Bayesian-Based Decision Making for Object Search and Characterization

Transcription

1 9 American Control Conference Hyatt Regency Riverfront, St. Loui, MO, USA June -, 9 WeC9. Bayeian-Baed Deciion Making for Object Search and Characterization Y. Wang and I. I. Huein Abtract Thi paper focue on the development of deciion making criteria for autonomou vehicle where the tak to be performed are competing under limited vehicle and enory reource. More pecifically, we are intereted in the earch and characterization of multiple object given a limited number of autonomou enor vehicle. In thi cae, earch and characterization are two competing demand ince an autonomou vehicle in the ytem can perform either the earch tak or the characterization tak, but not both at the ame time. Thi i a very critical deciion a chooing one option over the other may mean miing other, more important object not yet found, or miing the opportunity to atifactorily characterize a found critical object. Building on previou determinitic-baed work by the author, in thi paper we develop Bayeian-baed earch veru characterization deciion making criteria that reult in guaranteed detection and characterization of all object in the domain. I. INTRODUCTION Thi paper focue on the management of autonomou enor-equipped vehicle for the earch and characterization of multiple object, whoe number i unknown beforehand, over a given domain. In the cae where uch object are poibly in greater number than available enor vehicle, earch and characterization are two competing demand. Thi i becaue a enor vehicle can perform either the characterization tak or the earch tak, but not both at the ame time (earch require mobility and characterization contrain the motion of the vehicle to that of the object). Hence, a enor vehicle ha to decide on whether to continue earching or top and characterize once it find an object. Thi deciion may be very critical in ome application a in earch and recue, where, for example, finding and analyzing a nonhuman object may come at the cot of delaying or altogether miing a live human victim. Converely, a vehicle may come acro a human victim and, at the cot of miing it, and decide to continue the earch tak. Building on the determinitic framework developed by the author in [], in thi work we develop Bayeian-baed earch and characterization metric and deciion making algorithm that guarantee that all object in the domain will be found and atifactorily characterized. We firt review ome of the related literature. Inpired by work on particle filtering, in [] the author develop a trategy to dynamically control the relative configuration of enor team under a probabilitic framework. The goal i to get optimal etimate for target tracking through enor fuion. In [3], the author ue the Beta ditribution to model the level of confidence of target exitence for an unmanned aerial vehicle (UAV) earch tak in an uncertain environment. The Beta ditribution defined for each cell i a function of the prior probabilitie which i updated through Baye theorem. In [4], the above uncertainty meaurement are extended by uing the Modified Baye Factor, and prediction of future meaurement i alo taken into account to calculate the poible uncertainty reduction in UAV earch operation. An alternate approach for earching in uncertainty environment i called SLAM. The paper [5] preent a paradox of combining mapping and localization at the ame time, whoe olution require explicit repreentation of all the correlation between the etimated vehicle poition and known geometric feature. Coordinated earch and tracking under probabilitic framework ha been tudied mainly for optimal path planning in the literature. In [6], the author invetigate earchand-tracking uing recurive Bayeian filtering with foreknown target poition with noie. A vehicle will keep earching until the target detection probability i above ome preet threhold. However, the target might be lot and need to be found again due to meaurement noie. The reult are extended in [7] for dynamic earch pace baed on forward reachable et analyi. In [8], the author propoe a Bayeian-baed multienor-multitarget enor management cheme. The approximation trategy, baed on probability hypothei denitie, maximize the quare of the expected number of target. For the ame objective, in [9] the author eek to maximize the probability of finding a target with ome foreknown location information in the preence of uncertainty. Vehicle are contrained to chooe from a et of available control and limited communication channel during each time tep. However, there i no explicit deciion making trategy for earch and tracking propoed in the above literature. In thi paper, we propoe effective deciion making trategie for earch and characterization under a probabilitic framework. During the earch proce, an uncertainty map i built baed on the probability of object preence over the earch domain. The probability of object preence over the domain i updated uing Baye theorem given enor meaurement. A characterization uncertainty function i alo defined for each found object. The metric for both earch and characterization are baed on the correponding uncertainty function. A probabilitic framework i deirable to be able to take into account enor error, a well a allow for future incorporation of other tak uch a object tracking, data aociation, data fuion, enor regitration, and clutter reolution []. The paper i organized a follow. In Section II, Bernoulli ditribution are firt introduced to model earch and /9/$5. 9 AACC 964

2 characterization enor model. We then derive expreion for the poterior probabilitie of target preent over the entire domain, and probabilitie of claification for found object baed on Baye theorem. Uncertainty earch and characterization function uing information entropy, along with aociated metric are defined. In Section III, we develop a deciion making trategy for earch and characterization. In ection IV, a et of imulation reult are provided to how the effectivene of the propoed deciion-making trategy. The paper i concluded with a ummary of current and future work in Section V. II. PROBLEM FORMULATION A. Setup and Senor Model There are two baic objective in a earch and characterization operation. The firt objective i to find each object and fix it poition in pace. The econd objective i to oberve each found object and collect the deired amount of information that i ufficient for it characterization. Thi paper focue on the claification of tatic object and future reearch will focu on mobile object. Characteritic of interet for immobile object may be geometric hape, and/or nature of electromagnetic emiion. Let D R be a domain in which object to be found and characterized are located. Let q be an arbitrary point in D. Let N o > be the number of object, however, both N o and the poition of the object in D are unknown beforehand. We will aume that there exit a ingle autonomou enor-equipped vehicle (denoted by V) that perform the earch and characterization tak. Future reearch will focu on a team of enor-equipped vehicle. The current cenario i an extreme cae in which the reource available are at a minimum (a ingle enor vehicle a oppoed to multiple cooperating one). At any time t, the vehicle can either perform the earch tak or the characterization tak, but not capable of both at the ame time. Initially, the vehicle tart in the earch mode. Aume that we are given ome earch veru characterization deciion making trategy. Since the number of object i potentially very large, with a poor choice of deciion making trategy, the vehicle may end up exceively characterizing one ingle object while there may till exit unfound, and more important, object in the domain. In thi paper, we invetigate policie that guarantee that every tatic object within the domain will be found and each found object will be characterized by the autonomou vehicle until a minimum atifactory claification performance i achieved. Let the poition of the tatic object O j, j {,,..., N o }, be p j, which i unknown beforehand. The vehicle V atifie the following imple firt order dicretetime equation of motion q(t + ) = q(t) + u(t), where q D R repreent the poition of V, and u U R i the control input, U i the et of allowable control. In thi work, for both the earch and characterization procee, we ue a enor model with Bernoulli ditribution, which give binary output, however, with different obervation content: object preent or not preent for earch, and property G or B for characterization. Thi i a implified but reaonable enor model becaue it abtract away the complexitie in enor noie, image proceing algorithm error, etc. In the earch proce, let V = {v, v } be the et of two poible enor output, where v correpond to object detected, and v correpond to no object detected. Let S = {, } be the et of two poible tate type, where correpond to object preent, and correpond to object not preent. The actual obervation V i taken according to the probability parameter β of a Bernoulli ditribution. Since there are two tate in all, two Bernoulli ditribution are ued and the following matrix (which i called the emiion probability matrix in the Hidden Markov Model (HMM) literature []) for earch tak i given by [ v p B = = β, p v = β ], p v = β, p v = β (), where p v i, i, j =,, decribe the probability of j meauring vi given tate j. For the ake of implicity, we can aume that the enor probabilitie of making a correct meaurement are the ame. That i, we have p v = pv = β. The value of β i aumed to depend on the range between the enor and the oberved point. Without lo of generality, here we aume a imple model for β that i a fourth order polynomial function of = q(t) q within the enor range r and b n =.5 otherwie, { ( ) M β () = r r 4 + bn if r, () b n if > r where M + b n give the peak value of β if q being oberved i located at the enor vehicle location, which indicate that the probability of ening correctly i highet exactly where the enor i. The parameter r i the range of the earch enor. The ening capability decreae with range and become.5 outide of the limited enory range W, implying that the enor return an equally likely obervation of preent or not preent regardle of the truth of whether there i an object at that location or not. Figure how the β function over a quare domain of ize 4 4. Note that β i a function of, and i a function of the vehicle poition q(t) and the location q of interet. For the characterization proce, we alo define binary obervation output for each found object: v c and vc that correpond to tate type c (property G ), and c (property B ), repectively. The obervation proce i aumed to be Bernoulli and i aumed, for implicity, to obey the ame functional form a the detection model above: { Mc ( ) β c () = r r c 4 c + bn if r c, (3) b n if > r c 965

3 β qy Fig.. Correct ening probability function β with q =, M =.4 and r =. where M c + b n and r c are the peak enory capacity and limited enory range for the characterization proce. When an object of interet i within the enor effective characterization radiu r c < r c, thi object i aid to be found, and the vehicle ha to decide whether to characterize it or continue earching. Remark: ) If we have more than two poible claification propertie, the binary-type Bernoulli enor model i no longer appropriate. In thi cae, one can model the enor obervation uing a multinomial random variable that can take one of K dicrete value and expand the emiion matrix to dimenion K K. ) A key feature of the propoed approach i that the enor may have a limited range. Previou work on cooperative coverage control uually aume that the enor have an infinite range []. Thi aumption i not made here. Outide the enor domain W, the enor i ineffective (with β =.5). Thi i very important in application where D i large-cale (i.e., too large to be covered by a ingle et of tatic enor agent). B. Bayeian Update for Search and Characterization For both earch and characterization procee, we employ Baye theorem to update the probability of object preence at q, or of a found object k having the property G. Let u firt conider the object detection Bayeian update equation. Given an obervation, Baye theorem give, for each q, the poterior probability p (S,t+ = v j ; q), j after the obervation have been taken at time tep t: p (S,t+ = v j; q) = α p (v j S,t = ; q) p (S,t = ; q) (4) where p (S,t+ = v j ; q) i the poterior probability of object being tate type given that obervation vj ha jut been taken at time tep t, p (vj S,t = ; q) i the probability of the particular obervation vj being taken given that the object tate type at time tep t i, which i given by the emiion matrix () and the β function (), p (S,t = ; q) i the prior probability of type being correct at t, and α erve a a normalizing function that enure that the poterior probabilitie p (S,t+ = i v j ; q) um to one over the tate type et S = {, }. For brevity, we let p ( q, t + ) denote p (S,t+ = v j ; q) and p ( q, t) denote p (S,t = ; q). It can be qx hown that the object preence probability update equation at q i given by β p ( q, t) p ( q, t + ) = y β p ( q, t) β p ( q, t) + + ( β )p ( q, t) ( y) β p ( q, t) + β + p ( q, t), (5) where y i defined a follow { if V = v y = if V = v. (6) The probability of object not preent i p ( q, t + ). For the characterization proce, we ue a imilar update equation a (5) to expre the poterior probability of a found object k at location q k having property G : β c p c ( q k, t) p c ( q k, t + ) = y β c p c ( q k, t) β c p c ( q k, t) + + ( β c )p c ( q k, t) ( y) β c p c ( q k, t) + β c + p c ( q k, t), (7) where q k i the poition of object k. The probability of having property B i p c ( q k, t + ). Recall that β c i a function of q(t) and q. Remark about extenion to multiple enor vehicle. When we have multiple autonomou vehicle, each Berboulli type enor will give it own obervation for a certain location q. Hence, there are m combination for the obervation et V if we have m enor in all. We will need to olve for the explicit expreion for α l, l {,,, m } and obtain the correponding update equation of the poterior probability p ( q, t+, l) imilar to Equation (5). C. Uncertainty Map For the earch proce, we ue an information-baed approach to contruct the uncertainty map for every q within the earch domain. The information entropy function of a probability ditribution i ued to evaluate uncertainty. The uncertainty map will be ued to guide the vehicle in the earch domain. Let the probability of the occurrence of an event be p, then the information i meaured a I(p) = log b (/p), (8) where b i the bae (we ue b = e in in thi paper). In our cae, there are ditinct tate value for the dicrete probabilitie. Therefore, the probability ditribution P i given by P = {p, p }. We define the weighted average of information I(p) a the information entropy ditribution for dicrete probability ditribution P at q at each time tep t: H (P, q, t) = p ( q, t)lnp ( q, t) ( p ( q, t))ln( p ( q, t)). (9) When p ( q, t) = or, there i no uncertainty about object exitence or lack thereof and, therefore, H =, which i the deired uncertainty level. Maximum uncertainty H,max =.693 i when p ( q, t) =.5. The initial uncertainty ditribution i aumed to be H,max reflecting the fact that at the outet of the earch miion there i poor certainty level (in other word, a uniform ditribution for object exitence). The greater the value of H, the bigger the uncertainty i. Figure () how the 966

4 Fig.. H p( q, t) Information entropy function H for the earch proce. information entropy function (9) a a function of p ( q, t). The information entropy ditribution at time tep t over the domain form an uncertainty map at that time intant. For the characterization proce, we define a imilar entropy function H c (P c, q k, t), with P c = {p c, p c }, for every found object k (located at q k ) to evaluate claification uncertainty. H c (P c, q k, t) = p c ( q k, t)lnp c ( q k, t) ( p c ( q k, t))ln( p c ( q k, t)). () There are a many calar H c a there are found object k up to time t. The initial value for H c for every found object k can alo be et a H c = H c,max =.693. If the vehicle find target k and decide to characterize it, H c will decreae a the characterization probability increae according to the Bayeian update equation derived above. When a vehicle ha collected enough information baed on the available reource at that time tep, it leave the object and H c remain contant until the vehicle come back to characterize it when poible. Thi i repeated until the deired H d (to be dicued below) characterization certainty i achieved. D. Search and Characterization Metric In thi ection we develop metric to be ued for the earch veru characterization deciion making proce. In the event of object detection and a deciion not to proceed with the earch proce, but, intead, topping to characterize the found object, the aociated cot i defined a D J (t) = H (P, q, t)d q. () H,max A D The cot J i proportional to the total integral of the earch uncertainty over D. We divide the integral by the area of the domain A D multiplied by H,max in order to normalize J (t). According to thi definition, we have J (t). Initially, J () =, ince H (P, q, ) = H,max for all q D. If for ome t we have H (P, q, t ) = for all q D, then J (t ) = and the entire domain ha been atifactorily covered and we know with % certainty that there are no object yet to be found. For the characterization proce, let No (t) be the number of object found by the autonomou enor vehicle up to time t. For each found object j {,,, N o (t)}, define the characterization metric H d ( q j, t) to be H d ( q j, t) = ǫ c J (t), () where ǫ c i a preet upper bound on the deired uncertainty level for characterization. H d depend on how uncertain the vehicle i of the preence of more undetected object in D through J (t). Initially, J () = and the vehicle will attempt to characterize it until the claification uncertainty i maller than ǫ c. On the other hand, if J (t ) = for ome time t >, the vehicle can pend a much time characterizing the object becaue the vehicle ha achieved % certainty that it ha found all critical and noncritical object in the domain. If the vehicle find an object O j (i.e., within the effective characterization radiu r c ) and decide to characterize it, the vehicle will continue characterizing until achieving the characterization condition H c (P c, q j, t) < H d ( q j, t). (3) The vehicle V then top characterizing the found object and witche to earching again. The vehicle can reume characterizing an object that ha been detected and completely or partially characterized in the pat if it find it again during the earch proce. When thi occur, the value of H d will be maller than the lat time the objected ha been detected. III. SEARCH VERSUS CHARACTERIZATION DECISION-MAKING We will conider a earch/characterization deciion making trategy that guarantee finding all object in D (i.e., achieve J = ) and characterizing each object with an upper bound on the characterization uncertainty of ǫ c. Let u firt conider a earch trategy. The goal in the earch trategy i to attain an uncertainty level uch that the earch cot J (t) ǫ for all q within D and all t t for ome t >. Let the control u(t) be retricted to a et U. For example, U could be the et of all control u(t) R uch that u(t) < u max, where u max i the maximum allowable control peed. Baed on thi contraint on the control, we define Q W (t) a the et of point in W reachable from the current location of the vehicle at time t: Q W (t) = { q W : q q(t) U}. (4) For the earch proce, we ue a control law that drive the vehicle to ome point q Q W (t) that ha the highet uncertainty, and witch to a perturbation control law when the vehicle i trapped in a region where no uch point exit. Let u firt conider the following condition, whoe utility will become obviou hortly. Condition C. H (P, q, t) ǫ, q Q W (t), where ǫ i a preet threhold of ome mall value. Conider the following { control law ū(t) if C doe not hold u (t) = (5) ū(t) if C hold where ū(t) i the nominal control law, and ū(t) i the perturbation control law. Let q be the point that ha the highet uncertainty within Q W (t), that i, q (t + ) = argmax q QW(t) H (P, q, t). (6) The nominal control law i then et to be ū(t) = q (t + ) q(t) U. (7) Thi choice for the nominal control law i inpired by the nominal control law in [3]. 967

5 Note that according to Equation (6), q (t + ) might be a et of point holding the ame maximum uncertainty value. Rule to pick the bet point are immaterial a far a thi work i concerned and in thi paper we aume there i only one uch point for the ake of implicity. When the uncertainty H of all the point q Q W (t) i le than ǫ, Condition C hold, and no uch q (t +) exit. Thi mean that the vehicle get trapped in a region where H ǫ if retricted to applying only the nominal control law ū. Note that thi doe not imply that the entire domain D ha been fully earched yet (hence, the need for the perturbation control law which will be dicued hortly). The reaon we retrict our choice of q to W (a oppoed to D) in the definition of Q W (t) (cauing ū to become a local controller) are a follow: ) Uing W intead of D limit the computation involved in finding q to a maller pace and, hence, i more computationally efficient. Thi i epecially true in the cae of large cale domain, where much of the domain D i unreachable from where the vehicle i becaue of the retriction on the control u U. ) Although in thi paper we aume that the vehicle ha full knowledge of the domain D and the earch uncertainty function H (P, q, t) for all q D, D may not be known in real time. In thi cae, all the information the vehicle could obtain i within it limited enory domain W. Note that the application of the local controller i conitent with our previou work [4] [7]. If Condition C hold, then the perturbation controller ū(t) i ued: ū(t) = k(q(t) q ) where < k i the controller gain, and q Q D (t) := { q D : q q(t) U} uch that H (P, q, t) > ǫ. The controller i ued to drive the vehicle out of the region with low uncertainty ǫ to ome q Q D (t) uch that H (P, q, t) > ǫ, if uch a point exit. There are only two cenario that can arie. The firt i when the et U allow for motion from any point in D to any other point, and we have Q D (t) = D, t >. If thi condition i held for all t and if at ome time t f there i no point q Q D (t f ) = D uch that H (P, q, t f ) > ǫ then we ay that the miion i complete a every point in the domain ha been earched with a atifactory certainty level (below ǫ). In the econd cenario, the et U may be uch that Q D (t) D (but Q D) for ome t. In other word, there are location in D that the vehicle can not reach given the contraint on the control velocity ū. Under thi cenario, the miion may never be completed. For the purpoe of thi paper, we will aume that U i uch that Q D (t) = D for all time t. Since there may be many uch point q, a choice of only one uch q need to be made. There are everal way uch a choice can be made. We provide one uch choice that i efficient energy-wie than other poibilitie. Let D ǫ (t) := { q Q D (t) : H (P, q, t) > ǫ}, which i an open et of all q for which H (P, q, t) i larger than a preet value ǫ. Let D ǫ (t) be the cloure of D ǫ (t). Let D ǫ,v (t) be the et of point in D ǫ (t) that minimize the ditance between the poition vector of vehicle V, q, and the et D ǫ (t): D ǫ,v (t) } = { q D ǫ (t) : q = argmin q Dǫ(t) q q(t). Other choice of the et D ǫ,v (t) may alo be conidered, but thi choice i efficient ince the perturbation maneuver eek the minimum ditance for redeployment. Similar a the choice of q (t + ) in Equation (6), the et D ǫ,v (t) may contain more than a ingle point and we will imply aume that there will exit at mot one uch point. If D ǫ (t) i empty, thi mean that the ditribution H (P, q, t) < ǫ everywhere over the domain and the earch miion i complete. Once the vehicle find an object and decide to characterize it, it witche to a characterization tak and will not carry out any earching until H c (P c, q j, t) < H d ( q j, t). After achieving at leat the deired upper bound of characterization uncertainty ǫ c, the vehicle will witch back to become a earch vehicle and leave it characterization poition to find new object. Under the aumption that U i uch that Q D (t) = D for all time t, the earch and characterization control policy given by equation (5) and (3) will guarantee that J converge aymptotically to zero, which i equivalent to guaranteeing that all vehicle be found. The maximum value of characterization uncertainty acceptable i given by ǫ c. IV. SIMULATION RESULTS In thi ection we provide a numerical imulation, which illutrate the performance of the deciion making trategy. We aume the domain D i quare in hape with ize 3 3 unit length. There are 5 target with object, 3 and 5 have property B, and object and 4 have Property G, with a randomly elected initial deployment. We et r = r c = 8 and r c = 6 a hown by the magenta and green circle in Figure 3.The parameter M = M c of the enor i et a.4, which give the highet value for β a.9, i.e., there i 9% chance that the enor i ening correctly at the location of the vehicle and gradually to.5 according to the model dicued above (Equation (), (3)). Let the deired upper bound for claification uncertainty ǫ c be.. Here we ue the control law in equation (5) with control gain k =.5. The et U i choen to be D, o that Q W (t) i given by the interection of U and W, i.e., W and Q D (t) = D which guarantee the full coverage of the entire domain. Figure 3 how the evolution of H. From Figure 3(b), we can conclude that at mot H = 4 ha been achieved everywhere within D. Figure 4(a) how the evolution of J (t) under the control trategy and can be 968

6 x pc pc t.8 (a) (b) t Fig. 3. Uncertainty map (dark red for highet uncertainty and dark blue for lowet uncertainty) and the vehicle motion at t = and 7 (with initial uncertainty H = H max at t = ): (a) Uncertainty at t = and (b) Uncertainty at t = 7. Fig. 5. Probability of object having Property G p c for object and object. J(t) (a) t Fig. 4. (a) Evolution of the earch cot J (t), (b) Poterior probabilitie for every q within D at 7. een to converge to zero. All the object have been found with the probabilitie of object preent a and zero earch uncertainty. Thoe cell that do not contain an object end up with zero earch probability and uncertainty. Figure 4(b) how the detection of all object at time tep 7. For all the 5 found object, object, 4 have been characterized with probability of having Property G a and zero claification uncertainty. Object, 3, 5 have been characterized with probability of having property G a and zero claification uncertainty. Figure 5 how the etimated characterization of the propertie of object (which ha property B ) and of object (which ha property G ). p( q, t) y V. CONCLUSION Baed on a probabilitic framework, a deciion-making and control trategy wa developed to guarantee the detection of all object in a domain and the characterization of each object until a preet mall value of claification uncertainty i achieved. Numerical imulation demontrated the operation of the trategie. Future reearch will focu on locating and characterizing dynamic object. The quetion of unknown environment geometrie (i.e., unknown D) will alo be addreed. Mot importantly, optimizing the control and deciion making law with repect to ome cot function will be invetigated a the current reult provide ome olution to the deciion making problem, albeit with guaranteed performance (i.e., guaranteed detection and characterization of all object) under appropriate aumption. (b) x [] J. R. Spletzer and C. J. Taylor, Dynamic Senor Planning and Control for Optimally Tracking Target, The International Journal of Robotic Reearch, no., pp. 7, January 3. [3] L. F. Bertuccelli and J. P. How, Robut UAV Search for Environment with Imprecie Probability Map, Proceeding of the 44th IEEE Conference on Deciion and Control, and the European Control Conference, December 5. [4], Bayeian Forecating in Multi-vehicle Search Operation, AIAA Guidance, Navigation, and Control Conference and Exhibit, Augut 6. [5] J. J. Leonard and H. F. Durrant-Whyte, Simultaneou Map Building and Localization for an Autonomou Mobile Robot, in IEEE/RSJ International Workhop on Intelligent Robot and Sytem IROS 9, Oaka, Japan, November 99, pp [6] T. Furukawa, F. Bourgault, B. Lavi, and H. F. Durrant-Whyte, Recurive Bayeian Search-and-Tracking uing Coordinated UAV for Lot Target, Proceeding of the 6 IEEE International Conference on Robotic and Automation, May 6. [7] B. Lavi, T. Furukawa, and H. F. Durrant-Whyte, Dynamic Space Reconfiguration for Bayeian Search-and-Tracking with Moving Target, Autonomou Robot, vol. 4, pp , May 8. [8] R. Mahler, Objective Function for Bayeian Control-Theoretic Senor Management, I: Multitarget Firt-Moment Approximation, Proceeding of IEEE Aeropace Conference, 3. [9] M. Flint, M. Polycarpou, and E. Fernández-Gaucherand, Cooperative Control for Multiple Autonomou UAV Searching for Target, Proceeding of the 4t IEEE Conference on Deciion and Control, December. [] M. K. Kalandro, L. Trailovic, L. Y. Pao, and Y. Bar-Shalom, Tutorial on Multienor Management and Fuion Algorithm for Target Tracking, American Control Conference, 4. [] L. R. Rabiner, A Tutorial on Hidden Markov Model and Selected Application in Speech Recognition, Proceeding of the IEEE, vol. 77, no., pp , February 989. [] B. Grocholky, Information-theoretic control of multiple enor platform, Ph.D. diertation, The Univerity of Sydney,. [3] I. I. Huein, A Kalman-filter baed control trategy for dynamic coverage control, Proceeding of the American Control Conference, pp , 7. [4] I. I. Huein and D. Stipanović, Effective Coverage Control for Mobile Senor Network with Guaranteed Colliion Avoidance, pecial iue on multi-vehicle ytem cooperative control with application, IEEE Tranaction on Control Sytem Technology, vol. 5, no. 4, pp , 7. [5] Y. Wang and I. I. Huein, Awarene Coverage Control Over Large Scale Domain with Intermittent Communication, 8 American Control Conference, 8. [6], Cooperative Viion-baed Multi-vehicle Dynamic Coverage Control for Underwater Application, Proceeding of the IEEE Multiconference on Sytem and Control, 7, invited paper. [7], Underwater Acoutic Imaging uing Autonomou Vehicle, 8 IFAC Workhop on Navigation, Guidance and Control of Underwater Vehilce, April 8. REFERENCES [] Y. Wang, I. I. Huein, and R. S. Erwin, Awarene-Baed Deciion Making for Search and Tracking, American Control Conference, 8, invited Paper. 969