MODEL-BASED APPROACH TO CHARACTERIZATION OF DIFFUSION PROCESSES VIA DISTRIBUTED CONTROL OF ACTUATED SENSOR NETWORKS

MODEL-BASED APPROACH TO CHARACTERIZATION OF DIFFUSION PROCESSES IA DISTRIBUTED CONTROL OF ACTUATED SENSOR NETWORKS Kevn L. Moore and YangQuan Chen Cener for Self-Organzng and Inellgen Sysems Uah Sae Unversy Logan Uah presened a 1s IFAC Symposum on Telemacs Applcaons In Auomaon and Robocs TA 2004 21-23 June 2004 Helsnk Unversy of Technology Espoo Fnland Ths work suppor by Uah Sae Unversy s Space Dynamcs Laboraory

Oulne Inroducon and Movang Examples Conrol-Theorec Problem Formulaon Addng Acuaed Acuaors Oher Applcaon Scenaros An Expermenal Tesbed and Prelmnary Resuls Techncal and Theorecal Challenges

Neworked Sensors Through hsory many echnologes have become ubuous: Moors Mcroprocessors Today a new echnology has he same promse; Neworked sensors Due o advances n n bology elecroncs nanoechnology wreless communcaons compung neworkng and robocs we can now: Desgn advanced sensors and sensor sysem Use wreless communcaons or elemery o more effecvely communcae sensor daa from a dsance han ever before Buld neworks of sensors usng wreless communcaons and compuer neworkng echnology ha can provde he capably o oban spaally-dsrbued measuremens from low-power sensors whch communcae and relay nformaon beween each oher Develop reconfgurable or adapable neworks of dsrbued sensors by provdng mobly or acuaon o he ndvdual sensors n he nework

Example Sensor Nework From Neworked Sensors for he Obecve Force by Mr. John Ecke U.S. Army Research Laboraory

Example: Cooperave UA Search

Moble CBR Threa Awareness Sysem ThreaWATCH Sensor-carryng UAs and UGs assess and rack he developmen of a hazardous plume resulng from a CBR errorsm ac.

A conamnaon even occurs resulng n a developng plume.

An nal predcon of he plume s made from a physcs-based model ha accouns for: - Geographc and oher consrans e.g. buldngs - Weaher condons wnd humdy pressure... - Dffuson convecon/advecon... Sysem dynamcs gven by: z y x f z y x u z y D x z y x u z y x u + Δ Δ +Δ

A sem-auonomous swarm of acuaed sensors s deployed o collec conamnan samples. The model-based predced conamnan concenraon s used as an aracor poenal feld for he swarm whch confgures self unformly

The acuaed sensors are characerzed as -Infrasrucure sensor nework -Wreless -Auomaed commanded by cenral -Auonomous pah-plannng ably -Roboc

As he conamnaon even connues he plume spreads. Samples are aken by he acuaed sensor swarm a he mos recen bes esmae of he plume boundary.

Usng he samples aken by he acuaed sensor swarm a new plume esmae s compued.

The sensor swarm s now deployed o he new predced plume boundary

The sensor swarm s now deployed o he new predced plume boundary where new samples are aken.

Dsrbued Sensor Nework To mplemen a dsrbued sensor nework we need A sensor relevan o he applcaon a hand Some ype of ypcally wreless communcaon capably Suable communcaon and daa flow conrol proocols Algorhms for sensor placemen and daa nerpreaon and use ncludng mul-modal daa fuson Furher a presumpon of he ueson where should he sensors be placed s ha hey can ndeed be placed eher Manually human-n-he-loop Robocally In wha follows we consder robocally-deployed sensors

Dsrbued Acuaed Sensor Nework Le us defne: An acuaed sensor s a sensor ha can move n space eher hrough self-logc or n response o a command from a supervsor. An acuaed sensor nework s a neworked collecon of acuaed sensors whch are workng ogeher o acheve some ype of nformaon collecon and processng. Noes: Use erm acuaed raher han moble Also dsngush beween auonomous and acuaed Consder anoher movang example o llusrae he use of such a nework: real-me amospherc plume denfcaon

Issues Relaed o Dsrbued Sensor Nework Developmen If we consder ssues relaed o developng a nework of acuaed sensors we can denfy he followng: 1. Approprae sensor 2. Communcaon hardware 3. Communcaon and daa conrol proocols 4. Acuaon mechansms 5. Coordnaon sraeges Here we dscuss he laer: how does one decde where o deploy a dsrbued nework of sensors?

Problem Formulaon - 1 Formulae he general problem of Coordnaon of dsrbued neworks of acuaed sensors For real-me spaal dffuson characerzaon. Mos exsng relaed work on coordnaon sraeges for swarm-ype neworks Based on he dea of ndvdual sensors followng some ype of a-pror energy funcon or graden. We propose a new dea: model-based coordnaon sraegy: Models are becomng ncreasngly well-developed n a varey of applcaon arenas. One should use all he nformaon ha s avalable when ryng o solve a problem.

Problem Formulaon - 2 A Sensor Ne: We begn by assumng we are gven a nework of acuaed sensors NS made up of a collecon of ndvdual sensors ha are defned as follows: A S : an acuaed sensor wh he followng characerscs: T 3 - locaed n space a x y z R - can communcae wh all ohers and wh a supervsor. - can generae a measuremen of neres o he applcaon defned by s whch s assumed o be a funcon of boh space and me as defned below. - can move freely n hree dmensons wh dynamcs gven by & f u A where u s he moon conrol npu for sensor S.

Problem Formulaon - 3 Sysem o be Characerzed: Nex we assume ha here exss a space-me dsrbuon of neres ha we wsh o characerze wh he dsrbued acuaed sensor nework. We denoe he dsrbuon as whch s assumed o be he soluon a known PDE wh a known nal condon 0 0. The plan dynamcs are assumed o be of he followng form whch akes no accoun dffuson and ranspor phenomena effecs such as convenon/advecon expressed n sandard vecor calculus: + Δ F Δ D Δ + g 0 0 0 where F denoes he effec of exernal possbly varable npus on he plan dynamcs e.g. wnd ran dus humdy ec. D s he dffuson funcon for he specfc problem g reflecs he effecs of consrans e.g. gravy buldng erran ec. and denoe he nal condons. 0 0 0

Problem Formulaon - 4 A Samplng Acon: I s assumed ha he oupu of he sensor S defned above as s s a measuremen of he dsrbuon of neres a wherever he sensor s locaed n space. Thus we can wre: s Exernal Inpus F Consrans g Inal Condons 0 0 0 Sysem Dynamcs PDE Oupu Dsrbuon Moon Conrol Inpu u Acuaed Sensor Dynamcs Sensor Locaon Acuaed Sensor Measuremen s Sensor Oupu

Problem Formulaon - 5 Predcon: The nex sep n he problem formulaon s o defne he predcon. Of course f we had perfec knowledge he problem would be rval. However n fac we only have esmaes of he nal condons of he exernal npus and of he consrans. Le s defne hese esmaes as F ˆˆ g ˆ and ˆ respecvely of course here are oher sources of uncerany such as parameers n he dffuson 0 funcon D bu for now we wll assume hese are known. Then we can compue he esmaed dffuson ˆ as he soluon of ˆ + Δ F ˆ ˆ Δ D Δˆ + gˆ ˆ ˆ 0 0 0 ˆ s for all and all s s s s Noce he nroducon of he acual sensor measuremens a sample pons and sample mes as s consrans for he paral dfferenal euaon.

Problem Formulaon - 6 Conrol: The nex pece we add n hs secon s he moon conrol of he acuaed sensor. There are varous ways o approach hs pece. For nsance one could ake conrol acons o be a funcon of he error beween he predced samples and he acual samples. Tha s gven a se of samples we make a predcon abou he dsrbuon. We hen move o a new pon n space and ake new samples. The error beween wha we expec o measure and wha we acually measure deermnes where we ake our nex samples. However for he momen we consder a smpler approach. We smply move he sensors so hey are unformly dsrbued relave o he predced dsrbuon. Thus we can wre sp u& H ˆ h where H denoes a ype of feed-forward energy funcon ha has he effec of compung a se of unformly dsrbued locaons around he dsrbuon and h s he conrol law used o drve he acuaed senor o s sp new sepon. sp

Problem Formulaon - 7 Goal Saemen: Fnally we need o defne he goal of he conrol acon. Ideally one would lke o acheve lm ˆ for all However hs s ue ambous. Insead may be beer o hope for makng he predcon mach a he sample pons. Thus we can defne a cos funcon J lm h ˆ g where h s a posve funcon g

4b ˆ 4a 3b 3a and all for all ˆ 2c 0 ˆ 0 0 ˆ 2b ˆ ˆ ˆ ˆ ˆ 2a 0 0 0 1b 1a subec o : ˆ lm mn sp h u H sp s s s u f s s s s s g D F g D F J h H + Δ Δ + Δ + Δ Δ + Δ & &

Exernal Inpus F Consrans g Inal Condons 0 0 0 Sysem Dynamcs PDE Oupu Dsrbuon Moon Conrol Inpu u Acuaed Sensor Dynamcs Sensor Locaon Acuaed Sensor Measuremen s Sensor Oupu Conrol Compuaon Esmaed Exernal Inpus F ˆ ˆ ˆ Predced Oupu Dsrbuon Esmaed Consrans Esmaed Inal Condons gˆ ˆ 0 0 0 Predcor

One Oher Idea We would lke o go one sep furher: Suppose we can acuae an acuaor I.e. There s a robo ha can mpac he dffuson of he plume

Based on he plume feaures predced by he swarm s measuremens a nework of moble acuaors s deployed o apply dspersal agens o counerac he effec of he conamnan.

One Oher Idea We would lke o go one sep furher: Suppose we can acuae an acuaor I.e. There s a robo ha can mpac he dffuson of he plume Suppose A A : an acuaed acuaor wh he followng characerscs T 3 - locaed n space a x y z R - can communcae wh all ohers wh all sensors and wh a supervsor. a - can generae an effec of neres o he applcaon defned by d whch s assumed o be a funcon of boh space and me. - can move freely n hree dmensons wh dynamcs gven by & a f u a A where u s he moon conrol npu for acuaor A. a

Acuaor Moon: For hs se of acuaors we defne a moon conroller gven by sp u& a a d H ˆ a h sp a We pon ou ha n he case of an acuaed acuaor he funcon H s prmarly a comparaor and d he desred dsrbuon can ypcally be aken as zero.e. we don wan any conamnan!. Conrol Goal: Whou gong no he deals we propose he followng cos funcon for he desgn of he a a funcons H and h c J lm d ˆ d Ths coss seeks o drve he predced dsrbuon o he fnal dsrbuon everywhere n space. Fnal Archecure and Problem Saemen: The euaons below gve he fnal form of he problem. Noce ha we have acually saed wo coupled problems. The sensor moon conrol problem s based on he oupu of he predcon. Bu he effec of he acuaed acuaors s shown n he dffuson funcon used n he predcon. We denoe hs as funcon a w D d d because n general he effec of a dspersal agen may no necessarly be lnear. A hs me he effec of hs couplng s no clear. One would hope o see he sandard separaon prncple emerge bu ha may no be possble. Deep research s needed o undersand hs problem. Fgure 13 shows he complee archecure.

5c ˆ 5b 5a 4b ˆ 4a 3b 3a and all for all ˆ 2c 0 ˆ 0 0 ˆ 2b ˆ ˆ ˆ ˆ ˆ 2a 0 0 0 1b 1a : subec o ˆ lm mn ˆ lm mn sp a h a u d a H sp a u a f sp h u H sp s s s u f s s s s s g d D w F g D F d d c J a h a H g h p J h H + Δ Δ Δ + + Δ Δ Δ + & & & &

F g 0 0 0 Sysem Dynamcs PDE Oupu Dsrbuon Acuaed Acuaor Acon a a d Acuaed Acuaor Dynamcs a u Acuaed Sensor Dynamcs u Sensor Locaon Acuaed Sensor Measuremen s Sensor Oupu Conrol Compuaon Conrol Compuaon Desred Oupu Dsrbuon F ˆ ˆ gˆ ˆ 0 0 0 Predcor ˆ Predced Oupu Dsrbuon

Oher Applcaons The deas presened here are wdely applcable o a large number of applcaons. Framework can be appled o any problem where here s a spaal dffuson process for whch here s an neres n predcon and conrol and where here are a lmed number of samples and/or acuaon pons avalable. Such applcaons could nclude for example Mappng he dffuson of arborne conamnans Mappng he spread of waer-borne conamnans Mappng of amospherc and space-based feaures of he earh Problems such as spaal vbraon suppresson on arplane wngs Weed managemen n an agrculural seng Anenna array coverage Ec.

Coordnaed flee of surface shps acng as a dsrbued sensor nework collec samples used o deermne he boundary of an ol spll. Coordnaed arcraf acng as an acuaed acuaor nework apply dspersan o he ol spll.

A coordnaed saelle consellaon as a dsrbued sensors nework mappng he Earh s magneosphere no drawn o scale!.

Weed Managemen Applcaon Opmal Inellgen and Co-operave pah and msson plannng Usng an arcraf or saelle map of he regon user assgned asks are opmzed usng he nellgen pah and msson planner The sysem adaps o unexpeced obsacles or erran feaures by re-plannng opmal msson and pah assgnmens Technology developed for use on varous auonomously conrolled vehcles usng dgps navgaon Prooypes eupped wh sol samplng eupmen chemcal applcaors radaon deecors ec.

Challenges and Research Opporunes for Moble Acuaor-Sensor Neworks MAS-Ne Technologcal: for he mos par mos of he echnology needed o feld a MAS-Ne sysems s COTS

Prncpal Sysem Componens UA/UG Acual ehcle Compung Plaform Handheld Conroller Sensor Payload ehcle Conrol Sys ehcle Comm Sys Ground Saon Comm Sysem HMI Sofware Sysem Operang Sysem Comms/Neworkng Proocols HMI Daabase Mechancal Assembly Avoncs/Elecroncs Sofware Deploymen Sysem Sensor Processng Plume Dynamcs Command and Conrol Algorhms UA GNC/Plannng

Challenges and Research Opporunes for Moble Acuaor-Sensor Neworks MAS-Ne Technologcal: for he mos par mos of he echnology needed o feld a MAS-Ne sysems s COTS Theorecal: a number of challenges exs ncludng: Samplng heorem: how ofen where and how close ogeher should a dffuson process be sampled so s rackable? Ths s echncally he problem of observably of a dsrbued sysem When s possble o elmnae a plume? Ths s he problem of conrollably of a dsrbued sysem Wha f we wan o conrol he shape of a plume? Ths s he problem of regonal conrollably or boundary conrol. A relaed problem s he so-called zone conrol for dsrbued sysems. Does a separaon prncple exs? Can dsrbuon predcons be done uckly enough o mplemen he sysem? Ths s a problem of compuaonal complexy

Concluson We have nroduced he dea of moble sensor neworks va several movang examples For he case of dffuson processes e.g. plume rackng we have presened a conrol-heorec problem formulaon We have also suggesed he dea of addng moble acuaors Oher possble applcaon scenaros were dscussed We have descrbed an expermenal esbed and some prelmnary resuls Fnally we menoned some of he echncal and heorecal challenges ha mus be addressed o feld a MAS-Ne sysem