, 990], and n D a general geometry 3-dof robot manpulator arm (wth only revolute and/or prsmatc jonts) may have up to two postures for a

4 gven pose. To see how ths s possble, consder a planar RRR seral system wth the end-effector fxed n some pose. The mddle revolute jont can then adopt two confguratons wthout changng the pose of the end-effector, thereby leadng to two postures for that one pose (Fgure ). Fgure. Postve and negatve angle for a revolute jont, and a schematc representaton. We can show ths algebracally. Thus wth three revolute jonts, R, R, and R 3 n seres, there are two closure equatons: x = a cos( θ ) + a cos( θ + θ ) + a cos( θ + θ + θ ) () y = a sn( θ ) + a sn( θ + θ ) + a sn( θ + θ + θ ) () where a j are the lnk lengths, θ ( =,,3) are the jont angles, and ( x, y ) are the coordnates of a pont on the end-effector wth respect to a global coordnate frame. From eqn. () and eqn. () we obtan two solutons for θ, ( cos( φ) ) ( sn( φ) ) x a + y a a a θ =± arccos aa (3) where φ = θ+ θ + θ3 s the orentaton of the end-effector wth respect to a global coordnate frame. The two solutons for θ gven by eqn. (3) determne exactly two postures of the RRR manpulator. Smlarly, consder a planar RPR seral system wth the end-effector fxed n some pose. The prsmatc jont can then adopt two confguratons wthout changng the pose of the end-effector, agan leadng to two postures for that one pose (Fgure 3). In ths case the prsmatc jont must be constructed so that t allows sldng n the negatve drecton and hence can have a negatve value for the jont varable. Agan we can show ths algebracally. Thus wth one revolute jont R, one prsmatc jont P, and a second revolute jont R 3, n seres, there are two closure equatons. In ths case, the coordnates of a pont on the end-effector are: x = a sn( θ ) + S cos( θ ) + a cos( θ + θ ) (4) 34 3 y = a cos( θ ) + S sn( θ ) + a sn( θ + θ ) (5) 34 3

5 where a j are the lnk lengths, θ ( =,3) and S are the jont varables, and ( x, y ) are the coordnates of a pont on the end-effector wth respect to a global coordnate frame. From equatons (4) and (5) we obtan two values for S, [ φ ] [ φ ] 34cos( ) 34sn( ) ( 3) S =± x a + y a a a (6) where φ = θ+ θ3 s the orentaton of the end-effector wth respect to a global coordnate frame. The two solutons for S gven by eqn. (6) determne exactly two postures of the RPR manpulator. Fgure 3. Postve and negatve dstance for a prsmatc jont, and a schematc representaton Table shows the number of postures obtaned n ths way for the RRR and RPR, and addtonally for sx other planar three-jont systems consstng of just revolute and prsmatc jonts. Each of the four systems contanng at least two revolute jonts has two postures, whereas each of the remanng four systems contanng at least two prsmatc jonts has just one posture. In Table a pose or posture s denoted by the symbol L j, where L represents the end-effector lnk, the subscrpt j ndexes the pose and the superscrpt ndexes the posture. Ths notaton s a general one and t s also used later n Tables and 3 for parallel and hybrd systems, respectvely. In contrast to the stuaton wth seral systems, parallel knematc systems are usually consdered (correctly) to have several poses assocated wth a gven posture, but are also consdered (ncorrectly) to always have just one posture assocated wth any gven pose. For example the Stewart platform may have up to possble poses for a gven posture [Lazard and Merlet, 994], or the general Stewart type platform up to 40 possble poses [Husty, 996]. In general a parallel manpulator system may have more than one pose for each posture and smultaneously more than one posture for each pose. Ths s shown schematcally n Fgure where several postures (one from each contorton) map to each pose and where each posture maps to several poses (one n each formaton). To see how ths s possble, consder one of the legs of a three-legged 3-RRR parallel system wth the platform fxed n some pose.

6 Table. Examples of dfferent postures of planar seral manpulators. SERIAL MANIPULATORS Jontspace / POSTURES RRR RPP RRP PRP PRR PPR RPR PPP

7 Table. Examples of dfferent poses and postures of planar parallel manpulators. PARALLEL MANIPULATORS Workspace/ POSES Jontspace/ POSTURES L 3-RRR L L 6 L 3 L L L RPR 5 6 L L3 L L

8 Table 3. Examples of dfferent poses and postures of a planar hybrd manpulator. HYBRID MANIPULATOR Workspace/ POSES Jontspace/ POSTURES (RPRRR)R L L 3 L 4 As wth the seral system consdered earler (Fgure ), the mddle revolute jont n each leg can adopt two confguratons wthout changng the pose of the platform, thereby leadng to eght postures n total for that one pose. Wth general geometry ths 3-RRR system also has up to sx poses for each posture, as s well known [Hunt, 983]. The upper half of Table shows a partcular example of a 3-RRR parallel manpulator system that has specal geometry. Ths system has only four poses for each posture but a full complement of eght postures for each pose. (Agan the Lj notaton s used here to label and dstngush the dfferent confguratons.) The planar three-legged 3-RPR parallel system may be treated n a smlar way to the 3-RRR system f the prsmatc jonts n the former are physcally desgned to allow negatve-valued jont dsplacements. As wth the seral system consdered earler (Fgure 3), the prsmatc jont n each leg can adopt two confguratons wthout changng the pose of the platform, thereby leadng to eght postures for that one pose. Wth general geometry ths 3-RPR system (lke the 3-RRR) also has up to sx poses for each posture, as s well known [Hunt, 983; Gosseln and Merlet, 994]. The lower half of Table shows a partcular example of a 3-RPR parallel manpulator system that has specal geometry [Duffy, 996]. Ths system has only four poses for each posture but a full complement of eght postures for each pose. (Agan the Lj notaton s used here to label and dstngush the dfferent confguratons.) Fnally, f we consder hybrd (combnatons of seral and parallel) knematc systems we fnd that (as wth the parallel case) a hybrd system has n general more than one posture for each pose and more than one pose for each posture. Table 3 shows the (RPRRR)R hybrd system, where agan the Lj notaton s used to label and dstngush the dfferent confguratons.

9 5 Workspace and Jontspace Structure Snce n general the mappng between jontspace and workspace s many-many (Fgure ) the geometrcal and the topologcal structures of workspaces and jontspaces are often complcated. However, they may be explored n terms of pose, posture, formaton and contorton. As a frst step we consder brefly the RRR and RPR seral systems. Fgure 4. Jontspace (contorton ) for the RRR planar seral manpulator. Fgure 5. Workspace of the RRR planar seral manpulator. Fgure 4 shows one of the two contortons (of postures) n the jontspace of the RRR planar seral manpulator. Fgure 5 shows the sngle formaton (of poses) n ts workspace, correspondng to both contortons n the jontspace. Smlarly, Fgure 6 shows one of the two contortons (of postures) n the jontspace of the RPR planar seral manpulator, and Fgure 7 shows the sngle formaton (of poses) n ts workspace, correspondng to both contortons n the jontspace.. A further paper on the structure of workspaces and jontspaces s planned. Fgure 6. Jontspace (contorton ) for the RPR planar seral manpulator. Fgure 7. Workspace of the RPR planar seral manpulator.

10 6 Dscusson and Conclusons The paper has examned some aspects of the relatonshp between jontspace and workspace for robot manpulators. It has concentrated on planar knematc systems for clarty but the approach apples equally to spatal systems. The concepts of pose and formaton for workspace, and posture and contorton for jontspace have been ntroduced and explored for a range of seral, parallel and hybrd systems. Workspace and jontspace structures have been examned brefly, and a further paper s planned to explore ths n more detal and to apply the concepts n the wder context of forward and reverse knematcs. References Duffy, J. (996). Statcs and Knematcs wth Applcatons to Robotcs. Cambrdge Unversty Press. Duffy, J., Crane, C (980). A dsplacement analyss of the general spatal 7-lnk 7-R mechansm,. Mechansm and Machne Theory 5: Gosseln, C.M., and Merlet, J-P. (994). The drect knematcs of planar parallel manpulators: specal archtectures and number of solutons. Mechansm and Machne Theory 9(8): Hunt, K.H., (983). Structural knematcs of n-parallel-actuated robot-arms. Journal of Mechansms, Transmssons, and Automaton n Desgn 05: Hunt, K.H., and Prmrose, E.J.F. (993). Assembly confguratons of some on-parallel-actuated manpulators. Mechansm and Machne Theory 8():3 4. Husty, M., (996). An algorthm for solvng the drect knematcs of general Stewart-Gouth platforms. Mechansm and Machne Theory 3(4): Lazard, D. and Merlet, J-P. (994). The (true) Stewart platform has confguratons. Proceedngs of IEEE Internatonal Conference on Robotcs and Automaton. San Dego: Merlet, J-P. (996). Drect knematcs of planar parallel manpulators. Proceedngs of the IEEE Internatonal Conference on Robotcs and Automaton, Mnneapols, Mnnesota: Raghavan, M. and Roth, B. (989) Knematc analyss of the 6R manpulator of general geometry. In Mura, H. and Armoto, S. (eds), The Ffth Internatonal Symposum on Robotcs Research, MA:MIT Press, Rooney, J., and Duffy, J. (97). On the closure of spatal mechansms. Proceedngs of the th ASME Mechansms Conference & Internatonal Symposum on Gearng and Transmssons. San Francsco, CA, USA: paper no. 7-Mech-77. Rooney, J., and Earl, C.F. (983). Manpulator postures and knematc assembly confguratons. Proceedngs of the Sxth World Congress on Theory of Machnes and Mechansms, New Delh, Inda: Tanev, T.K. (998). Forward dsplacement analyss of a three-legged four-degree-of-freedom parallel manpulator. In Lenarcc, J. and Husty, M.L. (eds), Advances n Robot Knematcs: Analyss and Control, Kluwer Academc Publshers, Dordrecht:

ROBOT KINEMATICS. ME Robotics ME Robotics

ROBOT 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 information

Inverse kinematic Modeling of 3RRR Parallel Robot

Inverse 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 information

Analysis of Continuous Beams in General

Analysis 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 information

WORKSPACE OPTIMIZATION OF ORIENTATIONAL 3-LEGGED UPS PARALLEL PLATFORMS

WORKSPACE 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 information

R s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes

R 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 information

Sensory Redundant Parallel Mobile Mechanism

Sensory 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 information

DETC ANALYSIS OF THREE DEGREE OF FREEDOM 6 6 TENSEGRITY PLATFORM

DETC 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 information

Kinematics of pantograph masts

Kinematics 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 information

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1)

For instance, ; the five basic number-sets are increasingly more n A B & B A A = B (1) Secton 1.2 Subsets and the Boolean operatons on sets If every element of the set A s an element of the set B, we say that A s a subset of B, or that A s contaned n B, or that B contans A, and we wrte A

More information

A mathematical programming approach to the analysis, design and scheduling of offshore oilfields

A 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 information

Parallel manipulator robots design and simulation

Parallel 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 information

PLANAR PARALLEL 3-RPR MANIPULATOR

PLANAR 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 information

An Optimal Algorithm for Prufer Codes *

An 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 information

ISSN 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 information

1 IRCCyN: UMR CNRS 6596, Ecole Centrale de Nantes, Université de Nantes, Ecole des Mines de Nantes

1 IRCCyN: UMR CNRS 6596, Ecole Centrale de Nantes, Université de Nantes, Ecole des Mines de Nantes he Knematc Analyss of a Symmetrcal hree-degree-of-freedom lanar arallel Manpulator Damen Chablat and hlppe Wenger Insttut de Recherche en Communcatons et Cybernétque de Nantes, rue de la Noë, 442 Nantes,

More information

SLAM Summer School 2006 Practical 2: SLAM using Monocular Vision

SLAM 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 information

The Greedy Method. Outline and Reading. Change Money Problem. Greedy Algorithms. Applications of the Greedy Strategy. The Greedy Method Technique

The Greedy Method. Outline and Reading. Change Money Problem. Greedy Algorithms. Applications of the Greedy Strategy. The Greedy Method Technique //00 :0 AM Outlne and Readng The Greedy Method The Greedy Method Technque (secton.) Fractonal Knapsack Problem (secton..) Task Schedulng (secton..) Mnmum Spannng Trees (secton.) Change Money Problem Greedy

More information

6.854 Advanced Algorithms Petar Maymounkov Problem Set 11 (November 23, 2005) With: Benjamin Rossman, Oren Weimann, and Pouya Kheradpour

6.854 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 information

FEATURE EXTRACTION. Dr. K.Vijayarekha. Associate Dean School of Electrical and Electronics Engineering SASTRA University, Thanjavur

FEATURE EXTRACTION. Dr. K.Vijayarekha. Associate Dean School of Electrical and Electronics Engineering SASTRA University, Thanjavur FEATURE EXTRACTION Dr. K.Vjayarekha Assocate Dean School of Electrcal and Electroncs Engneerng SASTRA Unversty, Thanjavur613 41 Jont Intatve of IITs and IISc Funded by MHRD Page 1 of 8 Table of Contents

More information

Mathematical Model for Motion Control of Redundant Robot Arms

Mathematical Model for Motion Control of Redundant Robot Arms Mathematcal Model for Moton Control of Redundant Robot Arms EVGENIY KRASTEV Department of Mathematcs and Informatcs Sofa Unversty St. Klment Ohrdsky 5, James Boucher blvd., 1164 Sofa BULGARIA eck@fm.un-sofa.bg

More information

Data Representation in Digital Design, a Single Conversion Equation and a Formal Languages Approach

Data Representation in Digital Design, a Single Conversion Equation and a Formal Languages Approach Data Representaton n Dgtal Desgn, a Sngle Converson Equaton and a Formal Languages Approach Hassan Farhat Unversty of Nebraska at Omaha Abstract- In the study of data representaton n dgtal desgn and computer

More information

Atlas Based Kinematic Optimum Design of the Stewart Parallel Manipulator

Atlas Based Kinematic Optimum Design of the Stewart Parallel Manipulator 20 CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 28,aNo. 1,a2015 DOI: 10.3901/CJME.2014.0929.155, avalable onlne at www.sprngerlnk.com; www.cjmenet.com; www.cjmenet.com.cn Atlas Based Knematc Optmum Desgn

More information

Parallelism for Nested Loops with Non-uniform and Flow Dependences

Parallelism 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 information

ON 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, 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 information

F Geometric Mean Graphs

F Geometric Mean Graphs Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 2 (December 2015), pp. 937-952 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) F Geometrc Mean Graphs A.

More information

Sum of Linear and Fractional Multiobjective Programming Problem under Fuzzy Rules Constraints

Sum of Linear and Fractional Multiobjective Programming Problem under Fuzzy Rules Constraints Australan Journal of Basc and Appled Scences, 2(4): 1204-1208, 2008 ISSN 1991-8178 Sum of Lnear and Fractonal Multobjectve Programmng Problem under Fuzzy Rules Constrants 1 2 Sanjay Jan and Kalash Lachhwan

More information

Range images. Range image registration. Examples of sampling patterns. Range images and range surfaces

Range images. Range image registration. Examples of sampling patterns. Range images and range surfaces Range mages For many structured lght scanners, the range data forms a hghly regular pattern known as a range mage. he samplng pattern s determned by the specfc scanner. Range mage regstraton 1 Examples

More information

Machine Learning: Algorithms and Applications

Machine Learning: Algorithms and Applications 14/05/1 Machne Learnng: Algorthms and Applcatons Florano Zn Free Unversty of Bozen-Bolzano Faculty of Computer Scence Academc Year 011-01 Lecture 10: 14 May 01 Unsupervsed Learnng cont Sldes courtesy of

More information

A Binarization Algorithm specialized on Document Images and Photos

A 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 information

Six-axis Robot Manipulator Numerical Control Programming and Motion Simulation

Six-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 information

Compiler Design. Spring Register Allocation. Sample Exercises and Solutions. Prof. Pedro C. Diniz

Compiler 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 information

VISUAL SELECTION OF SURFACE FEATURES DURING THEIR GEOMETRIC SIMULATION WITH THE HELP OF COMPUTER TECHNOLOGIES

VISUAL 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 information

2x x l. Module 3: Element Properties Lecture 4: Lagrange and Serendipity Elements

2x 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 information

Step-3 New Harmony vector, improvised based on the following three mechanisms: (1) random selection, (2) memory consideration, and (3)

Step-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 information

3D vector computer graphics

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 information

An Iterative Solution Approach to Process Plant Layout using Mixed Integer Optimisation

An Iterative Solution Approach to Process Plant Layout using Mixed Integer Optimisation 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 An Iteratve Soluton Approach to Process Plant Layout usng Mxed

More information

Machine Learning 9. week

Machine 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 information

Content Based Image Retrieval Using 2-D Discrete Wavelet with Texture Feature with Different Classifiers

Content 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 information

Learning the Kernel Parameters in Kernel Minimum Distance Classifier

Learning 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 information

Support Vector Machines

Support Vector Machines /9/207 MIST.6060 Busness Intellgence and Data Mnng What are Support Vector Machnes? Support Vector Machnes Support Vector Machnes (SVMs) are supervsed learnng technques that analyze data and recognze patterns.

More information

DESIGN OF A HAPTIC DEVICE FOR EXCAVATOR EQUIPPED WITH CRUSHER

DESIGN OF A HAPTIC DEVICE FOR EXCAVATOR EQUIPPED WITH CRUSHER 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

More information

Resolving Ambiguity in Depth Extraction for Motion Capture using Genetic Algorithm

Resolving 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 information

Load-Balanced Anycast Routing

Load-Balanced Anycast Routing Load-Balanced Anycast Routng Chng-Yu Ln, Jung-Hua Lo, and Sy-Yen Kuo Department of Electrcal Engneerng atonal Tawan Unversty, Tape, Tawan sykuo@cc.ee.ntu.edu.tw Abstract For fault-tolerance and load-balance

More information

Module Management Tool in Software Development Organizations

Module Management Tool in Software Development Organizations Journal of Computer Scence (5): 8-, 7 ISSN 59-66 7 Scence Publcatons Management Tool n Software Development Organzatons Ahmad A. Al-Rababah and Mohammad A. Al-Rababah Faculty of IT, Al-Ahlyyah Amman Unversty,

More information

PROBLEMS AND PROCEDURES FOR KINEMATIC DESIGN OF MANIPULATORS

PROBLEMS AND PROCEDURES FOR KINEMATIC DESIGN OF MANIPULATORS 第八屆全國機構與機器設計學術研討會 台北科技大學 2005 年 12 月 2 日 PROBLEMS AND PROCEDURES FOR KINEMATIC DESIGN OF MANIPULATORS Marco Ceccarell LARM: Laboratory of Robotcs and Mechatroncs DMSAT - Unversty of Cassno Va D Baso 43,

More information

Type-2 Fuzzy Non-uniform Rational B-spline Model with Type-2 Fuzzy Data

Type-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 information

CHARUTAR VIDYA MANDAL S SEMCOM Vallabh Vidyanagar

CHARUTAR VIDYA MANDAL S SEMCOM Vallabh Vidyanagar CHARUTAR VIDYA MANDAL S SEMCOM Vallabh Vdyanagar Faculty Name: Am D. Trved Class: SYBCA Subject: US03CBCA03 (Advanced Data & Fle Structure) *UNIT 1 (ARRAYS AND TREES) **INTRODUCTION TO ARRAYS If we want

More information

Four-cable-driven parallel robot

Four-cable-driven parallel robot 2013 13th Internatonal Conference on Control, Automaton and Systems (ICCAS 2013) Oct. 20-23, 2013 n Kmdaejung Conventon Center, Gwangju, Korea Four-cable-drven parallel robot XueJun Jn 1, Dae Ik Jun 1,

More information

INVERSE DYNAMICS ANALYSIS AND SIMULATION OF A CLASS OF UNDER- CONSTRAINED CABLE-DRIVEN PARALLEL SYSTEM

INVERSE 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 information

Parallel matrix-vector multiplication

Parallel matrix-vector multiplication Appendx A Parallel matrx-vector multplcaton The reduced transton matrx of the three-dmensonal cage model for gel electrophoress, descrbed n secton 3.2, becomes excessvely large for polymer lengths more

More information

Analysis on the Workspace of Six-degrees-of-freedom Industrial Robot Based on AutoCAD

Analysis 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 information

Computational Issues in the Planning and Kinematics of Binary Robots Abstract 1. Introduction 2. Workspace Analysis and Optimization

Computational 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 information

Kinematics Modeling and Analysis of MOTOMAN-HP20 Robot

Kinematics 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 information

Electrical analysis of light-weight, triangular weave reflector antennas

Electrical analysis of light-weight, triangular weave reflector antennas Electrcal analyss of lght-weght, trangular weave reflector antennas Knud Pontoppdan TICRA Laederstraede 34 DK-121 Copenhagen K Denmark Emal: kp@tcra.com INTRODUCTION The new lght-weght reflector antenna

More information

Rigidity analysis of T3R1 parallel robot with uncoupled kinematics B. C. Bouzgarrou, J.C. Fauroux, G. Gogu, Y. Heerah

Rigidity analysis of T3R1 parallel robot with uncoupled kinematics B. C. Bouzgarrou, J.C. Fauroux, G. Gogu, Y. Heerah Rgdt analss of T3R parallel robot wth uncoupled nematcs B. C. Bouzgarrou, J.C. Faurou, G. Gogu, Y. eerah Laboratore de Recherche et Applcatons en Mécanque avancée (LaRAMA) Insttut Franças de Mécanque Avancée

More information

The motion simulation of three-dof parallel manipulator based on VBAI and MATLAB Zhuo Zhen, Chaoying Liu* and Xueling Song

The 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 information

Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings

Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings Stffness modelng for perfect and non-perfect parallel manpulators under nternal and external loadngs Alexandr Klmchk, Damen hablat, Anatol Pashkevch o cte ths verson: Alexandr Klmchk, Damen hablat, Anatol

More information

An Application of the Dulmage-Mendelsohn Decomposition to Sparse Null Space Bases of Full Row Rank Matrices

An 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 information

Esc101 Lecture 1 st April, 2008 Generating Permutation

Esc101 Lecture 1 st April, 2008 Generating Permutation Esc101 Lecture 1 Aprl, 2008 Generatng Permutaton In ths class we wll look at a problem to wrte a program that takes as nput 1,2,...,N and prnts out all possble permutatons of the numbers 1,2,...,N. For

More information

Jeha Ryu* and Jongeun Cha. Jeha Ryu* is with Department of Mechatronics, Kwangju Institute of Science and Technology (K-JIST),

Jeha Ryu* and Jongeun Cha. Jeha Ryu* is with Department of Mechatronics, Kwangju Institute of Science and Technology (K-JIST), Volumetrc Error Analyss and Archtecture Optmzaton for Accuracy of HexaSldeype Parallel Manpulators Jeha Ryu* and Jongeun Cha Jeha Ryu* s wth Department of Mechatroncs, Kwangju Insttute of Scence and echnology

More information

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points;

Subspace clustering. Clustering. Fundamental to all clustering techniques is the choice of distance measure between data points; Subspace clusterng Clusterng Fundamental to all clusterng technques s the choce of dstance measure between data ponts; D q ( ) ( ) 2 x x = x x, j k = 1 k jk Squared Eucldean dstance Assumpton: All features

More information

Math Homotopy Theory Additional notes

Math Homotopy Theory Additional notes Math 527 - Homotopy Theory Addtonal notes Martn Frankland February 4, 2013 The category Top s not Cartesan closed. problem. In these notes, we explan how to remedy that 1 Compactly generated spaces Ths

More information

Accounting for the Use of Different Length Scale Factors in x, y and z Directions

Accounting 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 information

Multi-objective Optimization for Upper Body Posture Prediction

Multi-objective Optimization for Upper Body Posture Prediction Mult-objectve Optmzaton for Upper Body Posture Predcton Jngzhou ang *, R. Tmothy Marler, HyungJoo Km, Jasbr S. Arora, and Karm Abdel-Malek ** Vrtual Solder Research Program, Center for Computer-Aded Desgn,

More information

Multi-posture kinematic calibration technique and parameter identification algorithm for articulated arm coordinate measuring machines

Multi-posture kinematic calibration technique and parameter identification algorithm for articulated arm coordinate measuring machines Mult-posture knematc calbraton technque and parameter dentfcaton algorthm for artculated arm coordnate measurng machnes Juan-José AGUILAR, Jorge SANTOLARIA, José-Antono YAGÜE, Ana-Crstna MAJARENA Department

More information

NUMERICAL SOLVING OPTIMAL CONTROL PROBLEMS BY THE METHOD OF VARIATIONS

NUMERICAL 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 information

A high precision collaborative vision measurement of gear chamfering profile

A 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 information

Cluster Analysis of Electrical Behavior

Cluster 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 information

A SYSTOLIC APPROACH TO LOOP PARTITIONING AND MAPPING INTO FIXED SIZE DISTRIBUTED MEMORY ARCHITECTURES

A SYSTOLIC APPROACH TO LOOP PARTITIONING AND MAPPING INTO FIXED SIZE DISTRIBUTED MEMORY ARCHITECTURES A SYSOLIC APPROACH O LOOP PARIIONING AND MAPPING INO FIXED SIZE DISRIBUED MEMORY ARCHIECURES Ioanns Drosts, Nektaros Kozrs, George Papakonstantnou and Panayots sanakas Natonal echncal Unversty of Athens

More information

CHAPTER 2 DECOMPOSITION OF GRAPHS

CHAPTER 2 DECOMPOSITION OF GRAPHS CHAPTER DECOMPOSITION OF GRAPHS. INTRODUCTION A graph H s called a Supersubdvson of a graph G f H s obtaned from G by replacng every edge uv of G by a bpartte graph,m (m may vary for each edge by dentfyng

More information

XY-Theta Positioning Table with Parallel Kinematics and Unlimited Theta Rotation

XY-Theta Positioning Table with Parallel Kinematics and Unlimited Theta Rotation XY-heta Postonng able wth Parallel Knematcs and Unlmted heta Rotaton Ilan A. Bonev 1, Aleander Yu 2, Paul Zsombor-Murra 2 1 Department of Automated Manufacturng Engneerng, École de echnologe Supéreure,

More information

Multiobjective Design Optimization of 3-PRR Planar Parallel Manipulators

Multiobjective Design Optimization of 3-PRR Planar Parallel Manipulators Multobjectve Desgn Optmzaton of 3-P Planar Parallel Manpulators aza Ur-ehman, Stéphane Caro, Damen Chablat, Phlppe Wenger To cte ths verson: aza Ur-ehman, Stéphane Caro, Damen Chablat, Phlppe Wenger. Multobjectve

More information

Lecture 5: Multilayer Perceptrons

Lecture 5: Multilayer Perceptrons Lecture 5: Multlayer Perceptrons Roger Grosse 1 Introducton So far, we ve only talked about lnear models: lnear regresson and lnear bnary classfers. We noted that there are functons that can t be represented

More information

Reducing Frame Rate for Object Tracking

Reducing 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 information

REFRACTION. a. To study the refraction of light from plane surfaces. b. To determine the index of refraction for Acrylic and Water.

REFRACTION. 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 information

GSLM Operations Research II Fall 13/14

GSLM Operations Research II Fall 13/14 GSLM 58 Operatons Research II Fall /4 6. Separable Programmng Consder a general NLP mn f(x) s.t. g j (x) b j j =. m. Defnton 6.. The NLP s a separable program f ts objectve functon and all constrants are

More information

Mathematics 256 a course in differential equations for engineering students

Mathematics 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 information

Contour Error of the 3-DoF Hydraulic Translational Parallel Manipulator. Ryszard Dindorf 1,a, Piotr Wos 2,b

Contour 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 information

Hermite Splines in Lie Groups as Products of Geodesics

Hermite 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 information

A Fast Content-Based Multimedia Retrieval Technique Using Compressed Data

A 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 information

We 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 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 information

TPL-Aware Displacement-driven Detailed Placement Refinement with Coloring Constraints

TPL-Aware Displacement-driven Detailed Placement Refinement with Coloring Constraints TPL-ware Dsplacement-drven Detaled Placement Refnement wth Colorng Constrants Tao Ln Iowa State Unversty tln@astate.edu Chrs Chu Iowa State Unversty cnchu@astate.edu BSTRCT To mnmze the effect of process

More information

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION

MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION MULTISPECTRAL IMAGES CLASSIFICATION BASED ON KLT AND ATR AUTOMATIC TARGET RECOGNITION Paulo Quntlano 1 & Antono Santa-Rosa 1 Federal Polce Department, Brasla, Brazl. E-mals: quntlano.pqs@dpf.gov.br and

More information

UNIT 2 : INEQUALITIES AND CONVEX SETS

UNIT 2 : INEQUALITIES AND CONVEX SETS UNT 2 : NEQUALTES AND CONVEX SETS ' Structure 2. ntroducton Objectves, nequaltes and ther Graphs Convex Sets and ther Geometry Noton of Convex Sets Extreme Ponts of Convex Set Hyper Planes and Half Spaces

More information

COMPARISON OF TWO MODELS FOR HUMAN EVACUATING SIMULATION IN LARGE BUILDING SPACES. University, Beijing , China

COMPARISON OF TWO MODELS FOR HUMAN EVACUATING SIMULATION IN LARGE BUILDING SPACES. University, Beijing , China COMPARISON OF TWO MODELS FOR HUMAN EVACUATING SIMULATION IN LARGE BUILDING SPACES Bn Zhao 1, 2, He Xao 1, Yue Wang 1, Yuebao Wang 1 1 Department of Buldng Scence and Technology, Tsnghua Unversty, Bejng

More information

Computer Animation and Visualisation. Lecture 4. Rigging / Skinning

Computer 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 information

Kinematics and Numerical Algebraic Geometry

Kinematics and Numerical Algebraic Geometry Knematcs and Numercal Algebrac Geometry Charles Wampler General Motors R&D Center Warren, Mchgan, USA Includng collaboratons wth: Andrew Sommese Jon Hauensten Dan Bates Notre Dame Teas A&M Colorado St.

More information

Probabilistic Map Building by Coordinated Mobile Sensors

Probabilistic Map Building by Coordinated Mobile Sensors Probablstc Map Buldng by Coordnated Moble Sensors Jen-Yeu Chen, Student Member, IEEE, and Jangha Hu, Member, IEEE Abstract In ths paper, we develop an effcent algorthm for coordnatng a group of moble robotc

More information

K-means and Hierarchical Clustering

K-means and Hierarchical Clustering Note to other teachers and users of these sldes. Andrew would be delghted f you found ths source materal useful n gvng your own lectures. Feel free to use these sldes verbatm, or to modfy them to ft your

More information

Steps for Computing the Dissimilarity, Entropy, Herfindahl-Hirschman and. Accessibility (Gravity with Competition) Indices

Steps 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 information

A Fast Visual Tracking Algorithm Based on Circle Pixels Matching

A 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 information

The Codesign Challenge

The 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 information

Chapter 6 Programmng the fnte element method Inow turn to the man subject of ths book: The mplementaton of the fnte element algorthm n computer programs. In order to make my dscusson as straghtforward

More information

Problem Definitions and Evaluation Criteria for Computational Expensive Optimization

Problem 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 information

We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors

We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors We are IntechOpen, the world s leadng publsher of Open Access books Bult by scentsts, for scentsts 3,900 116,000 120M Open access books avalable Internatonal authors and edtors Downloads Our authors are

More information

Needed Information to do Allocation

Needed Information to do Allocation Complexty n the Database Allocaton Desgn Must tae relatonshp between fragments nto account Cost of ntegrty enforcements Constrants on response-tme, storage, and processng capablty Needed Informaton to

More information

LOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit

LOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit LOOP ANALYSS The second systematic technique to determine all currents and voltages in a circuit T S DUAL TO NODE ANALYSS - T FRST DETERMNES ALL CURRENTS N A CRCUT AND THEN T USES OHM S LAW TO COMPUTE

More information

Complex 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. 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 information

Solving two-person zero-sum game by Matlab

Solving two-person zero-sum game by Matlab Appled Mechancs and Materals Onlne: 2011-02-02 ISSN: 1662-7482, Vols. 50-51, pp 262-265 do:10.4028/www.scentfc.net/amm.50-51.262 2011 Trans Tech Publcatons, Swtzerland Solvng two-person zero-sum game by

More information

Cordial and 3-Equitable Labeling for Some Star Related Graphs

Cordial and 3-Equitable Labeling for Some Star Related Graphs Internatonal Mathematcal Forum, 4, 009, no. 31, 1543-1553 Cordal and 3-Equtable Labelng for Some Star Related Graphs S. K. Vadya Department of Mathematcs, Saurashtra Unversty Rajkot - 360005, Gujarat,

More information