Multi-UAV Task Allocation using Team Theory

Transcription

1 Proceedngs of the 44th IEEE Conference on Decson and Control, and the European Control Conference 2005 Sevlle, Span, December 12-15, 2005 MoC03.6 Mult-UAV Task Allocaton usng Team Theory P. B. Sut, A. Snha and D. Ghose Abstract A multple UAV search and attack msson n a battlefeld nvolves allocatng UAVs to dfferent target tasks effcently. Ths task allocaton becomes dffcult when there s no communcaton among the UAVs and the UAVs sensors have lmted range to detect the targets and neghbourng UAVs, and assess target status. In ths paper, we propose a team theoretc approach to effcently allocate UAVs to the targets wth the constrant that UAVs do not communcate among themselves and have lmted sensor range. We study the performance of team theoretc approach for task allocaton on a battle feld scenaro. The performance obtaned through team theory s compared wth two other methods, namely, lmted sensor range but wth communcaton among all the UAVs, and greedy strategy wth lmted sensor range and no communcaton. It s found that the team theoretc strategy performs the best even though t assumes lmted sensor range and no communcaton. I. INTRODUCTION Unmanned aeral vehcles are beng extensvely used for mltary purposes, lke search, survellance and as muntons n the battlefeld [1] - [10]. They play a crucal role n nformaton gatherng from hostle and unknown regons. These UAVs can also be used as muntons to search for, attack and destroy targets n unknown regons. The UAVs used for these applcatons may have lmted capabltes and may not have the requred stealth capablty and ammunton payload to complete the task sngle-handedly. Hence, there s a case for such UAVs to be deployed n swarms. A desrable feature for these UAV swarms would be to have autonomous decson makng and coordnatng capablty. As the UAVs perform search, they may fnd several targets n the search regon. The number of UAVs may be more than the number of targets avalable or the number of targets avalable may be more than the number of UAVs. In ether case, we need an effcent task allocaton method for assgnng the UAVs to the targets. However, ths algorthm must be decentralzed and sutable for mplementaton n a multple agent UAV swarm. An effcent task allocaton strategy should complete the msson (that s, destroy all targets) n mnmum tme by cooperatng and coordnatng wth other UAVs [1]. Cooperaton can be acheved by communcaton wth neghbourng UAVs, explctly or mplctly. When the UAVs do not communcate wth each other, decson makng The authors would lke to acknowledge the fnancal support receved from the IISc-DRDO Program on Advanced Research n Mathematcal Engneerng. A. Snha and P. B. Sut are Graduate students n the Department of Aerospace Engneerng, Indan Insttute of Scence, Bangalore , Inda, Emal: {sut,asnha}@aero.sc.ernet.n Debassh Ghose s a Professor n the Department of Aerospace Engneerng, Indan Insttute of Scence, Bangalore , Inda, Emal: dghose@aero.sc.ernet.n becomes a dffcult task. The classcal soluton for task allocaton problem would be to have a centralzed task allocaton system that generates the necessary commands for the UAVs. But, centralzed task allocaton system have well known lmtatons and do not address scalablty ssues too well. Hence, there s a necessty to develop a decentralzed task allocaton algorthm. Here, we use concepts from team theory to develop such a decentralzed task allocaton algorthm for multple UAVs that do not communcate wth each other whle performng search and attack tasks n an unknown regon. The UAVs that we consder are small n sze, have lmted fuel capacty (lmted flght tme), and lmted sensng capabltes. The UAVs can detect the presence of neghbourng UAVs and targets wthn ts sensor range only. The UAVs do not communcate wth ther neghbours and make ther decsons based only on the nformaton they receve from ther sensors. All the UAVs are assumed to be homogeneous, have constant speed and have no turn radus constrants. The UAVs have to carry out the msson wthn the gven flght tme. Collson avodance between UAVs s not an ssue here. The UAVs can perform search, attack, speculatve and battle damage assessment (BDA) tasks. Search task refers to searchng for targets n the unknown regon. Once a target s found by the UAV, t executes a speculatve task to ensure that the target s a real target and not a false target. The target that has been verfed as a real target s attacked by the UAV. After attackng the target, battle damage assessment s carred out. The BDA task gves an estmate about the amount of damage caused to the target. The speculatve and BDA tasks yeld nformaton about the target status, the former before the attack and the latter after the attack s performed. Snce there s no communcaton among UAVs, a UAV does not have any nformaton about whether a target whch s not n ts sensor range has been attacked by any other UAV. So, t has to perform a BDA wth some probablty. Snce the BDA task and the speculatve tasks are smlar n nature, we classfy the BDA task also as a speculatve task. The speculatve task s performed n the followng way: Once a UAV fnds a target, t estmates the status of the target wth some probablty. The target can have three dfferent status (a) Not Attacked (NA) (b) Partally Destroyed (PD) (c) Completely Destroyed or False target (CDF). The probablty of the target status s a functon of the dstance between the UAV and the correspondng target. The estmate about the status of the target s updated as the UAV moves towards the target. So, the speculatve task s performed on ts way to the target, at every tme step. Each UAV performs decson-makng ndependently, based /05/$ IEEE 1497

2 on the estmate of the target status. The decson taken by the UAV also depends on the number of neghbourng UAVs. Here, we assume that the UAVs do not have suffcent memory to remember the path travelled so far, as well as the locaton of the targets already attacked. A. Lterature Task allocaton of UAVs s an actve research area for the past few years. Nygard et al. [1], propose a network flow optmzaton model for allocatng UAVs to targets. The network optmzaton problem s formulated as a lnear programmng problem to obtan decsons for allocatng the UAVs. The authors assume that global communcaton between UAVs exsts. The network flow model has been further extensvely studed by Schumacher ([2], [3], [4]) for wde area search muntons wth varable path lengths, assgnment wth tmng constrants and path plannng. Chandler et al. ([5], [6]), explore varous other technques lke teratve network flow, auctons, lnear programmng, and mxed nteger lnear programmng, for mult-uav task allocaton. The effect of communcaton delays on the task allocaton usng the teratve network flow model s dealt wth n Mtchell [7]. Curts [8] presents a task allocaton methodology for smultaneous search and target assgnment, where the search and task assgnments are posed as a sngle optmzaton problem. Turra et al. [9] present a task allocaton algorthm for multple UAVs performng search, dentfcaton, attack, and verfcaton tasks n an unknown regon for targets that move n real tme. These authors also address the problem of obstacle avodance for the UAV. Jn et al. [10] propose a probablstc task allocaton scheme for the scenaro presented n [5], [6]. In most of the algorthms presented n the papers cted above, global communcaton between agents s assumed although the agents themselves have lmted sensor range. So, nformaton obtaned by an agent s communcated to all the other agents. However, the task allocaton decson algorthm s autonomously executed by the agents. The team theoretc approach allows the UAVs to perform decsonmakng ndependently when there s no exchange of nformaton wth other UAVs, or when there s no communcaton between UAVs. The UAVs can only sense the locaton of ther neghbours. Radner [11] was the frst to show that decentralzed optmal team decson problems can be formulated and solved usng lnear programmng technques. An example of applyng team theory to a manufacturng frm and obtanng team optmal decsons s descrbed n [12] and [13]. Waal and Van Schuppen [14] provde optmal team decson soluton for team problem wth dscrete acton spaces. Ranarayan and Ghose [15] pose a multple agent search problem as a problem n the team theory framework and propose optmal soluton to determnaton of search regons. Rusmevchentong and Van Roy [16] show that local nformaton sensng wth a chan of agents can produce near optmal decsons for the entre team of agents. In ths paper, we present a task allocaton algorthm for multple UAVs performng search, attack, speculatve, and battle damage assessment tasks n an unknown regon usng concepts from team theory for the scenaro gven n the next secton. Ths s one of the very few applcatons avalable that explots the esoterc team theoretc results to solve a practcal problem of decson-makng. B. Problem Scenaro Consder a planar search space consstng of an unknown number of targets. The locaton of the targets are not known a pror to the UAVs. A search and destroy msson would be undertaken by sendng a fleet of UAVs to search a regon and destroy as many targets as possble wthn flght endurance tme of the UAVs. The task nvolved n such mssons are search, attack, and speculate/battle damage assessment (BDA). A search task nvolves searchng the envronment for targets, whle attack task nvolves attackng the target, speculate/bda task nvolves estmatng the value of the target. The UAVs have to coordnate among each other so as to accomplsh the msson faster. Coordnaton between UAVs has to be acheved wthout communcaton. The UAVs also have lmted sensor range. The UAVs can sense the exact poston of all the targets wthn ts sensor range, but not the exact target values. The locaton of all the neghbourng UAVs wthn a UAV s sensor regon are also assumed to be detected. Ths nformaton s utlzed to accomplsh the msson. The UAVs should perform task allocaton so that as much of the msson as possble s completed. C. Bascs of Team Theory Team theory deals wth problems where there are several decson makers who have dfferent but correlated observatons about a random state. Each decson maker uses pre-determned strateges to make a decson based on hs observatons. Dependng on the decson taken, the team realzes a common payoff or ncurs a common cost. The goal s to mnmze ths total cost or mze the global proft n an expected sense. Let T = {1, 2,...,N} denote a team of N decson makers and S denotes the set of alternate states of the world or the envronment. We consder the set S to be fnte,.e., there are only a fnte number of confguraton of the envronment. Moreover, there s a probablty functon γ(s) defned on the set S of the possble states of the envronment. Each decson maker receves nformaton about a state sɛs. The nformaton receved by the th decson maker s gven by y = η (s) (1) where η s called the nformaton functon of the th decson maker. The set of all nformaton that the th decson maker can receve s gven by Y = {y }. The set η = {η 1,η 2,...,η N } s called the nformaton structure for the team. On the bass of the receved nformaton y, the th decson maker takes decson x whch s gven as x = δ (y ) (2) 1498

3 where, δ s called the decson functon. Let X = {x } be the set of alternatve decsons that the th decson maker can take. Then, δ maps Y X. The vector δ = {δ 1,δ 2,...,δ N } s the team decson functon. Dependng on the problem, the team decson x = {x 1,x 2,...,x N } may be constraned to satsfy some condtons,.e., x may be forced to reman wthn some closed convex set k(s) R N. The outcome of the team s determned by the state s and the team decson x and t s gven by ω = u(s, x) (3) where, ω(s, x) s called the payoff functon. Snce, the state of the envronment s a random varable wth a gven probablty dstrbuton, we fnd the expected payoff E[ω(s, x)]. Thus, the obectve of the decson maker s to x k(s) E[ω(s, x)] (4) If the payoff functon s lnear, ω(s, x) can be wrtten as ω = C x, where C s a functon of the state and t s a random varable. Then, the obectve functon s gven as x k(s) E [ C x ], (5) II. PROBLEM FORMULATION Consderng the scenaro descrbed n Secton I, let N number of UAVs be deployed for the search and attack operaton. The obectve of the UAVs s to attack and destroy the mum number of targets wthn ther endurance tme. Each UAV s an autonomous decson maker. We assume that there are M targets n the search space whose exact locaton or number s not known to the UAVs. The state of the envronment, S, conssts of the UAV poston (q x,q y ), target poston (t x,t y ) and the target values V, =1,...,M. A UAV can sense the presence of a target and estmate ts value wth probablty p(d ), whch depends on the dstance d between the UAV and the target T. Let us assume that at tme step t s, UAV can sense m number of targets and n number of UAVs wthn ts sensor range. The th UAV calculates the probabltes p(d ), =1...,m for m targets values. The UAV has to decde on ts acton usng ths nformaton. The decson that the th UAV takes s gven by the decson vector x = [x,1,x,2,...,x,m ], where x {0, 1} denotes whether the th UAV wll perform the task or not. The decson of the th UAV s based on the beneft C obtaned by performng task. The th UAV uses nformaton of only those of ts neghbourng UAVs that are wthn ts sensor range. So, the obectve of the team s to mze the total beneft whch s gven by ω = C x, =1,...,n =1,...,m +1 (6), where, tasks =1, 2,...,m denote whether UAV wll attack target T, and =(m +1) s the search task. The obectve functon ω and the constrants are lnear. Hence, we can use the lnear programmng algorthms to solve the above optmzaton problem. Each UAV s at a dfferent geographcal poston and the envronment sensed by each UAV may be dfferent. Hence ω for each UAV would also be dfferent. Moreover, each UAV can perform only one task at any one tme nstant, so x =1 (7) For the msson to be effectve, t s necessary that only one UAV should be assgned to one target at a tme step. So, we also have the followng condton, x =1, =1,...,n, =1,...,m +1 (8) But, wth the above constrant, the soluton mght stll become nfeasble as t may so happen that the number of targets present s more than the number of UAVs and hence t may not be possble to assgn all the targets. Hence, we relax the above constrant to x 1 (9) Thus, the problem can be framed as an LP problem wth each UAV solvng ts own LP. The optmzaton problem s rewrtten as: w = C x (10) = 1,...,n, =1,...,m +1 subect to x = 1,, =,...,m,m +1 x 1, =1,...,n x = {0, 1} The above LP problem s formulated wthout usng any team theoretc concepts. Now, we descrbe the LP formulaton usng team theory. III. TEAM THEORETIC FORMULATION The problem defned n Secton II assumes that the optmzaton problem s solved globally. However, n the scenaro that we consder, the UAVs do not have global nformaton. Each UAV solves the optmzaton problem wth only local nformaton avalable to t. The benefts that the th UAV calculates for dfferent tasks are defned as follows: Search task: tme left C s = (11) total flght tme Attackng target : C = V T w r S t (12) where, V T = value of target T, w r = the weght gven to search task over the task of attackng a target, S t = (tme to reach the target T )/(total flght tme). However, the th 1499

4 UAV knows the values of the target wth some probablty. The probablty dstrbuton s assumed to be lnear and s shown n Fgure 1. Let p r (d ) defne the probablty of target to have a value r at a dstance d. Here, r = {0, 0.5, 1} where, when r =1the target s not attacked, when r =0.5 the target s partally destroyed, and when r =0the target s fully destroyed. Thus, C s are random varables wth probablty p(d )={p r (d )}. Speculaton/BDA: Snce speculaton on the target s done at every tme step, and s reflected on the value of targets, we are not attachng a separate beneft for the speculatve task. Each UAV also estmates the benefts that ts neghbourng UAVs (say the k th UAV) wll get from the dfferent tasks that t can perform as follows: Search task: The search task s smlar to that defned above, hence the search value s same for all UAVs. Attackng target : If target s wthn the sensor radus of the k th UAV then probablty 1 1_ 3 Fg. 1. p p, p k sr dstance probablty dstrbuton of the values of the targets Fg. 2. b P d^ a UAV UAV Determnaton of vrtual targets sr C k = V t w r S t (13) where, tme to reach the target by UAV k S t = (14) total flght tme If, target s not n the sensor range of the k th UAV then C k =0. Here, we have assumed that all the UAVs have the same sensor range and hence the th UAV can estmate whether the th target s wthn the sensor range of k th UAV. Attackng vrtual target: The concept of vrtual target s used to estmate the envronment beyond the sensor range of the th UAV (see Fgure 2). The th UAV cannot see the shaded regon whch th UAV can see. Dependng on the number of targets present n that shaded regon, the behavour of the th UAV wll vary. To estmate the number of targets that mght be there, we assume that the targets are unformly dstrbuted. We take nto consderaton the combned effect of all these target, whch we assume to be placed at a pont p, equdstant from pont (a, b). Ths combned target s called the vrtual target for the k th UAV. The beneft that the k th UAV gets for attackng ths vrtual target ˆk s C kˆk = (average value of target)n k w r S ˆd (15) where, n k s the number of targets that can be present n the shaded regon. Therefore, n k = n (area of shaded regon)/π(s r ) 2 and C lˆk = 0, l = 1,...,n l k, and s r s the sensor range. That s, for any other UAVs, the beneft of attackng the vrtual target ˆk of the k th UAV s zero. Snce, C s are random varables, the th UAV wll mze the expected payoff. The expectaton s calculated on the bass of the ont probablty P (s) of the state. Here, we assume that the value of the targets are ndependent events, therefore m P (s) = p(d ) (16) =1 The obectve s to mze the expected payoff E(ω) wth the constrants defned n Secton II, thus each UAV solves the followng lnear programmng problem: E( c x ) (17) =1,...,n =1,...,m,m +1, (m +1)+1,...,(m +1)+(n 1) subect to x =1, x 1 x =0,,ĵ, ĵ = vrtual targets where = m +1 s a search task, ĵ = =(m +1)+ 1,...,(m +1)+(n 1) represents the vrtual targets. IV. SIMULATION RESULTS We demonstrate the effectveness of usng team theory for a mult-uav task allocaton problem usng a smulaton envronment. Consder a geographcal search space of wth 20 targets present n the geographcal regon, as shown n Fgure 3. The search and attack operaton s carred out for 200 tme steps, whch also represents the flght tme of the UAVs. The sensor range of each UAV s 20. The locaton of the target are not known a pror to the UAVs. All the targets n the search space have the same target value for these set of smulatons, however, n general, the target may have dfferent target values dependng on ther threat level. The targets are located randomly n the search space. We use 7 UAVs for the msson. The UAVs perform search, attack and speculatve tasks on the target. We compare the results when UAVs use team theory based decson makng wth other types of task allocatons, namely, greedy allocaton, and lmted sensor range wth full communcaton. 1500

5 Search Regon Targets UAVs % Value of target destroyed Performance vs No. of steps Team Theory Greedy wth communcaton No. of steps % target destroyed Fg Search regon wth UAVs and targets Performance vs No. of steps greedy team theory communcaton No. of steps Fg. 4. Number of targets destroyed completely A. Greedy allocaton In ths allocaton scheme, each UAV decdes to move to a target that would gve mum beneft. Snce the value of the targets are random varables, we consder the expected value of the target to calculate the beneft C. Hence, th UAV s decson s gven by: where S t = C = [E(V )w r S t ] (18) tme to reach the target total flght tme B. Lmted sensor range wth full communcaton Here, each UAV has lmted sensor range s r but can communcate wth all the other UAVs. Whenever a new nformaton s sensed by a UAV, the UAV broadcasts the nformaton to all the other UAVs. We assume that there are no communcaton delays. Hence, all the UAVs have the same nformaton about the state of the envronment at any gven tme. So, all the UAVs solve the same LP problem. Moreover, the concept of vrtual target does not apply here, as the th UAV knows the number of target present n the neghbours sensor regon through communcaton. Smlar to greedy strategy, the UAV would lke to mze the expected value of the target. The th UAV solves the followng problem C x (19) x subect to x =1 x 1 (20) where =1,...,N and =1,...,t a, wth t a representng all the targets detected so far. Fg. 5. Average target value destroyed; performance for averagng over 20 dfferent maps % Value of target destroyed Performance vs sensor radus Sersor radus Fg. 6. Performance of target value destroyed wth varaton n sensor range for the UAVs Fgure 4 shows the performance curves for 7 UAVs performng search and attack tasks on a search space shown n Fgure 3. For evaluaton of the performance by each strategy we use the percentage values of the target destroyed (T d ). For nstance, at tme step t, f, say, t c targets are completely destroyed (hence ther value s equal to 0), t h targets are half destroyed and t n targets are not attacked, then T d = t c +0.5t h +0t n (21) The target value destroyed (T d ) provdes an nsght about how many targets are half and full destroyed n the search space. We can see that as tme passes the number of targets beng destroyed ncreases and hence the target value destroyed (T d ) ncreases. The performance of greedy strategy s the worst compared to other two strateges as expected. However, team theoretc strategy performs the best n spte of ther beng no communcaton between UAVs. Fgure 4 show the performance of a partcular smulaton. To obtan the average performance of all the strateges, we carry out the smulaton for 20 dfferent random target maps for 200 tme steps each wth same UAV postons. Durng the search task, t s logcal that, after some tme durng whch search s carred and f no targets are found, the UAV has to change ts drecton, so that there s a better chance of fndng a target. Hence, after every 10 steps of search task, the UAVs change ther drecton of search by a random angle. Hence, the performance of the target destroyed sometmes depends on the random change n search drecton. Hence, to average out the randomness of search we smulate each target map 1501

6 three tmes and consder the average performance. Fgure 5 shows the average performance of each strategy for 20 such randomly generated target maps. From the fgure we can see that ntally all the strateges perform almost at the same level but wth tme, team theoretc strategy outperforms the other strateges. Ths s a sgnfcant outcome snce the team theoretc strategy assumes no communcaton between UAVs and has lmted sensor range. In case of full communcaton, the communcaton costs are ncurred and the computatonal costs are more wth respect to the team theoretc strateges as the UAV has to consder all the UAVs nformaton about the targets. The greedy strategy has a tendency to move n groups and of not effectvely usng the resources of havng multple UAVs for the msson. Team theory perform better and s scalable to large scale systems as the nformaton sensng s local and consequently the computatonal effort s less. Fgures 4 and 5 have shown that the team theoretc strategy performs better than the other strateges. Another study examnes the effect of sensor radus on T d (Fgure 6). Here, we consdered a random target map and carred out three smulatons for each sensor radus. The effect of sensor radus shown s the average of the three smulatons. The fgure shows that for ths partcular case sensor radus of about 25 gves the best performance than any other sensor radus. The performance of team theory, greedy and full communcaton strateges depends on sensor range. If the sensor radus s small, a UAV can sense very small area and the decson taken wll not be effectve. We expect that wth ncrease n sensor range the performance wll also mprove. In the case of team theory, ths s not true because f we consder a large sensor range, the estmated value of the vrtual target wll be ncorrect. Ths s because the area sensed by the k th UAV can nclude regons beyond the search regon space where there are no targets. But, the th UAV does not consder ths fact and assumes equal densty of targets everywhere. Ths unnecessarly gves more weghtage on the vrtual target and the overall performance decreases. Ths effect can be seen n Fgure 6. Ths problem can be resolved f we consder other parameters such as target densty gradents or restrcton to the search space. These aspects are beng nvstgated and wll be reported later. The rato of search value to the target value also plays a crucal role. If we gve equal prorty to search and target then the UAV may opt for search task even though there s a target near t. On the other hand, f we ncrease the value of the target then there s a possblty that the UAV may loter around a target whch s already destroyed. In our smulatons, we consdered search value to be 25% of the target value and ths seemed to yeld good results. But, a more focused study s necessary to study ths aspect of the problem. V. CONCLUSION In ths paper, we proposed a team theoretc strategy for effcent task allocaton for multple UAVs performng search and attack task n an unknown regon consstng of unknown number of targets wth no communcaton between UAVs and havng lmted sensor range. The performance of team theory for task allocaton studed through smulatons show that team theory performs better than other strateges. The scheme s applcable to stuatons were communcatons delays or lack of communcaton becomes a decdng factor n UAV task performance as ths scheme does not requre any communcaton at all. The task allocaton algorthm can be scalable to large number of UAVs and does not have communcaton overhead. Ths s one of the few applcatons n the lterature where team theory has been used effectvely to solve a practcal problem. REFERENCES [1] K.E. Nygard, P.R. Chandler, M. 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