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- - - -- ---- - - -- --- -- - - , -..l_

- A n Historic Centerfold: A/~

SIT! AIBD, S/TR

09>

o 74470 93568 1

- - - -- -~-- ---_._.._ ---- -

. THOSE WHO CAN . . .

LEARN

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The Rug Warrior Pro·

m

lrhe Brains... The Brawn .

0

(/processing,memory andsensorcircuitry)

o

Powerful Motorola MC68HC II Microcontroller

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Two-line Alphanumeric LCD Display

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32 K of Battery Backed R AM

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RS-232 Serial Port

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Collision Detector

P Photoresistor Light Sensors

p Infrared Obstacle Detectors

~ ~ Microphone

Piezoelectric Buzzer

f

Two-Channel Motor Driver Chip ( Dual Shaft Encoders

? Free Interactive C Software I with Manual

... and more

Brain sold separately: $359(}Q

(wheels, motors, chassis,etc)

• Two 6 V olt Gear Motor

• Two 2 1/2" Wheels

• Custom Caster Wheel

• Custom Chassis Plate

• Clear Plastic Skirt Body

• Mounting Hardware, Cables , Tie straps, etc.

• Custom Decals

Brawn sold separately: $240(}Q

Personal Robotics: RealRobotsto Construct, Program, and ExploretheWorld

byRichard Raucci

Familiarity with robots willsoon be asimportant as computer-and internet-literacyisnow.Here'sa handy COI1$Wnl'TRltidetohelp readersfind therobot that'sright for them.The authorincludessuggest ionsforprojects suited to the robotsreviewed.Thishand y guide will helpyou avoid the frustrati on sthat comefrom workingwith the

wrongkit-whether it'stoodifficultto assemble, or perhaps ~_---'

rooeasy to besufficientlychallenging.Ifit'snotreally arobot, thenit's not in thisbook.250 PI" Paperback . $25

TNI ' • • • ONAL 10_OT

NAVIGATOR ThePersonal Robot Navigator byMer!K.Miller, Nelson B.Wink lessllI, Joseph H.Bosworth & KentPhelps

A book andsoftware combinat ion thatpresentsthe world of personal robotnavigati on.The authorscover what wecan expectfrom robotsin theway of intelligence and navigation.RoboN av'software (included) ena bles '---'-'-'---'---' you, therobotmasrer,tomake a mapofyour housewith

furniture,record corridors your robot can travel,calculate best paths,&

simulate the robot followingthepath whilemonitoring compass,sona r, wheel turn and triangulation indicators.Freeze act ion, printscreen ,and study thenavigationlog.204 PI" Paperback.Incl.PCDisk. $44.95

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Publis hers of Science and Technology 63 South Ave,Natick,MA 01760

Vis it ourwe b-s ite :www.akpete rs. com Orderby phone:(508)655-9933,Man- Fri,9 - 5EST or by fax(508) 655-5847 Visa/MasterCard:Be sure toinclude both card number and expodate. Checks:inSUS or by InternationalPostal Money Order Shipping:(US)$5for firsttitle,$2for eachadditional title International:Pleaseinquire about postal charges.se rvice@ a kpe te rs .com Anunprecedent ed referen cework that compiles into one

conv enient sourceeveryth ing the student or experienced developm entalengineerneedsto know about themany technologies associated with thisrapidly evolving field.

Presentinginamanner which often parallelsstrategies of roboticdevelopm ent,Everettprovides a comprehensive and understand ableexplanati on of the theoryofsensoroperation.

Objectiv ereviews of prototype and commerciallyavailable

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Mobile Robots:Inspirationto Implem entation 2nJEdition,1999

byJosephL.Jones,AnitaM.Flynn,BruceA.Seiger Roboti cshasmadequantumleaps since thefirst edit ionof MobileRobots:InspirationtoImplementation.With thisnew edit ion , the authors keeppacewith the ever-growingand rapidlyexpandingfieldofrobotics.Reflectstechnological development s and includesprograms andactivit iesfor robot en t h us ias ts. Usin g photogr aph s, illustrati ons, and inform ativ e text ,MobileRobotsguides read ersthrough the step-by-step process ofconstructing twodifferent,inexpen sive and fullyfunction alrobots.

Updatedby several new ch apters with project s andapplicat ions. 457 PI'.

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Sen sorsforMobileRobots:Theoryand Application byH.R.Everett

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._~---~._---~

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Deceleration TIme

Detector Vertical 3"

6"

Detector Horizontal '2"

ROBOTSCIENCE&TECHNOLOGY 24"

13

48"

36"

4

iL- - - - - - L- - - - - - -lr-+Time

58 39

Cover: Eric Sander

~-~----_...

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36

26

7

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FIRST

Robotics

FIRST National

Championships at EPCOT

Thousands of students, hundreds of robot s.

Teammembers,theirfamilies,friendsandotherspectators fill the stands at Walt DisneyWorld'sEPCOTCenter. They!)rovide a colorful backdropfortheopening

ceremonies of the1999 FIRSTnational championshipelimina tionround.

Under the rules of the elimina tion round, the top 16 qualificati on seeds picked their all ianc e partn er, an d then the partners picked athirdteam.AcesHighpickedTeam 1, The Juggernaut s from the Oakl and by Floyd

Painter

The annual FIRST (For Inspiration and Recognition of Science and Technology) National Champion sh ip tournament was held at Walt Disney World's EPCOT Center at Orlando, FL April 22,24. Two hundre d seven teams from the United States and Canada competed in the series, which was won by an alliance of hi gh sch ool teams from Connecticut, Michigan and Ohio. Several thousand high school te am members and their sponsors, familie s and friends spent three days enjoying Florida sunsh in e and tough competition.

There are several things about a FIRST tournament that you can depend on: It will be spirited, it will be exciting, and it will be colorful. This year' s championship series was no exc eption. In just five years, this national tournament ha s grown to become the largest event of the year at on e of the world's maj or entertainment complexes. FIRST is growing phenomenally, so the sho w will not o n ly go on, it will get bigger.

The Winning Alliance

In the highlight of the tourna me n t , an alliance leadbyAcesHigh,Team 176 from Windsor Locks, CT, won the 1999 FIRST Nati on al Champ io nsh ip. Aces High was comprised of team memb ers and spo nsors from Windsor Lock s High Schoo l an d Suffield High Schoo l. The team and their robot, Maverick, finished 15th among the 20 7 te am s in the qualific ati on round, wherein team s compe ted with allies that were randoml y selec ted.

ROBOT SCIENCE&TECHNOLOGY

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The tournam ent came down to the third and deciding match of the riveting ch ampionsh ipseries. Match3 wasTeam 176/1/48 all theway, and as theclocktickedaway the final seconds, the crowd nearthe stage begantosurge with exci te me nt. When the results were an no unced, the crowd wentwild and the stage wasrushed byclassmat es and sponsors of the winning alliance . Analliance of threediverseteam shad wontheFIRSTnati on al cha mp ionsh ip throu gh an ext raord ina ry displ ay of coordinati on an d team play. Their suppo rte rscrowded the stage , danced , The opposition in the finals was Team 45, led by last year's FIRST nationalchampion,theTechnoKats from Kokomo High School, IN and their robot, TKO. The 'Kats were allied with Team Ill,from Rolling Meadows and Wheeling high schools in Schaumburg,IL, and their robot WildStang. Team 45's third team partner was'Team 84, from Wyalusing,Athens,Towanda, Troy, Northeast and Sayre high schools, Troy, PA and their robot,Chuckrt,

Both all ia nces were ext re me ly aggressive in the final series, and the hittingwasparti cularlyhard in thefirst match. Team 45/111/84 won that mat ch , but Team 176/1/48 gath ered itselfmagnific ently, and beat the odds bywinningthe last two matchesand the cha mpionsh ip. Theteamprevailed in mat ch two,tyin gtheround inspite of thefactthatJuggernautandMaverick wer e che wing at each ot he r while tryin g to climbon to the puck.

The Final Series

defender," and that the hallm ark of Team ELITE's Xtremachen II was its

"versatilityandaggressiveness."Oth ers noti cedTeam48's ada pta bility too;the judges awarded theBestDefen sivePlay Award for thenati onalchampionship seriesto analliance that included the team.

The 176/1 partne rs then picked team number48,TeamELITE,fromWarren G. Harding High School in Warr en, OH, to roun d ou t what ultimately became the win n ing trio.

The Victorious Robots

Those scouti ng repor tsled Team 176 very quic k ly to its partne rs for the eliminati on round. The reportsnot ed thatJuggernautwas an "awesom epuck

Partnering for Success

Techn ical Center (OTC) Northeast, Ponti ac,MI, a blendofst uden ts from Ponti ac Cen t ra l, Roch est er, Oxford and PontiacNorthernhigh schoolsand OTe.

The pro c ess of selec t ing allia nce partnerswas oneof therealcha llenges of this year's FIRST tourna men t. The lead enginee rfor Team 176 told RS&T,

"Our scoutsevaluatedand record edthe st re ng ths and weaknesses of all the ot he r team s so that our drive team never ste pped onto the playin g field withoutknowing all thedet ails abo ut our all iance partner s as well as our oppo ne nts."

The winning robots were impressive.

Inaddi t iontoMaverick,Team 176 had in its stable the OTCJuggernaut,and Team ELITE's Xtremachen("Extrem e- Mach ine") II.Thisformidable lineup needed all the skill and firep ower it could muster todefeat its oppone n ts in the fina lcha mp ionsh ip mat chup.That series provedbeyonddou btthatFIRST robotics is a con tac t sport. Jon Gallo, sen io r proj ec t eng inee r for Delphi Pack ardElectric and Team48captain, said,"T h isyear's competition requires te am s to bu il d a rob ot that can withst and vigo ro us amo u n ts of inte ra ct io n with ot he r robo ts. " Mr.

Gallo pro ved to be presci ent; the win n ingrobo tssurvive datremendous amo u n t of inter acti on during tourn am ent act iv ity, an d it was vigoro us withacapitalV.

ROBOTSCIENCE&TECHNOLOGY

~~- ..~--

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Some organi zation shave theresource and top-lev el attention that result it spo nsorsh ip of many teams, and tha involves funding, provision of sho j space and machinery, and voluntee timefrom engine ers andother mentors amongothe r things.This year,severa org an izati on s mad e extraordinar- nationwid e comm it me n ts to FlRS1 TheNati on al Aeron au tics and Spac. Administrati on (NAS A) spo nso re:

thirty-on e te ams, UTC sponso re:

twelv e, an d Delphi Autorn otiv.

Syste ms five.

NASA and FIRST

1999 FIRST national champion Team176,AcesHighfromWindsorLocks, CT. , is shownwithitsrobot,Maverick.Theteam,representingWindsor Locks and Suffield High Schools,fJlaced 15th in the qualificationround,gainingthe righttochoose

itsalliancepartners for the eliminationround.Team176 was sponsoredbythe Hamilton StandardDivisionof United Technologies Corporation .

laugh ed and cried and just gene rally madehappy over the scene , whiletheir now-rigid, silentglad iato rsstoo d frozen in time at the puck .

After things settle d down a bit, Jam es Crouse , direc tor of eng inee ring for Delph i Pa ck ard Electri c Syste ms, prai sed the alliance format , saying,

"T h is is a pe rfect examp le of how depending on partnerscan lead youto the top." Thom asRice, OTC instruct or andsponsorof Team 1,also praisedthe

"solid alliance, "and the waythe

176/

1/48

trioresponded tothepressure afte r beingdown foll owing the first match ofthefinal series.

Winning Sponsorship

The winning all ia nc e for 1999 provid ed a grea texampleof variet yin spo nso rsh ip. Hamilton Sun ds t ra n d (form erl y Hamilt on Stand ard) Division of industrial gian t Unit ed Techn ol o gi es Corpora t io n (UTC) spo nso re d Te am

176,

and Delphi Pack ard Electric division of Delphi Autom otive Syste mssponsored Team

48.

TheJuggernauts of Team

1

were spo nso red by 3-Dimens ional Services,

ROBOT SCIENCE&TECHNOLOGY

of Roch ester Hills,Ml.

Exper ie nce is a com mo n byw ord amo ng the spo nso rs of the winning allia nce. Delphi Autom oti ve Syste ms has spo nso red team s for eigh t years, fromthefirst yea rofcompe t it ion,and ha s a ste lla r success ra t e . United Techn ol o gi es Corpo ra t io n an d 3- Dimen sion al Servicesare in their fifth yearofsponso rsh ip.

Commitment

Corporatesponso rsh ipof FIRSTteam s comes in allsizes and varieti es, from govern me n t agen c ies to compa n ies, large andsma ll.

Occasiona lly, a sing le compa ny will back a team, but that israre, as in the case of 3-Dimensiona lServicesand the Juggernauts of Team 1.The company, located in Rochester Hills, Ml near Pontiac, is in the rapid prototyping busin ess, a perfect base for rob otics engineering.It has

170

employees, and in terest ingly, Aaron Bellore, amember of last year's OTC FIRST team, and three other form erteam memb ers, are employed there.

Dave Lavery, Program Execut ive fo Solar an d Plane t ar y Explo ra t ion a NA S A head qu arter s explai ned th.

NA S A ph ilosop hy: "Scie nce an, technology educat ion and outreac h i one of the agency's primary mission s Thus, the agency cha rte r sup po rt parti c ip ati on in pro gr am s suc h a FIRST which prom ote science an, technology educa t ion. But at aneve) more fun da me n ta l level , we beli ev. that suppo rt ing FIRSTis crit ica l totil, surviva lofthe agency.

(Continuedonpage 33.

This is what it's allabout! Threerobotson thepuck and lots of flopf>iesairborne.

(9)

Popular Micromouse Algorithms, Part V

In our last issue weintroduced youto theA*Algorithm.It's a greatalgorith m but here's abetter one. Perhaps you have discovered tha taltho ugh A *willprovide the sho rtestroute to the destination, it mayuseupallyourtimesolving themaze, but leave no time forthe robot to actua llyget to its destinati on .Well!That iscertainlyaturnoff! What to do ?

Try the C* (HC - star") Algorithm.With this method youcancall time outs while doingtheplann ing and make a move toward the destination. Themovemaynot bethe absolute best ,but it willget your robo ton its way.

Previous articles conce ntrated on the microm ouse com petiti on s.These competitions have been organ ized an n ually by various chaptersof the Institute of Electrical and Elect roni c Engin eers (IEEE), and are very popular. Depending on the con testants , the exact rulesmaydiffer. Themain objec t ive, however,remainsthesame: use aroboti cmouseto solve a maze as quicklyaspossible.The basic premiseis tha t themicromouse robot doesnotknowthe configura t ionofthemazebefore its firstrun.The coordina tesof the startingpointand destinati on,however, are known .The robo t is allowedto sto re informa- tion andrepea tsolving themaze with in a time limit. TheA* Algorith ms limitati on has already been discussed (take stoo much time planningand not eno ugh doing).The C* Algorithm isnot commo n ly used in these compet it ions altho ugh it could beif timeoutsareused judicio usly.The C* Algorithmdoeshave anadva ntage in that it can dealwith therealworld condit ionsof timeversus movementand the reforecould beappliedto variousrobot icact ionssuchas armor legmovem ents.

Backg round and Introduction

In previous issues, wediscussed theWall Hugging, Depth- first Search,and Flood-fill algorith ms.Then ,inour July1998 issue, we emp loyed the Wall Hugging Algorith m and dis- covered its mainfault.Inessence, ifthe robotswimsalong thesho rel ineof a lake, itwill neverreach an island destina- tion inthe middle.This failure is, of course,att ributab leto the limitations of th e algor ith m. In the Novemb er issue, anotherpopularalgorith mwasused to solve themicromouse maze , the Depth-firstSearch (DFS ).Themain adva ntageof

the DFS is that it guaranteesthat the robot willexploreall cellsthatcanbereach ed from its startingcell,and mapthem.

Unfortuna te ly,DFS doesno t provide the shortest path to the destinat ion .Inshort, DFS is effect ive but not efficien t.

A faster, lessintuiti ve method is a littl emore complica ted than the wall huggin g and DFS tech niq ues,but hasthe ad- vantageof findingthedestinati on withou thavin g to explore the ent ire maze.Thatmethod was oursubject in Janu ary - the Flood -fill Algorith m. Thismethod will findaway tothe destination witho utexploringallof the cells,and therefore save search time.However,itmaynot find theshortestpath.

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In our April issue , we examined the A

*

("A-star") Algo- rithmforpossible microm ou se applica t ions.Thisalgorith m finds the sho rtestpath in a sta te -space from an initialsta te toafinalstate. Altho ugh theA

*

Algorithm guaran tees to find the shortestpath ,it is complex an d requiresmorepro- cessing resou rces an d time.This complex ity mak estheA

*

Algorithminap plicabl einsma llercon tro llersan d maytake longer inthe aggregate thantheFlood-fillAlgorithm to ac- complish the en t ire task (path det ermination and travel time) .Indeed, if the re isnot eno ugh timefor theA

*

Algo- rithm to comp lete, nothing atall happ ens.

The algor ith m discu ssed in this art icle ,C*, is alsoa sta te- space-sea rc h algor it h m. However, unlike A*, the C* Algor ithm isrecursive and tries to find the sh or test path 'gradu ally.'TheC*Algorithm givessome answereven if it must be terminat ed before the opt ima l solut ion (i.e ., the shortes t path) isfound.Thusit ispossibl e tolimit the time of the C* search, make an appropriate mov em ent, rest art C*, make ano the r movement, etc. ,etc. , until the mazeor mov em en t is comple te d. The aggregate time of all the searchesand movementsmay givea sh or te r timetocomple- tionthan theA

*

Algorithm.

Robotic applica t ionsareofte ncons ide red 'real-time,'mean- ingthereis adeadlinetomeet.Therefor e,theC* Algorithm maybea more suita blesta te-s pace-se archalgor ith m insome real-time robo t icapplica tions .

The Algorithm

Befor ewedel veintothepseud o-cod e of the algor ith m , it is important to understand the two compo ne n ts ofC*.The first compo ne n t is an iterative algorith m (theC* Iterati on Algor ith m).This iterati ve algor ith m rep eat edl y calls the second compo ne n t , a recursive algo rith m (call ed the C*

Look -ah ead Algorithm) . The C* Look -ahead Algorith m esti mates the shortest distancetoa goalstate from the cur- rent sta tebasedon thelook -ah eaddepth.Asthelook -ah ead depth increases, the est ima te of the shortes t distan ce to a goalstate becomes more accurate .

Eachsuccessive iterat ion oftheC*Iterati onAlgorithmdeep - ens the lo o k -ah e ad depth using the C" Lo ok- ah ead Algorith m an d prod uces a more inform ed est ima te of the optimal move tha n the prev ious iteration. At the en d of each iteration , adec ision basedonthe inform ati onreturned by the C"Look-aheadAlgorith m is reache d.Thedecision includes the action that is estima ted to lead to the shortest path to agoalsta te an d an esti mate of the length of that

ROBOTSCIENCE&TECH NOLOGY

path .Thedecision is then saved. If the re isnot suffic ien time for another iteration , the C* Iter ation Algori thm i:

term ina te d. However,the saveddecision from the previou:

success ful iterati on is still availab le to gu ide the robot ir makingitsnext move.

The pseud o-cod e of the C* Iter ati on Algor ithm is showr asfoll ows:

C*Iteration(start,final) thisPathEstimate=h(start) rep eat

lastPathEstimate=thisPathEstimate thisPathEstimate=infinity

for eachact iona applicabl e at start nextState= a(start)

estimate=cost (a )+C*(nextState,final, lastPathEstimate-cost(a))

ifestimate<thisPathEstimate then thisPathEstimate=estimate actionToTa1<e=a

end if end for

latchedAction

T o

Ta1<e=action

T o

Ta1<e untilthis PathEstimate=lastPathEstimate en d iteration

TheC*Look -ahead Algorithmis as follo ws:

C*(start, final,left)

if(startinfinal) return0 else

min = infinity

foreach act ionaapplica bleatstartdo nextState= a(start )

if(cost(a)+h(nextState) >left) then estimate=cost(a )+h( nextState) else

estimate=cost(a )+C*(nextState,final, left-cost( a) )

en d if

ifestimate<min min

=

estimate en d if

end for returnmin end if

en d

c *

- - - -- ---~---~--~---~---:---_...._---_..._-----~

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Explanation

THE

NAVIGATOR

PERSONAL ROBOT

The C* Look -ah eadAlgorithmis arecursive algorith m that explores the sta te -space in adepth-firstmanner. It requires threepieces of information(calledthe parameters).The first paramet er,start, isthe sta rt ingsta te . Thesecon d parameter, final,is a setoffina lsta tes. The third par am et er,left,isthe upper bound that will be used if the search is allo wed to cont in uefurthe rexplora t ion. In return,the C*Look-ahead Algorithm returnsan estimated sho rtes t distancefrom the startsta te to one ofth esta tes in thefinalset.

Thefirstrecursionterminati on cond it ionoccurs whenstart mat ch es anyofthefinal sta tes. When this cond it ion is sat is- fied, we arealready atafinal sta te.Therefore ,the distance totravel is zero. Ze roisreturned.

01'"•. '••••• ••"U

I

"A good discussion of how robot navigationtechnology operates in therealworld...objects are not always in the same place, sensors not always accurate; but a good design allows the robot to complete its tasks."

- Paul Malenfant,Software Engineer

The secon d recursion terminati on conditi on for the C"

Look -ah ead Algorithm is when the sum of the cost of an action and theheuri sti c of thenextStateis grea te r than the upperboundleft.This cond it ion is expressedas

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estima te=cost (a)+h(nextState)

Note that the upper bound for nextState is left-cost(a) be- cause the act iona usesup cost tn )of the look -aheaddepth allo wan ce alloca te d for thestartsta te. The algor ith m per- forms this ana lysisfor all applicab leact ions from thestart state.Theminimumof all the est ima tes isthen returned to the calle r.

in the algor ith m. If th iscond it ion is sat isfied, weknow the real minimumcostfrom nextStatetoone of thefinal sta tes is more tha n left because theheuri sti c is admissible.In othe r word s,the act ualshortes t distan ce to afinal sta te through nextStatewill exceed the look -ah ead depth.At thispoint, we simply mak e anestimate usin gthefoll owing sta te me n t:

estimate =cos t (a )+C*(nextState,final,left-cost(a))

In essence, the C* Look- ah ead Algorithm returns the foll owing inform ati on:

If the cond it ion (cost( a)+h(nextState) >left)isnot sat isfied , the algor ith m recurses to get a mor e acc ura te est ima te of the sho rtes t distan cebetw een nextState an doneof the states infinal, expressed bytheelse sta te men t:

- -- -- ..._- - - ""- -- .._ - ---~

ROBOTSCIENCE&TECHNOLOGY

(12)

Assumingtheminimum distan cefrom thestartstate toone of thefinal states isnomore thanleft, the algorith m returns themost informed minimumest ima ted distan ce from the Algorith m.This algorith m callsthe C*Look -ahead Algo- rithm rep eat edl y, and uses the resul t of the previous C*

Look- ah ead Algorith m invoc ati on asthebound of the cur- ren tinvocat ionbeyondwhich it looks ahead. This gradua lly exte nds thelook -ah eaddepthperimet er as each invocati on returns a min ima lly larger and mor einform ed estima te. Fur- thermo re, the iteration algorith m also keeps track of the shortes t distan ceand the act ion leadingtothe sho rtes t dis- tan ce.This allows the robo t todecid ewhich acti ontotak e afte r the C* Iterati on Algorithm returns voluntarilyor is terminat edduetothetime limit.

The C* Iterati on Algorithm terminat esvoluntaril y when twoiterati onsindicatethe same distance.Thisis on ly pos- sible when the actua l sho rtes t distance to a final sta te is found. However, ifthere isnot sufficien t time to find the actua lsho rtes t distan ce, the C* Iterati on Algorithm saves theresults(estim at ed sho rtes t distan ce and theact ion lead- ingtoit) of thelast complete iterati on .

Thisresult ispossibly sub-opt ima l (not leadingtothe short- est path), but it is adecisionbased on the amo un t of time available to compute theresult.

An Example

Furtherm ore,therobot starts with facingsout h.

Let us use the same robot cha rac te r istics as in the A* example.

• The robo t tak es500 msto turn 90degrees.

• The robot tak es700mstomove one cell.

• Therobot tak es1200mstomove two cells.

Weusethe same heuri stics asin the A * example:

WHERE

h- theheuri stic.

GIVEN

(XnextSrare'Ynexrsrare) - coord inateofthe cell rep resented by nextState

(Xf)' Yf))- coord ina teof thedestination cell (only one in the exa mple)

THEN Let usrevisit an example presented in the A* Algorithm

art icle (seepp.17of the April 1999 issue ofRS&T).Let cell Sbethe start ingcellandcell0 bethedestinati oncell.The maze configura t ion is asfoll ows:

Figure1.Maze Setup

[§][AJlliJ

[Qmrn

[Q][B][Q]

o

1 2

o 1 2

(abstxnextSlale-xf)) )- isthehori zontaldistan ce between the cell repr esented bynextState and thedestinati on cell

(abs(ynext tateS -Yf))) - is the vert ica l distan ce betwee n the cellrepr esented bynextState and the destinati on cell 600 ms - Anytime estimate that isLESSthan or equal tothe timerequiredfora move ofa singlecell, in this case600ms.

Although it takes700 msto execute the'moveforward one cell'command, it takes on ly600 mstomove onecell whenthe robot executes the 'moveforward twocell'command.

abs - the abso lute valu e.

(abstxnextSrare-xf))+a bs(ynext.S'rare-Y/)))- Thisistheminimum number ofcellsto travel even ifthere wereno walls.The hori zontal offset of the cell repr esented bynextStatefrom the destination is

abstx

next.srate- Xl)) ' The robo t must move abs(xnext.srate-Xl)) cells hori zon tall y even if the reare nowalls.

Sim ilarly,abs(Ynexrsrare-Yf)) indicat estheminimum numberof cells totravel vert ica llyeven if thereare no walls.The sum

II.'

ROBOT SCIENCE&TECH N OLOGYI

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the exact sho rtest path , the A* Algorith m ismor e efficient than the C* Algorith m. However, if the robot has a time limit with in whic h it must mak e a decision ,the A*Algo- rithm maynot have eno ugh time to find the exactshor tes t path , and therefore can no t make any recommendati on s. On the othe r han d, the C*Algorith mcanat least est ima teand make a suggest ion. Forthefirstiteration of the C* Iteration Algorith m, the amo un t of timerequired ismerel ythe sum of time required to compute theheuri stics of the outco me ofeachact ionapplicab leat the curren tstate.

of hori zont al offsetand verti cal offset istheminimum num- ber ofcellsto trave l in order to reach thedestinati on cell from the cell repr esented bynextState.

Conclusion

The following is a parti al trace of the outco me of the C*

Iterati ve Algorith m. Not e that Xd (X den ot esthe celland can be S,A, B,C, E,F, G, Hand D, d den ot esthedirecti on the robotis facingandcan ben, e,s, w) repr esentsthe robo t being at cell X and facing directi on d. Each bold face lastPathEstimateassign ment indicat esthebeginning ofa C*

invocati on .The ste psofthe combine dalgorith msare illus- trat ed bythe curren tpath , the sumof the exact costof the path , and theheuri stic valueof thelast sta te in thepathjust prior tothe terminati on of recur sion.The boldface number (possibly moretha none) ind icates theleast est imateof this C* Iterati on Algorith m invocation, which will be used as thelastPathEstimateforthe next iterati on . See Figure 2 for illustrat ionsofiterat ion s.

The curiousreader canworkout therest of thetrace .Just to spoilthefun , letus discusswhatwill happen . At some point , thelastPathEstimatevalueis set to 3400. However,thevalu e oflastPathEstimateafter the iteration will not be increased anyfurt herbecause the pathSsSeBeBsDswithanexact cost of3400ms is kno wn . The 'until'cond it ionof the oute r loop isnow satisfied.Thealgorith mexitsknowin g theexactshor t- estpathcosts 3400 ms and recommends a turn to theeastat cellS.

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Besides the real-time nature of the C* Algorith m, it also doesnotinvolvethe complex ityoftheA*Algorithm.Even ifrecur sion is proh ibited (usuall yduetosome limitati on s of the CPU arch itect ure ), the sing le recur sion call in the re- cu rs ive C* Lo ok -ah ead Algorithm ena b les an easy tran slation toan iterat ive algorith m.

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Examples of Consecutive Iterations and T heir Recommendations:

First Iteration

(lastPathEstimate=2400)

Third Iteration

(las tPat hEstimate=2900)

Fourth Iteratio n

(lastPathEstimate=3000)

Ss 2400

SsCs 2500

SsSe 2900 SsSw 2900

recommendation: move south

Second Iteration

(lastPathEstimate=2500)

Ss 2400

SsCs 2500 SsCsCe 3000 SsCsCw 3000 SsSe 290 0 SsSw 2900

recommendat ion : turn east

Ss 2400

SsCs 2500 SsCsCe 3000 SsCsCw 3000 SsSe 2900 SsSeSs 3400 SsSeSn 3400 SsSeAe 3000 SsSeBe 2900 SsSeBeBs 3400 SsSeBeBn 3400 SsSw 2900 SsSwSs 3400 SsSwSn 3400

recommendation:

move south or turn east

Ss SsCs SsCsCe SsCsCeCn SsCsCeCs SsCs CeEe SsCsCw SsCsCwCn SsCsCwCs SsSe SsSeSs SsSeSn SsSeAe SsSeAeAn SsSeAeAs SsSeAeBe SsSeBe SsSeBeBn SsSeBeBs SsSw SsSwSs SsSwSn

2400 2500 3000 3500 3500 310 0 3000 3500 3500 2900 3400 3400 3000 3500 3500 31 0 0 2900 3400 3400 2900 3400 3400

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recommendation: move south or turn east

Readers want to thank Or Tak Auyeung for contributing the Popular MicroMouse Algo- rithms series,beginning in our July98issue.

Tak teaches the micromouse lab at the Uni- versity of California at Davis,where we met him during the IEEE Region6competition.

In his formerlife,he was the software developmen t group leader for embedded controllers at Zworld.

Or Tak's technical know- how will appear even more often: we promoted himto Contributing Editor, and forced him to write three '-. . .more articles for thisissu . Turn now to read his tech- nical review of Lego Mindstorms (p42),and his introductions to wire-wrapping (p 36).

~----_._---~

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Positio signal

Introduction

Radi o Con tro l, or RIC -t ype, servo - mot orshave becom e very popular in the fields of hobby an d ed uca t iona l roboti cs.Their size,ease of interfacing, andcostare themain reason sfortheir popul arit y.These easy-to- useservos are intern all y com p lex servo syste ms cons ist ingofamotor, a gearbox, motor driver circ u it, con t ro l circ u it , comma nd signal decoding circ uit ry, andapositi on sensor.

Microcon t roll ers and RIC Command

servos form apowerful duo signal

for the rob ot builder.

Micr o c ontroll er s ha ve multiplied thefeasibility of usin g servos. With the availa b ili ty of high -l e vel lan gu age s for micr o - contro lle rs, the difficulty level of programmingthem hasdecreaseddram ati call y.

The in teg ra tio n of inter-pr et ers and periphera lsontosing lesubst rates like theBASICStampsand the availabi lity of sma llsing leboardservocon tro llers have decreasedthecomplex ityof both hard ware and software.

This articlewillexplore how to con tro l and usetheRICservosto best suit the needs of sing le-and multi-axis robots and an imatron iccrea t ions. Let sbegin with anexplana tionof how servos work and how to con tro l them with the prop er signa ls.

A st udy of the phys ic al effects of motionwill follow, whichwill provide the groundwork for exam in ing the capabilit iesandsho rtcom ingsof these servos. Thisknowledgewill be used to crea te moti on profilesthat best suitour need s. Lastl y, an investi gation of variousmethods ofsynch ron izing the motion of multiple servos with each other and with internal and ext ernal even ts usin g a servo con tro ller will be conducted .

Figure1.Theclosedloop andself-adjusting nature of servo controlsystemsisshowninthisdiagram.

Servo Control

Some funda me nta ls of servo mo to rs sho uld bediscussedbefor e gett ing into themeat of the art icle .A servo ,sho rt for servo mo tor in this article, is a self- cor rec t ingcon trolsyste m in which the var ia b le bein g con tro lle d is a mechani cal positi on or moti on . The servo is a positi on al control syste m.

Figure I illustrat es the closed loop arch itec ture and self-adjust ing nature ofaservo con tro lsyste m.

The main compone n ts inside a servo are a set of gea rs, a motor, a poten- tiom eter, an d a circ u it bo ard . The circ u it bo ard per form s the control syste m functi on andafew othe r chores, as well. In most servos, the en t ire circuit, less afewdiscret e compo ne n ts, is on a single Integrated Circuit. In a ser vo con t ro l syste m , the error amplifier compar es the out put sha ft positi on informati on it gets from its pot entiom et er to that of a comma nd sig na l input. The differ en c e , know n as the erro r sig na l, is am p l if ie d in the gain stage. The amplifiederror signa l is then fed to a

Out~ut mo tor driver circ uit that

sha drive s the mo tor. The mot or moves the output 'sha ft an d the pote n- tiom et er tow ard the correct positi on until the pote n t iome te r output signa l matches the comma ndsigna l, thus elim ina ting posit ionerro r in the syste m.

The com ma nd signa ls that con t rol these servos are a spec ial type called PulseWidth Modul ati on(PWM).The inform ati on aPWM signa lconve ys is in the widthof itsdigit al pulses.The informati on con ta ine d in the pulse width is servo position.Thepulsewidth varies betw een abo ut 0.5 to 2.5 msfor correspo nd ing sha ft positi ons of 0 to 180degrees(seeFigure 2). Thesepulses

ROBOTSCIEN CE&TECHNOLOGY

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Deceleration Time

Maximum Velocity

' ! - - - -- - - - -L-- - - - - - ---k---.Time

Frictio n is atorqueload .Therearetwotypesto cons ider.

Sta t ic frictionisthat st ickytype of frict ion thatmust be overco me with a little extra torq ue befor e an object begins to mov e. Sta n da rd fricti on creates coun te racting torque,or torq ue loading,when a sha ft isrotating.The servo an d load joints(an y add it iona l jointsor pointsof con tac t in the robo t that theservoismoving) aresources of friction.Measuringfrict ion on a rota rysyste mcan be donewith mod er at e effor t. For prac t ica l purposes,keep friction losses low by usin g ball bearingsin both servo an d load jointsif planning to move heavyload s.More important is to cons ider these effects oftorqu e loads agains tyourtorq uesurplus.

Another sourceoftorque loadingisin ertia.Thisload is crea te d when the shaft is accele ra t ing or decel er ating.

Inerti a isthe prop ertythat causes an objec t in motion to stay in motion andan objectat rest to stay at rest.In thefishingpole examp le, imagine a 40-inch-long pole with a I-ounce sin ke r attached to the en d. Raise the pole to the 12 o'clock positi on, the n quickl y lower it and abruptly stop at the 3 o'clock posit ion.Since the poleisflexible,it willovershoo tthe3 o'clock positi ons, andyou willfeelan incr ease of torque loading. In fact , you'd have togrip thehandletighter becauseof it, and!

if you couldn 't provid e eno ugh holdingtorque, your hand mov em entswould contribute to overshoot ing. Newton's first lawof motion states tha t force eq ua ls mass times acceleration (F=MA).The rota tiona lequivalen t isT'-Ic, or torque (T) equalsmassmom ent of inertia (I) times rotati onalaccele ra t ion (ex).The amo untofine rt ia in a rota ry load is eq ualto the masstimesthe sq ua re of its distance to the cen te r of rotation (I=Mr2) , an d more accuratelyisthe sumoftheprodu ct s of eve ry particleof mass an d their individu aldistances to the cen te rofro- tati on sq ua red. Math em a ti c all y: 1=IM rn 2of every particlen. Inertiaincr eases thefur therout from the cen- ter anobjec t isbecau sethe object travelsmor edistan ce for the same rotat ional arc. Thus in linear units it is traveling faste r andaccele ra tingquicker. Thismean sthat ifyou tried the movem ents asdesc ribed with a l-Inch fishingpol e an d a40-ounce weight, it wouldn' tcrea te

Velocity Acceleration Rater Acceleration/

Time

1 / /

~----r---"

Torqu eis the rotary equivalen tof forc e.Anyimpediment to a servo 'soutput torque is known as a torque load.

Weight on alevered mechanism (like afishing poleor roboticarm ) producestorqu e. One exampleoftorque is abeam withone endattached to a shaft ,and the othe r weigh ted .The torque produced isjustlikethedownward turn ing force you feelwhen holding afishingpolewith a weighton the en d.Asmoreweightis adde d, thetorque increases.Thinkof the amo untofoutput torque available from a servo as a surplus. Thereis on lysomuch atyour disposal before it begins to affect performance.Torque load s,like the weightedbeam ,redu cethe surplus. There are severalother sources oftorqu e to cons ide r besides the stat ictorque loading caused by a weigh te d beam. We will disc uss three basic elements of motion: torq ue , frict ion ,and ine rt ia.

I 20 ms (50 HZ)i

- -1 r 1-2 ms I

-~ ~-

Figure2.A ty/Jicall-2 mspulsewidth commandsignalwithina20ms cycle timeof aPulseWidthModulation (PWM )controlsystem.

Physics of Motion

repeat abo ut every 20 to30 ms.Pulsewidthswere designed tobe10% or less of the totalrep etit ive cycle time to allowa sing le rad iotransm itter tomultiplex(combine)atleasteight pulsesin a row in each cycle , making it an eight-c han n el syste m. The receive r de-multip lexesthese signalsinto eigh t individu alpulses, one for eachservo. The exact pulsewidth variesalittlebetw een servo manufacturers,butmost ope rate in0.3to 2.3 and 0.7to 2.7 msran gesfor servo positi ons of 0 to 180 degreesrespectivel y.Thesepar am et er smay vary. For exam ple, measurem entsmade on an Airtronics94 102 servo yie lde da 0.5 to 2.25 msran ge, an da] RServoNES51 7servo yielded0.7 to 2.25msran ge.

The electr ica l requir em ent s of a servo are fairly stra igh tforward. Servos are design ed to work at 4.8 to 6.0 Volts.The high er the voltage , the more torque the servo can supp ly, and thefaster it will ope ra te. Some roboticists havebeen success ful usin gvoltages ashigh as7.2Volts. On the othe r hand, the servos quit working when the voltage fallsbelow abo ut3 Volts.

r I

I

I

m

ROBOTSCIENCE&TECHNOLOGYI

Figure3.Illustration of sequentialcomponents of amovefromA toB.

(17)

J

Graph1. CompzmsonofjJosition vs velocity for a ty!)icalservomovement.

This particul ar moti on profil e resul ted in an accelerati on time of 76.3 ms and a decel erati on time of 62 ms with a cons ta n t veloc ity time of 136ms,The tota ltrans it ion took 275ms or0.275 s.The servo hasnonlinear accele rat io nand decelerati on ramps,so calculati ng distancetraveled during thesetimesisnot straigh tfo rward. Takin gmeasurem ents from theTime vs. Positi on trace of Grap h 1 the veloc ity during cons ta n t veloc ity is calculated to be 60%.206 s. One can then calculate that the servo moved 39.6°(0.136/0.206 x 60°) duringthe consta ntveloc ityportionwith therem aining 20. 4° mo v em ent occu rr ing during accele ra t io n and decelerati onphases.

The acceleration and decelerati on times ofan yo ne servo are typicall y not symme t rica l. Some servos hav e quick er accelerat ion tha n decel erati on wh ile othe r servos are the opposite. Theran ge is from30 to 90 ms each for common servos, and abo ut 0.1 to 0.15 s comb ine d. Measur em ents tak en of severa l 600/0.22s servos indica t e that it tak es any whe re from0.28to 0.32 secondsto complete a 60°move from zeroveloc ity to zero veloc ity. Timingmeasurem ents of aHitecHS-300at4.8Volt s,rat ed at 60%.19s and performing a 60°move were tak en usin g a very light instrument grade potenti om et er attache d to the output sha ft of the servo. Results aresho wn in Grap h 1.

HS- 300sb~vo:60 degree mbve Acceleration:76.3ms'

I

-Con~hiriivelocity:136rns

I .

Deceleration:62 ms .Ma~.Vel::.206s'/6 0 de.

Transit time: 275 ms .

nearly the same amo untof torqu eduring accelerat ion anddecelerat ion. For prac t ica l purposes,keep masslow andas close to the cente rof rota t ionaspossibl e.Noti ce from the T=In formula tha t lower values of accele ra- tion(«)willalso lower the torquegene rated.Alpha(«) canbe eithe r negati ve orpositi vedepending on whether theload is accelerat ingordecele rating. So, cons ide r the directionof the gene rated torque whe n allocati ngyour torque budget.

Typica l Servo Specifications

POSITIVE LOGIC ENGINEERING

. --~ --~~._-~.._ -

. _-_

...._ - - .

Two importa ntperforma ncespec ificat ionssupp liedby servo man ufact urers are outp ut torque an d transit time (som e manufac tu rer s call it operating sjJeed ). Outp ut torque is specified in units of ounce -inc hes,or kilogram -centimet ers, and indica tes the load the servo can move before sta lling.

Standa rd size commo n servos have a torq ue rating of 40 ounce- inc hes (oz-in .}. A way to visua lize this isto use the fishi ngpoleanalogyagain.Attach inga40-ounce weigh ton a l-In ch pole would result in 40 oz-in. of torque. Othe r equ iva lents would be al-ounceweightto a40-in ch pole, or a 2-ounce weightona 20-inc hpole.

Ano the r important performa nce- rela tedservospec ifica t ion is transit time or operat ing speed .Scient ifica lly known as radialveloc ity,we'llcall itrotaryveloc ity.Commo nservos canrotateat a veloc ityof60 degrees every 0.22 seconds, or 272 degrees/seco n d, or 45 rpm, once it has reached full veloc ity. That isto saythatthis sameservocan no tsta rt from po int (A) at zero veloc ity and end up at zero veloc ity at poin t (B), 60degrees away, in 0.22 seconds.One hasto consider acceleration and decelerati on times, and duringthese times, the average velocity islessthan thenominalvelocit y of the servo. Figure 3 sequen tially illustrat es the compone nts of a comp lete movefrom sta rt (A) tofinish(B).

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ROBOTSCIENCE&TECHNOLOGY

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Aservo param eter of interestto the robo t design er,but not usu all y provid ed by manufacturers of servos, is power cons umpt ion. There are two major compo ne n ts in servos that utilize elec trica l power. One istheelectroniccircuitry.

Powerforthe circuitry, the standbycurrent, isalwaysrequired and istypicall y abo ut 5 to 10 mA. The othe rcompo ne nt that cons u mes pow er is the motor. The motor current requirem ent isdirectlyproportional to output torque. The outp ut torqu e ofa servo could bedetermined bymeasuring theinputcurren tan dsubtrac t ing the sta n dbycur ren t. This yiel dsthe relativ e output torque.Forsta nda rdservos, thisis on the order of 10 mA/oz-in.The measure ofa mot or's or servo'scurren tvs. torque isknown asitsTorque Cons ta n t. When a servo accelera tes an inerti al load , extra torque loadingisrealized, and high currents will result.High currents cancausea voltage drop across yourpowersource (typicall y a batter y pack).This can cause contro l probl em s if the voltage falls below that required to maintain the control system. The simplest cure is to use two batt er ypacks, one for the servosan dano the r for the con tro ls.

Servo and Systems

Performance Parameters

The stock acceleration an d veloc ity rat es of servos are of conce rn for mot ioncon tro lapp lications.Unlessdesigning a robot to imitat e a street mime ,it isnot a good idea to have high accelerations.Not on lydoes th is lookunnatural;itcan alsocauseovershoot and excessive stress on the gearsand othe rmecha n icalcompo ne nts.It canalsocause high current trans ients due to excessive torque from high inertia loads.

The more gadgetsattache d to the load ,theworse it gets due to the added iner t ia . The proble m can be allev iate d by decreasing the accelerat ion and decel er ati on rates of the servo.In fact, the high veloc ities are notmuch ofaproblem if you can contro l accele rat ion. With high inertia load s accelerat ion may have to be decreased to such an exte n t that maximum veloc ity maynotbeattainabl edue totime cons traints (seeFigure4).

Velocity

Maximum - - - - - - - Velocity

L;"---~-. Time

Figure4.High inertia loadsmaypreventreachingmaximum velocity before deceleration is requiredtostopat the!)ro!lerlocation.

II.

ROBOTSCIENCE&TECHN OLOGY I

Herewesee that alow accelerat ion rate precludesreaching maximumvelo citybeforedeceleration comme n ces inorder to achieve a complete stop at the correc t positi on within thetime cons tra int.

System Stiffness

St iffness is aver yimportant parame ter. The overallst iffness ofa servo isdet ermin ed bythene t sumof several electrical and mechanicalproperties.Theseinclude controlsyste mgain (electrical gain ), deadb and, backlash ,an den dplay.Gainand deadband are elec trica l prop erties ofservos. Backl ash and en dplay are mechanical prop erti es. These prop erties are explaine d individu all ybelow.

Control system gain isresponsibl efor the electrica lst iffness ofa servo. Gain isthe slope of a motor 's output tor qu e vs, ang ular positi on error. Aservowith atorque rat ingof40oz- in. does not output its full torque instantly when a small erro roccurs.It hap pens gradua llyand it maytake 10 to 2C degrees(withsta ndardservos)of ang ularpositionerro r before thefulloutput torqu eis app lied.An examplewould belifting with a robo t ic arma 20 oz-in.load usin g one servo with a st iffnessof0.5degree/oz-in.Itwould take a10-degree position erro r just to lift the objec t (0.5 degrees x 20 oz-in.), and its positi on would always rem ain at least 10 degrees in error, An II-degree move comma nd would lift the load just one degree.For systemswithvarying loads,alarge stiffnesserror would adve rse ly affect re pea tabil ity. Servos wit h higher out put torque , give n the same load , are genera lly stiffer.

Electrical gain is a produce rof stiffnessandislinear, whereas mechanicalprop ertiesdegrade stiffnessand arenonl in ear.

Deadband is an area of movem ent aroun dthe comma nded positi on where a servo does not respo nd.When a servo is close to itscomma n d posit ion and the error signa lis small.

some servosare design ed not to'respond.Thisis the case in some industri al applica t ions,espec iallythosewith high gain (very st iff) servo syste ms. It is used to reduce noise and ditheringnear the comma n dposit ion.Thisishard to verify

in thecaseofRICservos , but itcan befelt.

Backl ash . Manymanufacturersclaimtheir servos ha ve zerc backlash .The internal gear train actua lly doeshave some backl ash, but itseffectsare almos telim ina tedonthe system levelby the positi on feedback device (the potentiom et er) being directly attach ed to the out pu t shaft. The servo's con tro l syste m can corr ect its positi on to compe nsa te for mech ani calbacklash.Thepotentiom et ers also havebackl ash but it isusually avery sma llamo un t.When cha ng ingvelocity or direction, th e servo's con tro l system response time for backlash compensat ion maybepercei vabl e. The backl ash responsetimemay causeovershoot ing during acce lerat ion an d decelerati on, especi all yfor high inertialoads.For these

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