Cooperative and Active Sensing in Mobile Sensor Networks for Scalar Field Mapping

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1 3 IEEE Intenatonal Confeence on Automaton Scence and Engneeng (CASE) TuBT. Coopeatve and Actve Sensng n Moble Senso Netwos fo Scala Feld Mappng Hung Manh La, Wehua Sheng and Jmng Chen Abstact Scala feld mappng has many applcatons ncludng envonmental montong, seach and escue, etc. In such applcatons thee s a need to acheve a cetan level of confdence egadng the estmates at each locaton. In ths pape, a coopeatve and actve sensng famewo s developed to enable scala feld mappng usng multple moble senso nodes. The coopeatve and actve contolle s desgned va the eal-tme feedbac of the sensng pefomance to stee the moble sensos to new locatons n ode to mpove the sensng qualty. Dung the movement of the moble sensos, the measuements fom each senso node and ts neghbos ae taen and fused wth the coespondng confdences usng dstbuted consensus fltes. As a esult an onlne map of the scala feld s bult wth a cetan level of confdence of the estmates. We conducted compute smulatons to valdate and evaluate ou poposed algothms Keywod: Actve sensng, Senso fuson, Senso netwos. I. INTRODUCTION Actve sensng n MSNs has ecently attacted much eseach nteest, especally n contol engneeng []. Some actve sensng algothms fo souce seeng and adaton mappng have been developed [] [5]. The poblem of souce seeng s fst addessed n [], and then t s thooughly studed n [3], [4] fo the case when dect gadent nfomaton of the measued quantty s unavalable. Also, the poblem of chemcal plume souce localzaton s addessed by constuctng a souce lelhood map based on Bayesan nfeence methods [3]. Moeove, localzaton of a adaton souce usng only adaton ntensty measuements has been done usng a hybd contol stategy [4]. Addtonally, actve sensng fo adaton mappng s developed n [5]. The contol algothm taes nto account sensng pefomance and dynamcs of the obseved pocess theefoe t can stee moble sensos to locatons whee they maxmze the nfomaton content of the measuement data. In ou pevous wo [6], [7], we have developed a coopeatve sensng algothm fo an MSN to buld the map of the scala feld. Based on ou algothm, all moble sensos can fom a quas lattce fomaton and collaboate togethe to estmate the value at each cell of the feld assocated wth Ths poject s suppoted by the Depatment of Defense unde DoD ARO DURIP gant 5568-CS-RIP, USA; and the Vetnamese Govenment unde the MOET (Mnsty of Educaton and Tanng) 3 pogam. Hung M. La s wth the Cente fo Advanced Infastuctue and Tanspotaton (CAIT), Rutges Unvesty, Pscataway, NJ 8854, USA, Emal: hung.la@utges.edu. Wehua Sheng s wth the School of Electcal and Compute Engneeng, Olahoma State Unvesty, Stllwate, OK 7478, USA, Emal: wehua.sheng@ostate.edu. Jmng Chen s wth the State Key Lab. of Industal Contol Technology, Depatment of Contol, Zhejang Unvesty, Hangzhou, P.R.Chna, 37,Emal: jmchen@eee.og. Confdence (Weght) x Numbe Cell Index of Cells Fg.. Low confdence cells The confdence at each cell of the scala feld. ts own confdence of estmaton. Howeve the coopeatve contolle does not nclude onlne feedbac of the estmate confdence. Hence, the sensng pefomance o the confdence does not satsfy the desed one. Ths could affect some scala feld mappng applcatons such as tempeatue feld mappng, seach and escue, whee a need exsts to acheve a cetan level of confdence egadng the estmates at each locaton. As we can see fom Fgue, usng the nomal coopeatve sensng algothm developed n ou pevous papes [6], [7], we fnd that some cells have vey low confdence. Ths means that we may mss mpotant nfomaton at these locatons (cells). Fo example, n seach and escue opeaton the MSN may mss the objects at the locatons whee the confdence of the estmate s not suffcent. Ths motvates us to develop a coopeatve and actve sensng algothm fo MSNs so that each senso only nteacts wth ts neghbos and uses the local obsevaton to automatcally adjust the confguaton of the MSNs such as elatve locaton among sensos, oentaton and focal length of the sensos (camea), etc. to adapt to the envonments and mpove the sensng pefomance. To acheve ths goal the contolle should be desgned va the eal-tme feedbac of the sensng pefomance. By ths way the contolle can stee the moble senso to move to the ght locatons of the feld n ode to mpove the sensng qualty. Fo smplcty, n ths wo we only focus on adjustng the elatve locaton among sensos. Specfcally, ou poblem focuses on how to contol the movement of the moble sensos to ensue quas /3/$3. 3 IEEE 83

2 unfom confdence on the estmates. Hee by quas unfom confdence we mean that the confdence s bounded by a lowe and uppe bound. hee c v s the small postve constant between and. The eason of ntoducng c v s to avod the vaance V (t) beng zeo when the dstance q (t) qc equals to zeo. II. SCALAR FIELD AND MEASUREMENT MODELING In ths secton we pesent the model of the scala feld and the measuement model of moble sensos. A. Model of the Scala Feld We model the scala feld of nteest as F = ΘΦ T, () hee Θ = [θ,θ,...,θ K ], and Φ = [φ,φ,...,φ K ]. φ j, j =,..., K, s a functon epesentng a densty dstbuton, and θ j s the weght of the densty dstbuton of the functonφ j. We can model the functon φ j as a b-vaate Gaussan dstbuton φ j = det(cj )(π) e (x µj x )C j (y µ j y )T,j [,,...,K]. hee [µ j x µj y ] s the mean of the dstbuton of functon φ j, and C j s covaance matx (postve defnte) and t s epesented by: [ (σ j C j = x ) c o ] j σj xy c j σj xy (σy) j, whee c j s a coelaton facto. B. Measuement Model We patton the scala feld F nto a gd of C cells. Each senso maes an obsevaton (measuement) of the scala feld at cell ( {,,...,C}) at tme step t based on the followng equaton m (t) = O (t)[f (t)+n (t)], () hee n (t) s the Gaussan nose wth zeo mean and vaance V (t) at tme step t. We assume that n s uncoelated nose whch satsfes { Cov(n (s),n V (t)) =, f s = t, othewse, hee Cov s the covaance. O (t) s the obsevablty of senso node at cell at tme step t, and t s defned as O (t) = {, f q (t) q c s, othewse, hee q R s the poston of senso node ; qc R s the locaton of cell at ts cente; and s s the sensng ange of senso node. Ths defnton tells us that f cell s nsde the sensng ange, s, of senso node then cell can be measued o obseved. Othewse the obsevablty s zeo. Each moble senso node maes an measuement at cell coespondng to ts poston. We assume that the vaance V (t) s elated to the dstance between the senso node and the locaton of the measuement accodng to: { q(t) q (t) = c +c v (, f q s (t) q ) c s, othewse, V (3) (4) III. DISTRIBUTED SENSOR FUSION ALGORITHM A. Oveall Appoach In ths secton we pesent a dstbuted senso fuson algothm to allow each senso node to fnd out an estmate of the value at each cell of the scala feld based on ts own measuement and ts neghbo s measuements. Ou algothm has two phases. Fst, at tme step t, each senso node fnds an estmate of the value of the scala feld F. Second, each senso node fnds a fnal estmate of the value of the scala feldf at each cell dung ts movement. To acheve t, we use two consensus fltes. The consensus flte s to fnd out an estmate of the value of the feld F at each cell at tme step t. Snce each moble senso node maes ts own measuement at each cell wth ts own weght (confdence), the consensus flte s used to fnd out an ageement among these confdences. At each tme step t each moble senso node needs to fnd an estmate of the value of each cell based on consensus flte, and fnd an oveall confdence of ths estmate based on consensus flte. Ths pocess can be called the spatal estmaton phase. Then, dung the movement of each senso node, t wll have multple spatal estmates of each cell assocated wth the own confdences. Hence, these spatal estmates ae fused teatvely though the weghted aveage potocol, and ths pocess can be called the tempoal estmaton phase. B. Spatal Estmaton Phase In the spatal estmaton phase, the measuements of each senso node and ts neghbos at cell at tme steptae nputs of the consensus flte. Then, the output of ths consensus s the estmate of the value of the scala feld F at cell at tme step t. Also n ths phase, the confdences (weghts) of the measuements of each senso node and ts neghbos at cell at tme step t ae nputs of the consensus flte. Then, the output of ths consensus s the estmate of the confdence of the measuement of the scala feld at cell at tme step t. ) Consensus Flte : Dstbuted consensus [7], [8] s an mpotant computatonal tool to acheve coopeatve sensng. We consde dstbuted lnea teatons of the followng fom x (l+) = w(l)x (l)+ wj(l)x j(l), (5) j N (t) hee l s teaton ndex. The ntal condton fo the state s gven as x (l = ) = m (t). The weght, w (l), s the self weght o vetex weght of each senso to cell, and wj (l) s the edge weght between senso and senso j. Ou poblem hee s to estmate the value of the feld F at each cell at each tme step t. Snce each senso node maes the obsevaton at cell at tme step t based on ts own confdence (weght), the consensus should convege to the weghted aveage of all obsevatons (measuements) at 83

3 cell fom all senso nodes n the netwo. Ths weghted aveage s the estmate of the value at cell at tme step t, and t s computed as: n E = (t) = w (t)m (t) n = w. (6) (t) In ode to mae the consensus (5) convege to E n (6) we need to ensue that the sum of all weghts ncludng the vetex and edge weghts at each node satsfes the followng condton [6], [7]: w(l)+ wj(l) =. (7) j N (t) Fom Equaton (7) by assgnng the same value to all edge weghts we obtan: hee, w (l) s defned as wj (l) = w (l). (8) N (t) w (l) = cw (9) (t), V whee c w s a constant. If senso node does not obseve cell (O (t) = ) then the vetex weght w (l) s set to zeo. Theefoe we have the followng weght desgn c w wj V (l) = (t), f = j, w (l) N, f j,j N (t) (t), (), othewse. In ode to satsfy Equaton (7) we need the followng condton fo c w : < cw V <. () (t) Snce mn(v have: cv (t)) = ( when q s (t) q ) c =, we < cw c v < < c w < c v ( ( s () s) ). ) Consensus Flte : Snce each senso node has ts own confdence of the measuement of the value of the scala feld at each cell at each tme step t we need to fnd an ageement among the confdences of senso nodes. The consensus algothm s ntoduced to fnd the oveall confdence fom each tme step t. Ths oveall confdence s the estmated weght, W (t), of the weghted aveage potocol as shown n Equaton (7). Let y (l = ) be the confdence of the measuement of the value of the scala feld at cell at each tme step t fo senso node, o y (l = ) = w (t). Let y j (l = ) be the confdence of the measuement of the value of the scala feld at cell at each tme step t fo senso node j wth j N (t), o yj (l = ) = w jj (t). Then, we have the followng consensus flte y (l+) = w (l)y (l)+ j N (t) wj (l)y j (l), (3) In ths consensus flte, we use the Metopols weght [8] as wj(l) +max( N, f j,j N (t), N j(t) ) (t), = j N (t) w j (l), f = j,, othewse. (4) C. Tempoal Estmaton Phase Fom the consensus fltes and, to allow each senso node to on-lne estmate the value of the scala feld at each cell based on ts own measuement and ts neghbo s measuements, the tempoal estmate phase s used. Dung the movement of senso nodes, each senso obtan seveal spatal estmates (fom the spatal estmaton phase) of the value at cell assocated wth ts own confdence, hence the fnal estmate s teatvely updated based on these spatal estmates va the weghted aveage potocol. Fo detals, fst let l c be the teaton that both consensus flte and convege, then we have the estmates of cell : E (t) = x (l c); and W (t) = y (l c). We can fnd the fnal estmate of the value of the scala feld at cell based on followng equatons: - Update weght (confdence): W (t) = W (t )+W (t )+...+W () (5) - Update the fnal estmate (weghted aveage potocol): E (t = ) = E (t = ) = x (l c ) (6) E (t) = W (t )E (t )+W (t)e (t) W (7) (t )+W (t) IV. POTENTIAL CONTROLLER DESIGN FOR ACTIVE SENSING In ths secton we am to develop a potental contolle fo coopeatve and actve sensng, and the man dea of ou appoach s shown n Fgue. Ou pupose s usng the feedbac of the confdence of the estmate to adjust the movement of the sensos to adapt to the envonments so that they can mpove the sensng pefomance n a dstbuted fashon. Specfcally, the potental contolle s desgned to stee the moble sensos to the expected locatons n ode to acheve the quas unfomty of the confdence. Fst, we descbe the flocng contol algothm [9], [] whch s used to contol moble sensos to move togethe wthout collson. A. Flocng Contol We consde n moble senso nodes movng n two dmensonal Eucldean space. The dynamc equatons of each senso node ae descbed as: { q = p (8) ṗ = u, =,,...,n. hee (q, p ) R ae the poston and velocty of senso node, espectvely, and u s the contol nput of senso node. 833

4 Desed Confdence of Estmates + - Potental Contolle (u ) Potental Contolle Enhanced wth Attactve and Repulsve Foces Cuent Confdence of Estmates Moble Senso Scala Feld Fg.. Dagam of coopeatve and actve sensng based on the flocng contolle enhanced wth attactve and epulsve foces va confdence feedbac. The geomety of the MSN s modeled by an -lattce [9] that meets the followng condton: q j q = d,j N (t), (9) hee d s a postve constant ndcatng the dstance between senso node and ts neghbo j. Howeve, at sngula confguaton (q = q j ) the collectve potental used to constuct the geomety of flocs s not dffeentable. Theefoe, the set of algebac constants n (9) s ewtten n tem of σ - nom [9] as follows: q j q σ = d,j N (t), hee the constant d = d σ wth d = / c, whee c s the scalng facto. The σ - nom,. σ, of a vecto s a map R m = R + defned as z σ = ǫ [ +ǫ z ] wth ǫ >. Unle the Eucldean nom z, whch s not dffeentable at z =, the σ - nom z σ, s dffeentable evey whee. The flocng contol algothm whch conssts of the fomaton contol tem and the leade tacng contol tem s pesented as u = f +f t. The fomaton contolle [9] s used to contol the netwo to fom a quas lattce fomaton, and t s desgned based on a pawse attactve/epulsve foce. f = c φ ( q j q σ )n j +c a j (q)(p j p ), j N j N () whee c and c ae postve constants. Moe detals of how to compute f please see [9]. The leade tacng contolle s used to contol each moble senso to tac the vtual leade. The tajectoy of the vtual leade s planned so that the MSN can cove the ente scala feld. Ths contolle s pesented as f t = c t (q q t ) c t (p p t ) () heec t andct ae postve constant, andq t andp t ae poston and velocty of the vtual leade, espectvely. B. Desgn of Attactve Foce In ths subsecton, we ntoduce the attactve foce tem to ncease the confdence level. The attactve foce wll stee the moble sensos to the cells whch have low confdence. In ode to do ths, fst let qc be the locaton of the cell that has confdence lowe than the lowe bound, o O L (t), hee O L (t) s the subset of cells coveed by moble senso at tme t, whch have confdence lowe than the lowe bound. O L(t) Oc (t), hee Oc (t) s the set of cells coveed by moble senso at tme t, and t s defned as O(t) c = { ϑ O : qc q,ϑ s O = {,,...,} }. () At each tme t, the moble senso may have seveal cells whch have confdence lowe than the desed one. In ode to stee the moble senso to go to these low confdence cells, the vtual attactve foce ae geneated at these cells. If the cell has lowe confdence the bgge attactve foce s geneated. To expess the detals of the attactve foce desgn, fst let W L d be a lowe bound of the desed confdence of the estmates of all cells n the scala feld, and W L d s a vecto of C dmenson. Let L W (t) = WL d W(t) be the dffeence between the cuent confdence and the lowe bound (see Fgue 3), L W (t) = [ W (t), W (t),..., C W (t)]. Based on ths feedbac, L W (t), we can desgn a attactve foce as shown n Equaton (3). f att = O L (t) C att φ att ( qc q σ )n att, (3) hee, C att = c W (t) a +( W (t)), W (t) L W (t), and c a s a postve constant. C att s used to contol the ampltude of the attactve foce. Namely, f cell has low confdence o W (t) s lage, the the ampltude of the attactve foce s bg n ode to attact the moble senso to go to close ths cell. The attactve foce functon φ att ( qc q σ ) s desgned as: φ att ( q c q σ ) = ρ h ( q c q σ s O L (t). qc ) q σ + q c q σ hee, s = s σ ( s s sensng ange as defned befoe). Smla to [9], the bump functon ρ h ( q c q σ ) wth h s (,) s defned as,f q c q σ [,h) ρ h ( q c q s qc q σ σ s ) = [ + cos(π( s h h ))] (4) f q c q σ [h,] s, othewse. The vecto along the lne connectng qc ( OL (t)) and q s defned as: n att = (q c q )/ +ǫ qc q, O L (t). (5) hee, ǫ s small postve constant. C. Desgn of Repulsve Foce Based on the attactve foce desgn n the pevous subsecton, the confdence level can be nceased, howeve some cells may have too hgh confdence. Ths s unnecessay snce ths needs moe measuements, and causes moe enegy consumpton. Theefoe, t s desable f we can mantan 834

5 Confdence (Weght) Confdence of Estmates Uppe Bound Lowe Bound Fnally, the potental contolle fo the coopeatve and actve sensng s pesented as follows: u = f ep +f att +f +f t. (8) Cell Index Fg. 3. Illustaton of confdence feedbac fo quas unfomty of the confdence. The uppe bound and lowe bound ae used to ceate a quas unfom of the confdence. both lowe and uppe bound of the confdence pefomance, o a quas unfom confdence (see Fgue 3). Hence, we ntoduce a epulsve foce tem to the Potental Contolle n ode to stee the moble sensos to move away fom the cells whch have too hgh confdence. Let qc be the locaton of the cell that has confdence hghe than the uppe bound (see Fgue 3). Fo these cells we wll ceate the vtual epulsve foce to stee the moble sensos to move away. To expess the detals of the epulsve foce desgn, fst let W H d be a uppe bound of the desed confdence of the estmates of all cells n the scala feld, andw H d s a vecto of C dmenson. Let H W (t) = WH d W(t) be the dffeence between the cuent confdence and the uppe bound (see Fgue 3), H W (t) = [ W (t), W (t),..., C W (t)]. Based on ths feedbac, H W (t), we can desgn a epulsve foce as shown n Equaton 6. = f ep O H (t) C ep φ ep ( qc q σ )n ep, (6) hee, C ep = c W (t) +( W (t)), W (t) H W (t), hee c s a postve constance. O H (t) s the subset of cells coveed by moble senso at tme t, whch have confdence hghe than the uppe bound. Obvously,O H(t) Oc (t). Cep s used to contol the ampltude of the epulsve foce. Namely, f cell has hgh confdence, o W (t) s lage, the the ampltude of the epulsve foce s bg n ode to push the moble senso to move away fom ths cell futhe. The epulsve foce functon φ ep ( qc q σ ) s desgned as: φ ep ( qc q σ ) = ρ h ( q c q σ ) s qc q σ s ( ) +( q c q σ s ), O H (t). The bump functon ρ h ( q c q σ ) s defned as (4), but t s s now appled fo the hgh confdence cells o O H (t). The vecto along the lne connectng qc ( OH (t)) and q s defned as: n ep = (q c q )/ +ǫ qc q, O H (t). (7) V. SIMULATION RESULTS In ths secton, we test ou coopeatve and actve sensng algothm and compae t wth the nomal coopeatve sensng algothm [6], [7] n tems of the sensng pefomance. We model the envonment (scala feld F ) as multple vaate Gaussan dstbutons. The scala vecto Θ can be abtaly selected, fo example Θ = [ ], coespondng to fou multple vaate Gaussan dstbutons (K = 4), and each one s epesented as: φ = det(c )(π) e (x )C (y )T. [ ] hee we can select: C =, wth the coelaton facto c =.333. Fo the functons φ,φ 3,φ 4 : the means (µ x,µ y ) ae (, ), (4.3, [ 3.5), (3, -3), espectvely; ] the matx C = C 3 = C 4 = ; the coelaton facto c = c 3 = c = c. We set the lowe bound of the confdence level s 5, and the hghe bound of the confdence level s.9 5. The feld F has a sze of 9, and t s pattoned nto cells. The snapshots of multple senso nodes fomng a floc and buldng the map of the unnown scala feld ae shown n Fgue 4. The fnal confdence of the estmate n one dmenson at each cell of the feld F s shown n Fgue 5. In ths fgue we compaed thee methods togethe. Namely, Fgue 5 (a) shows the confdence of nomal coopeatve sensng (Potental Contolle wthout attactve and epulsve foces). Fgue 5 (b) shows the confdence of actve sensng wth the Potental Contolle wth attactve foce only. Fgue 5 (c) shows the confdence of actve sensng wth Potental Contolle wth both attactve and epulsve foces. Fom these esults, we can see that by usng both attactve and epulsve foce contolles we have bette unfomty of the confdence pefomance. Ths ndcates that all the cells of the scala feld ae obseved wth a cetan level of confdence. To see the advantages of the actve sensng we compae t wth the nomal sensng n tem of mappng eo as shown n Fgue 6. We can see that the eo between the ognal map and the bult map ove cells s small when applyng the actve sensng (see Fgue 6 (b)), but t s bgge when applyng the nomal sensng (see Fgue 6 (a)). VI. CONCLUSION Ths pape pesented coopeatve and actve sensng algothms fo moble senso netwos to buld the map of an unnown scala feld. The poposed dstbuted senso fuson algothm conssts of two dffeent dstbuted consensus 835

6 Fg. 4. Snapshots of buldng the map of the scala feld F usng the dstbuted fuson algothm and the coopeatve and actve sensng algothm (8). 3 x 5 3 x 5 3 x Confdence (Weght).5 Confdence (Weght).5 Confdence (Weght) Numbe of Cells Numbe of Cells (a) Cell Index (b) Cell Index (c) Numbe of Cells Cell Index Fg. 5. Confdence ove the cells n one dmenson: (a) fo nomal coopeatve sensng [6], [7]; (b) fo actve sensng wth Potental Contolle usng only attactve foce; (c) fo actve sensng wth Potental Contolle usng both attactve and epulsve foces (8) x Numbe of Cells Cell Index (a) x Numbe of Cells Cell Index Fg. 6. Eo between the ognal map and the bult map n one dmenson ove cells: (a) fo the nomal sensng [6], [7]; (b) fo the actve sensng. fltes whch can fnd an ageement on the estmates and an ageement on the confdence among senso nodes. Each senso node coopeates wth neghbong sensos to estmate the value of the feld at each cell. The fnal estmates of the values of the scala feld ae updated on-lne based on the weghted aveage potocol. Moe mpotantly, the moble sensos can automatcally adjust the movement to acheve quas unfom confdence though a potental feld based feedbac contol algothm. Smulaton esults ae collected to demonstate the poposed algothms. REFERENCES [] T. H. Chung, V. Gupta, J. W. Budc, and R. M. Muay. On a decentalzed actve sensng stategy usng moble senso platfoms (b) n a netwo. the 43th IEEE Conf. on Decson and Contol, pages 94 99, 4. [] C. Zhang, D. Anold, N. Ghods, A. Sanosan, and M. Kstc. Souce seeng wth nonholonomc uncycle wthout poston measument pat : Tunng of fowad velocty. IEEE Conf. on Decson and Contol, pages , 6. [3] S. Pang and J. A. Faell. Chemcal plume souce localzaton. IEEE Tans. on Systems, Man, and Cybenetcs Pat B, 36(5):68 8, 6. [4] C. G. Mayhew, R. G. Sanfelce, and A. R. Teel. Robust souce-seeng hybd contolles fo autonomous vehcles. Amecan Contol Conf., pages 85 9, 7. [5] H. G. Tanne R. A. Cotez and R. Luma. Dstbuted obotc adaton mappng. Expemental Robotcs The Eleventh Int.l Symposum, volume 54 of Spnge tacts n advanced obotcs, Spnge, pages 47 56, 9. [6] H. M. La and W. Sheng. Coopeatve sensng n moble senso netwos based on dstbuted consensus. the Sgnal and Data Pocessng of Small Tagets Conf., Poc. of SPIE,. [7] H. M. La and W. Sheng. Dstbuted senso fuson fo scala feld mappng usng moble senso netwos. IEEE Tans. on Cybenetcs, 43(): , Ap. 3. [8] L. Xao, S. Boy, and S. Lall. A scheme fo obust dstbuted senso fuson based on aveage consensus. Intenatonal Confeence on Infomaton Pocessng n Senso Netwos, pages 63 7, 5. [9] R. Olfat-Sabe. Flocng fo mult-agent dynamc systems: Algothms and theoy. IEEE Tansactons on Automatc Contol, 5(3):4 4, 6. [] H. M. La and W. Sheng. Flocng contol of a moble senso netwo to tac and obseve a movng taget. Poc. of the 9 IEEE Int. Conf. on Robotcs and Automaton (ICRA 9), Kobe, Japan, pages ,