AN INTERACTIVE ONLINE ROBOTICS COURSE. STEPHEN BRUDER Applied Technology Associates (ATA) 1300 Britt St. SE Albuquerque, NM 87123

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1 Intellgent Automaton and Soft Computng, Vol. 13, No. 1, pp , 2007 Copyrght 2007, TSI Press Prnted n the USA. All rghts reserved AN INTERACTIVE ONLINE ROBOTICS COURSE STEPHEN BRUDER Appled Technology Assocates (ATA) 1300 Brtt St. SE Albuquerque, NM AND KEVIN WEDEWARD New Mexco Insttute of Mnng and Technology Socorro, NM INTRODUCTION ABSTRACT Attemptng to convey concepts and deas n the subject area of robotc manpulators from wthn the confnes of a statc two-dmensonal prnted page can prove qute challengng to even the most gfted of authors. The nherently dynamc and mult-dmensonal nature of the subject matter seems better suted to a medum of conveyance wheren a student s allowed to nteractvely explore topcs n ths mult-dscplnary feld. Ths artcle descrbes the ntal development of an onlne robotcs course textbook whch seeks to leverage recent advances n Web-based technologes to enhance the learnng experence n ways not possble wth prnted materals. The pedagogcal approach employed heren s that of mult-modal renforcement wheren key concepts are frst descrbed n words, conveyed vsually, and fnally renforced by solctng student nteracton. Key Words: Educaton, Manpulator knematcs, Robots, Manpulator dynamcs, Vrtual realty, Symbolc computaton, Electronc publshng Educators have long snce heralded the advent of the Internet-era wheren onlne teachng would become commonplace, however, ths vson of the Internet as an educatonal medum s stll n the embryonc stage. Despte ths fact, varous colloqua [1], conferences [2], symposa [3], and specal ssues [4] have focused on the topc of robotcs educaton and some authors have addressed onlne educaton. Over the past decade, or two, robotcs educaton has bfurcated nto the prncpal sub-categores of moble robotcs and manpulator-based robotcs. The accessblty of small nexpensve moble robots has facltated the prolferaton of these devces n the classroom across a broad spectrum of educatonal levels [5]. Under the auspces of the KISS Insttute for Practcal Robotcs (KIPR), Sten [6] and her colleagues have ventured to expose even kndergarten students to the benefts of hands-on learnng through usng prmarly LEGO-based robotcs. Other authors, such as Wedeward [7], have focused on mddle to hgh school students and have developed complete outreach programs employng moble robotcs as an educatonal tool to expose the students to concepts n engneerng. Unversty level undergraduate [8] and graduate courses [9] reman the most common focus of educators. Many of these, and other smlar efforts, have employed the use of the Internet as a medum [9] to wdely dssemnate robotcs related educatonal materal, share deas wth fellow educators, and reach out to dstant students. Manpulator-based robotcs educaton has not enjoyed a commensurate growth curve due n part to the startup fnancal commtment requred to secure necessary equpment. By developng Internet-based laboratory envronments for teachng, smulatng, and studyng robotc manpulators, authors such as Candelas [10], Labov [11], McKee [12], and Rohrmeer [13] serve to provde a wder audence wth exposure to robots. In a specal journal ssue on robots n educaton, Murphy [14] promotes the use of 105

2 106 Intellgent Automaton and Soft Computng robotcs to teach artfcal ntellgence and presents a compellng argument for the ncluson of hands-on learnng and robot contests [15]. Sutherland [16] descrbes a successful approach to exposng undergraduates to robotcs relyng on a very lmted budget whle seekng a balance between research and fundamentals. Whle many authors have used the Internet n ther robotcs educatonal efforts some have specfcally focused on ths medum as a venue and have developed successful vsualzaton tools. The early vsualzaton tools were basc stand-alone software packages [17, 18], whch were later followed by sophstcated Internet-based vsualzaton tools such as RobotDraw [19], VRML 2.0 Robot [13, 20], Robolab [21], and RIO [11]. The desrablty of employng symbolc manpulaton software tools for analyzng robotc manpulators has been wdely recognzed [22, 23, 24] by numerous authors. However, a means by whch ths could be readly accomplshed over the Internet was not avalable untl qute recently [25]. The motvaton for the onlne robotcs course descrbed heren s derved from a convcton that robotcs educaton should be dynamc, nteractve, and at least three-dmensonal. Concepts n robotc manpulaton nherently nvolve temporal evoluton, and as such, n teachng ths subject the ncluson of a non-statc means of presentng such deas s desrable. In the opnon of the current authors, by solctng student nteracton n the learnng process the educatonal experence s enhanced, as the student then becomes an actve partcpant rather than a passve observer. As a result of the extensve ncluson of deas from spatal geometry beng embedded n the study of robot manpulators, a medum for llustratng these deas whch s capable of showng more than two-dmensonal statc projectons can enhance the vsual representatons used to convey concepts. Also, the goal of promotng ths subject area to the wdest possble audence led to the use of the Internet as a dssemnaton medum. The work descrbed heren seeks to draw on the lessons learned by earler efforts and to synergstcally combne recently avalable enablng Internet technologes to enhance the overall learnng experence and usablty of the materal. The organzaton of the remander of ths paper s next descrbed. Secton 2 descrbes the enablng technologes and gves some examples of ther usage. Secton 3 provdes an outlne of the course materal and focuses on partcular sub-sectons to promote the case for onlne educaton tools. Secton 4 dscusses future drectons and s followed by the overall concluson. 2. THE ENABLING TECHNOLOGIES The three prncpal technologes, whch facltated the development of ths onlne book, address the areas of vsualzaton, symbolc manpulaton, and mathematcal representaton of equatons on the Web. 2.1 Vsualzaton Currently there exst few canddate technologes whch are sutable for modelng and smulaton of robotc manpulators on the Web [19]. The Vrtual Realty Modelng Language (VRML) [26] was selected for the followng reasons: Requres a comparatvely low bandwdth due to small fle szes Provdes a set of basc prmtves for smple objects Inherently supports spatal transformaton and anmaton Supports clent-sde hardware accelerated graphcal renderng Accommodates the ablty to extend the language by addng nodes and scrpts Provdes a future mgraton path to X3D [27] (an XML-based superset of VRML) Supports an external authorng nterface (EAI) whch allows an external Java-based program to control propertes of the VRML scene The language allows an ntutvely appealng herarchcal approach to modelng robots, whch can be performed usng a Denavt-Hartenburg (D-H) type transformaton node. The robot shown n Fgure 1a was created usng the VRML code shown n Fgure 1b. The DHRotatonalJont node was created to extend the VRML language to allow a sngle lne transformaton usng the four D-H parameters wth access to a rotatonal or translatonal (DHTranslatonalJont) jont varable. The ndvdual lnks can be controlled by drvng the jont varables

3 An Interactve Onlne Robotcs Course 107 Fgure 1a. A VRML model of a smple robot arm. Lnk0-LynxArm {} CoordFrame {x_label "X0" y_label "Y0" z_label "Z0"} DHRotatonalJont { alpha 0.0 a 0.0 d 0.0 theta 0.0 chldren [ Lnk1-LynxArm {} CoordFrame {x_label "X1" y_label "Y1" z_label "Z1"} DHRotatonalJont { alpha 1.57 a 0.0 d 0.0 theta 0.0 chldren [ Lnk2-LynxArm {} CoordFrame {x_label "X2" y_label "Y2" z_label "Z2"} DHRotatonalJont { alpha 0.0 a 2.0 d 0.0 theta 0.0 chldren [ Lnk3-LynxArm {} CoordFrame {x_label "X3" y_label "Y3" z_label "Z3"} DHRotatonalJont { alpha 0.0 a 2.0 d 0.0 theta 0.0 chldren [ Lnk4-LynxArm {} Fgure 1b. VRML code requred to produce a robot. CoordFrame {x_label "X4" y_label "Y4" z_label "Z4"} wth jont slders or otherwse (anmaton scrpt or external Java code). The coordnate frames and manpulator lnks are also user-defned (prototyped) nodes. Ths envronment allows the student to alter hs/her vewpont on the 3-D scene and nteract wth the mage to see how the robot moves as the jonts are drven. Support for VRML renderng n standard Web-browsers s provded va one of many freely avalable plug-ns. 2.2 Symbolc Manpulaton Analyzng robotc manpulators can nvolve a sgnfcant amount of tedous mathematcs. The educatonal benefts of havng a student manually multply sx 4 4 matrces of trgonometrc functons once or twce mght be argued to have some redeemng value, however, after the tenth tme the value of

4 108 Intellgent Automaton and Soft Computng such an exercse mght become questonable. As an example, consder multplyng the followng sx matrces wheren, c = cos( θ ( t)) and s = sn( θ ( t)). The lkelhood of a smple error n manually calculatng the result s qute hgh. Furthermore, as ths s typcally the frst step n developng an analytcal model of a robot manpulator, the nterdependency of the analyss does not leave much room for error. Currently, there exst many capable computer-based symbolc manpulaton packages (e.g. Maple, Mathematca, Derve, MathCad, MATLAB, etc), each havng dfferent syntax and requrng a substantal learnng curve (cost not wthstandng). However, only recently have Web-based symbolc manpulaton capabltes become avalable wth applcatons such as MapleNet [28] and webmathematca [25]. Ths approach has the followng benefts over the non-web counterparts: Usage s free to the remote user No learnng curve as the complcated syntax s hdden from the user Compact task specfc code can be wrtten for the problem at hand Can also be used for more tradtonal tasks such as numercal calculatons, graphng, etc When development of the onlne materal was ntated the only optons were webmathematca and an ntal release of MapleNet as Mathcad Applcaton Server and MATLAB Web Server dd not provde symbolc calculaton capabltes. For the work descrbed heren webmathematca was selected, as t seemed to be the most mature and best suted to performng the necessary symbolc calculatons and provdng smplfed results n a compact format. An example of ths Web-based symbolc manpulaton s shown n Fgure 2 wheren a student can use a smple Web-based nterface to determne the often-nvolved calculatons necessary to generate a three-dmensonal rotatonal matrx. Fgure 2. An example of web-based symbolc manpulaton. Developng such onlne symbolc manpulaton materal n webmathematca s somewhat nvolved for all but the most seasoned Web-server admnstrators. Sgnfcant knowledge of Web-server technology, ncludng servlet contaners, HTML forms, Java programmng, and text-edtor based codng of Java server pages s unfortunately necessary. The future, however, holds the promse of tools to smplfy the authorng process.

5 An Interactve Onlne Robotcs Course Mathematcal Expressons on the Web When publshng scentfc materal on the Internet one must face the challenge of how best to represent mathematcal equatons. The Hyper Text Markup Language (HTML) provdes very lmted capabltes (subscrpts and superscrpts) n ths regard and many authors resort to convertng equatons to mages. The Portable Document Format (pdf fles) allows for farly acceptable formattng of equatons, however, ths approach requres a propretary vewer and does not ntegrate well wth other Web-based technology. In 1999 the Math for HTML effort of the W3C organzaton began to develop MathML [29] and the current verson (2.0) has receved natve support n browsers such as Netscape 7.0, Amaya, Mozlla, and others. Internet Explorer 6.0, however, has not yet embraced ths standard and requres the use of a free plug-n. MathML encodes both structure and presentaton of mathematcal expressons for the Web and allows equatons to be cut-and-pasted from a Web document nto other applcatons whle preservng ther mathematcal meanng. By so dong one can take MathML equatons from a Web document nto Mathematca (say) and use them for symbolc calculatons. Ths approach allows smaller fle szes and mproved renderng, both vsual and prnted, whle allowng tght format control. One mght say that MathML s an XML verson of TeX for the Internet. Unfortunately, ths technology s suffcently new that authorng tools are few and far between. Fnally, the R matrx generated, as shown n Fgure 2, s MathML code and hence the output generated by the Web-based symbolc manpulaton tool can be used as a begnnng for further analyss or documentaton. 3. THE ONLINE TEXTBOOK The current verson of the onlne materal can be found at and runs on the Apache Tomcat servlet contaner wth webmathematca 2.0. The source code conssts of XML fles contanng MathML 2.0 coded equatons and the llustratons use VRML 2.0 wth Javascrpt (for nternal NODES) and the EAI 2.0 wth Java for externally controlled smulatons. Users can vew the materal usng: Netscape 7 + a VRML plugn, or IE 6 + a VRML plugn + MathML plugn The outlne of the materal s as follows: Chap. 1 Chap. 2 Chap. 3 Chap. 4 Chap. 5 Introducton 3D Transformatons - 3D Postonal Relatonshps - 3D Orentatonal Relatonshps - Mnmal Descrptons of Orentaton - Poston and Orentaton Transformatons Robot Knematcs - Forward Knematcs - Inverse Knematcs Moton Knematcs - Angular Velocty Knematcs - Translatonal Velocty Knematcs - Summarzng the Approaches for Constructng the Manpulator Jacoban - Sngulartes of the Manpulator Jacoban Robot Dynamcs - Statc Forces and Moments - Lagrangan Dynamcs Appendces The followng sub-sectons provde representatve hghlghts from varous chapters n the onlne textbook. 3.1 Topcs n 3-D Orentaton In ths secton, students are ntroduced to the topc of three-dmensonal orentaton, rotaton matrces, and varous types of three-parameter descrptons of orentaton. The dstncton between fxed-axs (roll, ptch, and yaw) and relatve-axs (Euler angles) rotatons s often a pont of confuson for students.

6 110 Intellgent Automaton and Soft Computng Based on the experences of the current authors, presentng a three-step sequence of rotatons (Fgure 3) nterspersed wth statc mages leadng to an analytcal result allows most students to grasp the fundamental concepts. Fgure 3. A statc mage depctng rotatons. However, by supplementng ths statc presentaton wth an opportunty for a student to nteractvely select the sequence of rotatons (Fgure 4) whle vsually recevng dynamc stmulus on ther actons, the underlyng deas can be renforced. Proceedng one step further, the student s allowed to explore the analytcal result derved by performng varous types of rotatons (e.g. fxed, relatve, or angle-axs) usng ether/both numerc or/and symbolc angles. Ths s done usng the Orentaton Explorer shown n Fgure 2. As the fnal result s dynamcally generated as a MathML equaton t can be cut and pasted nto local software for documentaton or further manpulaton. 3.2 Topcs n Robot Knematcs The topc of robot knematcs typcally begns wth a procedure for assgnng coordnate frames to robot lnks. The most prevalent approach, commonly referred to as the D-H method, utlzes four parameters ( α,, 1 a 1 d, θ ) to defne a sx dmensonal spatal relatonshp between two adjacent coordnate frames by mposng two constrants. The ensung textual descrpton followed by an llustraton, such as shown n Fgure 5, can prove challengng to grasp. By provdng an anmaton of the sequental moton resultng from the transformaton nduced by the four D-H parameters, ther defntons and usage are substantally clarfed. The onlne anmaton shows the moton of a coordnate frame on an mage smlar to that of Fgure 5 (see onlne course Secton 3.1). These deas are then used to assgn coordnate frames to example robot desgns, such as the very low-cost commercally avalable arm llustrated n Fgure 1. The analyss then proceeds to calculate the homogeneous 4 4 transformaton matrx, whch relates the poston and orentaton of the base frame to the tool frame. Unfortunately, ths calculaton typcally nvolves the multplcaton of sx 4 4 matrces of trgonometrc functons. The lkelhood of an error when employng manual dervaton of such results s qute hgh and due to the nterdependency of later calculatons tolerance of such errors s very low. To assst n overcomng ths obstacle a Manpulator Knematc Explorer has been developed usng webmathematca [25] wheren the student can enter the D-H table characterzng the robot of nterest wthout havng to learn the syntax of the symbolc mathematcs program. An example sesson s shown below n Fgure 6 for the case of a commercal robot arm used on a moble manpulator. The secton, whch follows n the onlne textbook, employs smlar tools to address the topc of nverse manpulator knematcs.

7 An Interactve Onlne Robotcs Course 111 Fgure 4. The outcome of an nteractve sesson. Fgure 5. An llustraton of the four D-H parameters. 3.3 Topcs n Robot Dynamcs The fnal chapter n the onlne textbook presents an approach for developng a closed form model of the non-lnear dfferental equatons descrbng the dynamcs of a robotc manpulator, assumng rgd lnks and jonts. Ths topc draws upon most of the man deas prevously developed n the materal and s often not addressed n a frst undergraduate course prmarly due to the tme consumng nature of the calculatons nvolved theren. By presentng a systematc step-by-step approach, based on the Euler-Lagrange equatons appled to the energy of the robot, a straghtforward methodology for obtanng the dynamc equatons s ntroduced. The sx step procedure can be summarzed as follows (please consult onlne course materal for a detaled explanaton):

8 112 Intellgent Automaton and Soft Computng Fgure 6. The Manpulator Knematc Explorer. Step 1: Compute the nerta matrx for each lnk ( I ), n a coordnate system located at the lnk's center of mass (frame { c }, = 1,...,n) Step 2: Construct the D-H table, and thus the forward knematc relatonshps 1 T, 2T,..., nt. Transform these matrces to lnk center of mass coordnates: T( q, q,..., q ) = T( q, q,..., q ) T = 0,.., n 0 0 c c r r From these we can get 0 d, 0 ˆ c z, and 0 c R. Step 3: Construct v r 0 whch can be obtaned by dfferentatng c d r 0, and then transform r 0 c ω nto frame r 0 T 0 r c },.e. ω = R ω. { c c Step 4: Develop expressons for the knetc energy K = potental energy V = n V = 1 r r T, where V = g 0 dc m. n K = 1 1 r T r r T r, where K = ( m v v + ω I ω 2 ) Step 5: Apply the scalar Euler-Lagrange equatons to the Lagrangan L=K-V, = 1,...,n to develop: L() d L() = τ k ; k = 1,.., n qk dt q& k Step 6: Collect the terms and rewrte the expressons generated from Step 5 n the matrx form: r r Dqq ( )&& r r r + Cqqq (, & r )& r r + Gq ( ) = τ To allow students to check the fnal result obtaned and to encourage exploraton, an onlne Manpulator Dynamcs Explorer was developed. To demonstrate the use of the Manpulator Dynamcs Explorer consder the followng example nvolvng a smple two-lnk rotary/prsmatc (RP) robotc manpulator shown n Fgure 7. The D-H table for the robot s gven by: c c c c and

9 An Interactve Onlne Robotcs Course 113 The D-H frames are labeled wth numerc subscrpts and the center of mass coordnate frames are denoted by the subscrpts c. Fgure 7. A smple two-lnk robot. The followng nformaton must be entered nto the Manpulator Dynamcs Explorer as shown n Fgure 8: Fgure 8. Manpulator Dynamcs Explorer.

10 114 Intellgent Automaton and Soft Computng The D-H parameters, the lnk masses, the gravty vector, the Inerta matrces (n center of mass coordnates), and the transformaton matrces from D-H frames to center of mass coordnates. Ths smple example demonstrates the desrablty of employng symbolc manpulaton software. 4. FUTURE DIRECTIONS To accommodate a larger concurrent audence than s currently possble ths onlne book wll be hosted on dedcated servers at Sanda Natonal Labs and New Mexco Tech. The development of an onlne robot bulder whch would allow a student to desgn, analyze, and vsualze robots s currently underway, however, such an effort requres a hgher level of sophstcaton. It s the ntenton of the current authors that ths work serve as a startng pont for more advanced topcs n robotcs and as such wll undergo contnual mprovements. Ths paper s a frst dscusson of the onlne book and precedes ts formal dssemnaton n the classroom. It s the ntent of the authors to utlze the onlne book n the near future and encourage others to adopt t as well. Recognzng the value n assessng the book s effectveness, feedback from these mplementatons wll be collected, reported, and used to mprove the onlne materal. 5. CONCLUSION Ths artcle descrbes the development of an onlne ntroductory robotc manpulator book, whch leverages recent advances n Web-based technologes to enhance the learnng experence. The three underlyng enablng technologes were descrbed and examples of ther usage were gven. A flavor of the approaches employed n ths book was presented and justfcaton for the pedagogcal methodology provded. Further mprovements n these ntal efforts wll rely on the feedback receved from users of ths onlne book. ACKNOWLEDGMENT The authors wsh to recognze the support of the Intellgent Systems and Robotcs Center at Sanda Natonal Labs for facltatng the start of ths effort, Jacquelne Lacoursere as the man Web-content developer, and two NMT graduate students Steven Wasson and Scott Deare for assstance wth the onlne Java and webmathematca examples. REFERENCES 1. IEE Colloquum on Robotcs and Educaton, Robotcs Educaton Sesson, Robotcs Manufacturng Automaton and Control. Vol.14. Proceedngs of the Ffth Bannual World Automaton Congress (WAC 2002) ISORA 2002, ISIAC 2002 and ISOMA 2002, Orlando, FL, USA, AAAI Sprng Symposum on Robotcs and Educaton, Stanford CA, USA, IEEE Robotcs and Automaton Magazne: Specal Issue on Robotcs n Educaton, E. Kolberg and N. Orlev, Robotcs learnng as a tool for ntegratng scence technology currculum n K-12 schools, 31st Annual Fronters n Educaton Conference. Impact on Engneerng and Scence Educaton. Conference Proceedngs, Reno, NV, USA, D. P. Mller and C. Sten, So That's What P s For and Other Educatonal Epphanes from Hands-on Robotcs, n Robots for kds: Explorng new technologes for learnng experences. Drun, A. & Hendler, J. (Eds.) San Francsco, CA: Morgan Kaufmann, K. Wedeward and S. Bruder, Incorporatng robotcs nto secondary educaton, Robotcs Manufacturng Automaton and Control. Vol.14. Proceedngs of the Ffth Bannual World Automaton Congress (WAC 2002) ISORA 2002, ISIAC 2002 and ISOMA, Orlando, FL, USA, 2002.

11 An Interactve Onlne Robotcs Course N. M. F. Ferrera and J. A. T. Machado, RobLb: an educatonal program for robotcs, Symposum on Robot Control (SYROCO 2000), Venna, Austra, Volume: 2, pp , IEEE Robotcs and Automaton Magazne: Specal Issue on robots on the Web, Volume: 7, F. A. Candelas, S. T. Puente, F. Torres, G. Ortz, P. Gl, and J. Pomares, A vrtual laboratory for teachng robotcs, Internatonal Journal of Engneerng Educaton, Volume: 19, Issue: 3, pp , A. Lobov, J. L. M. Lastra, and R. Tuokko, A collaboratve framework for learnng robot mechancs: RIO-robotcs llustratve software, 33 rd Annual Fronters n Educaton, Boulder, CO, USA, G. T. McKee, The development of Internet-based laboratory envronments for teachng robotcs and artfcal ntellgence, 2002 IEEE Internatonal Conference on Robotcs and Automaton, Washngton, DC, USA, Volume: 3, pp , M. Rohrmeer, Web based robot smulaton usng VRML, Proceedngs of the 2000 Wnter Smulaton Conference, Orlando, FL, USA, R. R. Murphy, Robots and educaton, IEEE Intellgent Systems, Volume: 16, Issue: 6, pp , R. R. Murphy, Competng for a robotcs educaton, IEEE Robotcs & Automaton Magazne, Volume: 8, Issue: 2, pp , K. T. Sutherland, Undergraduate robotcs on a shoestrng, IEEE Intellgent Systems, Volume: 15, Issue: 6, pp , R. B. Whte, R. K. Read, M. W. Koch, and R. J. Schllng, A graphcs smulator for a robotc arm, IEEE Transactons on Educaton, Volume: 32, Issue: 4, pp , T. Raz, Graphcs robot smulator for teachng ntroductory robotcs, IEEE Transactons on Educaton, Volume: 32, Issue: 2, pp , M. F. Robnette and R. Manseur, Robot-Draw, an Internet-based vsualzaton tool for robotcs educaton, IEEE Transactons on Educaton, Volume: 44, Issue: 1, pp , VRML 2.0 Robot, Avalable: ROBOLAB, Avalable: J. F. Nethery and M. W. Spong, Robotca: a Mathematca package for robot analyss, IEEE Robotcs & Automaton Magazne, Volume: 1, Issue: 1, pp , K. Srdharan, Teachng computer graphcs and robotcs usng symbolc computaton software, Computer Applcatons n Engneerng Educaton, Volume: 8, Issue: 1, pp , N. Vra and E. Tunstel, Use of symbolc computaton n robotcs educaton, IEEE Transactons on Educaton, Volume: 35, Issue: 1, pp , webmathematca, Avalable: Vrtual Realty Modelng Language (VRML), Avalable: X3D, Avalable: MapleNet, Avalable: MathML, Avalable: ABOUT THE AUTHORS S. Bruder s a senor control engneer wth Appled Technology Assocates n Albuquerque NM, pror to whch, he was an Assocate Professor of Electrcal Engneerng specalzng n Robotcs and Control. He receved a Ph.D. n Electrcal Engneerng from Queens Unversty, Kngston, Ontaro, Canada n 1994 n mult-sensor robotcs.

12 116 Intellgent Automaton and Soft Computng K. Wedeward receved the Ph.D. degree n Mechancal Engneerng from New Mexco State Unversty, Las Cruces, NM, n He s currently an Assocate Professor of Electrcal Engneerng at the New Mexco Insttute of Mnng and Technology, Socorro, NM. Hs nterests are n engneerng educaton, robotcs and complex networks.