Optimal Sensor Placement for Cooperative Distributed Vision

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1 Opmal Senso Placemen fo Coopeave Dsbued Vson Lus E. Navao-Semen, John M. Dolan, and Padeep K. Khosla, Depamen of Eleccal and Compue Engneeng he Robocs Insue Canege Mellon Unves Psbugh, PA, USA {lenscmu, jmd, Absac hs pape descbes a mehod fo obsevng maneuveng ages usng a goup of moble obos equpped wh vdeo cameas. hese obos ae pa of a eam of small-sze (7x7x7 cm) obos confgued fom modula componens ha collaboae o accomplsh a gven ask. he cameas seek o obseve he age whle facng as much as possble fom he especve vewpons. hs wok consdes he poblem of schedulng and maneuveng he cameas based on he evaluaon of he cuen posons n ems of how well can he manan a fonal vew of he age. We descbe ou appoach, whch dsbues he ask among seveal obos and avods exensve eneg consumpon on a sngle obo. We exploe he concep n smulaon and pesen esuls. Kewods-senso placemen; coopeave sensos; dsbued vson; auomac suvellance. I. INRODUCION Suvellance, econnassance, and secu ae good examples of dffcul o edous undeakngs ha can benef fom he use of eams of oboc sensos capable of modfng he vanage pons. A eam of obos has dsnc advanages ove sngle obos wh espec o sensng. eam membes exchange senso nfomaon, collaboae o ack and denf ages, o even asss each ohe o ovecome obsacles. B coodnang s membes, a eam can explo nfomaon deved fom mulple dspaae vewpons. A sngle obo, hough poenall equpped wh a lage aa of dffeen sensng modales, s lmed a an one me o a sngle vewpon. Moeove, a eam of obos can smulaneousl collec nfomaon fom mulple locaons. One mpoan aspec of suvellance and vglance asks ha s fequenl addessed s ha of obsevng and ackng he movemens of people o vehcles navgang whn he confnes of a pacula aea. In he case of obsevng people, s ofen mpoan no onl o deec and ack a peson, bu also o denf hm/he, o a leas o poduce mages ha could be used n he fuue o deemne whehe a peson was pesen n a pacula aea a an gven me/dae. he coec placemen of a vdeo camea wh espec o he subjec o age s cucal o poduce a useful mage. A good phoogaphe alwas es o capue a scene fom he bes possble angle. hee ae seveal facos o be consdeed when evaluang how good a pacula camea poson s n ems of he chaacescs of he mage ha wll be poduced. Fo example, consde a convenonal mug sho made fo polce fles. If he suspec s locaed ehe oo close o o oo fa awa fom he camea, dsncve chaacescs of he suspec s face can be los n he pcue. In he same manne, s mpoan ha he suspec faces he camea a cean angles fo boh he fonal and pofle shos. Reseach n hs aea pcall consdes sac placemen of sensos, and deals wh ssues elaed o polgon vsbl [7]. Some ohe eseaches have consdeed he use of sensos ha shf he posons ove me o ensue ha ages eman unde suvellance a all mes [][]. Howeve, mos of hese appoaches do no ake no accoun ha some applcaons eque he senso o be posoned wh a pacula oenaon, and offe soluons n whch jus he deecon of a age s consdeed sasfaco. In hs pape we descbe some pelmna wok on an auomac age obsevaon ssem o be used pmal b ou eam of cenmee-scale obos, called Mllbos []. he Mllbos ae capable of cang dffeen pes of sensos whle mananng poson esmaes, and cuenl ae able o collaboae o exploe and map aeas naccessble o lage obos. We ae cuenl developng a ssem n whch vdeo cameas seek o obseve he age whle fonall facng as much as possble fom he especve vewpons fo suvellance asks. he same ssem can be used fo ohe applcaons ha eque he obsevaon of a movng age fo dffeen facng angles. II. PROBLEM DESCRIPION he Opmal Senso Placemen poblem suded n hs pape s defned as follows: gven S: A fne wo-dmensonal spaal egon, wh enances and exs. R: A subse of M obos equpped wh vdeo cameas, deploed as pa of a lage se of N obos R. { } R =,,, M : A se of K ages navgang whn S. { } S =,,, K

2 x x wh ange [,], whee x ( ) and x ( ) ae sae vecos ha epesen he Defne he evaluaon funcon E ( (), () ) poson and oenaon of obo (o camea) and age especvel. hs evaluaon funcon akes no accoun he camea s opcal confguaon (.e., focal lengh, feld of vew, ec.), he desed mage sze of he age, he dsance fom he camea o he age, and he angle beween he age s facng decon and he vew decon of he camea. A obo R s opmall placed wh espec o he age a me when he evaluaon funcon E( (), () ) = he evaluaon funcon E ( (), ()) x x. he goal s o maxmze he mean value of x x ove me hough he adequae selecon and maneuveng of he se of obos R, =,, M ove me seps. III. RELAED WORK he wok mos closel elaed o ous nvolves he concep of acve vson, whch mples compue vson mplemened wh a movable camea. Seveal eseaches have exploed he use of mulple cameas fo coopeave mulsenso suvellance; Collns e al. [8] descbe a mulcamea suvellance ssem ha allows a sngle human opeao o mono acves n a clueed envonmen usng a dsbued newok of acve vdeo sensos. Masuama e al. [7] nvesgae he use of evaluaon funcons fo plannng laou of mulple cameas n D sac scenes. he wok assumes ha he cameas eman n fxed posons; he senso placemen poblem s solved n he off-lne camea wok plannng. hs wok dffes fom ous n ha ou obos mus dnamcall shf he posons ove me o ensue a fonal vew of he age. Pake e al [] descbe he use of mulple obos fo coopeave obsevaon of ages. Howeve, hs wok assumes obos wh 6 feld of vew sensos, and does no enfoce an pacula senso-age aangemen. IV. APPROACH he aonale behnd ou saeg s smple: he obos wll eman opeaonal fo as long as he eneg souces can suppl he powe equed. I s well known ha one of he mos eneg-consumng asks ha an moble obo can pefom s o move fom one place o anohe. Consequenl, n ode o conseve eneg, we wan he obos o shf he posons as lle as possble. Fo hs eason, s cucal o know exacl whee he cameas should be placed, n ode o use he avalable eneg effcenl. I s easonable o assume ha he closes obo o he age should be he one assgned o obseve. he shoe he dsance a obo has o move, he bee n ems of eneg. Howeve, once a obo has moved o he opmal obsevaon poson, wll ve lkel become he closes obo o he opmal poson mos of he me, hus ceang a suaon n whch one obo s pemanenl assgned o obseve he age. Alhough hee ae a numbe of easons wh hs suaon ma be dsadvanageous, we ae mosl concened abou he exensve use of a sngle obo s eneg eseve. hs s paculal mpoan n he case of he Mllbos, snce he baees end o de fase when he shf he posons connuousl. Consequenl, we seek o dsbue he obsevaon ask among mulple obos. hee ae wo basc poblems nvolved n ou appoach: ) fndng he opmal senso placemen, and ) selecon of he combnaon of sensos o be used a an gven me. hese opcs ae descbed n he followng secons. A. Senso Evaluaon Funcon We have modfed he evaluaon funcons used n [7] and exended he concep fom sacall o dnamcall posoned cameas. All pons wh an unobsuced vew of a age ae evaluaed wh espec o wo vaables: dsance o age, and he angle beween he age s facng decon and he vew decon of he camea. he dsance o age affecs he appaen sze of he age n he mage. he opmal dsance o age dop s deemned befoehand, and akes no accoun he opcal confguaon of he camea, and he sze of he age. he desed angle beween he age s facng decon and he vew decon of he camea s ou pma concen, and s deemned b he naue of he applcaon. In hs pape we consde he full fonal facng angle o be opmal (.e., he age s facng sagh a he camea), alhough n some cases he use mgh wsh o obseve he age a a dffeen angle. Le us consde a age a me. he cuen age sae s descbed b x = x ϕ, whch ncludes s cuen poson and facng angle. Smlal, assume ha he sae veco descbng a vdeo camea caed b a obo s gven b x = x θ. he evaluaon of (, ) age s gven b ( x (), x ()) E ds exp x wh espec o s dsance o he = ( x x ) + ( ) d σ op Equaon () esembles a Gaussan dsbuon, whch peaks when he dsance beween ( x, ) and ( x, ) s equal o d op. he paamee σ adjuss how seveel he devaon fom he opmal dsance, d op, s penalzed. In ode o evaluae he angle beween he age s facng decon and he vew decon of he camea, he vew am decon ha cenes he age nsde he mage fame, θ, s compued fs. hs s smpl he angle of he un veco ha, x,, as adaes fom he pon ( x ) owad he pon ( ) ()

3 age ( x, ) Fgue. Geome of he Camea-age aangemen. am shown n Fg.. he compuaon of θ smplfes he calculaon of he opmal vew decon, snce educes he seach space fo he opmal soluon. We make he assumpon ha he cameas ae dven b a holonomc dve mechansm, so he can be oened equall well along an beang, nowhsandng he oenaon of he obo. he opmal vew decon of he camea occus when he age s facng sagh a he camea. As shown n Fg., when am am θ = θ he angula dsance θ ϕ povdes an ndcaon of how well he camea manans a fonal vew of he age. he evaluaon of ( x, ) wh espec o he facng angle s gven b am Efacng ( x (), x ()) = ( cos( ) θ ϕ ) () am Equaon () has a mnmum when θ = ϕ,.e., when boh he camea and he age ae ponng n he same decon. On he ohe hand, () peaks when he angula dsance equals π (o π), when he camea and age pon a one anohe. he oal evaluaon s hen compued b mulplng he effecs of boh evaluaon funcons () and (): ( (), () ) E x x = E E () oal ds facng he opmal camea poson fo a age can hen be deemned b fndng he poson n S ha maxmzes he evaluaon funcon: x = ag max E () op Camea ( x, ) ϕ oal am θ = θ ( x, ) am θ Fg. llusaes he use of () fo evaluang all pons suoundng a age. As expeced, he opmal camea poson s ndcaed b a global maxmum locaed n fon of he age, a a dsance d op. Y poson E oal : age (face angle = π/) - X poson Fgue. hs plo llusaes he pefomance of he evaluaon funcon. In hs plo, d op = and σ =.. he evaluaon funcon peaks a he pon (,), whch ndcaes he opmal camea poson. B mulplng he oal evaluaon funcon () compued ndvduall fo each age, s possble o deemne he opmal placemen of a camea wh espec o mulple ages: E = E, () combned oal K K Ls whee Ls denoes a ls of he objecs o be obseved b he camea. Fo example, consde he case n whch one camea s equed o obseve wo ages, as shown n Fg.. he opmal camea poson s compued fo each age sepaael, and hen he poduc of he ndvdual evaluaon funcons s calculaed. As expeced, hee s a pon n he (x, ) plane ha maxmzes he evaluaon funcon fo boh ages. Howeve, s neesng o noe ha hs pon, hough poduces he bes possble vew of wo ages a he same me, mgh no poduce a useful pcue of boh ages (fo nsance, n Fg. he opmal camea poson was evaluaed a onl 87%). Y poson - - Maxmum value = X poson ages Fgue.One camea obsevng wo ages. he bes mage poduced s evaluaed as 87% of he maxmum value.

4 Noneheless, he value of hs combned evaluaon funcon s sll a useful ndcao ha could be used o decde whehe one o wo cameas should be scheduled o obseve boh ages. B. Saeg fo Senso Selecon In hs secon, an algohm fo senso selecon and schedulng s pesened. As menoned befoe, he goal s o maxmze he mean value of he evaluaon funcon E ( x (), ()) x ove me hough he adequae selecon and maneuveng of obos R, =,, M ove me seps, whle educng he collecve use of bae powe. he evaluaon funcon () s used o fnd he opmal camea poson, and plas a cenal ole n ou algohm. he algohm s he followng: Gven R, S, and, and he opeaon paamees d op, σ,, execue he followng seps eve seconds:. Oban an esmae of x fo all navgang n S a me. (hs s usuall done usng ohe obos n R ).. Compue opmal camea posons fo all, usng (). If an opmal camea poson canno be found (.e. no sngle global maxmum s pesen), o he maxmum evaluaon numbe s below a cean heshold (.e., he vew s no good enough), ncease he numbe of cameas o obseve he ages b one unl a se of opmal posons s found.. Fnd he senso R ha s closes (Eucldean dsance) o each opmal poson found n sep, and assgn. If hee s a conflc (.e. one obo s closes o wo o moe ages ha canno be obseved smulaneousl), he nex closes obo s assgned.. Maneuve all assgned senso no he coespondng ages. he nex secon pesens smulaons ha llusae he pefomance of hs algohm. V. SIMULAIONS We have conduced a sees of smulaon expemens o valdae ou deas. he objecve s o llusae he compuaon of opmal camea poson usng evaluaon funcons. Ou expemens wee pefomed usng a Mllbo smulao. hs smulao has been exensvel used b ou eam, and esembles he mos elevan chaacescs of he Mllbos wh a good degee of fdel. I s assumed ha all sensos know he posons a all mes, as he Mllbos do. he Appendx descbes he Mllbos and he localzaon ssem n deal. he ackng conolle used s descbed n [6]. In he fs smulaon he goal s o manan a fonal vew of boh objecs as much as possble, usng as few cameas as possble. hs expemen nvolves wo objecs movng a consan bu dffeen speeds, as shown n Fg.. wo sees of bg ccles denoe he poson and oenaon of he wo objecs a eve me sep. he elave dsance beween consecuve ccles on each objec s pah s dffeen, snce he objecs move a dffeen veloces. wo cameas ae deploed n he aea. Boh cameas can dnamcall shf he posons. he squae maks ndcae he nal poson of he cameas. he sees of small ccles movng fom lef o uppe gh ndcaes he ajeco of he opmal camea poson, f a sngle camea wee used o obseve he wo objecs smulaneousl fo he duaon of he expemen. hs opmal poson s compued usng (). As shown n he op plo of Fg., dung he fs seconds he opmal obsevaon poson s no able o poduce an adequae mage of boh objecs. he evaluaon numbe emans below., whch was se as he heshold value. Consequenl, camea s nall assgned o obseve Objec, whle Objec s obseved b camea. he evaluaon of he opmal camea placemen evenuall eaches he heshold afe seconds, ndcang ha a camea s able b self o manan an adequae fonal vew of boh objecs smulaneousl. A ha me, camea s he closes o he opmal camea poson and consequenl s assgned o obseve boh objecs, whle camea s eleased and sopped. Boh camea evaluaons ae shown n Fg., boom plo. he second smulaon s smla. he goal s also o manan a fonal vew of boh objecs as much as possble, usng as few cameas as possble. hs expemen nvolves wo objecs movng fom lef o gh a consan bu dffeen speeds, as shown n Fg. 6. wo sees of bg ccles denoe he poson and oenaon of he wo objecs a eve me sep. he elave dsance beween consecuve ccles on each objec s pah s dffeen, snce he objecs move a dffeen veloces. Egh cameas ae deploed along an magna hallwa. hs me, he cameas can dnamcall shf he posons. he squae maks ndcae he nal poson and vew decon of he cameas. he sees of small ccles movng fom lef o gh ndcae he ajeco of he opmal camea poson, f a sngle camea wee used o obseve he wo objecs smulaneousl fo he duaon of he expemen. Y poson Objec Objec - 6 X poson Fgue. Obsevng mulple objecs. Inall he opmal obsevaon poson s no able o poduce an adequae mage of boh objecs. Evenuall, camea s assgned o obseve boh objecs. Opmal pah (fo a sngle camea obsevng wo objecs)

5 hs opmal poson s compued usng (). Inall, camea s able b self o manan an adequae fonal vew of boh objecs smulaneousl. hs s obseved n he ajeco of camea, whch nall follows he ajeco of he opmal camea poson. Due o he dffeence n speeds, he opmal obsevaon poson s no longe able o poduce a sasfaco mage of boh objecs and he evaluaon numbe dops below., whch was se as he heshold value. Consequenl, camea 6 s called no acon afe seconds. he esuls ae shown n Fg. 7. I s neesng o obseve n Fg.7 ha he evaluaon funcon fo camea eaches a sead sae below he maxmum of. hs s due o he fac ha he poson conolle used fo ackng fals o keep up he pace and lags wh espec o he desed poson. hs esembles he behavo obseved n he eal obos. I s also neesng o Y poson Camea evaluaon (one camea obsevng wo objecs) me, sec me, sec Camea evaluaon (one camea pe objec) Objec Objec Camea Camea Fgue.Camea evaluaon fo mulple objecs. he op plo shows he evaluaon of one camea obsevng boh ages. When he opmal poson s able o poduce a sasfaco mage, camea obseves boh objecs, and camea s eleased Opmal pah (fo a sngle camea obsevng wo objecs) X poson Fgue 6. Obsevng mulple objecs. Camea s nall able o obseve boh objecs smulaneousl. When he evaluaon of camea dopped below he heshold, a second camea was assgned o obseve Objec, whle Camea was assgned o obseve Objec. 7 Camea evaluaon (one camea obsevng wo objecs) me, sec.. Camea evaluaon (one camea pe objec) Camea Camea 6 me, sec. Fgue 7.Camea evaluaon fo mulple objecs. he op plo shows he evaluaon of camea obsevng boh ages. When he opmal poson was no able o manan a mnmum evaluaon, a second camea s called n, esulng n good obsevaon of boh objecs. noe ha he handoff ansen oveshoos fs, and hen falls befoe eachng he sead sae. hs s agan due o he behavo of he ackng conolle, whle he obo maneuves no he obsevng poson. VI. CONCLUSIONS AND FURHER WORK We have descbed a mehod fo obsevng maneuveng ages usng a goup of moble obos equpped wh vdeo cameas. We poposed an algohm fo schedulng and maneuveng he cameas based on he evaluaon of he cuen posons n ems of how well can he ake a fonal pcue of he age. We pesened smulaon esuls ha seem o ndcae he poenal of he suggesed appoach. he expemens descbed n he pecedng secon ae pelmna. he smulaons pesened do no accoun fo ohe obsacles n he envonmen, whch mos lkel wll affec he evaluaon funcon of pons n he plane. In addon, alhough he algohm s scalable, we need o fuhe es he pefomance fo seveal camea-age combnaons, and fo dffeen age maneuveng ndces. hee ae a numbe of decons n whch we would lke o expand hs eseach. In ode o be effecve, he algohm should ncopoae mechansms fo navgaon (.e. collson avodance, ec). Fuhemoe, he algohm could benef fom leanng abou he mos ansed pahs n he egon, so ha he sensos would gavae owads hgh-age-dens aeas. APPENDIX A. he Mllbos and he localzaon ssem he Mllbos ae small obos (7x7x7 cm) confgued fom modula componens. hs modula desgn allows he eam o be easl confgued o accomplsh he ask a hand. he cuen senso se ncludes RF communcaon, compuaon,

6 mobl, vdeo camea, sona (sho and long ange), IR angefnde, and PIR senso modules. Because of he small sze, he compuaonal and sensng capables of Mllbos ae lmed []. Noneheless, b explong he popees of specalzaon and collaboaon he dsadvanages mposed b small obo sze ae ovecome. B havng specalzed senso modules he eam as a whole can opmze on sze and esouces - specfcall powe. A senso s acvaed onl when he msson eques. Collaboaon s necessa o coodnae and collec nfomaon so ha he ndvdual membes of he eam can ac as a sngle logcal en. A cusom-bul localzaon ssem ha ulzes dead eckonng and ulasonc dsance measuemens beween obos enables he Mllbos o accomplsh asks such as mappng and exploaon []. he dsance beween wo obos s measued usng snchonzed ulasound and RF pulses. A concal efleco mouned above a low-cos ansduce allows he Mllbos o deec and ansm ulasonc pulses n an decon. Peodcall, each obo ha seves as a beacon ems smulaneousl a ado fequenc (RF) pulse and an ulasonc pulse. Usng he RF pulse fo snchonzaon, he dsance o he beacon s measued as he me-of-flgh of he ulasonc pulse mulpled b he speed of sound (m/s a C). he eam leade coodnaes he pngng sequence o ensue ha beacon sgnals fom mulple obos do no nefee wh one anohe. o mpove he accuac, hs pocedue s epeaed seveal mes and he sample mean s ulzed o esmae he dsance o he beacon. All he Mllbos ansm he dsance measuemens o he eam leade who calculaes he new obo posons. A maxmum lkelhood algohm deemnes he mos lkel poson of he obo gven he measued dsances o he cuen beacons. Assumng ha he dead eckonng and dsance measuemens ae nomall dsbued andom vaables, he lkelhood of beng locaed a a poson (x,) s gven b (, d, d, b(), b( ),, b( )) m P x x m ( d, σx ) ( d, σ ) ( () b (), σb ) N x x N N whee N(p,σ ) s a nomal dsbuon wh zeo mean and vaance of σ evaluaed a p, (x d, d ) s he poson measued = = (6) hough dead eckonng, () s he dsance fom he beacon o he Mllbo, m s he numbe of beacons, and b () s he sample mean of he dsance measuemens fom beacon o he Mllbo. he poblem of faul olean localzaon fo he Mllbos s addessed n []. hs wok focuses on deecng and solang measuemen fauls ha commonl occu n hs localzaon ssem. Such falues nclude dead eckonng eos when he obos collde wh undeeced obsacles, and dsance measuemen eos due o desucve nefeence beween dec and mul-pah ulasound wavefons. REFERENCES [] A. Howad, M. J. Maac, and G. S. Sukhame, Moble senso newok deplomen usng poenal felds: A dsbued, scalable soluon o he aea coveage poblem, In Poceedngs of he 6h Inenaonal Smposum on Dsbued Auonomous Robocs Ssems (DARS) Fukuoka, Japan, June -7,. [] L. E. Pake and B. Emmons, Coopeave mul-obo obsevaon of mulple movng ages, In Poceedngs of he 997 IEEE Inenaonal Confeence on Robocs and Auomaon, pp. 8-89, Albuqueque, New Mexco, Apl 997. [] L.E. Navao-Semen, C.J.J. Paeds, and P.K. Khosla, "A beacon ssem fo he localzaon of dsbued oboc eams," Inenaonal Confeence on Feld and Sevce Robocs, Psbugh, PA pp. -7, 999. [] R. Gabowsk, L. E. Navao-Semen, C.J.J. Paeds, and P. K. Khosla, "Heeogeneous eams of modula obos fo mappng and exploaon," Auonomous Robos, vol. 8, pp. 9-8,. [] R. nos, L.E. Navao-Semen, and C.J.J. Paeds, Faul olean localzaon fo eams of dsbued obos, Poceedngs of he IEEE/RSJ Inenaonal Confeence on Inellgen Robos and Ssems. Page(s): 6-66 vol.,. [6] S.O. Lee, Y.J. Cho, M.Hwang-Bo, B.J. You, and S.R. Oh, A sable age-ackng conol fo unccle moble obos, Poceedngs of he IEEE/RSJ Inenaonal Confeence on Inellgen Robos and Ssems, pp. 8-87,. [7]. Masuama,. Wada, and S. oka, Acve mage capung and dnamc scene vsualzaon b coopeave dsbued vson, Poc. s Inenaonal Confeence on Advanced Mulmeda Conen Pocessng AMCP98, pp.6-9, 998. [8] R. Collns, A. Lpon, H. Fujosh, and. Kanade, Algohms fo coopeave mulsenso suvellance, Poceedngs of he IEEE, Vol. 89, No., Ocobe,, pp

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( )

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( ) 5-1. We apply Newon s second law (specfcally, Eq. 5-). (a) We fnd he componen of he foce s ( ) ( ) F = ma = ma cos 0.0 = 1.00kg.00m/s cos 0.0 = 1.88N. (b) The y componen of he foce s ( ) ( ) F = ma = ma