Kinematic Synthesis of Multi-fingered Robotic Hands for Finite and Infinitesimal Tasks
|
|
- Jared Collins
- 8 years ago
- Views:
Transcription
1 Kiematic Sythesis of Multi-figered Robotic Hads for Fiite ad Ifiitesimal Tasks E. Simo-Serra, A. Perez-Gracia, H. Moo ad N. Robso Abstract I this paper we preset a ovel method of desigig multi-figered robotic hads usig tasks composed of both fiite ad ifiitesimal motio. The method is based o represetig the robotic hads as a kiematic chai with a tree topology. We represet fiite motio usig Clifford algebra ad ifiitesimal motio usig Lie algebra to perform fiite dimesioal kiematic sythesis of the multifigered mechaism. This allows tasks to be defied ot oly by displacemets, but also by the velocity ad acceleratio at differet positios for the desig of robotic hads. The additioal iformatio eables a icreased local approximatio of the task at critical positios, as well as cotact ad curvature specificatios. A example task is provided usig a experimetal motio capture system ad we preset the desig of a robotic had for the task usig a hybrid Geetic Algorithm/Leveberg- Marquadt solver. Key words: kiematic sythesis, multi-figered grippers, Clifford ad Lie algebra. 1 Itroductio The desig of ed-effector robotic tools has traditioally take place i a applicatioorieted fashio withi the framework of the mechaical desig theory [7]. Amog the rich variety of robotic ed-effectors, those geerally defied as robotic hads are cosidered suited ot oly for graspig, but also for dexterous maipulatio. We ca E. Simo-Serra Istitut de Robòtica i Iformàtica Idustrial (CSIC-UPC) esimo@iri.upc.edu A. Perez-Gracia Idaho State Uiversity, Pocatello, Idaho perealba@isu.edu H. Moo Texas A&M Uiversity, College Statio, TX hsmoo@eo.tamu.edu N. Robso Texas A&M Uiversity, College Statio, TX iarobso@tamu.edu 1
2 E. Simo-Serra, A. Perez-Gracia, H. Moo ad N. Robso defie a multi-figered robotic had as a ed-effector i which the base, or palm, spas several serial chais i a tree-like structure. There are a great variety of desigs for robotic hads. Some desigs mimic the huma had ad exhibit a high umber of degrees of freedom, [1] ad [15]; others are desiged for specific applicatios [4] ad may or ot be athropomorphic [5]. Most of the desigs have bee orieted either towards maximum athropomorphism or towards optimizig graspig, maipulability or workspace size. A good review o the efforts toward kiematic had desig ca be foud i [6]. As robotic hads become more commo i idustrial applicatios ad huma eviromets, it makes sese to thik that their desig will become more task-orieted. Soto Martell ad Gii [14] expose the eed for a task-based desig process for robotic hads. The use of kiematic sythesis for the desig of the multi-figered robotic had has bee applied to idividual figers, see []. We believe that the reaso why dimesioal sythesis has bee scarcely applied to robotic had desig is because of the lack of a method that takes a multi-figered task as the iput ad outputs a multi-figered desig. I this paper, we exted the work preseted i [13] by combiig it with the results o kiematic sythesis for ifiitesimal positios [8, 9] ad expressig the kiematics usig the Clifford algebra of dual quaterios [10]. Note that mechaical likages are traditioally sythesized by specifyig a task, cosistig of a umber of positios that the ed-effector has to move through, with the goal of determiig the desig parameters, i.e. fixed ad movig pivot locatios, as well as the size of the likage. The differece betwee the traditioal desig of mechaical likages ad the curret desig with cotact directio, used i this research, is basically i the task, which cosists ot oly of positios, but velocities ad acceleratios compatible with cotact ad curvature specificatios betwee the ed-effector/figers ad the object to be grasped. I compariso to the traditioal sythesis techiques, these velocities ad acceleratios yield to a more complicated system of positio, velocity ad acceleratio desig equatios, as well as more complicated trajectory plaig techiques. As a example, we apply this methodology to the desig of a multi-figered had for operatig a door kob. The motivatio for this desig arose from a idividual, who is cofied to a wheel chair after a accidet. He has limited movemet ad weakess i his hads, makig it difficult for him to grasp doorkobs at his workspace. The sythesis preseted here is the first step towards developig assistive maipulatio devices. Ifiitesimal Kiematics The geeric screw S for a twist ca be represeted as a elemet of the Lie algebra se(3) [1], S=λ(s;r s+ hs)=λ(s;s 0 + hs)=(ω;v) se(3) (1)
3 Kiematic Sythesis of Multi-figered Robotic Hads for Fiite ad Ifiitesimal Tasks 3 where s,r,ω,v R 3 with s s=1, s 0 = r s ad λ,h R. The relative velocities betwee a pair of rigid bodies form oe-dimesioal subalgebras of the Lie algebra se(3) [11]. The most geeric subalgebra is geerated by the screw or helical joit S which becomes a revolute joit S R =(s;s 0 ) with h=0 or a prismatic joit S P =(0;s) with the screw axis at ifiity. The biary operatio of the Lie algebra is the Lie bracket, which ca be expaded for screws as, [S 1,S ]=[(ω 1 ;v 1 ),(ω ;v )]=(ω 1 ω ;ω 1 v + v 1 ω ) () The velocity of the ed-effector for a serial articulated chai with joits i a give cofiguratio ca be writte as [1], dp dt =Ṗ= θ i S i (3) where Ṗ = (ω;v) with ω beig the agular velocities ad v beig the Cartesia velocities. The screwss i represet the ifiitesimal screws of each joit. The ifiitesimal screws ca be trasformed to a istataeous positio from a referece positio usig the Clifford algebra cojugatio actio, S k i = ( e ˆθ k i 1 S k i 1 )S i ( e ˆθ k i 1 S k i 1) = ( i 1 ) ˆθ k j e S j j=1 S i ( i 1 j=1 ˆθ k j e S j) (4) where ˆθ i k = ˆθ i k ˆθ i r with ˆθ i r is the joit parameter i the referece cofiguratio ads k i is the i-th screw i a serial chai at positio k. The velocity of a joit j i a chai is writte as the derivative of a fiite screw [3], ds j dt =Ṡ j = j 1 θ i [S i,s j ] (5) Cross terms ad the o-commutatio of the derivatio operator must be take ito accout as see by differetiatig each velocity compoet of (3) usig the chai rule. This ca be expaded to obtai the acceleratio of the ed-effector, d P dt = P= d dtṗ= ( θ i S i + θ i Ṡ i ) = 1 θ i S i + θ i θ j [S i,s j ] (6) j=i+1 where P=(α;a) with α beig the agular acceleratios ad a beig the Cartesia acceleratios. The approach is geeral i the sese that the chai rule ca be successively applied to obtai higher derivatives if ecessary.
4 4 E. Simo-Serra, A. Perez-Gracia, H. Moo ad N. Robso 3 Desig Equatios for Tree Topologies Tree topologies ca be see as may differet serial chais that share a umber of commo joits. The equatios ca be writte as for serial chais, but the task defiitio will vary with the topology. The fiite motio of a joit ca be expressed usig the expoetial map of a screw S. This ca be expressed usig the uit elemet of the Clifford eve subalgebra of the projective space Cl + (0,3,1) or dual quaterio, e ˆθ S =(cos θ d si θ ε)+(si θ + d cos θ ε)s=cos ˆθ ˆθ + si S. (7) where ε is the dual uit such that ε = 0. For a serial chai with joits, the forward kiematics of a serial chai ca be writte relative to a referece cofiguratio of the serial chai, ˆQ( ˆθ)= e ˆθ i S i = (cos ˆθ i + si ˆθ i S i) (8) where ˆθ i = ˆθ i ˆθ 0 with ˆθ 0 beig the joit parameters of the referece cofiguratio. For a task composed of fiite positios, the relative forward kiematics ca be compared to the relative motio from the referece cofiguratio to each positio ˆP 1k = ˆP k ˆP 1 1 [10], ˆP 1k = e ˆθ k i S i, k=,...,m p (9) where m p is the umber of positios cosidered ad ˆθ i k beig the referece cofiguratio. For a task with velocities, we ca use (3) to write, Ṗ k = = ˆθ k i θ 1 i, with k = 1 θ k i Sk i, k=1,...,m v (10) where Ṗ k is the absolute velocity iformatio for a give positio k i the form (ω;v). The istataeous joit screw axis S k i ca be calculated from (4). The same procedure ca be applied to acceleratio to obtai from (6), P k = θ i k S k i + 1 θ k i θ j[s k k i,s k j], k=1,...,m a (11) j=i+1 where P k is the absolute acceleratio for a give positio k i the form(α;a). The velocity ad acceleratio equatios ca be see as additioal pose iformatio that reduce the umber of poses eeded. Coutig the umber of idepedet ukows x ad idepedet equatios f we obtai,
5 Kiematic Sythesis of Multi-figered Robotic Hads for Fiite ad Ifiitesimal Tasks 5 x = s + j (m p + m v + m a 1) (1) f = c + d (m p + m v + m a 1) (13) where s is the umber of idepedet structural parameters, j the umber of joit degrees of freedom, c the umber of idepedet costraits ad d the degrees of freedom of the ed-effector motio. The umber of positios, velocities ad acceleratios are give by m p, m v ad m a respectively. If we cosider m=m p + m v + m a we obtai the familiar formula [10], m= s c d j + 1 (14) 4 Experimetal Set up ad Task Specificatio Sice the first step i our sythesis techique is related to choosig a specific task, the kiematic task selected for the desig is the operatio of a stadard door kob. I order to defie this kiematic task, the door kob graspig ad turig movemet was performed, from a start to ed spatial locatios. Durig the movemet, the subject emulates the opeig of the door motio with a apparatus show i Fig. 1a. The upper limb kiematics at specific poits of iterest are captured by a 3D Motio Capture System (Vico, OMG Plc., UK), available i our Huma Iteractive Robotics Lab at Texas A&M Uiversity. Three ifrared cameras track the positio of each marker relative to a predefied global coordiate frame, with a samplig rate of 100 Hz. Five movig frames are defied at the: elbow, wrist, ad tip of thumb, tip of idex ad tip of middle figers, respectively. Fig. 1b shows the marker attachmet. To oly sythesize the motio of the forearm, the positios chose were trasformed from absolute positios ˆP i to positios local to the elbow ˆP i j = ˆP 1 j ˆP i with ˆP J is the positio of the elbow. For velocities this ca be writte asṗ i j =Ṗ i Ṗ j. The obtaied positios ad velocities were the used as a task for the kiematic sythesis of the multi-figered robotic had. The kiematic specificatio cosists Fig. 1 1a The experimetal apparatus for emulatig the door kob task ad 1b the kiematic model cofigured i the 3D Motio Capture System. (a) (b)
6 6 E. Simo-Serra, A. Perez-Gracia, H. Moo ad N. Robso of set of three spatial displacemets defied by ˆP k = (ψ k,d k ),k = 1,,3, ad the associated agular ad liear velocitiesṗ k =(ω k ;v k ),k= 1, i two of the positios for each figertip. 5 Solvig Numerically The solver used is a updated versio of the kiematic sythesis solver for tree structures [13] updated to support the desig equatios (10) ad (11). The solver is composed of a Geetic Algorithm (GA) paired with a Leveberg-Marquadt (LM) local optimizer. For more details o the solvig approach see [13]. The full equatio system for a multi-figered robot with b figers formed by revolute joits ca be defied directly by maipulatio of the desig equatios, F(S, ˆθ, θ, θ)= ( c P c k θ k ˆP c 1k c Ṗ c k c c 1 i Sk i,c + e ˆθ k i S i,c, θ k i S k i,c, θ k i k=,...,m p c=1,...,b k=1,...,m v c=1,...,b c θ j k [Sk i,c,sk j,c ), ] k=1,...,m a c=1,...,b j=i+1 (15) where b is the umber of braches or figers, c is the umber of joits for a brach c, is the total umber of joits i the structure ad Si,c k are the istataeous axis of the joit i i the brach c for the frame k calculated by (4). A valid mechaism is said to be foud whe F(S, ˆθ, θ, θ)= 0. 6 Results The kiematic structure of the had cosists of a three degree of freedom palm+wrist complex (RRR), ad three figers, each of which is modeled as a two degree of freedom RR kiematic chai as see i Fig. a. This structure was chose for the kiematic sythesis of the task as it has fewer degrees of freedom tha the huma had while havig a o-fractioal umber of required samples. As this paper does ot deal with structural sythesis, a pre-determied topology is used. No additioal costraits were placed o the structure. For this kiematic structure with 9 revolute joits, a total of m=5 samples are eeded as obtaied from (14). The experimetal task cosists of may hudreds of frames of which m p = 3 were selected. For two of them velocity iformatio was also used providig m v =. Due to the ature of the door-kob opeig task, the acceleratios, related to curvature costraits (i.e. slidig motio of the figers alog the door-kob) are fairly small i compariso to the other task specificatios ad were ot take ito
7 Kiematic Sythesis of Multi-figered Robotic Hads for Fiite ad Ifiitesimal Tasks 7 (a) Topology (b) Full System (c) Idex Figer (d) Middle Figer (e) Thumb Fig. : The topology used ad overview of a solutio mechaism foud. accout. Therefore, our task cosists of positios, prescribed at the poit where the figers eed to grasp the door kob, ad velocities, describig the cotact of the figers with the door kob. The resultig equatio system has 90 ukows ad 10 equatios of which oly 7 are idepedet. A set of 50 solutios was obtaied takig a average of miutes per solutio ad eedig a average of geeratios per solutio with a populatio of 100 etities. A selected solutio mechaism of the doorkob task ca be see i Fig.. The thick joit axes are coected by thier lies at the itersectios of the commo ormals of the joits ad the joit axes. The origi is represeted by usig a square ad the ed-effectors are represeted by usig spheres. This solutio show is more compact tha the huma had as all the joits except oe are grouped together ad is able to perform the same task as the huma had. It was observed that geerally the solutios have a similarity betwee the idex ad middle figer, while the thumb has a differet shape, which is similar to how the huma had is desiged. 7 Coclusios This paper presets a ovel dimesioal sythesis methodology for articulated systems with a tree structure usig additioal costraits such as velocity ad acceleratio. It also presets a ew desig for umerically solvig kiematic systems usig these ew costraits, addig upo the previous work of umerically solvig tree structures with kiematic sythesis. The additio of velocity, acceleratio ad other derivatives at the positios allows a better local approximatio of the task motio, as well tasks with cotact ad curvature specificatios. For the selected kob-operatig task, a tree-like robot with three two-joited figers has bee desiged. Kiematic sythesis is just oe step i the desig process, oe that allows you to create iovative cadidates fitted for the kiematic tasks uder cosideratio. Eough solutios have bee foud to suggest that a method to aalyze ad rak those eeds to be a part of the desig process. These results show that the dimesioal sythesis of robotic multi-figered hads is possible. I additio, multi-figered hads appear ot to be redudat whe a task ivolvig several figers is to be performed.
8 8 E. Simo-Serra, A. Perez-Gracia, H. Moo ad N. Robso Ackowledgemets This work is partially supported by the Spaish Miistry of Sciece ad Iovatio uder project DPI Refereces [1] Borst, C., Fischer, M., Haidacher, S., Liu, H., Hirziger, G.: DLR Had II: Experimets ad experieces with a athropomorphic had. I: ICRA (003) [] Ceccarelli, M., Nava Rodriguez, N., Carboe, G.: Desig ad Tests of a Three Figer Had with 1-DOF Articulated Figers. Robotica 4, (006) [3] Cervates-Sáchez, J.J., Rico-Martíez, J.M., Gozález-Motiel, G., Gozález-Galvá, E.J.: The differetial calculus of screws: Theory, geometrical iterpretatio, ad applicatios. Proc. of the Istitutio of Mechaical Egieers, Part C: Joural of Mechaical Egieerig Sciece 3(6), (009) [4] Chalo, M.e.a.: Dexhad : a space qualified multi-figered robotic had. I: ICRA (011) [5] Dai, J.S., Wag, D., Cui, L.: Orietatio ad workspace aalysis of themultifigered metamorphic had-metahad. Tras. Rob. 5, (009) [6] Grebestei, M., Chalo, M., Hirziger, G., Siegwart, R.: A method for had kiematics desig. 7 billio perfect hads. I: ICABB (010) [7] Maso, M., Sriivasa, S., Vazquez, A., Rodriguez, A.: Geerality ad simple hads. Iteratioal Joural of Robotics Research (010) [8] Patarisky Robso, N., McCarthy, J.M.: Kiematic Sythesis With Cotact Directio ad Curvature Costraits o the Workpiece. I: IDETC (007) [9] Patarisky Robso, N., McCarthy, J.M.: Sythesis of a Spatial SS Serial Chai for a Prescribed Acceleratio Task. I: World Cogress i Mechaism ad Machie Sciece (IFToMM). Besaco, Frace (007) [10] Perez-Gracia, A., McCarthy, J.M.: Kiematic sythesis of spatial serial chais usig clifford algebra expoetials. Proc. of the Istitutio of Mechaical Egieers, Part C: Joural of Mechaical Egieerig Sciece 0(7), (006) [11] Rico, J.M., Gallardo, J., Ravai, B.: Lie algebra ad the mobility of kiematic chais. Joural of Robotic Systems 0(8), (003) [1] Selig, J.M.: Geometric Fudametals of Robotics (Moographs i Computer Sciece). SprigerVerlag (004) [13] Simo-Serra, E., Moreo-Noguer, F., Perez-Gracia, A.: Desig of oathropomorphic robotic hads for athropomorphic tasks. I: IDETC (011) [14] Soto Martell, J., Gii, G.: Robotic hads: Desig review ad proposal of ew desig process. World Academy of Sciece, Egieerig ad Techology 6 (007) [15] Ueda, J., Kodo, M., Ogasawara, T.: The multifigered aist had system for robot i-had maipulatio. Mechaism ad Machie Theory 45(), 4 38 (010)
Modified Line Search Method for Global Optimization
Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o
More informationSystems Design Project: Indoor Location of Wireless Devices
Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 698-5295 Email: bcm1@cec.wustl.edu Supervised
More informationCase Study. Normal and t Distributions. Density Plot. Normal Distributions
Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca
More informationConfidence Intervals for One Mean
Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a
More informationCantilever Beam Experiment
Mechaical Egieerig Departmet Uiversity of Massachusetts Lowell Catilever Beam Experimet Backgroud A disk drive maufacturer is redesigig several disk drive armature mechaisms. This is the result of evaluatio
More informationI. Chi-squared Distributions
1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.
More informationChatpun Khamyat Department of Industrial Engineering, Kasetsart University, Bangkok, Thailand ocpky@hotmail.com
SOLVING THE OIL DELIVERY TRUCKS ROUTING PROBLEM WITH MODIFY MULTI-TRAVELING SALESMAN PROBLEM APPROACH CASE STUDY: THE SME'S OIL LOGISTIC COMPANY IN BANGKOK THAILAND Chatpu Khamyat Departmet of Idustrial
More informationBasic Elements of Arithmetic Sequences and Series
MA40S PRE-CALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic
More informationConvention Paper 6764
Audio Egieerig Society Covetio Paper 6764 Preseted at the 10th Covetio 006 May 0 3 Paris, Frace This covetio paper has bee reproduced from the author's advace mauscript, without editig, correctios, or
More informationDetermining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
More informationChapter 7: Confidence Interval and Sample Size
Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum
More informationResearch Article Sign Data Derivative Recovery
Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov
More informationThe analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection
The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity
More informationStatistical inference: example 1. Inferential Statistics
Statistical iferece: example 1 Iferetial Statistics POPULATION SAMPLE A clothig store chai regularly buys from a supplier large quatities of a certai piece of clothig. Each item ca be classified either
More information. P. 4.3 Basic feasible solutions and vertices of polyhedra. x 1. x 2
4. Basic feasible solutios ad vertices of polyhedra Due to the fudametal theorem of Liear Programmig, to solve ay LP it suffices to cosider the vertices (fiitely may) of the polyhedro P of the feasible
More informationCHAPTER 7: Central Limit Theorem: CLT for Averages (Means)
CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:
More informationVladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT
Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee
More information5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
More informationSECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
More informationTrigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is
0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values
More informationEscola Federal de Engenharia de Itajubá
Escola Federal de Egeharia de Itajubá Departameto de Egeharia Mecâica Pós-Graduação em Egeharia Mecâica MPF04 ANÁLISE DE SINAIS E AQUISÇÃO DE DADOS SINAIS E SISTEMAS Trabalho 02 (MATLAB) Prof. Dr. José
More informationAnalyzing Longitudinal Data from Complex Surveys Using SUDAAN
Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical
More informationDepartment of Computer Science, University of Otago
Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS-2006-09 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly
More informationCHAPTER 3 DIGITAL CODING OF SIGNALS
CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity
More informationThe following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles
The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio
More information76 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 9 - NUMBER 1 - YEAR 2011 ISSN: 1690-4524
The Fuzzy ad Compartmet System Cocept for the Commuicatio System takig accout of the Hadicapped situatio M asahiroaruga DepartmetofHuma ad Iformatio Sciece,School ofiformatio Sciecead Techology,TokaiUiversity
More informationNATIONAL SENIOR CERTIFICATE GRADE 12
NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS
More informationDAME - Microsoft Excel add-in for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2
Itroductio DAME - Microsoft Excel add-i for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,
More informationAdvanced Methods for Security Constrained Financial Transmission Rights (FTR)
dvaced Methods for Security ostraied Fiacial Trasmissio Rights (FTR) Stephe Elbert, Steve.Elbert@PNN.gov Kara Kalsi, Kurt Glaesema, Mark Rice, Maria Vlachopoulou, Nig Zhou Pacific Northwest Natioal aboratory,
More informationLECTURE 13: Cross-validation
LECTURE 3: Cross-validatio Resampli methods Cross Validatio Bootstrap Bias ad variace estimatio with the Bootstrap Three-way data partitioi Itroductio to Patter Aalysis Ricardo Gutierrez-Osua Texas A&M
More informationDiscrete Mathematics and Probability Theory Spring 2014 Anant Sahai Note 13
EECS 70 Discrete Mathematics ad Probability Theory Sprig 2014 Aat Sahai Note 13 Itroductio At this poit, we have see eough examples that it is worth just takig stock of our model of probability ad may
More informationSequences and Series
CHAPTER 9 Sequeces ad Series 9.. Covergece: Defiitio ad Examples Sequeces The purpose of this chapter is to itroduce a particular way of geeratig algorithms for fidig the values of fuctios defied by their
More informationChapter 7 - Sampling Distributions. 1 Introduction. What is statistics? It consist of three major areas:
Chapter 7 - Samplig Distributios 1 Itroductio What is statistics? It cosist of three major areas: Data Collectio: samplig plas ad experimetal desigs Descriptive Statistics: umerical ad graphical summaries
More informationQueuing Systems: Lecture 1. Amedeo R. Odoni October 10, 2001
Queuig Systems: Lecture Amedeo R. Odoi October, 2 Topics i Queuig Theory 9. Itroductio to Queues; Little s Law; M/M/. Markovia Birth-ad-Death Queues. The M/G/ Queue ad Extesios 2. riority Queues; State
More informationTruStore: The storage. system that grows with you. Machine Tools / Power Tools Laser Technology / Electronics Medical Technology
TruStore: The storage system that grows with you Machie Tools / Power Tools Laser Techology / Electroics Medical Techology Everythig from a sigle source. Cotets Everythig from a sigle source. 2 TruStore
More informationIn nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
More informationBasic Measurement Issues. Sampling Theory and Analog-to-Digital Conversion
Theory ad Aalog-to-Digital Coversio Itroductio/Defiitios Aalog-to-digital coversio Rate Frequecy Aalysis Basic Measuremet Issues Reliability the extet to which a measuremet procedure yields the same results
More informationAutomatic Tuning for FOREX Trading System Using Fuzzy Time Series
utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which
More informationThe Canadian Council of Professional Engineers
The Caadia Coucil of Professioal Egieers Providig leadership which advaces the quality of life through the creative, resposible ad progressive applicatio of egieerig priciples i a global cotext Egieerig
More informationEvaluating Model for B2C E- commerce Enterprise Development Based on DEA
, pp.180-184 http://dx.doi.org/10.14257/astl.2014.53.39 Evaluatig Model for B2C E- commerce Eterprise Developmet Based o DEA Weli Geg, Jig Ta Computer ad iformatio egieerig Istitute, Harbi Uiversity of
More informationPartial Di erential Equations
Partial Di eretial Equatios Partial Di eretial Equatios Much of moder sciece, egieerig, ad mathematics is based o the study of partial di eretial equatios, where a partial di eretial equatio is a equatio
More informationEvaluation of Different Fitness Functions for the Evolutionary Testing of an Autonomous Parking System
Evaluatio of Differet Fitess Fuctios for the Evolutioary Testig of a Autoomous Parkig System Joachim Wegeer 1, Oliver Bühler 2 1 DaimlerChrysler AG, Research ad Techology, Alt-Moabit 96 a, D-1559 Berli,
More informationHypergeometric Distributions
7.4 Hypergeometric Distributios Whe choosig the startig lie-up for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you
More informationWeek 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable
Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5
More informationLesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig
More informationBiology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships
Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the
More informationEngineering Data Management
BaaERP 5.0c Maufacturig Egieerig Data Maagemet Module Procedure UP128A US Documetiformatio Documet Documet code : UP128A US Documet group : User Documetatio Documet title : Egieerig Data Maagemet Applicatio/Package
More informationA Combined Continuous/Binary Genetic Algorithm for Microstrip Antenna Design
A Combied Cotiuous/Biary Geetic Algorithm for Microstrip Atea Desig Rady L. Haupt The Pesylvaia State Uiversity Applied Research Laboratory P. O. Box 30 State College, PA 16804-0030 haupt@ieee.org Abstract:
More informationChair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics
Chair for Network Architectures ad Services Istitute of Iformatics TU Müche Prof. Carle Network Security Chapter 2 Basics 2.4 Radom Number Geeratio for Cryptographic Protocols Motivatio It is crucial to
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
More informationFOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10
FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 [C] Commuicatio Measuremet A1. Solve problems that ivolve liear measuremet, usig: SI ad imperial uits of measure estimatio strategies measuremet strategies.
More informationCHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
More informationAnnuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.
Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio - Israel Istitute of Techology, 3000, Haifa, Israel I memory
More informationAutomatic Design Algorithm of a Robotic End-Effector for a set of Sheet-Metal Parts
Automatic Desig Algorithm of a Robotic Ed-Effector for a set of Sheet-Metal Parts Avishai Sitov ad Amir Shapiro Abstract Robotic ed-effectors i automated productio lies are specially desiged ad built for
More informationCME 302: NUMERICAL LINEAR ALGEBRA FALL 2005/06 LECTURE 8
CME 30: NUMERICAL LINEAR ALGEBRA FALL 005/06 LECTURE 8 GENE H GOLUB 1 Positive Defiite Matrices A matrix A is positive defiite if x Ax > 0 for all ozero x A positive defiite matrix has real ad positive
More informationDomain 1 - Describe Cisco VoIP Implementations
Maual ONT (642-8) 1-800-418-6789 Domai 1 - Describe Cisco VoIP Implemetatios Advatages of VoIP Over Traditioal Switches Voice over IP etworks have may advatages over traditioal circuit switched voice etworks.
More informationDigital Enterprise Unit. White Paper. Web Analytics Measurement for Responsive Websites
Digital Eterprise Uit White Paper Web Aalytics Measuremet for Resposive Websites About the Authors Vishal Machewad Vishal Machewad has over 13 years of experiece i sales ad marketig, havig worked as a
More informationIncremental calculation of weighted mean and variance
Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically
More informationResearch Method (I) --Knowledge on Sampling (Simple Random Sampling)
Research Method (I) --Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact
More informationCreating an Agile BI Environment
White Paper Creatig a Agile BI Eviromet The rapidly chagig IT ecoomy has iflueced the Busiess Itelligece (BI) systems to look at iovative ways to be equally fast ad flexible. There is a eed to be more
More informationUsing Four Types Of Notches For Comparison Between Chezy s Constant(C) And Manning s Constant (N)
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - Usig Four Types Of Notches For Compariso Betwee Chezy s Costat(C) Ad Maig s Costat (N) Joyce Edwi Bategeleza, Deepak
More informationPROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM
PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics
More information1 Computing the Standard Deviation of Sample Means
Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.
More informationHow To Solve The Homewor Problem Beautifully
Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log
More informationTHE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction
THE ARITHMETIC OF INTEGERS - multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,
More informationChapter 7 Methods of Finding Estimators
Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of
More informationLecture 13. Lecturer: Jonathan Kelner Scribe: Jonathan Pines (2009)
18.409 A Algorithmist s Toolkit October 27, 2009 Lecture 13 Lecturer: Joatha Keler Scribe: Joatha Pies (2009) 1 Outlie Last time, we proved the Bru-Mikowski iequality for boxes. Today we ll go over the
More informationSoving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
More informationINVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology
Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology
More informationBaan Service Master Data Management
Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :
More informationInformation for Programs Seeking Initial Accreditation
Iformatio for Programs Seekig Iitial Accreditatio Aswers to Frequetly- Asked-Questios (from www.abet.org/ew-to-accreditatio/) Assurig Quality l Stimulatig Iovatio This documet iteds to aswer may of the
More informationCS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations
CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad
More informationHere are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio
More information19. LINEAR VISCOUS DAMPING. Linear Viscous Damping Is a Property of the Computational Model And is not a Property of a Real Structure
19. LINEAR VISCOUS DAMPING Liear Viscous Dampig Is a Property of the Computatioal Model Ad is ot a Property of a Real Structure 19.1 INRODUCION { XE "Viscous Dampig" }I structural egieerig, viscous velocity-depedet
More informationPSYCHOLOGICAL STATISTICS
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics
More informationhp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation
HP 1C Statistics - average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics
More informationDomain 1: Designing a SQL Server Instance and a Database Solution
Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a
More informationOverview on S-Box Design Principles
Overview o S-Box Desig Priciples Debdeep Mukhopadhyay Assistat Professor Departmet of Computer Sciece ad Egieerig Idia Istitute of Techology Kharagpur INDIA -721302 What is a S-Box? S-Boxes are Boolea
More informationCOMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S 2 CONTROL CHART FOR THE CHANGES IN A PROCESS
COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S CONTROL CHART FOR THE CHANGES IN A PROCESS Supraee Lisawadi Departmet of Mathematics ad Statistics, Faculty of Sciece ad Techoology, Thammasat
More informationAGC s SUPERVISORY TRAINING PROGRAM
AGC s SUPERVISORY TRAINING PROGRAM Learig Today...Leadig Tomorrow The Kowledge ad Skills Every Costructio Supervisor Must Have to be Effective The Associated Geeral Cotractors of America s Supervisory
More informationAsymptotic Growth of Functions
CMPS Itroductio to Aalysis of Algorithms Fall 3 Asymptotic Growth of Fuctios We itroduce several types of asymptotic otatio which are used to compare the performace ad efficiecy of algorithms As we ll
More information*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.
Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.
More informationRunning Time ( 3.1) Analysis of Algorithms. Experimental Studies ( 3.1.1) Limitations of Experiments. Pseudocode ( 3.1.2) Theoretical Analysis
Ruig Time ( 3.) Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Most algorithms trasform iput objects ito output objects.
More information1 Correlation and Regression Analysis
1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio
More informationOverview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals
Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of
More informationAbstract. Pawel Tadeusz Kazibudzki Jan Dlugosz University in Czestochowa, Poland E-mail: emailpoczta@gmail.com
AN EXPONENTIAL AND LOGARITHMIC UTILITY APPROACH TO EIGENVECTOR METHOD IN THE ANALYTIC HIERARCHY PROCESS: THE IDEA VALIDATION WITH EXAMPLE LOGISTIC APPLICATION problems 85 Pawel Tadeusz Kazibudzki Ja Dlugosz
More informationPattern Synthesis Using Real Coded Genetic Algorithm and Accelerated Particle Swarm Optimization
Iteratioal Joural of Applied Egieerig Research ISSN 0973-4562 Volume 11, Number 6 (2016) pp 3753-3760 Research Idia Publicatios. http://www.ripublicatio.com Patter Sythesis Usig Real Coded Geetic Algorithm
More informationProperties of MLE: consistency, asymptotic normality. Fisher information.
Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout
More informationTHE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n
We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample
More informationQuadrat Sampling in Population Ecology
Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may
More informationINVESTMENT PERFORMANCE COUNCIL (IPC)
INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks
More informationReliability Analysis in HPC clusters
Reliability Aalysis i HPC clusters Narasimha Raju, Gottumukkala, Yuda Liu, Chokchai Box Leagsuksu 1, Raja Nassar, Stephe Scott 2 College of Egieerig & Sciece, Louisiaa ech Uiversity Oak Ridge Natioal Lab
More informationMaximum Likelihood Estimators.
Lecture 2 Maximum Likelihood Estimators. Matlab example. As a motivatio, let us look at oe Matlab example. Let us geerate a radom sample of size 00 from beta distributio Beta(5, 2). We will lear the defiitio
More informationConfiguring Additional Active Directory Server Roles
Maual Upgradig your MCSE o Server 2003 to Server 2008 (70-649) 1-800-418-6789 Cofigurig Additioal Active Directory Server Roles Active Directory Lightweight Directory Services Backgroud ad Cofiguratio
More informationMeasuring Magneto Energy Output and Inductance Revision 1
Measurig Mageto Eergy Output ad Iductace evisio Itroductio A mageto is fudametally a iductor that is mechaically charged with a iitial curret value. That iitial curret is produced by movemet of the rotor
More informationiprox sensors iprox inductive sensors iprox programming tools ProxView programming software iprox the world s most versatile proximity sensor
iprox sesors iprox iductive sesors iprox programmig tools ProxView programmig software iprox the world s most versatile proximity sesor The world s most versatile proximity sesor Eato s iproxe is syoymous
More informationTHE problem of fitting a circle to a collection of points
IEEE TRANACTION ON INTRUMENTATION AND MEAUREMENT, VOL. XX, NO. Y, MONTH 000 A Few Methods for Fittig Circles to Data Dale Umbach, Kerry N. Joes Abstract Five methods are discussed to fit circles to data.
More informationConfidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
More informationEkkehart Schlicht: Economic Surplus and Derived Demand
Ekkehart Schlicht: Ecoomic Surplus ad Derived Demad Muich Discussio Paper No. 2006-17 Departmet of Ecoomics Uiversity of Muich Volkswirtschaftliche Fakultät Ludwig-Maximilias-Uiversität Müche Olie at http://epub.ub.ui-mueche.de/940/
More informationAdaLab. Adaptive Automated Scientific Laboratory (AdaLab) Adaptive Machines in Complex Environments. n Start Date: 1.4.15
AdaLab AdaLab Adaptive Automated Scietific Laboratory (AdaLab) Adaptive Machies i Complex Eviromets Start Date: 1.4.15 Scietific Backgroud The Cocept of a Robot Scietist Computer systems capable of origiatig
More information