TELEOPERATION OF MOBILE ROBOTS

Transcription

1 Lai Aerica Applied Research 36:79-86 (6) ELEOPERAION OF MOBILE ROBOS E SLAWIÑSKI V MU ad JF POSIGO Isiuo de Auoáica (INAU) Uiersidad Nacioal de Sa Jua A Liberador Sa Marí 9 (oese) J54ARL Sa Jua Argeia e-ail:{slawiski u jposigo}@iauusjeduar Absrac his paper proposes a sable corol srucure for bilaeral eleoperaio of obile robos he proposed corol srucure icludes a ie-delay copesaio placed o boh he local ad reoe sies of he eleoperaio syse eleoperaio experies hrough a siulaed ad real (usig Iere) couicaio chael are preseed o illusrae he perforace ad sabiliy of he proposed corol srucure Keywords asypoic sabiliy obile robos eleoperaio ie aryig delay I INRODUCION eleoperaio syses hae bee deeloped o allow hua operaors o execue asks i reoe or hazardous eiroes wih a ariey of applicaios ragig fro space o uderwaer uclear plas ad so o (Sherida 995) I geeral he bilaeral eleoperaio syses of obile robos are coposed by a local sie (where a hua operaor dries a hadcoroller deice); a reoe sie (where a obile robo ieracs wih he physical world); ad a couicaio chael ha liks boh sies he hua operaor geeraes elociy coads o he reoe obile robo while he posiio of he obile robo is back-fed o he hua operaor hrough he couicaio chael Perhaps he os ieresig case appears whe here exis a disace bewee he local ad reoe sies of a eleoperaio syse his geerally iroduces ie aryig delays addig disorio i he referece coads ad feedback sigals he presece of ie delay ay iduce isabiliy or poor perforace of a eleoperaio syse (Fiorii ad Oboe 997; Richard 3) I geeral i he desig of eleoperaio syses here is a rade-off bewee high rasparecy ad sufficie sabiliy argis (Lawrece 993) Mai corol sraegies proposed for bilaeral eleoperaio of delayed syses are described i Aderso ad Spog (989) Nieeyer ad Sloie (99) Oboe ad Fiorii (998) Oboe (3) Elhajj e al (3) ad Chopra ad Spog (3) I geeral he proposed corol srucures keep he passiiy or sabiliy a he expeses of reducig he syse rasparecy (Arcara ad Melchiorri ) his paper proposes a sable corol srucure for bilaeral eleoperaio of obile robos he proposed corol srucure is based o cobiig he elociy coad geeraed by he hua operaor i a delayed ie isa he receied posiio iforaio (which siulaes he operaor) i such oe ad he curre posiio of he obile robo o se he elociy referece of he obile robo he ie proposed delay copesaio is placed o he local ad reoe sies Moreoer experieces of eleoperaio of a obile robo are show o es he sabiliy ad perforace of he desiged eleoperaio syse he paper is orgaized as follows: Secio II gies he oaio used i his paper I secio III soe backgroud aerial o delayed differeial equaios is iroduced Secio IV preses he saee of he corol proble I Secio V a odel of he hua operaor for oio corol is preseed I Secio VI a sable corol srucure for bilaeral eleoperaio of obile robos is proposed I secio VII he sabiliy ad perforace of he proposed corol srucure are aalyzed hrough eleoperaio experies usig a siulaed ad real (Iere) couicaio chael Fially he coclusios of his paper are gie i Secio VIII II NOAION I his paper he followig oaio is used: h( ) R deoes he ie delay Here x( ) R x is he raspose of x x is he Euclidea or of x x (for a gie ie isa ) is he fucio defied by x ( θ ) = x( θ) for θ [ h( ) ] for exaple: x ( ) =x( ) x ( h) = x( h) ; ad he or is defied by x ( ) = sup x θ C () is he -diesioal space of h θ [ h() ] coiuous fucios o he ieral [ h() ] a ay ie he he fucio x C h O he oher had ( ) gie a o-liear differeiable fucio x ( ) = g( x( ) x( h) ) he icreeal gai of g is defied as g = if{ γ : g( x x ) g( y y ) γ [ x x ] [ y y ]} x x y y R III SABILIY OF DELAYED SYSEMS he robo eleoperaio syses are represeed by delayed differeial equaios I his secio we show sadard defiiios ad facs i he heory of delayed 79

2 Lai Aerica Applied Research 36:79-86 (6) fucioal differeial equaios (Krasoskii 963; Hale 977; Kolaoskii ad Myshkis 999) I addiio we propose a sabiliy codiio for syses wih ie delay which will be used i Secio VI for he sabiliy aalysis of he proposed eleoperaio syse Le s cosider he delayed fucioal differeial equaio gie by x () = f ( x ) f ( ) = () where x R x C h( ) R ad f R C h () R I is assued ha here exiss a soluio ( ) of () wih iiial daa [ ] x for θ [ h( )] wih ψ < H R which depeds coiuously o he iiial daa Fro ow o we will x ψ = x deoe he soluio or by ( ) ( ) ; Defiiio he soluio x = of () is said o be asypoically sable if a) For eery ε > ad each here exiss ρ = ρ( ε ) such ha ψ < ρ iplies ha x ( ; ψ ) < ε for all b) For eery here exiss ε = ε( ) such ha if ψ < ε he x ( ; ψ ) as If ρ ad ε are idepede fro he iiial ie he he zero-soluio is uiforly asypoically sable Fac (Krasoskii 963) Le s suppose ha he fucio f R : C h () R aps bouded ses of C h() i bouded ses of u ad w () are scalar coiuous posiie ad o-decreasig fucios If here exiss a coiuous fucioal V : R C h() R ad he followig codiios hold: u x ( ) V x x () R ad ha ( ) ( ) ( ) ( ) ( ) V ( x ) < w( x ( ) ) where V ( ) ) x (3) V alog he rajecories of (); he he soluio x = is uiforly asypoically sable Now le us cosider a o-liear syse wih ie aryig delay described by x () = f ( x() ) g( x( ) x( h) ) (4) where h( ) h ad ( ) <τ < x R R h x wih R h f :R R R ad g: R R R R I addiio we assue ha ( ) = ( ) = g for f ad Lea If a syse represeed by = f ( x) x is expoeially sable he here exis α λ R such ha λ x f ( x) λx x where x α x( ) e Proof If he syse x = f ( x) λ he i saisfies ha ( ) is expoeially sable x α x e ad herefore: λ ( ) e I x α x where I R wih I ( ) i = for < i Fro (5) he eoluio of x erifies ha λ x λα x( ) e I (6) Usig (5) ad (6) o λx x he followig ca be expressed: λ λ λ x x λ( α x( ) e )( α x( ) e ) I I x x = x f ( x) (7) Iequaliy (7) proes he proposed Lea heore Le us suppose ha he subsyse = f ( x) x of he syse (4) is expoeially sable wih rae λ he he followig codiio esures he asypoic sabiliy of he syse (4): 3 τ λ g < τ g R h <τ < (8) where λ ad ( ) he or g is he icreeal gai of he operaor g () Proof A fucioal V : R C h() R is proposed as follows g ( ) V x = x x ( ) ( ) > x x dθ (9) θ τ h() θ where he proposed fucioal icorporaes iforaio of he delayed dyaics ( g ) ha will help o reach a sabiliy codiio ha will direcly deped o he iederiaie of he aryig-ie delay ad he odelayed dyaics of he delayed syse Fro (9) ad cosiderig ha he delay h ( ) is bouded ( h( ) h ) ad ha x x = x ( ) x (by usig or properies) he he proposed fucioal V ( ) erifies codiio () gie by Fac - x ( ) V ( x ) x x h () g τ he ie-deriaie of V ( x ) alog he syse rajecories (4) is g g( h ) ( ) ( ) ( ( )) V x x f x x g x x h x x x ( h) x ( h) () τ τ Now he followig iequaliies are aaied usig or properies x ( ( )) ( ( )) g x x h x g x x h g x g x x( h) () g g 3 g x x x( h) g x g x( h) Puig () i () i yields g g h ( x ) x f ( x) 3 x x x ( h) x ( h) (3) V τ τ he hird er of he righ had i (3) is egaie defiie because h <τ < By applyig Lea o (3) (5) x 8

3 E SLAWIÑSKI V MU JF POSIGO ad orgaizig ers i yields 3 τ τ ( ) x λx x g x x (4) V Fro (4) codiio (3) Fac - is saisfied if 3 τ < τ λ g (5) Iequaliies () ad (4) erify he sabiliy codiios gie by Fac iequaliies () ad (3)- he he proposed heore is proe esurig he asypoic sabiliy of he syse (4) Figure shows he effec of he axiu deriaie of he ie delay o he sabiliy regio -gie by (5)- for hree arbirary alues g = 5 g = ad g = he achieed sabiliy codiio is idepede of he delay apliude ad i depeds o hree ai facors: he expoeial rae λ of he o-delayed syse x = f ( x) he or g of he delayed o-liear fucio g( x x( h) ) ad he axiu ie-deriaie τ of he ie delay Moreoer he greaer he eporal deriaie of he ie delay (τ ) he sroger he sabiliy of he o-delayed syse (higher λ ) o reach he sabiliy of he syse wih ie delay I addiio if g he he proposed sabiliy codiio eds o he sabiliy codiio of a o-delayed syse his is: λ < IV SAEMEN OF HE CONROL PROBLEM his secio describes he aalysed corol proble o a bilaeral eleoperaio syse of obile robos Figure shows a geeral diagra of a eleoperaio syse he hua operaor dries a obile robo hrough a had-coroller geeraig elociy coads o sed o he reoe sie which will be execued by he obile robo he obile robo ad obsacles posiio is isually back-fed o he hua operaor We suppose ha he obsacles posiio geeraes a ficiious force which depeds o he disace bewee he obile robo ad he obsacle Fig Geeral block diagra of a eleoperaio syse of a obile robo he ai sigals of he syse are he posiio x r ad force f r o he reoe sie he receied posiio x l ad force f o he local sie he elociy coad l geeraed i he local sie ad he elociy referece l r applied o he obile robo O he oher had he couicaio chael is represeed by a ie delay h coposed by a forward delay h (fro he local sie o he reoe sie) ad a backward delay h (fro he reoe sie o he local sie) ie h( ) = h ( ) h ( ) (6) We will cosider he obile robo as a uicycle locaed a a o-zero disace fro he objecie frae <g> I addiio aached o he robo here exiss he frae <a> as show i Fig 3 We cosider he ehicle posiio i Polar Coordiaes where he sae ariables are he polar coordiaes ρ α θ easured bewee he frae <g> ad he frae<a> he kieaic equaios ca be wrie as Fig Sabiliy regio i fucio of τ Fig3 Posiio ad orieaio of a obile robo 8

4 Lai Aerica Applied Research 36:79-86 (6) ρ = r cos α (7) si α α = r r ρ si α θ = r ρ Where r r are he liear ad agular elociies of he obile robo he objecie of he eleoperaio syse is ha a hua operaor (placed o he local sie) dries a obile robo (placed o he reoe sie) o reach he frae <g> i spie of he ie aryig delay his is ha he disace error (sae) i his case wihou fial orieaio- x : = [ ρ α] as sarig fro ay o-zero disace fro <g> V MODEL OF MOION CONROL OF HE HUMAN OPERAOR his secio preses a odel for he oio corol of he hua operaor which will be used laer (Secio VI) by he proposed delay copesaio A Hua operaor s odel for posiio corol he kieaic odel proposed for he posiio coroller of he hua operaor which geeraes elociy coads [ ] l = l l is he followig (Slawiñski e al 5): l = kρ (8) l = kα k siα where k k > Iroducig he hua coroller (8) io he kieaic equaios of he obile robo (7) we obai he followig closed loop equaios for he sae x := [ ρα ]: ρ = k ρ cos α (9) α = k α Lea he o-delayed eleoperaio syse (gie by (9)) of a obile robo (7) drie by a hua coroller represeed by (8) is expoeially sable wih rae λ = i{ k k } Proof he proposed Lyapuo cadidae fucio is V ( ρ α ) = ρ α () V alog he rajecories of he syse (9) is V = k ρ cos α k α () he ie deriaie of ( ) ρα Reark : he ie-deriaie of he fucioal V ( ρα) is egaie defiie () he he riial soluio is globally asypoically sable Reark : Fro (9) he soluio for α is k α () = α ( ) e he iiial codiio has a rage gie by α() π he proble o esablish a expoeial respose o ρ is resoled by seps: a) If he iiial codiio is α( ) dπ where d is a posiie arbirary cosa lower ha 5 - he () ca be expressed as ' V < k ρ k α () where k ' = k cos ( dπ ) > Fro () ad () is siple o deduce ha he o-delay syse is expoeially ' locally sable wih expoeial rae k { k k } = i b) If he iiial codiio is α( ) > dπ he here exiss a fiie ie defied by dπ = l (fro k π Reark ) which assures ha α( ) dπ c) We propose ha he respose of ρ is bouded by k ( ) ( ) e k ρ e ρ (3) d) If fro (3) ad cosiderig ha he syse is globally asypoically sable Reark - i yields k ( ) ( ) ( ) e k ρ ρ ρ e e) If > he α( ) < dπ -fro (b)- he fro (a) he respose of ρ is bouded by he expoeial respose gie by (3) Reark 3: Fro seps (a) (b) (c) (d) (e) ad Reark he equilibriu poi x = [ ρ α] = is expoeially sable wih rae λ = k We choose d ear zero such ' ha k k > he λ = k = i{ k k } B Ficiious force he echaical ipedace regulaio eeds he feedback fro he ieracio force bewee he robo ad is eiroe he ieracio forces iply physical coacs wih he eiroe which i he case of obile robos eas a collisio o aoid obsacles howeer i s ecessary o ierac wih he eiroe wihou causig ay collisio I such case he ieracio force is represeed by a ficiious force which depeds o he disace bewee he robo ad he obsacle as show he Fig 4 f() f() d() Obsacle β f() <g> Fig 4 Ipedace corol wih ficiious force y x 8

5 E SLAWIÑSKI V MU JF POSIGO he agiude of he ficiious force f is copued as f () = a bd() where a b are posiie cosas such ha a bd = d is he robo-obsacle axiu disace ad d () is he robo-obsacle disace ( d() d ) which is easured hrough ulrasoic or ype-caera sesors O he oher had he agle of he ficiious force is β (see Fig 4) he ficiious force o he reoe sie is f = [ f f ] r : (see Fig ) C Reacie corol ode wih decisio of he hua operaor he ipedace odel of he hua operaor is defied by Z = Bs K where B K are posiie cosas; while he referece error is defied by ~ x = Z f where f = f cos β is he copoe of f o he robo oio direcio he referece error ~ x is rasfored o a roaio agle ψ = x~ D () applied o he posiio referece (Mu e al ); where f = f si β is he copoe of f oral o he robo s oio direcio ad D () represes he hua operaor s decisio If he eiroe ad he ask are perfecly kow he he decisio could be prediced We assue ha he ask ad eiroe are accordig o D = sig( f ) Whe he ficiious force is zero he referece error is zero oo ad he he objecie of he oio corol is achieed D Reacie corol ode of he hua operaor Whe he eiroe or he ask are o kow he he ficiious force odifies he disace error ρ ad ~ he agular error α as: [ ρ ~ α] = [ ρ α] K [ f f ] where f is he copoe of f o he robo oio direcio f is he copoe of f oral o he robo s oio direcio ad he ipedace odel of he hua operaor is defied by K = diag[ K ρ K ] R where K K > α ρ α represe he hua operaor s elasiciy i respose o ficiious force geeraed by he disace robo-obsacle E Experieal alidaio of he hua operaor s odel o drie he obile robo Figure 5 shows he execued rajecories by he obile robo drie by a hua operaor i wo differe experieces ad also he rajecory usig a auoaic corol i is coposed by boh he posiio coroller posiio described i sub-secio A ad he ipedace coroller described i sub-secio C We coclude ha he proposed odel of he hua operaor is saisfacory he ipedace loop (he desired ipedace is represeed by a sable ad proper sricly liear filer) oly odifies he referece of he oio corol Howeer i wo be cosidered laer o siplify he sabiliy aalysis of he bilaeral eleoperaio syse (Secio VI) Fig 5 rajecories of he obile robo usig aual eleoperaio ad auoaic corol VI CONROL SRUCURE FOR BILAERAL ELEOPERAION OF MOBILE ROBOS his secio describes he proposed corol srucure applied o a bilaeral eleoperaio syse of obile robos he proposed delay copesaio does o odify he feedback posiio fro he reoe sie I addiio he local sie seds a sigal l ( ) Δ( h ) o he reoe sie; his sigal cobies he elociy coad geeraed by he hua operaor i a ie isa ad he receied posiio iforaio (which siulaes he operaor) i such oe I he reoe sie he proposed delay copesaio uses he curre posiio of he obile robo o odify he sigal l ( h ) ( ( )) Δ h h ad o esablish he elociy referece r ( ) Figure 6 shows a block diagra of he delayed bilaeral syse iroducig he proposed iedelay copesaio he delay copesaio is placed o boh he local ad reoe sies ad i is defied by a approxiaed odel of he local sie (Secio V) as follows Δ = k ρ c (4) Δ = k α k siα c c where k k are he paraeers of he delay c c copesaio ad he ecor = [ Δ Δ ] Δ is he oupu of he proposed delay copesaio Fig6 Block diagra of he eleoperaio syse wih delay copesaio 83

6 Lai Aerica Applied Research 36:79-86 (6) Now we aalyze he syse sabiliy usig he proposed delay copesaio ad also cosiderig ha he local sie is represeed by a ie-iaria kieaic odel We copued he ecor = [ ] r r r (Fig 6) which is applied o he obile robo (7) as follows = ( ( h h )) Δ ( ( h h )) Δ ( ) r l = [ ( ( h h )) Δ ( ( h h )) Δ ( ) ] r l Fro (7) he eoluio of he sae := [ ρα ] (5) x of he delayed syse is gie by ρ = r siα (6) α = r r ρ We pu (6) (8) ad (4) i (5) o obai a ierediae equaio which is icorporaed i (6) describig he delayed syse as follows: ρ() ( () ()) ( ( ) ( ) ( ) ( )) () = f ρ α g ρ α ρ h α h α k ρcos α (7) c f () = k α c ~ k ρ( h) ( h) g() = ~ ~ k α( h) k ( h) ( h) ρ N ~ ~ where k = k k k = k k ad si α siα( h) c c N = c ρ ρ( h) If he delay copesaio is a exac odel of he ~ ~ local sie he [ k k ] ad herefore g i (7) he fro (9) ad (7) he syse will represe he o-delayed real syse ad fro Lea he delayed syse will be asypoically sable ~ ~ O he oher had if [ k k ] g o siplify ~ his aalysis we suppose ha k = he fro (7) he icreeal gai is ~ g = k (8) Fro heore (gie by (8)) Lea ad (8) he sabiliy codiio is expressed as 3 ~ τ λ k < (9) τ he proposed corol srucure allows us o separae he delayed syse io he o-delay real syse ( f i (7)) ad a ew delayed subsyse (delayed fucio g i (7)) I he geeral case ( g ) he proposed corol sraegy allows esurig he syse sabiliy hrough a codiio iposed o he o-delayed syse (9) ha depeds o he axiu deriaie τ of he delay ad he gai g of he delayed o-lieariy of he syse VII EXPERIMENAL RESULS o illusrae he perforace ad sabiliy of he proposed corol srucure for obile robo eleoperaio experies hae bee coduced o a 84 Pioeer DX obile robo hrough a siulaed ad real couicaio chael he hua operaor receies isual feedback of posiio fro a Logiech webca placed o he reoe sie he objecie of corol is o achiee he posiio referece aoidig a ype cylider or cube obsacle placed o he workspace of he reoe sie I should be oiced ha he ipedace corol loop is acie whe he obile robo deecs a obsacle 5 usig ulrasoic sesors a a disace less ha [ ] A eleoperaio wih siulaed delay he had-coroller used i his experie is a Logiech Wiga joysick he iiial codiio is ρ ( θ ) = 37[ ] α ( θ ) = [ rad ] for θ [ h( )] he ie delay is siulaed by sofware he used paraeers for he delay copesaio are: B = [ N ] K = 3[ N s ] for rad rad he force copesaio (sub-secio C i secio V) ad k = 4[ ] k = 5π [ rad ] for he posiio c s c s copesaio (copesaio of posiio ad force i presece of ie delay) Figure 7 shows he execued rajecories by he Pioeer DX obile robo for dierse delays he adaage of usig he delay copesaio is clear Figure 8 shows he eoluio of he sae or x = [ ρα] of he delayed eleoperaio syse for arious delays O he oher had he Fig 9 shows he eoluio of he liear elociy of he obile robo he axiu liear elociy aries bewee 4 ad 5 for he dierse experies sec he respose of he delayed eleoperaio syse usig he delay copesaio is siilar o he aual eleoperaio wihou ie delay (referece respose); herefore he perforace of he syse is good B eleoperaio hrough Iere bewee Brazil ad Argeia Now he perforace of he proposed corol srucure for bilaeral eleoperaio of a obile robo (Pioeer DX) drie by a hua operaor hrough Iere bewee Sa Jua (Argeia) ad Vioria (Espírio Sao Brazil) is preseed he had-coroller used is Fig 7 rajecories of he obile robo usig he delay copesaio for arious delays

7 E SLAWIÑSKI V MU JF POSIGO Fig 8 Eoluio of he or of he sae x Fig rajecory of he obile robo eleoperaed by a hua operaor hrough Iere Fig9 Liear elociy of he obile robo a coercial seerig wheel wih acceleraor pedal A obsacle ype-cube is placed o he workspace of he reoe sie he used paraeers for he delay copesaio are: K = 3 [ ] K = [ rad ] for he force copesaio (subsecio D i secio V) ad ρ α N N k = 4 k = π rad for he posiio [ ] 5 [ ] c s c s copesaio (copesaio of posiio ad force i presece of ie delay) Figure shows he eoluio of he ie delay h ad h (which is esiaed usig a differeiaor filer) Figure shows he rajecory of he obile robo for his experie he hua operaor dries he obile robo o reach he objecie posiio aoidig he obsacle placed i he reoe sie Fig ie-aryig delay for he experie B usig Iere o lik he local ad reoe sies Fig eporal eoluio of he disace error ρ O he oher Fig shows he eporal eoluio of he disace error ρ i eds o zero as he respose of he eleoperaio syse is saisfacory i spie of he ie aryig delay added by Iere C Sabiliy Now we aalyse he sabiliy of he eleoperaio syse he axiu ie-deriaie of he ie delay added by he siulaed ad real (Fig ) couicaio chael is approxiaely τ = O he oher had he expoeial rae of he o-delayed syse is λ = i { k k } = 4 (see Lea ) Fro (9) we ca express he sabiliy codiio o k ~ as 3 ~ ( ) ~ 4 (3) k < k < 88 ( ) Fro (3) ad he alue of k we ca coclude ha he odel used by he delay copesaio could hae paraeric errors o a perceage of % VIII CONCLUSIONS I his paper i has bee proposed a sable corol srucure for bilaeral eleoperaio syses of obile robos he proposed sraegy icludes a delay copesaio placed o he local ad reoe sies of he eleoperaio syse ad i uses a odel of he local sie Seeral experies hae show a sable respose 85

8 Lai Aerica Applied Research 36:79-86 (6) wih good perforace ad rasparecy I addiio a obile robo was drie by a hua operaor wih isual feedback hrough a siulaed ad real couicaio chael i a coiuous way Fro hese resuls we ay coclude ha he applicaio of he proposed corol srucure o a idusrial or coercial syse is feasible he fuure work will be icorporaig he dyaic odel of he hua operaor o he proposed corol srucure I addiio he paraeers of he hua operaor will be ideified o iproe he perforace of he eleoperaio syse REFERENCES Aderso RJ ad M Spog Bilaeral corol of eleoperaors wih ie delay IEEE rasacio ad Auoaic Corol (989) Arcara P ad C Melchiorri Corol schees for eloperaio wih ie delay: A coparaie sudy Roboics ad Auooous Syses () Chopra N ad M Spog Bilaeral eleoperaio oer he Iere: he ie Varyig Delay Proble Proceedigs of he Aerica Corol Coferece Deer Colorado Jue (3) Elhajj I N Xi W Fug ad Y Liu Superedia- Ehaced Iere-Based eleroboics Proceedigs of he IEEE (3) Fiorii P ad R Oboe Iere-Based eleroboics: Probles ad Approaches ICAR 97 Moerey CA July (997) Hale JK heory of Fucioal Differeial Equaios Spriger Verlag New York (977) Kolaoskii VB ad A Myshkis Iroducio o he heory ad applicaios of fucioal differeial equaios Dordrech: Kluwer Acadey (999) Krasoskii NN Sabiliy of Moio Saford Uiersiy Press (963) Lawrece A Sabiliy ad rasparecy i Bilaeral eleoperaio IEEE rasacios o Roboics ad Auoaio (993) Mu V J Posigo E Slawiñski ad B Kuche Bilaeral eleoperaio of obile robos Roboica Cabrige Uiersiy Press 3- () Nieeyer G ad JJE Sloie Sable Adapie eleoperaio IEEE Joural of Oceaic Egieerig (99) Oboe R ad P Fiorii A Desig ad Corol Eiroe for Iere-Based eleroboics he Ieraioal Joural of Roboics Research (998) Oboe R Force Reflecig eleoperaio Oer he Iere: he JBI Projec Proceedigs of he IEEE (3) Richard JP ie-delay syses: a oeriew of soe rece adaces ad ope probles Auoaica (3) Sherida B eleoperaio eleroboics ad elepresece: A Progress repor Corol Eg Pracice (995) Slawiñski E V Mu ad J Posigo Bilaeral eleoperaio of obile robos wih delay Proceedig of he IEEE Ieraioal Coferece o Mecharoics ad Auoaio (ICMA 5) Niagara Falls Caadá July (5) 86 Receied: Sepeber 5 Acceped for publicaio: March 3 6 Recoeded by Gues Ediors C De Agelo J Figueroa G García ad J Solsoa