IJITCE October 2012

INTERNATIONAL JOURNAL OF INNOVATIVE TECHNOLOGY AND CREATIVE ENGINEERING (ISSN:2045-8711) VOL.2 NO.10 OCTOBER 2012


UK: Managing Editor International Journal of Innovative Technology and Creative Engineering 1a park lane, Cranford London TW59WA UK E-Mail: [email protected] Phone: +44-773-043-0249

USA: Editor International Journal of Innovative Technology and Creative Engineering Dr. Arumugam Department of Chemistry University of Georgia GA-30602, USA. Phone: 001-706-206-0812 Fax:001-706-542-2626

India: Editor International Journal of Innovative Technology & Creative Engineering Dr. Arthanariee. A. M Finance Tracking Center India 17/14 Ganapathy Nagar 2nd Street Ekkattuthangal Chennai -600032 Mobile: 91-7598208700

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IJITCE PUBLICATION

INTERNATIONAL JOURNAL OF INNOVATIVE

TECHNOLOGY & CREATIVE ENGINEERING

Vol.2 No.10

October 2012

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From Editor's Desk

Dear Researcher, Greetings! Research article in this issue discusses about Electric Discharge Machine, Scan Matching Technique. Let us review research around the world this month; The well-known startup supporting website, Kickstarter helps businesses raise money to get their design or idea off the ground and running into reality. The creators of Geode are using this site to raise funds to provide with an LED light designed to illuminate your photos. Watches can be so incredibly boring and with smartphones or mobile devices period, watches really need to step up their ante to grab our attention like they use to. Imagine peering into the abyss; a dark searing black hole that once touched lights up in small LED blue and white dots to show you the time, but you have to decode it since there are no numbers to give you a helping hand. Ever get stressed out when losing your house key or have you had to turn your car around to double check that you locked your door? We all have, but that doesn’t look to be what we will need to worry about in the near future. In March of next year, the very first batch of Lockitron will be available to the public, a keyless way to lock and unlock your door from your phone. You are able to reserve yours now and will not be charged until your Lockitron is ready to go. Do you think it makes us more secure or more susceptible to danger? The majority of us are not as able to get outdoors as we should or need to in order to catch some natural vitamin D from the sun. We work and play from our computers and spend little time outside, so why not bring it indoors? The Sunlight table/desk could be the answer to all of our problems as it could become a true asset to workforces and even added within our homes. The fibre optic grid gains source from another grid that is placed near a window which then feeds the light to the table mimicking what happens outside onto the desk giving you a nature feel within your work environment. It has been an absolute pleasure to present you articles that you wish to read. We look forward to many more new technology-related research articles from you and your friends. We are anxiously awaiting the rich and thorough research papers that have been prepared by our authors for the next issue. Thanks, Editorial Team IJITCE


Editorial Members

Dr. Chee Kyun Ng Ph.D Department of Computer and Communication Systems, Faculty of Engineering, Universiti Putra Malaysia,UPM Serdang, 43400 Selangor,Malaysia. Dr. Simon SEE Ph.D Chief Technologist and Technical Director at Oracle Corporation, Associate Professor (Adjunct) at Nanyang Technological University Professor (Adjunct) at Shangai Jiaotong University, 27 West Coast Rise #08-12,Singapore 127470 Dr. sc.agr. Horst Juergen SCHWARTZ Ph.D, Humboldt-University of Berlin, Faculty of Agriculture and Horticulture, Asternplatz 2a, D-12203 Berlin, Germany Dr. Marco L. Bianchini Ph.D Italian National Research Council; IBAF-CNR, Via Salaria km 29.300, 00015 Monterotondo Scalo (RM), Italy Dr. Nijad Kabbara Ph.D Marine Research Centre / Remote Sensing Centre/ National Council for Scientific Research, P. O. Box: 189 Jounieh, Lebanon Dr. Aaron Solomon Ph.D Department of Computer Science, National Chi Nan University, No. 303, University Road, Puli Town, Nantou County 54561, Taiwan Dr. Arthanariee. A. M M.Sc.,M.Phil.,M.S.,Ph.D Director - Bharathidasan School of Computer Applications, Ellispettai, Erode, Tamil Nadu,India Dr. Takaharu KAMEOKA, Ph.D Professor, Laboratory of Food, Environmental & Cultural Informatics Division of Sustainable Resource Sciences, Graduate School of Bioresources, Mie University, 1577 Kurimamachiya-cho, Tsu, Mie, 514-8507, Japan Mr. M. Sivakumar M.C.A.,ITIL.,PRINCE2.,ISTQB.,OCP., ICP Project Manager - Software, Applied Materials, 1a park lane, cranford, UK Dr. Bulent Acma Ph.D Anadolu University, Department of Economics, Unit of Southeastern Anatolia Project(GAP), 26470 Eskisehir, TURKEY Dr. Selvanathan Arumugam Ph.D Research Scientist, Department of Chemistry, University of Georgia, GA-30602, USA.

Review Board Members

Dr. Paul Koltun Senior Research ScientistLCA and Industrial Ecology Group,Metallic & Ceramic Materials,CSIRO Process Science & Engineering Private Bag 33, Clayton South MDC 3169,Gate 5 Normanby Rd., Clayton Vic. 3168, Australia Dr. Zhiming Yang MD., Ph. D. Department of Radiation Oncology and Molecular Radiation Science,1550 Orleans Street Rm 441, Baltimore MD, 21231,USA Dr. Jifeng Wang Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign Urbana, Illinois, 61801, USA Dr. Giuseppe Baldacchini ENEA - Frascati Research Center, Via Enrico Fermi 45 - P.O. Box 65,00044 Frascati, Roma, ITALY. Dr. Mutamed Turki Nayef Khatib Assistant Professor of Telecommunication Engineering,Head of Telecommunication Engineering Department,Palestine Technical University (Kadoorie), Tul Karm, PALESTINE.


Dr.P.Uma Maheswari Prof & Head,Depaartment of CSE/IT, INFO Institute of Engineering,Coimbatore. Dr. T. Christopher, Ph.D., Assistant Professor & Head,Department of Computer Science,Government Arts College(Autonomous),Udumalpet, India. Dr. T. DEVI Ph.D. Engg. (Warwick, UK), Head,Department of Computer Applications,Bharathiar University,Coimbatore-641 046, India.

Dr. Renato J. orsato Professor at FGV-EAESP,Getulio Vargas Foundation,São Paulo Business School,Rua Itapeva, 474 (8° andar) ,01332-000, São Paulo (SP), Brazil Visiting Scholar at INSEAD,INSEAD Social Innovation Centre,Boulevard de Constance,77305 Fontainebleau - France Y. Benal Yurtlu Assist. Prof. Ondokuz Mayis University Dr.Sumeer Gul Assistant Professor,Department of Library and Information Science,University of Kashmir,India Dr. Chutima Boonthum-Denecke, Ph.D Department of Computer Science,Science & Technology Bldg., Rm 120,Hampton University,Hampton, VA 23688 Dr. Renato J. Orsato Professor at FGV-EAESP,Getulio Vargas Foundation,São Paulo Business SchoolRua Itapeva, 474 (8° andar), 01332-000, São Paulo (SP), Brazil Dr. Lucy M. Brown, Ph.D. Texas State University,601 University Drive,School of Journalism and Mass Communication,OM330B,San Marcos, TX 78666 Javad Robati Crop Production Departement,University of Maragheh,Golshahr,Maragheh,Iran Vinesh Sukumar (PhD, MBA) Product Engineering Segment Manager, Imaging Products, Aptina Imaging Inc. Dr. Binod Kumar PhD(CS), M.Phil.(CS), MIAENG,MIEEE HOD & Associate Professor, IT Dept, Medi-Caps Inst. of Science & Tech.(MIST),Indore, India Dr. S. B. Warkad Associate Professor, Department of Electrical Engineering, Priyadarshini College of Engineering, Nagpur, India Dr. doc. Ing. Rostislav Choteborský, Ph.D. Katedra materiálu a strojírenské technologie Technická fakulta,Ceská zemedelská univerzita v Praze,Kamýcká 129, Praha 6, 165 21 Dr. Paul Koltun Senior Research ScientistLCA and Industrial Ecology Group,Metallic & Ceramic Materials,CSIRO Process Science & Engineering Private Bag 33, Clayton South MDC 3169,Gate 5 Normanby Rd., Clayton Vic. 3168 DR.Chutima Boonthum-Denecke, Ph.D Department of Computer Science,Science & Technology Bldg.,Hampton University,Hampton, VA 23688 Mr. Abhishek Taneja B.sc(Electronics),M.B.E,M.C.A., M.Phil., Assistant Professor in the Department of Computer Science & Applications, at Dronacharya Institute of Management and Technology, Kurukshetra. (India). Dr. Ing. Rostislav Chot•borský,ph.d, Katedra materiálu a strojírenské technologie, Technická fakulta,•eská zem•d•lská univerzita v Praze,Kamýcká 129, Praha 6, 165 21


Dr. Amala VijayaSelvi Rajan, B.sc,Ph.d, Faculty – Information Technology Dubai Women’s College – Higher Colleges of Technology,P.O. Box – 16062, Dubai, UAE

Naik Nitin Ashokrao B.sc,M.Sc Lecturer in Yeshwant Mahavidyalaya Nanded University Dr.A.Kathirvell, B.E, M.E, Ph.D,MISTE, MIACSIT, MEN GG Professor - Department of Computer Science and Engineering,Tagore Engineering College, Chennai Dr. H. S. Fadewar B.sc,M.sc,M.Phil.,ph.d,PGDBM,B.Ed . Associate Professor - Sinhgad Institute of Management & Computer Application, Mumbai-Banglore Westernly Express Way Narhe, Pune - 41 Dr. David Batten Leader, Algal Pre-Feasibility Study,Transport Technologies and Sustainable Fuels,CSIRO Energy Transformed Flagship Private Bag 1,Aspendale, Vic. 3195,AUSTRALIA Dr R C Panda (MTech & PhD(IITM);Ex-Faculty (Curtin Univ Tech, Perth, Australia))Scientist CLRI (CSIR), Adyar, Chennai - 600 020,India Miss Jing He PH.D. Candidate of Georgia State University,1450 Willow Lake Dr. NE,Atlanta, GA, 30329 Jeremiah Neubert Assistant Professor,Mechanical Engineering,University of North Dakota Hui Shen Mechanical Engineering Dept,Ohio Northern Univ. Dr. Xiangfa Wu, Ph.D. Assistant Professor / Mechanical Engineering,NORTH DAKOTA STATE UNIVERSITY Seraphin Chally Abou Professor,Mechanical & Industrial Engineering Depart,MEHS Program, 235 Voss-Kovach Hall,1305 Ordean Court,Duluth, Minnesota 55812-3042 Dr. Qiang Cheng, Ph.D. Assistant Professor,Computer Science Department Southern Illinois University CarbondaleFaner Hall, Room 2140-Mail Code 45111000 Faner Drive, Carbondale, IL 62901 Dr. Carlos Barrios, PhD Assistant Professor of Architecture,School of Architecture and Planning,The Catholic University of America Y. Benal Yurtlu Assist. Prof. Ondokuz Mayis University Dr. Lucy M. Brown, Ph.D. Texas State University,601 University Drive,School of Journalism and Mass Communication,OM330B,San Marcos, TX 78666 Dr. Paul Koltun Senior Research ScientistLCA and Industrial Ecology Group,Metallic & Ceramic Materials CSIRO Process Science & Engineering Dr.Sumeer Gul Assistant Professor,Department of Library and Information Science,University of Kashmir,India Dr. Chutima Boonthum-Denecke, Ph.D Department of Computer Science,Science & Technology Bldg., Rm 120,Hampton University,Hampton, VA 23688 Dr. Renato J. Orsato Professor at FGV-EAESP,Getulio Vargas Foundation,São Paulo Business School,Rua Itapeva, 474 (8° andar) 01332-000, São Paulo (SP), Brazil


Dr. Wael M. G. Ibrahim Department Head-Electronics Engineering Technology Dept.School of Engineering Technology ECPI College of Technology 5501 Greenwich Road - Suite 100,Virginia Beach, VA 23462

Dr. Messaoud Jake Bahoura Associate Professor-Engineering Department and Center for Materials Research Norfolk State University,700 Park avenue,Norfolk, VA 23504 Dr. V. P. Eswaramurthy M.C.A., M.Phil., Ph.D., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 007, India. Dr. P. Kamakkannan,M.C.A., Ph.D ., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 007, India. Dr. V. Karthikeyani Ph.D., Assistant Professor of Computer Science, Government Arts College(Autonomous), Salem-636 008, India. Dr. K. Thangadurai Ph.D., Assistant Professor, Department of Computer Science, Government Arts College ( Autonomous ), Karur - 639 005,India. Dr. N. Maheswari Ph.D., Assistant Professor, Department of MCA, Faculty of Engineering and Technology, SRM University, Kattangulathur, Kanchipiram Dt - 603 203, India.

Mr. Md. Musfique Anwar B.Sc(Engg.) Lecturer, Computer Science & Engineering Department, Jahangirnagar University, Savar, Dhaka, Bangladesh. Mrs. Smitha Ramachandran M.Sc(CS)., SAP Analyst, Akzonobel, Slough, United Kingdom. Dr. V. Vallimayil Ph.D., Director, Department of MCA, Vivekanandha Business School For Women, Elayampalayam, Tiruchengode - 637 205, India. Mr. M. Moorthi M.C.A., M.Phil., Assistant Professor, Department of computer Applications, Kongu Arts and Science College, India Prema Selvaraj Bsc,M.C.A,M.Phil Assistant Professor,Department of Computer Science,KSR College of Arts and Science, Tiruchengode Mr. G. Rajendran M.C.A., M.Phil., N.E.T., PGDBM., P GDBF., Assistant Professor, Department of Computer Science, Government Arts College, Salem, India. Dr. Pradeep H Pendse B.E.,M.M.S.,Ph.d Dean - IT,Welingkar Institute of Management Development and Research, Mumbai, India Muhammad Javed Centre for Next Generation Localisation, School of Computing, Dublin City University, Dublin 9, Ireland Dr. G. GOBI Assistant Professor-Department of Physics,Government Arts College,Salem - 636 007 Dr.S.Senthilkumar Post Doctoral Research Fellow, (Mathematics and Computer Science & Applications),Universiti Sains Malaysia,School of Mathematical Sciences, Pulau Pinang-11800,[PENANG],MALAYSIA. Manoj Sharma Associate Professor Deptt. of ECE, Prannath Parnami Institute of Management & Technology, Hissar, Haryana, India RAMKUMAR JAGANATHAN Asst-Professor,Dept of Computer Science, V.L.B Janakiammal college of Arts & Science, Coimbatore,Tamilnadu, India


Dr. S. B. Warkad Assoc. Professor, Priyadarshini College of Engineering, Nagpur, Maharashtra State, India Dr. Saurabh Pal Associate Professor, UNS Institute of Engg. & Tech., VBS Purvanchal University, Jaunpur, India Manimala Assistant Professor, Department of Applied Electronics and Instrumentation, St Joseph’s College of Engineering & Technology, Choondacherry Post, Kottayam Dt. Kerala -686579 Dr. Qazi S. M. Zia-ul-Haque Control Engineer Synchrotron-light for Experimental Sciences and Applications in the Middle East (SESAME),P. O. Box 7, Allan 19252, Jordan Dr. A. Subramani, M.C.A.,M.Phil.,Ph.D. Professor,Department of Computer Applications, K.S.R. College of Engineering, Tiruchengode - 637215 Dr. Seraphin Chally Abou Professor, Mechanical & Industrial Engineering Depart. MEHS Program, 235 Voss-Kovach Hall, 1305 Ordean Court Duluth, Minnesota 55812-3042 Dr. K. Kousalya Professor, Department of CSE,Kongu Engineering College,Perundurai-638 052 Dr. (Mrs.) R. Uma Rani Asso.Prof., Department of Computer Science, Sri Sarada College For Women, Salem-16, Tamil Nadu, India. MOHAMMAD YAZDANI-ASRAMI Electrical and Computer Engineering Department, Babol "Noshirvani" University of Technology, Iran. Dr. Kulasekharan, N, Ph.D Technical Lead - CFD,GE Appliances and Lighting, GE India,John F Welch Technology Center,Plot # 122, EPIP, Phase 2,Whitefield Road,Bangalore – 560066, India. Dr. Manjeet Bansal Dean (Post Graduate),Department of Civil Engineering,Punjab Technical University,Giani Zail Singh Campus,Bathinda -151001 (Punjab),INDIA Dr. Oliver Juki• Vice Dean for education,Virovitica College,Matije Gupca 78,33000 Virovitica, Croatia Dr. Lori A. Wolff, Ph.D., J.D. Professor of Leadership and Counselor Education,The University of Mississippi,Department of Leadership and Counselor Education, 139 Guyton University, MS 38677


Contents

Experimental Investigation and optimization of Mate rial Removal Rate on Electric Discharge Machine for EN-19 Alloy Steel by Manish Vishwakarma, Vishal Par ashar, V.K.Khare ……......…………...…………..………[1]

Autonomous Navigation by Robust Scan Matching Techn ique by D. Banerji, R. Ray, J. Basu, I. Basak ……[2]


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Experimental Investigation and optimization of Material Removal Rate on Electric

Discharge Machine for EN-19 Alloy Steel Manish Vishwakarma1*, Vishal Parashar1, V.K.Khare1

1Mechanical Engineering Department,M.A.N.I.T,Bhopal-51 (India) *Corresponding author: [email protected]

Abstract :

In this study, experiments were performed to

determine parameters effecting Material Removal rat e (MRR) along with performance measurement analysis with respect to respect to input machining paramete rs. Experimental work was conducted on EN-19 alloy stee l with Copper as tool electrode and EDM oil as dielec tric fluid. The data observed during experimentation has been used to yield responses in respect of material removal rate (MRR). The objective of this paper is to study the influence of operating input parameters o f copper electrode on material removal rate of EN-19 material followed by optimization for confirmation test purpose. The effectiveness of EDM process with copper electrode is evaluated in terms of the mater ial removal rate. In this work the influence of the parameters such peak current, voltage gap, pulse on time, duty cycle and flushing pressure. Material removal rate (MRR) in this experiment was calculate d by using mathematical method. The result of the experiment then was collected and analyzed using Minitab software. This was done by using the respon se surface method and Anova analysis. Keywords : Material Removal Rate, Response Surface Methodology, Regression.

I.INTRODUCTION

Electric discharge machining has extensive applications for manufacturing dies and tools to produce mouldings, die casting, and sheet metal dies etc[1][2].Implementation of EDM process will awaken manufacturing engineers, product designers, tool engineer and metallurgical engineers about unique capabilities and benefits of this process[3].EDM can be used for machining of high precision of all type of conductive material (metals, alloys, graphite, ceramics etc.) of any hardness. In EDM process [4], material removal from work piece is done by means of a series of electrical discharges. This paper presents work on machining by EDM for EN-19 alloy

steel. Certain parameters in EDM process directly

influence the process outputs. Setting appropriate values for such parameters requires the implementation of many machining trials. This leads to time consuming and expensive experimental work. Response Surface Methodology (RSM) has been used for modelling EDM machining of rectangular slot size 15 mm x 20 mm on EN-19 material using copper electrode tool [5, 6-9]. Response surface method is employed to signify relationships between inputs and significant outputs based on minimum number of experiments. This paper presents a mathematical modelling of EDM machining process on EN-19 alloy steel using RSM approach.

II. EXPERIMENTAL WORK

The material used for this work is EN-19 alloy steel

square plate of size 100mm x 100mm x 20mm with density 7.85 g/cm3. The specimen is machined on conventional milling at depth of cut 0.25 mm to produce a plane surface. Copper electrodes (99.97% pure, density 8.96 g/cm3 and melting point of 1086 •C), parallelepiped shaped 20mm x 15mm 100mm is used in the experiment. The machine used is ENC EDM Microcut make with NC control in Z-direction with EDM oil as dielectric medium.

III. EXPERIMENTAL PLAN

Experiments are planned on the basis of RSM technique used in experimental design. The codes are calculated as functions of the range of interest of each factor as shown in Table 1. A central composite design with five input variables having five levels between (• = ±2) coded values and 32 experimental runs were performed. Different variables represented by x1, x2, x3, x4, x5 and their levels are given in Table 2.The coded numbers for the variables used in tables are obtained from the following relationship[10] :


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Code Actual Value of variable -• xmin

-1 [(xmax + xmin)/2] – [(xmax – xmin)/2•] 0 [(xmax + xmin)/2 +1 [(xmax + xmin)/2] + [(xmax – xmin)/2•] • xmax

Table 1. Coded & actual values[10]

The numbers of test required are chosen with the standard 2k full factorial central composite design. CCRd provides as much as information as a five level factorial, requires many fewer tests and has been shown to be sufficient to describe the majority of process responses [11, 12, 13].Each experiment is performed using copper electrode, with a particular set of input parameters chosen randomly from the planned set of experiments. The polarity of the electrode is set as negative. The depth of machining is set at 2mm for all sets of experiments.

Factor Level

-2 -1 0 1 2 x1 10 30 50 70 90 x2 6 9 12 15 18 x3 3 4 5 6 7 x4 5 15 25 35 45 x5 0.1 0.2 0.3 0.4 0.5

Table 2. Coded levels

IV. REGRESSION MODELLING & ANALYSIS

According to the experimental plan a total of 32

experiments are conducted, each having the combination of various values of process variables x1, x2, x3, x4, x5. Each of the responses is fitted into a linear equation represented by:

Y (MRR) = •0 +•1x1 + •2x2 + •3x3 + •4x4 + •5x5---- (1)

Where, Y is the response and x1, x2, x3, x4, x5 are

coded levels of the variables. The coefficients •0, •1, •2,

•3, •4, •5 can be calculated by solving the following equation:

• = (xTx)-1 xTY-------------------- (2)

where, • is the matrix of parameter estimates, x is

the matrix of independent variables, xT is the transpose of X matrix and Y is the matrix of measured responses. Table 3 gives the design matrix and the responses. Analysis of variance (ANOVA) is performed to test the adequacy of the proposed models. The variance ratio denoted by F in ANOVA tables, is the ratio of the mean square due to a factor and the error means square. In this robust design F

ratio can be used for qualitative understanding of the relative factor effects. A large value of F means that the effect of that factor is large compared to the error variance. So the larger value of F, the more important that factor is in influencing the response [14].

In this work from Table 4, Anova table shows the most important factor is input current with 311.69 F ratio and pulse on time with F = 6.59. F ratio of other factors is not significant and has minimum effect.

Run x1 x2 x3 x4 x5 MRR

1 0 0 0 0 0 54.54

2 -1 -1 1 -1 -1 102.00

3 -1 1 -1 -1 -1 120.00

4 -1 -1 -1 -1 1 44.00

5 0 0 0 0 0 74.30

6 0 0 0 -2 0 106.00

7 1 1 -1 1 -1 140.00

8 1 -1 -1 1 1 69.95

9 -1 -1 1 1 1 63.29

10 1 1 1 -1 -1 108.00

11 2 0 0 0 0 59.36

12 0 0 0 2 0 112.00

13 0 0 2 0 0 99.50

14 0 0 0 0 0 131.00

15 0 0 0 0 -2 109.00

16 -1 1 1 -1 1 110.00

17 -1 1 1 1 -1 126.00

18 -1 1 -1 1 1 112.00

19 0 0 0 0 2 56.79

20 0 0 0 0 0 74.30

21 1 1 1 1 1 85.00

22 -2 0 0 0 0 103.00

23 1 -1 -1 -1 -1 122.94

24 1 -1 1 1 -1 125.00

25 0 -2 0 0 0 100.28

26 -1 -1 -1 1 -1 94.30

27 1 1 -1 -1 1 128.50

28 0 0 0 0 0 124.59

29 1 -1 1 -1 1 79.30

30 0 0 0 0 0 130.28

31 0 2 0 0 0 96.79

32 0 0 -2 0 0 101.30

Table 3. Design matrix and Response

Anova is used to test the null hypothesis with

regard to the data gained through experiments


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[16].Empirical models are fitted for the stated responses material removal rate. Analysis of variance is carried out on all the fitted models for a confidence level of 95%. The fitted model of material removal

rate is given by Eq. (3) and its analysis of variance is in Table 4.

MRR = 6.8 + 0.202 Ton + 0.401 Vgap + 1.48 DC + 2.79 Ip + 0.2 Fp ------------------ (3)

Source DF Seq SS Adj SS Adj MS F P Ton 1 393.5 393.5 393.5 6.59 0.016 Vgap 1 34.7 34.7 34.7 0.58 0.453 DC 1 52.5 52.5 52.5 0.88 0.357 Ip 1 18619.4 18619.4 18619.4 311.69 0.000 Fp 1 0.0 0.0 0.0 0.00 0.992 Error 26 1553.1 1553.1 59.7 Total 31 20653.2

Table 4 Anova of MRR

From Equation 3, the factors gap voltage, input

current, duty cycle, pulse on time have an additive effect on the material removal rate where as flushing pressure has minimum impact on MRR. Analysis of the residuals of the model shown in Equation 3 is performed to test assumptions of normality, independence and constant variance figure 1 of residuals. The quantitative test methods mentioned earlier are employed again, and none of the assumptions are violated.

20100-10-20

99

90

50

10

1

Residual

Percent

1501251007550

10

0

-10

Fitted Value

Residual

12840-4-8-12-16

8

6

4

2

0

Residual

Frequency

3230282624222018161412108642

10

0

-10

Observation Order

Residual

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for MRR

Figure 1. Residual plots for MRR

Regression analysis is carried out to ensure a least squared fitting to error surface in Minitab 15 environment. Regression analysis has been performed to find out the relationship between input factors and MRR. During regression analysis it is assumed that the factors and the response are linearly related to each other. The general first order model is proposed to predict the surface roughness over the experimental region can be expressed as Equation 1.

In general, the R2 adj statistic will not always increase as variables are added to the model. In fact, if unnecessary terms are added, the value of R2 adj will often decrease. When R2 and R2 adj differ

dramatically, there is a good chance that no significant terms have been included in the model [15]. For this experiment the R2 value indicates that the predictors explain 95.50 % of the response variation. Adjusted R2 for the number of predictors in the model was 91.0 % both values shows that the data are fitted well. The prediction model was then validated with another set of data.The verification of the tests results for material removal rate is shown in Table 5. The predicted machining parameters performance is compared with the actual machining performance and a good agreement is observed between these performances. In Table 5 process factors are given in terms of natural factors and their corresponding coded factors. In order to assess the accuracy of the prediction model, percentage error and average percentage error were recorded. Percentage of prediction errors is shown in the last column of Table 5. The maximum prediction error was 17.38 % and the average percentage error of this method validation was about 6.87%. As a result, the prediction accuracy of the model appeared satisfactory.

Run

Ton

Vga

p

DC

Ip

Fp

Pre

dict

ed

MR

R

Exp

.MR

R

Err

or(%

)

1 30 15 4 15 0.2 60.68 54.54 11.25 6 50 12 5 25 0.3 98.92 106.00 6.67

11 30 15 6 15 0.4 69.68 59.36 17.38 14 30 9 6 35 0.4 123.07 131.00 6.05 17 30 15 6 35 0.2 125.44 126.00 0.44 23 70 9 6 35 0.2 131.11 122.94 6.64 27 70 15 4 35 0.2 130.56 128.50 1.60 30 70 15 6 35 0.4 133.66 130.28 2.59 32 50 12 3 25 0.3 91.92 101.30 9.25

Table 5. Error Prediction


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7550

50

75

100

0

125

2515

30 045

MRR

Ton

Ip

Surface Plot of MRR vs Ton, Ip

Figure 2. Surface Plot for MRR Vs Ton & Ip

1550

75

100

100

125

2550 5

75

MRR

Vgap

Ton

Surface Plot of MRR vs Vgap, Ton

Figure 3. Surface Plot for MRR Vs Ton & Vgap

1550

75

100

100

125

1530 5

45

MRR

Vgap

Ip

Surface Plot of MRR vs Vgap, Ip

Figure 4. Surface Plot for MRR Vs Vgap & Ip

Figure 2 show that material removal rate increases with the increase in input current. Though, there is low MRR at the low Ip and low Ton which gives direct linear relation but there after it is increased with rise in current and pulse on time. Figure 3 show similar relationship between MRR versus Ton and Vgap in which it clear that there is linear relation of Vgap with MRR. The influence of Fp is minimum on material removal rate. And Figure 4 show the relation between Ip and Vgap. In this graph the high peaks show that the there is increase in MRR with increase in Vgap.

V. OPTIMIZATION OF MRR

The designed experiments involve determination of optimal conditions that will produce the "best" or “optimum” value for the response (MRR). Depending on the design type (factorial, response surface, or mixture), the controllable operating conditions may include one or more of the following design variables: factors, components, process variables, or amount variables. Optimal settings of the design variables for one response may be far from optimal or even physically impossible for another response. Response optimization is a method that allows for compromise among the various responses. The optimization is carried by obtaining the individual desirability (d) for each response combining the individual desirability to obtain the combined or composite desirability (D) thereby maximizing or minimizing the composite desirability and identifying the optimal input variable settings. Here in case of surface roughness optimization, it single response optimization where the overall desirability is equal to the individual desirability.

V (a) INDIVIDUAL DESIRABILITY

As in this case of MRR we need to optimize single

response, so here individual desirability (d) for material removal rate is obtained using the goals and boundaries for MRR that is given in Minitab session window. There are three optimization goals desired as follows:

• minimize the response • target the response • maximize the response

For material removal rate (MRR) it is desirable to

obtain maximum value for better surface finish of material. As response MRR is desired to be maximizing for which determination of target value and an allowable maximum response value is provided to response optimizer. The desirability (d=1) is one for MRR response below the target value: above the maximum acceptable value the desirability (d=0) is zero.

In the below Table 6, y is the response value, T and

L are the target and lower boundaries (i.e. minimum and maximum acceptable values for the response), respectively, and T is the target. For the MRR(y) to maximize by:


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f i(y) =

0 Y< L

y-L/ T-L L • y • T

1 Y > T

Table 6 Maximization of response by individual desi rability

5(b) RESPONSE OPTIMIZATION Goal Lower Target Upper Weight Import MRR Maximum 85 175 175 0.1 1

Table 7 EWR Range Starting Point: Ton = 50; Vgap = 12; DC = 5; Ip = 25; Fp = 0.3

Ton = 90 Vgap = 18 DC = 7 Ip = 45 Fp = 0.5

Table 8.Global Solution Predicted Responses as shown in Minitab session window. MRR = 168.053, desirability = 0.992000 Composite Desirability = 0.992000

CurHigh

Low0.99200D

Optimal

d = 0.99200

Maximum

MRR

y = 168.0534

0.99200DesirabilityComposite

0.10

0.50

5.0

45.0

3.0

7.0

6.0

18.0

10.0

90.0Vgap DC Ip FpTon

[90.0] [18.0] [7.0] [45.0] [0.50]

Figure 5.Optimization Plot

Each response in the research work are expressed

separately as linear and non linear functions of input variables such as Ip, Ton, Vgap, DC, Fp. Now aim is to maximize the response MRR and simultaneously maintain other responses in EDM process. As shown in Table 8 global solution of input parameters is obtained by response optimizer. To determine global

solution of input variables in order to satisfy the above criteria of MRR maximization, it had been solved by Response optimizer desirability maximization function in Minitab 15 environment. The individual desirability for MRR material removal rate is 1. To obtain this desirability, the optimum values factor levels can be set as shown under Global Solution in the Minitab Session window in Table 8. That is, Ip= 45, Ton=90, Vgap=18, DC=7, Fp= 0.5.The optimum predicted value for MRR = 168.053 obtained for 99.2 % desirability. If it is further desired to improve this initial solution, you can use the plot. Move the red vertical bars to change the factor settings and see how the individual desirability of the responses and the composite desirability change.

VI. RESULT AND DISCUSSION

Results show that input current, pulse on time, duty cycle, voltage gap are significant factors for MRR and flushing pressure has minimum effect on the material removal rate of EN-19 alloy steel material. Finally, a mathematical model was developed using multiple regression method to formulate the input current, gap voltage, and pulse on time, and flushing pressure to the MRR.

VII. CONCLUSIONS

From this analysis we can conclude that the most

significant EDM process variable influencing all the stated machinability parameters of EN-19 alloy steel is pulse current. The significance order of other parameters is gap voltage followed by pulse on time and gap voltage. These models can be effectively utilized by the process planners to select the level of parameters to meet any specific EDM machining requirement EN-19 alloy steel within the range of experimentation.

REFERENCES

[1] Payal H S & Sethi B L,”Non-conventional machining

processes as viable alternatives for production with Specific reference to electric discharge machining”, J Sci Ind Res, 62(2002) 678- 682.

[2] Pandey P C & Jilani S T, “Electrical machining

characteristics of cemented carbides, Journal of Material Processing Technology 116 (1987) 77-88.

[3] Singh S, Maheshwari S & Pandey P C, “Some

investigations into the electric discharge machining of hardened tool steel using different electrode materials”, J Mater Process Technol, 149 (2004) 272 277.


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[4] Heuvelman C J, Horsten H J A & Veenstra P C, “An introductory investigation of the breakdown mechanism in electro-discharge machining”, Annals CIRP, 20 (1971) 43-46.

[5] Kuppan, P., Rajadurai, A. and Narayanan, S. (2007)

Influence of EDM process parameters in deep hole drilling of Inconel 718. Int. J. of Advanced Manufacturing Technology, Vol. 38, No. 1-2, pp. 74-84.

[6] Kanagarajan et.al. (2008) Influence of process

parameters on electric discharge machining of WC/30% Co composites. IMechE, Part B: Engineering Manufacture, Vol. 222, pp. 807-815.

[7] Shabgard, M.R. and Shotorbani, R.M. (2009)

Mathematical modelling of machining parameters in EDM of FW4 welded steel. Proc. of World Academy of Science, Engineering and Technology, ISSN: 2070-3740, pp. 403-409.

[8] Chiang, K.T. (2008) Modelling and analysis of effects of

machining parameters on the performance characteristics in the EDM process of Al2O3+TiC mixed ceramic. Int. J. of Advanced Manufacturing Technology, Vol. 37, pp. 523-533.

[9] Habib et.al.(2009) Study of the parameters in electrical

discharge machining through response surface methodology approach. Applied Mathematical Modelling, Vol. 33, pp. 4397-4407.

[10] N.Aslan (2008) Application of response surface

methodology and central composite rotatable design for

modelling and optimization of multi-gravity separator for chromite concentration, Powder Technology,Vol 185, Issue 1, 10 June 2008, Pages 80-86.

[11] Obeng et.al. (2005) Application of central composite

rotatable design to modelling the effect of some operating variables on the performance of the three-product cyclone, Journal of Mineral Processing 76 (2005) 181-192.

[12] Cilliers JJ, Austin RC, Tucker JP(1992) An Evaluation of

formal experimental design procedures for hydrocyclone modelling, 4th International conference on hydrocyclones, pages 31-49.

[13] R.D Crozier. Flotation Theory, Reagents and Ore Testing, New York: Pergamon Press, 1992. [14] Jayswal et.al. (2011)Behaviour of copper and aluminium electrodes on EDM of EN-8 alloy steel

International Journal of Engineering Science and Technology, Vol. 3 No. 7 pp 5492-5499. [15] Mitra et.al. (2011): Pareto optimization of Electro

discharge machining of titanium nitride-aluminium oxide composite material using Genetic algorithm, Advanced Materials Research Vols. 264-265 (2011) pp 985-990.

[16] Parashar et.al. (2010): Statistical and regression analysis

of Material Removal Rate for wire cut Electro Discharge Machining of SS 304L usng design of experiments. International Journal of Engineering Science and Technology Vol. 2(5), 2010, 1021-1028.


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Autonomous Navigation by Robust Scan Matching Technique

D. Banerji1, R. Ray2, J. Basu3, I. Basak4 1,2Scientist, CSIR-Central Mechanical Engineering Research Institute, Durgapur, India

{1dbanerji, 2ranjitray}@ cmeri.res.in 3Professor, Mechanical Engineering Dept., Birbhum Institute of Technology, India

[email protected] 4Professor, Mechanical Engineering Dept., National Institute of Technology, Durgapur, India

[email protected] Abstract—For effective autonomous navigation, estimation of the pose of the robot is essential at every sampling time. For computing an accurate estimation , odometric error needs to be reduced with the help o f data from external sensor. In this work, a technique has been developed for accurate pose estimation of mobile ro bot by using Laser Range data. The technique is robust to noisy data, which may contain considerable amount of outl iers. A grey image is formed from laser range data and th e key points from this image are extracted by Harris corn er detector. The matching of the key points from conse cutive data sets have been done while outliers have been rejected by RANSAC method. Robot state is measured by the correspondence between the two sets of keypoint s. Finally, optimal robot state is estimated by Extend ed Kalman Filter. The technique has been applied to an operational ro bot in the laboratory environment to show the robustness o f the technique in presence of noisy sensor data. The performance of this new technique has been compared with that of conventional ICP method. Through this method, effective and accurate navigation has been achieved even in presence of substantial noise in t he sensor data at the cost of a small amount of additi onal computational complexity.

Keywords —Autonomous Navigation, Laser data, Scan Match, Kalman Filter

I. INTRODUCTION For effective navigation of a mobile robot, pose

estimation of the robot in the environment is an essential task. The purpose of the pose estimation is to keep track of the position and heading of mobile robot with respect to a global reference frame. By using the encoder data, pose of the robot can be computed, but due to various systematic and unsystematic odometric errors like wheel slippage etc, error is accumulated without bound. Practically, within a short period, the pose error becomes so high that it cannot be used for a purposeful

navigation. To overcome this problem, the robots pose needs to be computed with some suitable external reference at a specific sampling time interval. In this context, the relevant external references may be the natural landmarks or a set of distinguishable features present in the environment, which do not change position with time. For acquisition of these relevant data from the environment, various types of external sensors are used by mobile robots. In this work Laser range data has been used for the perception of the environment.

Laser data have been used in various ways in

different techniques for navigation purpose by scientists and researchers. The central issue of all these techniques is the proper correspondence of the data sets in the consecutive time steps. In other words, accurate data association is one of most important issue in this area. The problem becomes more critical when the data sets contain substantial amount of noise or outliers. One strength of Laser scan technique is that the entire sensor scan data may be considered as a feature, no information is lost and any arbitrary shape in the environment can be represented without aggregating all measurements within a given region into a single value [1]-[4]. But this involves processing of large amount of sensor data which make the computational and storing process more complex. The said complexity can be reduced by introducing occupancy grid concept [5-7]. Here data association which is the most critical part of simultaneous localization and view-based metric map building can be performed by various methods. Scan matching is one of the important methods which are dealt with in the present work.

In the scan matching approach, the full batch of data

obtained from local sensors is associated with the global map data in terms of correlations between the two sets. However, the scan matching technique is applied in a variety of ways for mobile robot navigation. Puttkamer E. et al. [8]-[9] explored a cross-correlation based scan matching technique from the derivatives of range-finder


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to determine the position and orientation without any geometric relationship with any feature. Tomono M. [2] proposed a geometric hashing scheme based global localization technique applicable to an environment having many curved features. Lu F. and Milios E. [1] developed a local scan matching approach by LRF data considering the relative pose of the robot. Albert Diosi and Lindsay Kleeman [3] proposed a Scan Matching approach in the polar coordinate system of a laser scanner, thereby eliminating expensive search for corresponding points in other scan match approaches. Censi A. et al. [10] suggested a feature data matching approach in Hough domain. Another approach is the correlation based image intensity based occupancy grid map building [11] where the matching problem can be solved by the establishment of the correspondence between two images transformed from the LRF data using occupancy grid concept. However, the most popular method is the Iterative Closest Point (ICP) algorithm [12-13] based on an iterative process to compute the correspondences between the scans, and then compute the sensor displacement by minimizing the distance error. Besl and McKay [12] described a general-purpose iterative closest point (ICP) algorithm for shape registration based on closest point rule and also proved that the ICP algorithm always converges monotonically to a local minimum with respect to the least-squares distance function. Moreover, regardless of the type of the model, the convergence speed of the algorithm is always very slow when the distance function approaches a local minimum. To accelerate the ICP algorithm, Besl and McKay used a line search method to heuristically determine the transformation variables based on their values in two or three recent iterations. Although this improves the convergence speed near a local minimum, the problem of obtaining a poor solution for the rotation component still exists. It has been observed that, if the rotation is small, the ICP algorithm is good at solving the translation. Again, in ICP method which is based on least square minimization technique, best matching result depends on the fit of the model data with the data. If the data sets having a lot of outliers/noise, the final matching result will be definitely influenced and will produce an erroneous matching. Hence the match technique is less robust. In [3] [13], some pre-processing technique was adopted to reduce the outliers. But, still rejections of all the outliers/noise from the data are very tedious job. So, rather than believing on the fit of all the elements of model with data, it’s better to match by fitting some key elements from the data. Here, key elements may be defined as corner points or interest points. In this paper, an attempt is made to accurately measure the global pose of a mobile robot by a new technique of laser scan matching and to use this measurement for optimal pose estimation.

The deliberations of the paper are organized as follows. In section II, the kinematic model for pose prediction has been stated. Then, the process of image

formation from LRF data, key point extraction and matching has been discussed and finally robot pose has been found by RANSAC method. In section III, the odometric information & measurement information has been fused by Extended Kalman filter for optimal estimation of pose. Subsequently, the testing & experimental results are elaborated in section IV. Finally, conclusion has been drawn in Section V. The scheme of the proposed method is shown in Fig. 1.

Fig. 1. Schematic diagram of the proposed method

II. MEASUREMENT OF ROBOT POSE

For a differential drive system the pose of the robot is

predicted by the following kinematic equations, ( )

1ii1icosSxx ++ θ∆+= (1)

( )1ii1i

sinSyy ++ θ∆+= (2)

θ∆+θ=θ + i1i (3)

where, T

i,i,i }yx{ θ is the pose at ith instant and T

1i,1i,1i }yx{ +++ θ is the predicted pose at (i+1)th instant after

giving the inputs to the driving wheels. The predicted pose vector { T

1i,1i,1i }yx +++ θ will be denoted by '

1iX + in

section IV.

e

RL

nr2

)NN(DS

+π=∆ (4)

Bnr2

)NN(D

e

RL−π=θ∆ (5)

where, D= wheel diameter, B= vehicle width, n = gear ratio, re = encoder resolution (pulse per revolution)

And R,L NN are the inputs to the driving wheels and

these are obtained from encoder data of the left and right wheels of the robotic vehicle at that sampling time.

Now, due to various types of systematic and unsystematic odometry errors like wheel slippage, unequal wheel diameters etc the pose computed by


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equations (1),(2) & (3) is erroneous. Next, the robot pose is measured with LRF data by a new technique in the following part of the section.

The range data acquired from the LRF is transformed

into a local occupancy grid map and then it is converted into an image. It is the fact that all the identical feature points on a particular object may not be usually traced by the LRF in successive scanning. Identical feature points may be within very close proximity, but not exactly in the same position for two successive scans. Moreover, there may be occlusions. These anomalies, in fact, create the outliers. Presence of outliers can be drastically reduced if the features are considered as an area object instead of a point. This is a novel method for reducing outliers. Two sub-images are constructed from the current and previous instant (reference) of LRF data and then key points are extracted utilizing ‘Harris corner point’ detection method [14] as described later on. Based on the two set of key points, current image is aligned with the reference image using Random Sample Consensus (RANSAC) method [15].

A. Construction of Image from LRF data

From the real time navigation point of view, occupancy grid framework is more robust and unified approach compare to any other framework. Also grid concept reduces the possibility of outliers in an image. In this work, occupancy grid framework is adopted, but in different form. Here, the tessellated space is transformed to a gray image considering each cell (a × a) of the tessellated space to be a pixel and the pixel intensities are determined based on whether the cell is occupied or unoccupied. 2D Laser data { }n

1iii,d =θ are

converted from the polar to the Cartesian form as written in (6). Here the assumption is that LRF is mounted at the geometric centre of the robot.

)sin(dyyy

)cos(dxxx

iici

iici

ϕ+θ+δ+=ϕ+θ+δ+=

(6)

where (xc, yc) is the previous robot position derived from the reference image map and (•x, •y, •) is the current increment as shown in Fig. 2. (xi, yi) is the Cartesian global position of the point object

iP which is

acquired by the LRF as ),d(ii

θ in local polar coordinate.

Fig. 2. Encoder based robot pose at tth & (t+•t)th instant

Fig. 3. Uncertainty in grid occupancy

If the LRF data is taken as true then occupied cells

can be calculated considering cell size of (axa) as

1a/)2/ay(int)(gc

1a/)2/ax(int)(gr

ii

ii

+−=+−=

(7)

having robot (LRF) position at cell {0, 0}. LRF data is highly accurate compared to sonar and other acoustic sensors, but still have some noise with standard deviation •.

Therefore, during conversion from cartesian point obtained from LRF data to cell, there is a probability to occupy more than one cell. As shown in Fig. 3, the point marked 1 is so placed that the uncertainty circle is overlapped on two consecutive cells.

The point may lie on any one of the two cells, whereas the point marked 2 is well inside the cell. Here, a simple heuristic rule is formulated as follows:

if, [ σ−+−≤<σ+−− 2/aa)1gr{(x}2/aa)1gr{( iii

&& σ−+−≤<σ+−− 2/aa)1gc{(y}2/aa)1gc{( iii ]

,255)gc,gr(I ii =

else 0)gc,gr(I ii = ;

End

Hence, an image is being formed by considering each cell of size (a × a) equivalent to one pixel having a value either 0 if empty or 255 if occupied, as shown in Fig. 4.

Fig. 4. Plot of 2D Laser data into a tessellated space


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In the figure, white cells represent the regions which are occupied by the features and black region shows the empty regions in the environment.

The number of rows and columns of the image are computed as follows,

1}gcmin{}gcmax{colT

1}grmin{}grmax{rowT

ii

ii

+−=+−=

(8)

and the center of robot is given as

}gcmin{CenY_Robot

}grmin{CenX_Robot

i

i

−=−=

(9)

B. Key point extraction Image is formed by transforming cartesian points

derived from LRF data to image pixel as described earlier. In this transformation, each pixel represents a constant area in XY plane. Size of any object in the image containing number of point features will remain constant though their orientation may change because of different view angle. Hence, there is no scale variation among the features within the images developed in different time instant. Only the orientation has changed depending on the robot’s pose. Therefore, conventional Harris corner detector which is invariant to rotation and computationally very fast, is sufficient to evaluate the stable key points. In this work, Harris corner point detector technique [14] is adopted.

C. Data association by RANSAC method

Data association is one of the most difficult area of map building. Finding the correct correspondences between the previously stored key points and those extracted from current sensor data is a complicated task. Especially, it becomes more challenging in the presence of huge amount of noise to find the correct matches with least error in statistical sense. However, it is true that any image is always having some type of noises and consequently, the key points extracted from the image are associated with positional uncertainty. Though, majority of the points are having Gaussian error, but there is a fair chance that a number of points are extremely deviated and logically these points should be considered as outliers. Otherwise, the accuracy of the result would be critically degraded. By applying RANdom SAmple Consensus these outliers are removed and the pose of the robot is computed indirectly with least error.

Here, localization problem has been formulated as a

hypothesis testing problem, where multiple pose hypotheses are considered and only the pose which can match the maximum number of features or key points in the current sensor data is accepted as the best probable candidate for the pose.

The idea of RANSAC is to generate a set of model

hypotheses by selecting randomly subsets of the

extracted key points containing the minimum number of data points sufficient to define a model. For each hypothesis a set of data points which fits the hypothesized model within a suitable tolerance is determined, called the consensus set. The hypothesis corresponding to the maximum consensus set is considered to be the most probable one. Here, minimum one pair of key points at a time from the image is used to generate model hypothesis. The method has been applied as follows.

1) Initial Key Point matching: For the initial correspondence, the key points on both the current image {Xc,Yc} and reference image {Xr, Yr } are projected to the global image map and then compared. Here, association of key points between current and reference image largely depend on the process noise. With lower process noise, two sets of data to be matched are within close vicinity and the corresponding association problem becomes simple. But in real situation, especially when the vehicle takes turn, large process noise is generated due to skidding. The odometer data is utilized for computing the search space for the correct key point. In this work, tentative key points are associated as follows.

(i) ( ii)

Fig. 5. Tentative keypoints matching between i) Reference & ii) Current Images

For a reference key point, nearest neighbourhood key point in current image is searched out using the euclidean distance as follows:

2

cr

2

crmin)YY()XX(d −+−= (10)

Now searching for all key points in current image

within the range ]wX,wX[xcc

+−∈ and

]wY,wY[ycc

+−∈ around the nearest neighbourhood

key point ( )cc

Y,X in current image is done, where w depends on the process noise. In this method of tentative matching, sometimes, more than one correspondence may be established for a reference key point as shown Fig. 5. The fake correspondences are rejected in the subsequent steps and only the correct match is retained.

2) Computation of the tentative robot poses: Two tentative matches are selected randomly from the tentative matching list and then evaluated the alignment parameters ),Y,X(

cococoφ as follows:


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From the first pair,

φφ−φφ

−

=

j

j

coco

coco

i

i

co

co

Y

X

cossin

sincos

Y

X

Y

X (11)

φφ−φφ

−

=

'

j

'

j

coco

coco

'

i

'

i

co

co

Y

X

cossin

sincos

Y

X

Y

X (12)

where, Pi )Y,X(

ii and Pi’ )Y,X( '

i

'

i are two randomly

selected key point positions on reference image and Pj )Y,X( jj and Pj’ )Y,X( jj

′′ are the corresponding pairs on

current image. By equating two matches, the following equations are derived:

φφ−φφ

=

B

A

cossin

sincos

D

C

coco

coco (13)

where, '

jj XXA −= , jj YYB ′−= , '

iiXXC −= ,

'

iiYYD −=

Now if the tentative matches are correct, then the relative positions of Pi, Pi’ and Pj, Pj’ are invariant and

hence 2222DCBA +≈+ . This method facilitates the

early elimination of wrong matches. From (13), co

φ is

obtained as shown in (14).

+−=φ −

BDAC

ADBCtan

1

co (14)

By substituting this value in (12), )Y,X(coco

are obtained.

3) Computation of support: Now, it is checked how many tentative matches support the tentative robot pose ),Y,X(

cococoθ .

First the current key point positions )Y,X( jpjp in the

matching list are computed for each match k by (15).

−−

φφφ−φ

=

cok

cok

coco

coco

jp

jp

YY

XX

cossin

sincos

Y

X

(15)

Then modified current key point positions are compared with the tentative matching pair of in the reference key point positions. If the deviation is within the limit, then it is considered as a supporting match.

4) Hypothesis with Most support: Steps from 1 to 3 are repeated n times. The alignment parameters

),Y,X(cococo

φ with most support, is the selected hypothesis and it is considered as the best measurement of the robot pose. It is denoted by

1iX + in

the next section, where optimal pose is estimated.

The required number of iterations (n) is calculated from the probability of a good matching • for RANSAC as

nj))1(1(1 ε−−−=δ (16)

where, • is the ratio of false matches to total matches, j is the sample size.

III. ROBOT STATE ESTIMATION

In section III, we have indirectly measured the robot state from Laser data. Similar to the odometer error, the measurement obtained from LRF data is also associated with some Gaussian error, which is called measurement error. By using Extended Kalman Filter, the odometer data & observed data from Laser scan, is fused to compute the optimal estimate of the robot pose. It is done iteratively by prediction and correction of the robot pose. Here, the robot state is predicted by encoder data (equation 1-3) and the state covariance is also predicted as

T

uu

T

viv

'

1iQJJJPJP +=+ (17)

where,

iP is the state covariance at ith instant and '

1iP+

is the predicted state covariance at the (i+1)th instant

respectively.vJ and

uJ are the Jacobians of the

nonlinear state transition function with respect to vehicle state and process noise respectively. Q is the process noise covariance.

Innovation is computed as

1i

'

1i1iXXv +++ −= (18)

where, '

1iX + is predicted pose from equation (1) and

1iX + is the observed pose from equations (12) - (14).

Now, Innovation covariance,

RHHPST

1i1i+= ++ (19)

where, H is Jacobian of observation matrix. The

measurement covariance R is the residual error of the robot pose computed by the method [3] and it is ( )25.0,p1,p1( 0 , where p is pixel i.e., 50mm.

Kalman_gain,

1i

T

1i1iSHPW +++ = (20)

Hence, the update of the robot pose and the

associated covariance are computed by equation (21) & (22) respectively.

1i1i

'

1i1ivWXX ++++ += (21)

T

1i1i1i

'

1i1iWSWPP +++++ −= (22)

After computing the updated robot pose, modified

current sub-image is superimposed on the previous reference image by co-positioning the robot position at both the current and the previous reference images. For superimposing the current image on the global image, the reference image is zero padded if the local image falls beyond the boundary of the reference image at a


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particular robot position. This updated global image is now stored as the reference image for the next iteration.

IV. EXPERIMENTS AND RESULTS

The performance of the proposed technique has been tested in the laboratory by conducting experiments with operational mobile robot. The performance has been compared with the conventional ICP method [16]. Real world data were captured by a Pioneer P3-DX robot with an on-board SICK LRF in the laboratory as shown in Fig. 6. The robot was moved through the working environment in a predefined path such that every possible corner of the environment could be explored. Over 3300 set of LRF and pose data were captured at an interval of 200ms with average speed of 200 mm/s. The global map based on raw odometer and laser data is plotted in Fig. 7 which shows that it is associated with huge process noise.

Fig. 7. Map generated by the data of odometer and LRF

All sample data sets were converted to image

considering grid size 50mmX50mm and matched using ICP [16] and proposed method respectively without any rejection of outliers. Residual errors are computed with the help of the technique used in [3] taking unit weight factor for both the cases. Scan matching using ICP method produces larger errors when vehicle take sharp turn as shown in Fig. 8(i). ICP method has a natural tendency to converge towards local minima. In fact, it’s a drawback of ICP method [1]. In the proposed method, few keypoints may be outliers and also some tentative matching may be erroneous. But, in due course, all the fake keypoints and miss-matching are eliminated in the form of outliers while seeking for maximum support in

RANSAC method and finally converges to actual matching point as shown in Fig. 8(ii).

Residual errors are represented in the form of pixel.

Here one pixel error is equivalent to maximum 50mm error. Residual errors are as per with different golden approach [3][13].

For testing the robustness of the proposed method

random noise is gradually injected to the current LRF data set. It has been observed that up to 43% of noisy

i) ii)

Fig. 8. Match at the instant where (•x, •y, ••) = (43mm, 27mm, 14.63°) by i) ICP (30 iteration), ii) proposed method considering •=0.9, •=0.7, j=2, m=37, matches = 23. Here red dotted points depict the reference feature points whereas blue line for current. Residual error (•x, •y, ••) = (1p, 1p, 0.25°), where p is pixel.

data out of 181 data in each scanning, the proposed method gives almost same result and after that residual errors are unpredictable.

Fig. 9. Generated global image map

The trajectory of robot and the final global map is generated and plotted in Fig. 9. Here, the parameters are taken as 50mm x 50mm grid cell, • = 5 mm.

V. CONCLUSION

The paper presented a new technique of autonomous localization by robust scan matching of LRF data. LRF data has been converted into a grey image and key points of the image have been used as landmarks for localization. By this process, the volume of data to be processed has been reduced considerably. By using RANSAC, the outlier data has been rejected and higher

Fig. 6. Real environment for conducting the test at robotics laboratory


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accuracy and robustness have been achieved. Experimental results has been compared with that of conventional ICP method to show the strength & usefulness of the proposed method.

REFERENCES

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