Capable. Inexpensive. Easy . Build and program all designs shown, and many, many more.

lJ. Grand Prize 1997 and 1 998 S ME Na tional Student Robot Competitions

"We were up and runninginm

time ,giddy with ideas!... An Erector Set for the Next

Generation!"

Wired Magazine ~

"Iamso pleasedwith the

Robix" [RCS-6]Ipurchased from you two months ago thai have decided to purchase8J

secondas a gift."

John Ruttenberg, Principal Engineer,Silico n Graph ics

"We've had fivesets for over<

yearand ourstudentsarejus:

fascinatedwith these robots.' Michael Janecek, Technoloqy Teacher,Palmer High School,

Palmer, Alaska

"I teach Machine DesigninUP(

Industrial Tech Department81 Illinois State University andf wanted you to know how muct

we have enjoyed yourRobix"

RCS-6 kit...Your kits have been getting quitea lotof pres as Illinois State,Southern tuino University and Illinois Wesley©]

~ are all using them."

Harry McBurney, Illinois Stat®

"We purchased two RCS-6 systems last month and wantt

order another. My class of12

Industrial Electronics studentsa

so enthusiasticabout it thai they areworking overtimeand don'twant to slow them down.

JimRic herson,Ass ociate Prof es sor of Electronics,BILD@

Ridge CommunityCollege, Wey ers Cave,Virginia

Capable. Inexpensive. Easy . Build and program all designs shown, and many, many more.

"Two weeks ago we ran theCommissionerof Educationfrom Japan (!)through our program...showed him the Meccano

curriculumwe were developing,and our US First robot competition entry, trophy, and videos -- ho hum,yawn. But when he and hisentourage saw ourRobix" RCS-6 demo,

they were riveted."

Mic hael H.Bast o ni, Technology Teacher PlymouthNo rt hHig h School, Plymouth, Massachusetts

"No science class or technical college should be without one.

Students at all levels would probably find the RCS-6 to be the best class activityof the year." H

Popular Electronics Magazine,Cover Story ~

'T he mostuser-friendly

equipmentand learning info for students that I have everused."

Dennis Skurulsky,President, Wisconsin Technology Education

~Association

"I'mdelightedwiththe product!

Masterfu/!"

Scott Robbins,Technol ogy Teacher,Winship JuniorHigh

"Our studentshavereally enjoyed workingwithyour kit. It

has givenoursmall-town,very rural studentsachance to see

technologyfromanew perspe ctive." ~ Larry White,Technology CoordinatorlTeacher, Sterling City

High School, Sterling City,Texas

"You sent us one of those

educational robots and we've hadso much funwith it and we've gottenso good that now we'vegone out and bought the

real thing.I don'tthinkwe'dhave 1...._ .. . .

been able to doit without first seeinghow easyit wasto

do. Wereallyappreciate it."

James O'Halioran,Chairman, Radius Toothbrush, Kutztown,Pennsylvania

"Faced with atight deadline we

decided to try the Robix" RCS-6 Controller to operate our

custom-built trade show animatronic. We were running almostas soon as we opened

the box. Great Product!"

Steve Hyman, Hyman Enterprises, Las Vegas, Nevada

U 5 E

R R A V

E

R E V I E

W ~============~

5

!

F E A T U R E 5

o

R D E R 5

The RCS-6 Hardwareincludeseverythingneededto work with your DOS PC-whether it's an oldPC-XTor aPentiumor something in between. The RCS-6comes with6servomotors,controllerincluding an8channel 8bitAID;power supply;20 custom extruded,machined and anodized aluminum "links"(-5'total);steel/nylonjoints , clamps and guides;

"arm" and"breadboard"constructi on bases ;parallel-jaw gripperlwrist assembly;all needed tools,safety goggles and safety markingtape;40 minute video and 80+ page manual including 25+ pages ofillustrated proj ects;laminatedreferencecard;parallel portcable;"props"for robots to handle;and aruggedcompartmented polytool casethatstores it all.

Advanced Design,Inc.

6052N. Oracle Road, Tuc so n, AZ.85704,USA tel:5205442390 fax 520 5750703

I

e~ail: desk~robix.c~m

I

L www.rOb.x.com--.J

The RCS-6 Softwareislayered ,starting with a"no typing" teac hmode;adding macros for loop and nesting;and finally adding C-LanguagecallsfOI logicand use of sensors.Software layersoffers utili'l;

at Grade SchoolthroughUnivers ity level,allowing a singleproduct to serve broad needs.

THE RCS-6 Video isFree

to

Educator~

(others pay just $3 for priority postage), so you can see the setin action and in detail before you buy.

Just call or fax on your letterhead to request a copy.

*

THE RCS-6 Priceis$550complete +$8S/Il. Surprised? Don'tbe --

Wedesign,manu fa ct ure,and sell direct.

And we look forward to hearing from you soon.

YOUR RobOT is WAiriN(j...

Fluffy, The Convertible Robot

by Chris Harriman

Acool upgradefc your Hexapod using the BasicX Microprocessor.

Build Your Own Hexapod Walker Robot - Part I

by George York and Shelley Christopher

How to assemblethe chassis and legsto give the buildera base for conceptualizing the skins describ ed in The Hexapod Walker Comes

to LIFE.

The A * Algorithm - Part IV

byTakAuyeung, PhD

A planni ngmethod for finding the fastest path in a microm ou semaze.

Fourt h in the series by our friend at the Unive rsity of Califo rn ia at Davi s.

•

58

/

!/

FIRST Robotics- A Robot Is Born

by Floyd Painter

High schoo l students engineer and build their competitio n robot - the story of C-Force.

The Hexapod Walker Comes to LIFE - Part I

byGeorgeYork and Shelley Christopher

Spiceup your bot in skins thatmake yours CRA W L.

Intelligent Evolving Soccer Robots - Part II

by Mohammed Jamshidi, PhD,

Denise Padilla, and Marco de Oliveira

Soft comp uti ng- enhancing robots' ability to play soccerat NASA'sACE, University of New Mexi co.

Constructing a Combat Robot - Part II

by Ronni Katz

Second Step: Cuttingand fitt ing, plus L...~_~~~~~_...J whereto get help and parts.

x

f

I

I I I

Cover Design:JulieA. Knudsen.FluffYisa convertibl ewalkin grobot built on a Lyn xm otion H2-KTHexapod/IWalkerkitchassis. It can function auto nomously withoutajoystick, or be operated manuall y with it. Photo byJack Schoofof NetMedia, Inc.

OUR MODULES••••YOUR ROBOTS

The R PC modu Ie is an intelli gen t transce ive rwhic hena blesaradi onetw orklink tobe simply implem ent edbet weena number of dig ital devices.The modul e combines an RF circuitwith processor-intensivelow -levelpack etfo rmattin g andrecoveryfunc tio nality,req uiringonlya simple antennaand5V supp ly to ope ratewithamic rocontroll er oraPc.

SAW controlled FM transmitter and superhet receiver Reliable 30m in-building range, 120m open gronnd

Built-in self-test/diagnostics/sta tus LEDs Complies with ETS 300-220 regulations

40kbitfs half duplex Free format packets of 1-27 bytes

Packetframing and error checking are user transparent Collision avoidance (listen before transmit)

Direct interfa ce to 5VCMOS logic Single5V supply@<20mA

Power save mode Ava ila ble in 418 and 433 Mhz

TheBiM moduleintegrat es alow powe rUHFFM tran s mitt er and matching supe rhe t recei ver with datareco ver y andTX/RXcha ngeover circui tsto providealow costsolutio n toimplem e ntin g abi-direct ion al sho rt rangeradi odata link.

ETS 300-220 tested forEuropean use SAW-cont rolled FM transmissionat -6dBm ERP

Double conversionsuper het receiver -107dBm receivesensitivity Single 4.5 to 5.5Vsupply<15mA(tx or rx)

Reliable 30m in-building range Half duplex data at up to 40kbitfs Direct interface to 5VCMOS logic Fast Imspower up enable for dutycyclepowersaving On-Board dataslice r,supplyswitched and antenna change over

Available in 418 and 433 Mhz

NEW!TheTX2 and RX2rad io tran smitter andreceiver pair ena ble thesimple implem entati on ofa datalink at upto40bit/s at distanc esup to 75m in- bui ldi ngand300mope ngrou nd . Bothmodul es combine fullscree ning withexte nsive intern alfilteringto ens ureEMCcomplia nceby minimiz ingspurio us radi at ion s andsusce ptibilities. TheTX2 and RX2modules willsuitone- to-o ne and multi-nod e wireless links inapplica tio ns inc ludin g car andbuild ingsecurity,EPOS andinve ntory trackin g,rem ote industria l processmonit orin g andcomputer network ing.Bec au se ofthe ir sma llsizeand low power req uireme nts, both modul es are idealforport abl ebatt ery-p oweredapplicat ion s suc hashand-heldtermi nal s.

Trans mitter • TX2 EMC conformant to ETS 300-683

Type Approved to ETX 300-220

Two-stage, SAW controlled, FM modulated at up to 40kbitfs Operation from 2.2to 6V

IOmW on 433.92MHz,ImW on 418MHz Improved frequency and deviation accuracy

Availa ble in 418 and 433 Mhz Receiver - RX2 Double conversion FMsuper het SAW front end tilter,image rejection 50dB

Supply3.0 to 6.0V^@ 13mA

40kbitfs,-F version ,-100dBmsensitivity@ I ppm BER 14kbitfs,-Aversion , -107d Bm sensitivity@ I ppm BER

LO leakage<-60d 11m Available in 418 and 433 Mhz

TYPICAL APPLICATIONS

robotics •environmental monitoring •remote process monitoring•wireless PC printer links •energy management in-vehicle sensing high integrity security• EPOS & stock control•group response systems•data networks

data transfer through hazardous environments •commercial& domestic security• fire alarms•medical alert•mobile panic attack

======- - . '....

For North American sales, contact:

Lemos International Co. Inc.

tel: (508) 798-5004 fax: (508) 798-4782 lemosint@ma.ultranet.com. www.lemosint.com

ROBOTSCIENCE&TECHNOLOGY

from the publisher

The Rob otics Mini-FAQ isnow online tohelp beginners get immersed in robotics withoutbeing swamped byafull-sizedFAQ.Con tribut inged ito r JohnPiccirillo con- ceived it, wrote it, and we'readdingthosepagesto our bigger, better, con ten t-filled web sit e . Bonus: We also put samples of our back issues on line. Check it out at www.Rob otMag.com.

Mypersonal thanks to Jen n ifer Duffek and Vince Wilczynskifor all thehard work assist ing the judges at the FIRST Californ ia regional. That was the highli ght of our year!

The World 's Best Organized Compe tition hosted thou sands ofst ude nts in seven cit ies duringthe last thirty days.Ifyou haven't yet becom einvol ved with theFIRST Foundation,doit now!They are revitalizingwhole commun it ies, re-en ergizing edu- cato rs,and putting exc ite me n t back into learning. (See RS&T Jan, page 6and this issue,page25.)

Most dram ati c result: Some youngfolk saregettingoff the stree ts, burning off their tato os, andgett ing back into class. It's obvious why I'msopleased to suppo rt thisfirst- rate program , For Insp irat ion and Recognition of Scien ce and Technol ogy. See www.usfirst. org,Iand the RS&T staff willsee you at FIRST'snat ional cha mpionsh ip at EPCOT in Orlando,April 22-24.

Sony's Hom eEntertainmentRob ot is oneve ryone 's mind.Tuneinto robotmag.com forthelatest breakingnews.

It painsme gre atly tosay that RS&T isnot yetamonthlymagazine.Sowe aresch ed- uling bi-month ly issues until our advert ising incom e let susprint monthly. Expect your next issuesto arrivein May,July,September,November and December.Related issue:we're add ing a full-timeadvertisingrep to service advertisers'needs.It'sasyn er- gist ic thing.

What's the Status ofyour Su bsc ription?What'sin the next issue ?When will it be sh ipped?Check out our new Frequently Asked Questi ons at www.Rob otM ag.com.

No mod em ?Noproblem! Call usat 888-510- 7728 (US/C an ada) or916-632 - 1000.

Our custo me rservice haspleasantly surprised folk s who need help with their sub- script ions. Sowhenever a magazinedoesn't show up, call or write. (We aren' t abig corp oration with nameless subscribe rs,and we take great pridein making you happy, one reader at a time.)

Robot Science&Technology(ISSN 1096-4754)ispublish ed monthly at 3875 Taylor Road , Suite200 Loomi s, CA 95650;916.660. 0480; Fax: 916.660.0730; info@RobotM ag.com.Subscr ipt ion inquiries U.S. and Canada 888.5 10.7728; all othe rcoun tries916.66 0.0482. Issue price; $5.95 (U.S .) $6,g,~

(C an ada).Subscription rat es:12 issues $39U.S.,$49Cana da (U.S.funds) . Othe rcoun tr iesseepage 49. Per iodi calspostage paid at Rocklin, CAand addi t iona l mail ing offices. POSTMASTER: Sent', cha ngeof add ressto:Rob ot Science&Technology, 235 1 Sunset Blvd#170-253,Rockli n , CA95765.

Contributing Edi JohnPiccirillo,

Kristine Wills,

Contributor Tak Auyeung,Ii Shelley Christo

Chris Harrim The Iconocla Mohammed Jamstf Ronni Kat Marco de Olivei

Denise Padill George Yor I

~

I

j

No part of this publi reproduced bymechanica or electronic process,or electronicrecording, nor aretrieval system, transmitt copiedfor publicor private the written permissionof the~

Advertisers, see _~ 916.632.10 publisher@robotm

Writers, see pa Send manuscri

L

Robot Science & Te

~35 1 Sunset Bouleva Rocklin,CA 9 editor@_robotma~

Subscribers and I!I See page 4 Educators 916.660.0480 fo

byChris Harriman

Fluffy has a split personality. The six-legged walker is a popular walking robot upgraded with an integrated microprocessor system and sonar. When a standard computer joystick is attached, Fluffy is manually controlled. Without the 'stick a panning Polaroid sonar gives it the capability to operate autonomously while exploring its environment. This dual personality is the result of an evolutionary build-and-rest process you too can use to build a convertible.

Fluffy is aLynxmotionH2-KT HexapodII Walker configured withaPolaroid sonarsensorsystem.ThePolaroid scanner is showninitsleft-lookposition.

ROBOTSCIENCE&TECHNOLOGY

For years,abasictruth abo ut walk- ing rob ot kits sta te d that the programmablemicrop rocessorsthat were availablecould nothandlethe servo mo tors and have capacity left fora soph ist icatedsensorsuite. I had built walking robot s, but had usu- ally be en disapp oint ed in their performan ce.The 'drea m walk er 'I always wantedtobuild would avoid obstaclesand not run intowalls.It was a project put off, because the required processin g capa bility was not available. That cha nge d with the introduction of the BasicX mi- cro p rocesso r syste m, which has raised the bar as far as spee d, ran- dom access mem ory andcodespace are conce rn ed. This new syste m's capa bility rekindled myinterest in crea t ingacoolwalking robo t,and I soon found myselfbuilding an H2- KT Hexa/Jod 11 Walker kit from

J

a va!

800.422.4265

Shown here:

RB5Xhaseunit,

RFtransm itte r hcat/light/solmdkit, video,and5-axisarm;

fullyR'«:mbled.

got We've

www.edurobot .com

•'Java'is a registered trademark of Sun Microsystems RB5X' Mby theGeneral RoboticsCorporation'"

Does yourrobot have sonar, infrared, 8 tactile sensors, and voice synt hesis?

Perhaps, but can you program your robot from your web browser?With our new Java-based robot control system, it's as easy as point & click,

copy& paste.TheRB5X^n, baseunitis

alsoavailableasan inner-componentkit.

Twomajor cha nges tothebasic Hexa- podch assis kit were mad ethatwerenot in the instru ctions. First, to increase batter ylife, aGuardianOG-63,6-volt The problem is manageabl e, and the risk of poor align me n tcan beredu ced duringthe cons truc t ion process.This is accomplishe d by insuring that the mov em ent(ran ge of moti on), andser- vomo tor align me n t of all six legs are identical. Do this bybuilding the leg units for one side , an d using on e of them as analign me n tand jointmove- ment gu ideto build the threelegunits for the oppo site side. Finally, once all thelegunits are equalin term s of move- ment an d al ig n me n t, finish the cons truc t ion bymountingthem tothe chass is.

work is required on the pre -cut plasticpieces,but it just involve s rem ov al of flash . Viewed as acol- lection of parts, the Hexa/)()d kit lo oks com p le x , but thank s to good eng inee r- ing,the assembly pro c e ss is very st ra igh tfor wa rd.

You will spen d a The Guardian DG -63batteryismountedbetween Fluffy'smain lot of time bolt- deck !>lates.This viewshowstheservomotors,controllerboard and ing togethe rand theback ofthePolaroidsonarsensorsuite.

align ingassemblies because of the she er three ampe re- ho urgel-ce ll batter ywas number of joints that require bolts, used . It is mounted over the robot's wash ers, and nuts.The cruc ialste p in cen te rof gravi ty bet weentheupper and the assem bly processisthe align me nt. lowe r chass is plat es. Second,a pan n ing It is very important to be sure that all Polaroid sona r sensor from an old in- thejointsmove smoo th lyand the ser- sta n tcame ra was adde d. An identical vom otor s are properly inst all ed an d sensor, the R14-Sonar1 is ava ilableas aligne d . Without proper joint move- a pack age (sensor,driver board , an d ment an d align me n t of the leg an d interface cable ) from Acroname, Inc.

sho ulde r joints in relati on to the ser- (seeResources) . vom otors, the Hexapodwill not walk

stra igh t. It will stagge ror drift to one side , which isunacceptabl eifyou plan touse adeadreck oningnavigati on sys- tem.

Thanks to a well -written instru ction manual,most robo t icists will not hav e any trouble with the build-up of the Hexapodchass is.Some lightfinishing

Under The Hood

Lynxmotion,Inc.IntegratingtheBasicX syste m with the kiteasily metthepro- cessing requirements of the walk er servo mo tors, and provided the add i- tiona lcapac ity need ed torun obstacle avoida ncesenso rs.

Ittookabouttwo weeksto builda walk- ing robo t thatdidn'tstagge r, which in itselfwas areal accomplish me n t. The fact thatI was able to control thewhole thing withone BasicXprocessor on my owncusto m- builtcontrolle r board was icing onthe cake . Infact, the robo t is a conve rt ible because of the approa ch tak en toperfectitswalking ability.On thefirst custo mcontro ller board, ajoy- stic k port was used to aid in the progra m m ing of the walk in g algo - rithm s. Using the joyst ic k to test algor ith msan d makerequired cha nges was easy. Once the walking program was perfec ted , the final con t ro lle r boardwith add it iona l input/output ca- pa bilit y for a senso r su ite was constructed .At thispointin its evolu- tion,the robot wasmanuall y controlled and a very com pe te nt walk er, with expa n da bility,

TheH2-KTHexapodIIrobo t is awell - design ed six- legged walking robo t kit thathas alot to offer the robo t icist. For locom otion ,it usestwo servo mo tors to con tro leachof itslegs, and walk swith atripod gait. The cen te r legfrom one side ,and the front and back legsfrom the oppos ite side move as a set , while the ot he r three legs remain on the ground forbalanc e.TheHexa/Jodis able to walk forw ard or backw ard , and can turn left or right within its own foot- print. The robo t is abo ut 12 inches long, 11 incheswide, almos t 6 inches tall an d has abo ut 3 1/2 inches of ground clearance.

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ROBOTSCIENCE&TECHNOLOGY

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comp ilingan d downloading your pro- gra ms . The BasicX progr ammi n g language closelymirrorsthat ofVisual Basic.In fact , most pro gram sthat run on theBasicXch ip would runeq ually well on yourBasicfor Windows.

Using BasicX to control a servomotor

Figure1.Polaroid Sonar Mounting Assembly.

A servo motor is comp risedofadirect- current (DC) motor, apositi on sensor on the sha ft, a gear-red uc t ion set, and an integrat ed circ uit.To ope ra te a ser- vomo tor you need two things, power (between4.5 and6.5volts )andadata signal. Theimpor tantelements ofthe servo moto r'sdata signa lare:

• The positi on signal- the high sig- nal(+5v). Thedurat ion of thishigh pulse can be anywhe refrom 1-2 ms.

Thisisthe com ma n d that tells the servo mo torwha t posit ion to be in , or move to, if it 'snot alrea dy there.

• The refresh rate - the tota l length of time it tak es the data signa l01

pulse st rea m to go fromsta rtofhigh , throu gh to low, an d back to sta rtol high again. It is typicall y between 10-20msin length .

~Front piece

~ Bottompiece Bad piece---7

Tobuild Fluffy,you will needtheBasicX Development System.Thisis akit with all the mat er ials required to program the ch ip. It con ta ins one BasicXch ip and devel opment/downloaderboard , as well as softwa re for creat ing, ed it ing ,

The controller board,showing thePolaroid sonarsensorconnectorsat thelowerleftandslightlyleft ofcenterat the top,theBasicX Chip mountedin the centeroftheboard,thethirteen servomotor

connectors(sixat thetopand sevenat thebottom),andthe joystickconnectorat theright.

SideviewofSonarbrack etMounted onaservo

- -- ----r- - - - -,---.J <::----Hexapod upper Bottompiece

2.15" - - ----'

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The BasicX Chip

The BasicXis a sing lech ip Basicpro- gra m ma b le micr o c ontr oll er that requires on lyan exte rnalcrystalanda 3-6 volt power source to run. It was usedfor thisprojectbecau seit has:(1) tremendou s spee d ,65,000 lines ofBa- sic cod e per secon d, (2) a large elec tro n ica llyerasa ble programmabl e read on ly mem ory(EEPROM)foruser code sto rage , (3) rand om ac c ess mem or y(RAM),(4) multitaskingca- pability, and (5) 32 input/output(I/O) pins.This ch ip incorporat esnew an d upgradedtechnologicalfeatures absen t from man y of its predecessors.

Thepanning sona rsuite wasaddedby cutt ing asq ua re holein theupperplat e an d add ing a 13thservo mo tor to the upperfront of theHexapodchass is. The th ree piecesthat makeup themount- ing assem b ly for the senso r an d its driver board wer e crafte d from some of thelefto ver kit plasti c .Thesewere supe r-gluedtogethe r (seeFigure 1)and fast ened tothe top of the servo mo to r's con trolhornwith two sma llscrews.

M:I ROBOTSCIENCE&TECHNOLOGYI (continued onpage 35)

Build Your Own Hexapod Walker Robot! ^{Part I}

by George York an d Shelley

J.

Chr istopher

Constructing a robot doesn't h ave to be co mp lica ted.

Build-it-yourself robot k its are availab le for robot icists at every level, from t he novice t o the expert . To prove that just about anyone can build the ir own bo t, t his series will provide thorough ste p-by-ste p instruct ions on constructing an affordab le, introdu ctory syste m.

sho rt , with fullste p- by-step instru ctions onskinfabricat ion.

You can build theHl-KThere, and bring itto lifethere.

This art icle isPart 1of the basicH1~KTconst ruct ion pro- cess. Part 2 of the series wil l focu s on the elec tro n ics, includingtheInfrared ProximityDet ector (IRPD), and will explain programming andsoftware.

Before beginning any constr uct ion projec t, inve n to ry the mat eri als andverify that allof the piecesare included in the kit.Thecon stru cti onprocess will begin with themechani- calsect ion , which includes the servos and hardw are pieces (Part1).

Sandpaperoremery board Xacto knife Double-s ide dFoam Tape

(Scotch / 3MHeavy Duty Mounting Tape foundat most officesupplystores)

Straight-edge MarkingPen Phillips screwdrive r CyanoacrylateGlue

(super glue) Support Structure

Materials Required to Get Started

It isuseful to categorize these sect ionsasPart1and 2 sothat theproject can be coord ina ted. Thiswill help theinexperi- ence d robo t icist to visua lizewhe re theywillstart and how they will finish . Be care-

ful NOT to rem ove the compo n e n ts that are on the an ti-sta tic pad in the bag.Sta t icsens it ivesemi- con d uc to rs can be damagedbyimproper han- dling.

Since this proj ect is run- ning con currentl y with the skin fabricati on series, some proceduralmodifica- tions were required. For simplifica t io n purpo ses, the Hexapodfabricati on Since thisHexapodhasthepot ential to resemble an alien

insectoid creat ure , this construct ion series will run concur- ren tly with art icles on how to bring your bot to life by crea t ing roboticoute r coverings, or "sk ins." In that series (see The Hexapod Walker Comes ToLIFE on page 58), the H1~KT will becom e a Mantid Hexaptera,or MH6for To getyouth in king , theH1~KTkit provid es allof the com- pon en ts necessaryto assembleafullyfuncti on alrobot.Also provided isan illustrat ed assembly manu al. However, any robot icseng inee r will admit that robot construct ion isre- pletewith modifi cati on andexperime n ta t ion. In this series, we will deviate from the assembly manu al, but the result willsti llbe a fullyfunc tio na lHexa[Jod Walker.

Jim Frye of Lynxmotion, Inc. explains on their web site (lynxmotion.com)tha tthe ir kits are design edforpeopl ewith some mod el orelectron ic kit assemblyexpe rience ,and they know of high schoolstude n tsand parent/child team swho have successfullyassembled their kits.Lynxmotion'sgoal is to man ufactureand distribute affordab le, high qualitykits to un ivers it ies,high schoo ls, and othe r robo t icists. Their kitsare design ed to filla gap in the educa t iona l, hobb y or 'person al' roboticsarena ,and they caut ion thattheirproject s havebeen known to spa rk imagin ati on s aswell as to make one th ink .

We will be build ing Lynxmotion, Inc.'s HI~KT Hexapod Walker Irobot, provid ing det ail edinstru cti ons and illustr a- tio ns tha t will guide you throu gh every fac et of the fabricationprocess.How to modifythe HexapodWalkerby adding an Infrared Proximit yDetector (IRPD) which allows the robottoreact to its env iron me nt , willalso be covered.

ROBOTSCIENCE&TECHNOLOGY

3. Identify one side of the bod v st ruc t ure as the "top" side andone side as the "bo tt o m."

4. On the bottom of the bod y struct ure , measur e 3-3 /8s inch es(85.7mm) from thenose of thebod y(thenar ro w end ) toward the cente r of thebody.Withamarkingpen, mark thispoint.Draw a line perp endi cul ar to the longi- tudinal axisacross the str uc t ure, at themark.Thismea- sure me nt will be the refer ence for theplacem ent of the cen ter servo mo to r.

PhotoI

begins her e wit h the cons t ruct ion of the HexajJOd Walker bod y and legs, and the attac h me n t of the servo mo tors. As the mechanical struct ure tak es form, the fabrica tor will see whe re and how the elect ronic circu its will fit for Part 2.

Whenthe st ruc t ure is comple te it will be available for mea- sure me ntan d visua lizat ion ofwhat the "creat ure" will look likethat isbeing con te mpla te dfor the compa n ion art icle.

5. A second refer en ce line isrequired on thebottomof the bod y st ruc t ure. Thistime,measure I inch(25.4mrn )from thetail of thebod y(the wide en d) tow ard the cen te rof thebod y.Withamarkingpen ,place amark at thispoin t.

Now draw an o the r perpendi cul ar line across the struc - ture at the mark.Thisreference line will help with the placem ent oftheright and left servo mo tors (seePhot o 2).

Setting the Servomotors to Mid Position (90 degrees)

Photo 3

A First Ste p gu ide is provided for set t ing the servo mo tors to mid positi on by usin gthemicrocontroll er (the servo mo- tor s m ust be in mid , . . . - - - , positionbeforeattaching

them to the robo t body st r uc t u re ) . The se in- st r uc t io ns co u ld be followed, but thatwould require be ginnin g the cons t r uc t io n pro c ess with the elec tro n ics as-

sem b ly. Below is aI_ IIIIIIJIII"

sh or tc u t that you can use. Have ava ilable the

servo mo to rs, plastic cou-

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• • • • • • • •• • • •

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piers, plasti c horns, and

mounting screws. (Thismay look like man y ste ps, but the processisreallyquite easy.)

I.Tak ethe plast ic pan el that hastheHexapod'spiecesma- ch ine d into it an d cut the pieces from the pan el usin g a sharpXactoblade.Cutt ingout thepiecesis suggeste d he- causesnap pingortwistingthemfrom thepan el could dis- tort or ruin their sh ape. Once rem ov ed fro m the panel, ther e sho uld be eigh t piecesthatwill form thehinges, six legs, and three pieces for thehori zon tal leg assem bly (see Photo I). (NOTE: Donotlose anyofthesepieces!Extra pieces are not included in the kit and every piece has a spec ific purpose. )

2. Oncethe partsare rem o ved, theywill req u iresome clean upatthepoints whe re theywer e con nec te dto thepan el.

With a pieceofsand paper,or an eme ry hoard , sand the edges of thepiecesuntilsmoot h.

Getting Started

2. Se lec t a co uple r (the sma ll, white plastic piec e that is sq uare , but hasacirc ular hole in themiddle) and pressits round back on to the servocoup linggea r. By hand, rotate the attac he d coupler on the servo coupling gear clock- wise until the gear sto ps.When the gea rsto ps, remove theco upler by gently pulling it from the servo coupling gear. Thisprocess sets the servoat

a

^degrees.

I. Hold a servoso that the coup linggear (thewhiteround piece protruding from the serv o ) is at the top. The manufacturer 'slab elislocat edbeneaththe servocoupling gear (seePhoto 3).

Centering Two Servomotors

Photo 2

• ROBOTSCIENCE&TECHNOLOGY

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3. St ill holding the servo , place the coupler back on the servo coup ling gear, with the coupler's edge d sides as near to par allel as possible, to the lon g sides of the servo. The "op en" sides of the couple rare nearly par allel to the top and bottom of the servo (see Photo4).

4. Repeat ste ps 1 through3 above on one more ser- vomoto r. The third ser- vomo tor isreserv ed for later.

Photo4

bemark ed with "cen te rservo" and "leftservo" st icke rs for identification purposes.

Aligning the Right Servomotor

1.Thethirdservo moto r willfunction astheRIGHT servo. Presstheround back ofacoupler onto the servocoupling gear. Rotat e the attac he dcoup leron the servo coup ling gear counterclockwi se untilthe gea r sto ps. Rem ov e the couplerby gentlypullingitfrom the servocouplinggear.

Thisprocesswillset theright servo mot or at0degrees.

2. St illholdingthe servo , placethe coupler back on the servo couplinggea r, with thecoupler'sedge dsides asnear par- alle lto the sidesof the se rvoaspossibl e(the opensidesof thecouplerwillbe nearl yparall el to the topand botto m of the servo. )

Aligning the Center Servomotor

1.Selectoneof thetwo servo mo to rsset at 0 degree sto func- tion asthe CEN T ER servo . Byhand ,rotat ethe coupler coun te rclockwise90 degree s(until theedge dsidesofthe couplerare parallel tothe top and bottom sho rt sides of the servo ).

2. Select aplasti c horn and place iton the coup lerso that the horn is poin t ing totheleft. Thehornhas aridged or

"teethed" side, which willdirectly engage thecoupler.This allows foranadjusta ble fit that willseat properlyandse- curely. Be sure that thehorn isplaced on thecoup ler so that theflat endof thehornisflushwiththeright edgeof the coupler. Thiswillgive thehorn eno ugh clearanceto functi on onceattac he d to the robo t body.Fastenthehorn onto the coupler witha screw using aPh illips screwdriver.

Tightenuntilsn ug, but nottootight(minoradjustme n ts maylat er berequired) (see Phot o 5).

Aligning the Left Servomotor

1.The secondof thetwo servo moto rs thatwere setat 0 de- grees will func t ion as the LEFT side servo. Rot at e the couplercounte rcloc kwise 90 degrees(unti lthe edgedside isnowparall elto the top and bottom of the servo ).

2. Place a plasti c horn on the couplerso that the horn is pointing left (as in ste p 2 above ). HOW EV ER,be sure that thehorn isplaced on the couplerso that the screw attaches the horn at the center of theadjustableopen- ing.Fasten thehorn onto the coupler with a mounting screwand tighten untilsn ug.Donot over-tighten.

Place the cente rand left servo moto rs aside an d be sure that they can be identified later.Itis suggested thatthese servos

3. Rot at ethe couplerclockwi se 90 degrees.

4. Place a plastic horn on the coup lerso that the horn is pointingto theright .Attachthehorn to the coup ler. Be sure that the screw is placed at the cente r of the open adjustme n tof thehorn.Attachuntil sn ug.

5. Mark the right servo for identificati on.

Attaching the Servos to the Robot's Body Structure

There are now three servos set at 90 degrees read y to be attached to thebottom of thebod y struc ture.

1. Placethecente rservoaftof thelinethat wasdrawn at3- 3/8s inch es. The servo 's horn will be pointing upward.

Place the side of the servo that is oppos ite the attac hed hornat the line. The sideof the servo that hasthehorn attached will be facingthe back -end of the robot bod y

Photo5

ROBOTSCIENCE&TECHNOLOGY

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(see Photo 6). The servo must be centered at this line.

Attach the servo in placewith the doubl e-sticktape . 2. Place theleft servo and right servo on thebody str ucture

for atrialfit.Each servo 's horn coupler must pointdown- ward (with therobot resting on itsback).Placethemfor- ward of the line that wasdrawn 1 inch from the back of the robot bod y structure. Laythem on their side,so that thehorns poin t down andappea r to"han g" over the side of the bodystr ucture.

3. Oncetheservos havebeen positioned sat isfactor ily, mark theirplacem entwithamarkingpen. Attach theservos to thebod y structure with doubl e-stick tape.

4. When the servos have been taped in place as sho wn in thephoto graphs,placethebod ywithattachedservos on a suppo rtstructure,suchas alarge rolloftape.The servo- motors sho uld be touch ing the suppo rt structu re so that the adjustable horns are not support ing the en t ireassem- bly.The servossho uld nowbe "h ang ing" underneath the upsidedown bod y str ucture.

Constructing the Vertical Leg Assembly (For the Center Legs)

To construct the vert ica l leg assembly, have available the two plastic brac kets, the sma ll rectan gular space r, and the twoleg piecesthat havetheprotrudingplastictabswith three holes, all prev iously cutfrom the plasti c pan el. Also, have available twoplastic screwsand nuts.Thefoll owingprocess

Photo 6

ROBOTSCIENCE&TECHNOLOGY

Photo 7

isperform ed while the robo t isresting on the suppo rtstruc- ture, and the servos are"han gin g"undern eaththerobot body. 1. Usin gthe twoplastic brack et s and the sma ll rectan gular spacer,sandwich the sma ll rect an gular spacer bet ween the twobrack et s(seePho to7).Therectan gular space rsho uld be adjusted to fit at a center placem en twhilebetw eenthe bracket s.

2. While holding the sandwich in place , insert one ofthe plasti clegs, hole end first, into one end ofthe sandwich. Be sureto align theholes onall threepieces(thetwobrack- etsand theleg) .

3. Insert a plasti c screw through the aligne d holes.Attach the nut on the oppos ite side and screw into place for a sn ug fit. Thisprocessmay cause therectangular spacerto mov e from itscentered, in-between placem entwith the twobrack et s.However, once the second legis securedat theoppos iteend, therect an gul arpiece willsn uglyfitbe- tween the two bracket s.Take,the second leg (with the same protruding plastic tab with th ree holes) and com- plet etheprocess.

4. Once the center leg assemb ly is complete lyconstructed, it is super-gluedonto thebod y struc ture. Theleg assembly will beplaced in thepre-cut slot on the bod y.Not e that the brack et s will fit sn ugly into the slots. First ,confirm proper placem ent.Then dab supe rglueon themiddle of the sandwich , alo ng the brack ets and the rectangular space r, where the leg assembly will directl ycontact the bod y structure. Usethe supe rglueconse rva t ivel y,and do not allowglue to touchthejoints of theleg assembly, where the plastic screws havebeen placed (see Photo 8).

5. Hold the legassemblyin placeuntilsecure.

Ideas ^I Links Books Articles Examples Part Sources Robot Gallery Surplus Motors H-Bridge Drivers Sharp IR Rangers Polaroid Rangers Eltec Pyroelectrics

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mo E asier Robotics

What's Next?

theleg all thewaythroughthe slits until it is "seate d"and firmly in place. Complete thisprocessfor therem aining legs(seePhot o9).

Photo 9

Author'sbiographies sho wnon page 62.

First, therewastheHl-KTkit.Nowthereis aparti all y con- structed'bot. We enco urageyou tofollow along in this spec ial two-part series. Also, takea look at how you can bringthis 'bot to lifewith roboti c skin fabricati on on page58 .

The HexapodWalkerhasjust begun to take sha pe. The six legsare attache daswellastheservo mo tors . However,thisis on ly the beginning of the exc it ingrobot icconstruct ion pro- cess! Part 2of thiscon struction series will feature working with the electron icsand programming of the assembly.

2. Repeat this processfor each corne r. (NOTE:The small holes of thetwohinges attache d tothe backof the struc- ture faceforward , toward thefrontof therobotbod y.)The sma ll holes of the twohinges attache d to thefrontof the bod y structure will facebackw ard, toward the aft end of the robot bod y. Check your work closely. It will be too late to make correc tions once the leg is glued in at the next ste p.

Photo 8

Attaching the Horizontal Leg Assemblies

1. Take two of the plastic pieces which will form a hinge, and hold them ataback corne rof therobot (it doesnot matter which side ). The robot body will be sandwich ed betw een thetwo suppor t hinges.NOTE: There are three holesineach hinge:two sma ll holes andone larger hole (thehingepoint).Be sure that thehinges to be attache d tothebackofthe robotstruc tureare placed with the sma ll holes facing forward toward the front of the body struc- ture.Put a screw throughthehingepointand plasticbody struc tu re,andattach with anut .

Eight plastic pieceswill form the four hingesto be used in the fabri cati on of the horizont al leg assemblies (aswell as four screwsand nuts). In thisprocess,thefour legswill be adde d tothebod y structure. Thisis acco mplish ed while the robot bod yisresting on the support structure, with theservo motor s "unde rnea th " theupsidedown bod y structure.

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3. There arefour legsrem aining to be attache d. Applysuper gluetothe topand bottom edgeof thenot ched endof the leg.Seatthetabintothe slotof thehorizontalhinge.Push

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phone: 303·258·3181 fax: 303-247-1892

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Popular Micromouse Algorithms , Part IV

Introduction

Thisisthefourth in a seriesofart icles abo ut various algo- rithms ("algorith m" is afan cy term for "method") used by mic rom ouse robo tstosolve themicromousemazeincotnpeti- tion.These competit ions have been organ ized an n ua llyall over the U.S.by variouscha pte rsof IEEE.Theyhav eproven to be verypopular. Depend ingon theintend ed contesta nts, the exact rulesmaydiffer amo ng the compet it ions. Themain object ive, however,rem ainsthe same: use arobotic "mo use"

tosolvethe maze as quicklyas/)ossible.Thebasic premise of the problem is that the microm ou se robo t does not know the config urationof the maze befor e itsfirst run.The coor- dinateof the destination , on the othe r hand,isknown.The robotis allowed to store informati on and rep eat solving the maze with in a time limit.

Most micro mo use robotscanon lysense whether there is a wall direc tly ahead , to the left an d to the right. Based on such limi ted informa tion ,therobotmustrely on proven al- gorith msto syste matica llyexplore themaze to find apath to the destinati on. A sma rtroboteven tries tofind theshort- est path to the destinat ion tominimize thetime it takesto travelthere. In previo us issues, wediscu ssed the WallHug- ging, Depth-first Search ,an d Flood-fill algor ith ms. In the July 1998 issue, we emp loyed theWall Huggin g algor ith m and discovered itsmain fault. Inessence, if therobot swims

along the shore lineofalak e,it will never reach an islandin the middle .Ther efore , if theisland isitsdestinati on,it will fail. The failure is, ofcourse, attributable tothe inad equ ate algor ith m. In the November issue , we discu ssed ano ther popular algor ith m used to solve themicromou se maze ,the Depth-first Search (DFS ).Themain advantageof theDFS isthat itguara n tees that the robot willexp lore allcells that can bereachedfrom its start ingcell,an d map the m. Un for- tunat el y, DFS does not provide the shortest path to the destinati on.A faste r, less intuitive method is a little more comp lica te d than the wall huggin g and DFS techniqu es, but hasthe adva ntage of findingthedestination without hav- ing to explo re the entire maze.That method wasthe subject of theJanuaryissue's algor ith mart icle- theFlood -fill algo- rithm. This method may fin d a way to the dest ina t ion without explor ingallof the cells,and the reforesave search time.However,it maynotfind thesho rtestpath,anecessity for accomplish ing the objectiveofthe com petit ion- tosolve themaze asquicklyaspossible.

Finding the Shortest Path

Given two robo ts that can move at the samespeed,the one that tak es a shor ter path will yield a sho rte r run time.It is, therefore,importanttofind the shortest pathfromthe start ing

III

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The act ua l number ofdistinc t act ions ,or mo ves, availa ble to the robot islimited on ly by its physical ability.Some ro - bots must sto p to turn. That act ion has a grea te rcos t value than if it were able to turn on the gowithout stopp ing. Two heuri sticformulaswill bediscussed,thefirst assumes therobot sto ps before turning and can no t mo ve diagonall y, and the sec o ndassumes diagonal mov ement ispossible.Theheuris- tic function app lica ble to the diagonal-c apable case is automatically an underestim at e for the other one. There- fore, the heuristi cfunctionthat usesthe lengthof thest ra igh t line is applicableto both the diagonalcapa ble and diagonal incapable cases.

IROBOTSCIENCE&TECHNOLOGY

'lEI Notations and Variables

Also, not e that in the algor it h m, wetalk abo ut "rea cha ble sta te N from state X viaact ion A."Ther e isno mentioning ofce lls in the algorith m. Thisisbecau se anact ion mayleave the rob ot in the same cellor a few cellsaway from the cur- rentcel t. A90-deg ree turn lea vesthe robo t in the same cell, whilea "mo ve forward three cells" act ion leaves the rob ot three cells from the currentcel t.

cdc rate . If the rob ot is to mov e forwa rd two cells, it can acc el era te to a high er spee d, the n deceler at e to slow and stop at the end of the second celt. These are not the on ly cons ide ra t ions when a robotmo ves.

Let usfirst exp lain the notation an d varia bles involved in this algor it h m . Thealgor ith m keep strack ofsta tesand other information aboutstat es via item swith fivecompo ne nts (for the lackof a better term, ca ll theseitems quint-tuples) .In a quint-tuple (X,Y,P,D,A), the componentshave the follow- ing meanings:

Co mpo ne n t I:thestat e X.This co mpo ne n t indicatesthe stat e to which the information in the quint-tuple belongs.

Co m po n en t2:theprevious sta te Y.This co mpo n e n t indi- cates that sta te pre vi ou s to this sta te when the ot he r compo n en tsarccom pute d.

Co mpo ne n t 3: P. The exact known minimum cost from the sta rt ing sta te to sta te X. Note that this is the exact costof one of possibl yman ypaths from the sta rt ingsta te to sta te X.

Co mpo ne nt 4:D.Theesti ma tedcost ofa path from the sta rt ing sta te through sta te X to adestinati on.Thisis al- ways an underestimat e of the act ua lcost. In othe r words, this compo ne n t is always lessthan the sho rtes t pathfrom thesta rt ing sta te through sta te X to a destination . Co mpo ne nt 5: A. The action taken at state Y to reach sta te X.

state (i.c., thescarringcelland theinitialdirection) to the des- tination cel t.

Assuming the entire maze is known (such as from a DFS exploration) ,the A

*

algor it h mgua rantees to find thesh or t- est path. ore that theA

*

algor ith m isaplanningmethod , not aneX!llorationmethod. Duringthe execution of the wall huggin g,DFSor flood-fillmethods,the robotac t ua lly moves around.However,during the executionof the A

*

algorithm, the rubor doe s nor move. Instead, the robot just plan sthe shor test path based on the knownco n figura t io n of the maze.

The A

*

algorithm dealswith"states" insteadof just"cel ls."

A state representsthe robot being at a cellandfacinga certain direction. In other words, the ruhot at cell X facingnorth is in a differentstate from the robot at cell X facing south.

In order to express the A

*

algor it h m, it ishelpful to intro- duce asorred lise.Asorte d list,asthe nameimplies,isa list of items that isordered bysome criterion. Asitems are inserted or deleted from the list ,adjustmentsare made to ensure the list remains so rte d. In the following discu ssion, wecan as- sume theheadof thelist isthe item with the leastvalue.For our discussion, each item in the list has an assigned value derived from a group of data.This data group includes: a state; the previous state; the "action"that getsfrom the pre- vious state to this state; the known minimum cost to get from thestart ing state to thisstare (computed and known);

and the value from thesta rt ingsta te to this state added to theunderestimated valueto reachthe destinationfrom this state.

In thisalgorithm , "cos t l A)"isthecostof an arbit ra ryac t ion A,and h(X) istheest ima ted distancefrom an arbit rarysta te X to thedestinati on. It isimportant to realizethat the ac- tions beingevalu ated are not confined to moving forward one cell and making 90-degree turns. Moving ahead two cellsisnotthesame asmoving ahead one cell twice.Mov- ing ahead two cells is a more efficient action with its own lower total cost ,because it takestime to accelerate and de- In addition to"sta tes," the A

*

algorithm relicson abeuristic function,or rule-of-thumb, to estimate the length from any state to the destination.Furthermore,the A

*

algorithm re- quiresthe heuristic processto provide an admissibleestimate.

"A d m issible" ismer ely a fancyterm for "unde rest imat ing ."

In other words,the A

*

algor ith m reliesonarule-of-thumb that always underestimatesthe act ua l distancefrom a sta te to thedestination.

The Method

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In the algorith m, "cons ide red" is a set of quint-tuplesthat represen t states that have beencons ide red. A"frontier"is a sortedlist of quint-tup les thatrepr esent sta tes that are being cons idered. Thelistis sorted in increasin g valueorde r, first tolast , by the fourt h compone n t ofthequint-tuple.Effec- tively, the firstquin t- tupleof"frontier "repr esentsthemost prob able state under cons ide rat ion that sho uld be on the sho rtestpathfromthe sta rt ingsta te to adestinati on.

Inpseudocode the algor ith m reads asfollows:

update(X,P)

for all (Z,X,PI,O,A)in conside redor fron t ierdo if (Ps-costfA) <PI) then

remove(Z,X,P I,O,A)

insert(Z,X,P+cost(A), P+cost(A)+ h( Z),A )tofront ier update(Z,P+cost(A) )

end if end for endupd ate A*(S)

empty the cons ideredset

create (S,null,O,h(S), n ull) in thesorte d list front ier wh ilethe destina t ion isno t consi de reddo

remove the first item (X,Y,P,O,AI) from fronti er put (X, Y,P,O,A I) tocons idered

for eachstate Nreachable fromsta teX wit han action A do

if (N,XI,P I, Dl,A2) does not exist infront ier or cons ide red

add (N ,X,P+cost(A) ,P+cost(A)+h (N),A) to frontier

else

if (PI> P+cost( A) ) the n delete(N,X I, P I,O I,A2 )

add (N,X,P+cost(A),

P+cost(A)+h(N),A) to frontier upd at e (N ,P+ cost (A ))

end if endif end for endwh ile end A*

RegardingtheA

*

algor ith m, themost cruc ialsta te me n tsto understand are theboldedones. Theselines associate state N with twonumbers. One of the possibly man y exact costs from thestart ingstateSto sta teXisP. As aresult, the exact costofone of thepossiblyman ypathsfrom the sta rti ngstate throu gh sta te X to sta te N isP plus the cost ofthe act ionA (Ps-costf.Aj).Notethatthis exactcost maynotbethe costof the shortest pathfrom the startingstate^to stateN. Thisiswhy we need to check ifapath to N has already beenfound. Ifone exists, the exact costsof the two paths arecompa red, and on ly the sho rtes t one is stored. Furthermor e, if a path to sta te N is already found , it implies that the pathsof other sta tes from sta te N mayhave been computed (represented byquint-tuplesin the "cons ide red" set or"fro ntier" sor ted list) . The utility procedure update recompu tes the quint- tuples of all states whose exact cost depends on the path from the sta rt ingstate to N.

Heuristic Functions

First ,weneed to decid e wha t actionscan be taken and the associatedcosts:

• Moveforw ard one cell: 700 ms.

• Move forward two cells: 1200 ms.

• 90-deg ree turn: 500 ms.

It isthe programmer 'sresponsibili ty to dete rm ine theheu- risticfunction (h).

Two Heuristic Examples

Thisfirstheuri sticfuncti onis applicable (admissible) if the robotsto ps beforeturning andcan no t move diagona lly.

h = 600 ms

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(abs( xl -x2) +abs( yl -y2) ) WHERE

h- theheu ristic.

(x1,y1)- coord inat e of the cell representedby the currentstate

(x2,y2) - coord ina teof thedestinati on

600 ms- any time est ima te that isLESSthan or equalto

the timerequired foramove of a sing lecell, in this case 600 ms.Although it takes 700 ms to execute the "move forw ard one cell"comma nd, it takes on ly600 ms tomove onecell whenthe robotexecutes the "move

forward two cell"command.

abs- the absol ute value.

abs(x l-x2 )+a bs(y l -y2 )- This isthe minimum number of cellstotravel even if therewerenowalls.Thehori zontal offset of the curre n tcell from the dest inat ion is abs(x 1- x2), the robot must move absfx l-xZ) cells hori zontally even if there are no walls.Similarly,abs(yl-y2) indicat es