FUZZY LOGIC BASED UAV ALLOCATION AND COORDINATION

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1 FUZZY LOGIC BASED UAV ALLOCATION AND COORDINATION James F. Smith III, ThanhVu H. Nguyen Code 57, Naval Reseach Laboatoy, Washington, DC, , USA Keywods Abstact decision suppot systems, distibuted contol systems, fuzzy contol, knowledge-based systems applications, softwae agents fo intelligent contol systems A fuzzy logic esouce allocation algoithm that enables a collection of unmanned aeial vehicles (UAVs to automatically coopeate will be discussed. The goal of the UAVs coodinated effot is to measue the atmospheic index of efaction. Once in flight no human intevention is equied. A fuzzy logic based planning algoithm detemines the optimal tajectoy and points each UAV will sample, while taking into account the UAVs isk, isk toleance, eliability, and mission pioity fo sampling in cetain egions. It also consides fuel limitations, mission cost, and elated uncetainties. The eal-time fuzzy contol algoithm unning on each UAV endes the UAVs autonomous allowing them to change couse immediately without consulting with any commande, equests othe UAVs to help, and change the points that will be sampled when obseving inteesting phenomena. Simulations show the ability of the contol algoithm to allow UAVs to effectively coopeate to incease the UAV team s likelihood of success. INTRODUCTION Knowledge of meteoological popeties is fundamental to many decision pocesses. Due to pesonnel limitations and isks, it is useful if elated measuement pocesses can be conducted in a fully automated fashion. Recently developed fuzzy logic based algoithms that allow a collection of unmanned aeial vehicles (UAVs and an intefeomete platfom (IP (Smith 005 to automatically collaboate will be discussed. The UAVs measue the index of efaction in eal-time to help detemine the position of an electomagnetic souce (EMS. The IP is actually an aiplane with an intefeomete onboad that measues emissions fom the electomagnetic souce whose position is to be estimated. Each UAV has onboad its own fuzzy logic based eal-time contol algoithm. The contol algoithm endes each UAV fully autonomous; no human intevention is necessay. The contol algoithm aboad each UAV will allow it to detemine its own couse, change couse to avoid dange, sample phenomena of inteest that wee not peplanned, and coopeate with othe UAVs. Section povides an oveview of the meteoological sampling poblem and a high level desciption of the planning and contol algoithms that ende the UAV team fully autonomous. Section 3 discusses the electomagnetic measuement space, UAV isk, and the planning algoithm. Section 3 also discusses the UAV path constuction algoithm that detemines the minimum numbe of UAVs equied to complete the task, a fuzzy logic based appoach fo assigning paths to UAVs and which UAVs should be assigned to the oveall mission. Section descibes the contol algoithm that endes the UAVs autonomous. Section also descibes the pioity fo helping (PH algoithm, a pat of the contol algoithm based on fuzzy logic that detemines which UAV should help anothe UAV equesting help. The thee subclasses of help equests ae also discussed in this section. Section 5 discusses expeimental esults including UAV path detemination, UAV path assignment, detemination of which UAVs should fly the mission and the esult of a equest fo help duing the mission. Finally, section 6 povides a summay.

2 METEOROLOGICAL SAMPLING AND COOPERATIVE AUTONOMOUS PLATFORMS Fo many applications it is useful to be able to make meteoological measuements in eal-time. Examples include detemining the index of efaction of the atmosphee to facilitate geolocation (Smith 005; detemination of the pesence and extent of such phenomena as adio holes and ducts, which may intefee with communications; tacking atmospheic contaminants (Speas 005; and sand suspended in the atmosphee that can intefee with sensos. The fuzzy logic based planning and contol algoithms that have been developed allow a collection of UAVs making up the UAV team to engage in coopeative sampling of the atmosphee in eal-time without human intevention. Each UAV will have its own contol algoithm allowing it to detemine new optimal tajectoies in eal-time subject to changing conditions. Also, the contol algoithm on the UAVs will allow them to coopeate to incease the pobability of mission success. Thee will be two diffeent types of coopeation allowed by the contol algoithm and thee classes of help equests which ae discussed in section. 3 PLANNING AND RISK The measuement space consists of the electomagnetic popagation envionment whee UAVs and the IP make thei measuements. This envionment includes sample points and the desiable neighbohoods that suound them. The sample points o the desiable neighbohoods ae whee the UAVs will make measuements. The method of detemining the sample points and desiable neighbohoods is descibed below. The measuement space also includes taboo points and the undesiable neighbohoods that suound them. The taboo points ae points of tubulence and othe phenomena that could theaten the UAVs. The undesiable neighbohoods suounding them also epesent vaious degees of isk. The method of specifying taboo points and quantifying the degee of isk associated with thei undesiable neighbohoods employs fuzzy logic and is discussed in this section. The planning algoithm allows the detemination of the minimum numbe of UAVs needed fo the mission subject to fuel constaints, isk, UAV cost, and impotance of vaious points fo sampling. Risk efes to tubulent egions oegions undesiable fo otheeasons, e.g., the pesence of enemy obseves o physical obstuctions. The planning algoithm automatically establishes the ode in which to send the UAVs taking into account the UAV s value; onboad senso payload; onboad esouces such as fuel, compute CPU and memoy; etc. The pioity of sample points and thei desiable neighbohoods ae taken into account. The planning algoithm also calculates the optimal path aound undesiable egions outing the UAVs to o at least nea the points to be sampled. In the planning phase, the location of the EMS is unknown. Some positions ae moe likely than othes fo the EMS s location. When establishing likely positions fo the EMS, human expets ae consulted. The expets povide subjective pobabilities of the EMS being located at a numbe of positions. These likely EMS locations ae efeed as hypothesis positions. Ray-theoetic electomagnetic popagation (Blake 986 is conducted fom each hypothesis position to each intefeomete element on the IP. The points on the sampling gid neaest the points of each ay s passage ae the sample points. The pioity of a sample point is elated to the subjective pobability of the hypothesis position fom which the associated ay emeges. Sample points aising fom the highest pobability hypothesis positions have pioity one; sample points associated with lowe pobability hypothesis positions, pioity two; etc. Each sample point is suounded by what ae efeed to as desiable neighbohoods. Depending on local weathe, topogaphy, etc., the desiable neighbohoods ae geneally concentic closed balls with a degee of desiability assigned to each ball. The degee of desiability chaacteizes the anticipated vaiation in the index of efaction. A point may be labeled taboo fo a vaiety of easons. A taboo point and the undesiable neighbohoods containing the point geneally epesent a theat to the UAV. The theat may take the fom of high winds, tubulence, icing conditions, mountains, etc. The undesiable neighbohoods aound the taboo point elate to how spatially extensive the theat is. When detemining the optimal path fo the UAVs to follow both the planning algoithm and the contol algoithm unning on each UAV take into account taboo points and the undesiable neighbohood aound each taboo point. The path planning algoithm and contol algoithm will not

3 allow a UAV to pass though a taboo point. Both the concepts of isk and isk toleance ae based on human expetise and employ ules each of which cay a degee of uncetainty. This uncetainty is bon of linguistic impecision (Tsoukalas 997, the inability of human expets to specify a cisp assignment foisk. Risk is epesented as a fuzzy decision tee (Blackman 999; Smith 00a, 00b, 003, 00a, 00b. The isk subtee defined below is a subtee of the lageisk tee that was actually used. The isk tee is used to define taboo points and the undesiable neighbohoods suounding the taboo points. The oot concepts on the isk tee use the membeship function defined in (-3, α ( qtaboo,x =,, 3, if if 0,, if if q taboo if = x, 0 < l l < l < > = 0 3 l l 3 l ( ( q taboo = position of taboo point. (3 whee the taboo point, q taboo is the point at which the isk phenomenon has been obseved. The oot concepts used on the isk subtee ae given in (, and the subscipt α is an element of the oot concept set, RC, i.e., α RC={Mountains, High Tension Wies, Buildings, Tees, Smoke Plumes, Suspended Sand, Bids/Insects, Othe UAVs, Ai Pollution, Civilian, Own Militay, Allied Militay, Neutal Militay, Cold, Heat, Icing, Rain, Fog, Sleet, Snow, Hail, Ai Pocket, Wind, Wind Shea, Hostile Action/Obsevation} The nom in equation ( is typically taken as an Euclidean distance. The values taken by the quantity l will be discussed in a futue publication. The fuzzy membeship function fo the composite concept isk is defined as isk ( q,x ( q,x taboo α RC taboo ( = max. (5 The best path algoithm is actually an optimization algoithm that attempts to minimize a α cost function to detemine the optimal tajectoy fo each UAV to follow, given a pioi knowledge. The cost function fo the optimization algoithm takes into account vaious factos associated with the UAV s popeties, mission and measuement space. Two significant quantities that contibute to the cost ae the effective distance between the initial and final poposed positions of the UAV and the isk associated with tavel. Fo puposes of detemining the optimal path, the UAV is assumed to follow a ectilinea path consisting of connected lines segments, whee the beginning and ending points of each line segment eside on the UAV s sampling lattice. Let A and B be two gid points on the UAV s sampling gid with coesponding position vectos, A and B, espectively. Denote the Euclidean distance between A and B as d( A, B. Let v( A, B be the speed at which the UAV tavels in going fom A to B. If both A and B ae sample points then the UAV tavels at sampling velocity, othewise it tavels at non-sampling velocity. The path cost is given by path _ cost d ( A,B = ntaboo ( A,B + isk ( ti,b i= v(,. β (6 A whee ntaboo is the numbe of taboo points, i.e., columns in the taboo point matix B [ t,t, K, ] Taboo (7 tn taboo and ti,i =,, K, ntaboo ae the taboo points detemined to exists in the measuement space when path _ cost( A, B is calculated. The quantity, β, is an expet assigned paamete. Note that path _ cost ( A, B is an effective time. When isk is n taboo not pesent, i.e., β isk ( ti, B is zeo, then i= path _ cost( A, B is the actual tavel time. When isk is pesent then the tavel time is inceased. The time incease will be significant if the isk is high. If the candidate path fo the mission consists of the following points on the UAV lattice given by the path matix in (8, Path =, (8 i [,, K, ] n

4 then the total path cost is defined to be total _ cost( n Pathi path _ cost( j,j+. j= (9 Detemining the optimal path fo the i th UAV consists of minimizing the total path cost given by (9 such that thee is enough fuel left to complete the path. The planning algoithm detemines the path each UAV will pusue, which points will be sampled, the minimum numbe of UAVs equied fo sampling the points and makes assignments of UAVs fo measuements at paticula points. UAVs ae assigned as a function of thei abilities to sample high pioity points fist. The planning algoithm detemines flight paths by assigning as many high pioity points to a path as possible taking into account elative distances including sampling and non-sampling velocity, isk fom taboo points, and UAV fuel limitations. Once flight paths ae detemined, the planning algoithm assigns the best UAV to each path using the fuzzy logic decision ule fo path assignment descibed in this section. The planning algoithm must assign UAVs to the flight paths detemined by the optimization pocedue descibed below in this section. This is efeed to as the UAV path assignment poblem (UPAP. The planning algoithm makes this assignment using the following fuzzy logic based pocedue. To descibe the decision ule it is necessay to develop some peliminay concepts and notation. Each UAV will fly fom lattice point to lattice point, i.e., gid point to gid point, let one such oute be given by the matix of points, [ P,P, K,Pn, P ] Path = (0 whee the odeing of points gives the diection of the oute, i.e., stating at P and ending at P. Let the taboo points be those given in (7. Let the degee of undesiability of the neighbohood associated with taboo points, ti,i =,, K, ntaboo be denoted isk ( ti, Pj fo the oute points Pj, j =,, K, n path. The definition of the mission isk is mission _ isk path n taboo npath ( Path ( t, P i= j= ( isk i j Within the path specified by (0, let thee be the following sample points to be measued, S, j =,, K,. Let the function pio assign j n sp pioities to the sample points, i.e, pio( S j is the pioity of the j th sample point. The values that can take ae positive integes with one pio( S j epesenting the highest pioity, two the next highest pioity, etc. The mission pioity fo Path is defined to be mission _ pio( Path. ( i= pio n sp ( S Futhemoe, let the ( UAV ( i,path T be the amount of time it will take UAV(i to fly and make measuements along Path. The fuzzy degee of eliability expets assign to the sensos of UAV(i is denoted as s ( UAV ( i. This is a eal numbe between zeo and one with one implying the sensos ae vey eliable and zeo that they ae totally uneliable. Likewise, ns ( UAV ( i is the fuzzy degee of eliability of othe non-senso systems onboad the UAV(i. This fuzzy concept elates to any non-senso system, e.g., populsion, computes, had disk, deicing systems, etc. The value of UAV(i in units of $ is denoted as V ( UAV ( i. The amount of fuel that UAV(i has at time t is denoted fuel ( UAV ( i,t. All the UAVs paticipating in a mission ae assumed to leave base at time, t = t o. Let UAV(i s fuzzy gade of membeship in the fuzzy concept isk toleance be denoted as isk tol ( UAV ( i. The quantity, isk tol ( UAV ( i, is a numbe between zeo and one and will be simply efeed to as UAV(i s isk-toleance. If the isk toleance is nea zeo then the UAV should not be sent on vey isky missions. If the UAV s isk toleance is nea one then it can be sent on vey isky missions. It seems natual to compae isktoleance to value. So the compaison can be caied out on the same footing, a fuzzy concept of value should be defined. The fuzzy gade of membeship in the fuzzy concept Value of each UAV that can be assigned to the mission is defined as i

5 ( ( i { Value( UAV ( j } Value UAV V ( UAV ( i. (3 max j The max opeation in (3 is taken ove the set of all possible UAVs that can be assigned to the mission. The advantage of the concept of isk-toleance is that it gives the use an exta concept to exploit. If the UAV is not of geat elative value, but it still might be needed fo a cucial mission afte the cuent one, it might be useful to give it a low isk toleance so that it is not lost on the cuent mission. This may allow it to be used on the following mission. The final concept and elated fuzzy membeship function that must be defined is slow. A UAV is said to be slow if it takes a long time to tavel a paticula path. The fuzzy membeship function fo the concept slow is defined as follows: slow ( UAV ( i, Path T ( UAV ( i, Path max { T ( UAV ( j, Path }. j ( A slow UAV expeiences a higheelative mission isk since it is in the field longe and may be exposed to isk longe. To constuct the fuzzy membeship function fo the fuzzy concept assign UAV to Path (AUP make the following definitions: f χ ( UAV ( i,path fuel( UAV ( i,t + ε T( UAV ( i,path ( o fuel. f min ( UAV ( i,path mission _ pio denom UAV min ( ( i,path [ s ( UAV ( i, ns ( UAV ( i ]. ( ( i,path + [ isk tol ( UAV ( i, V ( UAV ( i ] slow ( UAV ( i,path mission _ isk( Path. denom UAV ( UAV ( i,path f( UAV ( i,path f ( UAV ( i,path. num (5 (6 (7 (8 The Heaviside step function denoted as χ in (5 takes the value one when its agument is geate than o equal to zeo and is zeo othewise. The quantity ε fuel is added to the fuel tem to make sue the UAV selected has moe than enough fuel. Given the definition of num ( UAV ( i,path the fuzzy membeship function that gives the gade of membeship of UAV(i in the fuzzy concept assign UAV to Path is defined as AUP ( UAV ( i,path j ( ( i,path ( ( j,path, num UAV max num UAV (9 whee the max opeation in the denominato of (9 is taken ove the set of all UAVs that can be assigned to the path. CONTROL ALGORITHM Each UAV has a eal-time algoithm onboad it that allows ecalculation of paths duing flight due to changes in envionmental conditions o mission pioities. These changes typically become appaent afte the planning algoithm has un duing the peflight stage. As in the case of the planning algoithm the contol algoithm uses an A-sta algoithm (Russel 00 to do the best path calculation, employs fuzzy logic and solves a constained optimization poblem. Although this can equie a numbe of minutes of computation on a two to thee gigahetz compute, this is consideed adequate given the equied UAV flight time between points. The contol algoithms ecalculation of flight paths can be tiggeed by a numbe of events such as weathe boadcasts that indicate new taboo egions o changes of pioity of sample points. Fo those changes that do not equie UAVs suppoting each othe, the contol algoithm does not diffe fom the planning algoithm. The contol algoithm is faste by vitue that it only need pocess those pats of the measuement space whee thee have been changes elative to sample o taboo points. A UAV may equests help if it discoves a potential elevated system like a adio hole, malfunctions o suspected malfunctions. All of these conditions can esult in help messages being tansmitted between the UAVs. These help

6 messages can esult in inteactions between the UAVs based on tansmission of the esults of pioity calculations foendeing suppot to the equesting UAVs. Cuently in the contol stage, when a UAV discoves an inteesting physical phenomenon, is malfunctioning, o suspects due to intenal eadings that it is malfunctioning, it sends out a equest fo help. Each UAV eceiving this message calculates its pioities fo poviding assistance to the UAV in need. This pioity calculation gives ise to a numbe between zeo and one, inclusive, which is subsequently tansmitted to the oiginal UAV desiing suppot. The equesting UAV sends out an omni-diectional message with the ID of the UAV with highest pioity fo contibuting suppot. The high pioity UAV then flies into the necessay neighbohood of the equesting UAV to povide help. Thee ae thee classes of help equest. The fist occus when a UAV, the equeste, detemines it may have discoveed an inteesting physical phenomenon. This phenomenon may be an elevated duct, adio hole, ain system o some othe type of system with physical extent. The equeste desies to detemine if the phenomenon has significant extent. It will equest that a helping UAV o UAVs sample likely distant points within this phenomenon. The second class of help equest elates to a UAV that accoding to intenal diagnostics may be expeiencing a senso malfunction. This UAV will equests that anothe UAV o UAVs measue some of the points that the equesting UAV measued. This will help detemine if the UAV is actually malfunctioning. If the equesting UAV is detemined to be malfunctioning, then it will fly back to base, if it is capable. The detemination of whethe it is actually malfunctioning equies some consideation. Since the second UAV will pobably be measuing a distant point at a time diffeent than the oiginal equesting UAV made its measuements, potential vaiation in the index of efaction ove time must be taken into account. When a UAV sends out an omni-diectional equest fo help, those UAVs eceiving the message will calculate thei fuzzy pioity fo helping, denoted as PH. The UAV that will ultimately help the equeste is the one with the highest fuzzy pioity fo helping. The fuzzy pioity fo helping takes into account a vaiety of popeties of the potential helpe. The set of UAVs that eceive the equest fo help fom UAV(i at time t is denoted as help ( i, t. If UAV(i equest help at time t and UAV(j eceives the message then UAV(j will take into account the amount of time, denoted, help _ time( UAV ( j, it will take it to fly fom the point whee it eceived the equest to the point whee it would povide suppot. It also takes into account the amount of fuel UAV(j has left at the time of the equest, denoted fuel ( UAV ( j,t; UAV(j s fuzzy concept of pice denoted as pice, and UAV(j s fuzzy concept of mission pioity at time, t. Let the set of elevant UAV popeties be denoted as UAV _ pop and be defined as UAV _ pop = { help _ time, fuel,mission _ pio, pice} (0 The fuzzy pioity fo helping denoted as PH takes the fom ( UAV ( i,uav ( j = w ( UAV ( j PH α α α UAV _ pop ( The quantities w α and α fo α UAV _ pop ae expet defined weights and fuzzy membeship functions, espectively. The fuzzy membeship functions ae defined in (-5 and given below, help _time ( UAV ( i,uav ( j max k help( i,t fuel mission _ pio max k help( i,t = ( ( j { help _ time( UAV ( k } help _ time UAV ( UAV ( i,uav ( j = fuel( UAV ( j { fuel( UAV ( k } max k help( i,t ( UAV ( i,uav ( j pio( UAV ( j { mission _ pio( UAV ( k } mission _ = + + ( (3 (

7 pice ( UAV ( i,uav ( j k help( i,t ( ( j { Value( UAV ( k } Value UAV max = + (5 It is assumed that all evaluations ae pocessed at time, t, so time dependence is suppessed in (-5 fo notational convenience. A moe sophisticated vesion of the contol logic that takes path isk, changes in isk, UAV eliability, UAV isk-toleance and missed sample points into account will be the subject of a futue publication. 5 COMPUTATIONAL EXPERIMENTS The planning and contol algoithms descibed in the pevious sections have been the subject of a lage numbe of expeiments. This section povides a desciption of a small subset of these expeiments. They seve to illustate how the algoithms wee tested. Due to space limitations only expeiments involving up to thee UAVs ae discussed. UAV expeiments using only one UAV demonstate how the planning and contol algoithm will detemine the oute the UAV flies so that it is successful in making measuements at sample points in space, while the UAV avoids taboo points, that is points in space that could damage o destoy the UAV. Expeiments using two UAVs illustate how the contol algoithm allows the UAVs to automatically suppot each othe to incease the pobability thei joint mission is successful. Figues - use the same labeling conventions. Sample points ae labeled by concentic cicula egions coloed in diffeent shades of gay. The lighte the shade of gay used to colo a point, the lowe the point s gade of membeship in the fuzzy concept desiable neighbohood. The legend povides numeical values fo the fuzzy gade of membeship in the fuzzy concept desiable neighbohoods. If the fuzzy degee of desiability is high then the index of efaction is consideed to be close to the index of efaction of the sample point at the cente of the desiable neighbohood. This allows the UAV to make significant measuements while avoiding undesiable neighbohoods. Each sample point is labeled with an odeed pai. The fist membe of the odeed pai povides the index of the sample point. The second membe of the odeed pai povides the point s pioity. Fo example, if thee ae n sp sample points and the th q sample point is of pioity p, then that point will be labeled with the odeed pai (q,p. Points suounded by sta-shaped neighbohoods vaying fom dak gey to white in colo ae taboo points. As with the sample points, neighbohoods with dake shades of gay have a highe gade of membeship in the fuzzy concept undesiable neighbohood. The legend povides numeical values fo the fuzzy gade of membeship in the fuzzy concept undesiable neighbohood. UAVs with high isk toleance may fly though dake gey egions than those with low isk toleance. When compaing planning and associated contol pictues, if a point ceases to be taboo, the neighbohood whee it esides is maked by a vey dim gay sta as well as being labeled by a dialog box as being an old taboo point. New taboo points and thei associated undesiable neighbohoods ae labeled with dialog boxes indicating that they ae new. UAVs stat thei mission at the UAV base which is labeled with a diamond-shaped make. They fly in the diection of the aows labeling the vaious cuves in Figues -. Figue povides the sample points, taboo points and sample path fo one UAV as detemined by the planning algoithm. It is impotant to notice that the UAV s path passes diectly though each sample point, i.e., though the cente of the concentic ciculaegions epesenting the fuzzy degee of desiability of neighbohoods. Fotuitously, the taboo points and thei neighbohoods ae so positioned that they do not intefee with the UAV s measuement pocess o its etun to base. Figue depicts the actual path the UAV flies as detemined by the UAV s eal-time contol algoithm. The path detemined by the contol algoithm diffes fom the one ceated by the planning algoithm due to eal-time changes in taboo points. Afte leaving the UAV base new weathe data was acquied infoming the UAVs that the exact position of the thid sample point, i.e., the one labeled (3, actually esides within an undesiable neighbohood. Due to the high pioity of the sample point and the UAV s isk-toleance, the UAV flies into the taboo points undesiable neighbohood as indicated in Figue. In both the planning and contol algoithms the UAV measues sample points of two diffeent pioities, with the diection of the flight path selected so that the highe pioity points ae measued fist. By measuing high pioity points

8 fist, the likelihood of an impotant measuement not being made is diminished, if the UAV can not complete its mission due to a malfunction, change in weathe, etc. Also, due to movement of old taboo points o the emegence of new taboo points which ae maked New, the path detemined fo the UAV using the contol algoithm is significantly diffeent than the one ceated by the planning algoithm. The path change epesents the contol algoithm s ability to educe UAV isk. Figue 3 depicts the sampling path detemined by the planning algoithm fo an expeiment involving two UAVs. The fist, UAV( follows the dashed cuve; the second, UAV(, the solid cuve. The UAVs wee assigned to the diffeent paths by the fuzzy path assignment decision ule descibed in section 3. UAV( is assigned to sample all the highest pioity points, i.e., the pioity one points. UAV( samples the lowe pioity points, i.e.; those with pioity two. Due to the geedy natue of the point-path assignment algoithm, the highest pioity points ae assigned fo sampling fist. Figue depicts the actual flight path the UAVs take duing eal-time. Initially, UAV( is successful in measuing sample points one and two as assigned it by the planning algoithm. Just beyond sample point two, UAV( expeiences a malfunction. UAV( s eal-time contol algoithm subsequently sends out a help equest infoming the only othe UAV in the field, UAV( of the malfunction. UAV( s contol algoithm detemines a new path fo UAV( to fly so that the pioity one points, labeled (3, and (,, that UAV( was not able to sample ae subsequently measued. Afte UAV( measues sample point five, its new flight path allows it to measue sample points thee and fou. UAV( s contol algoithm detemined it was vey impotant that these pioity one points be measued. Unfotunately, due to the exta fuel expended in eassigning sample points thee and fou to UAV(, UAV( did not have enough fuel to measue sample points seven and eight which wee of pioity two. UAV( s ealtime contol algoithm detemined the best possible solution in the face of changing cicumstances and limited esouces. It is impotant to note that the contol algoithms unning on UAV( and UAV( diect both UAVs to alte theietun paths to the base due to the emegence of new taboo points making the planning algoithm detemined flight paths too dangeous. The contol algoithm uses each UAV s fuzzy isktoleance to detemine how nea each UAV may appoach a taboo point. Table : Details of thee UAV mission depicted in Figue 5. Locations UAV MISSION UAV MISSION UAV 3 MISSION Fly Mode Fuel Time Remain (minutes Locations Fly Mode Fuel Time Remain (minutes Locations Fly Mode Fuel Time Remain (minutes Base 90.0 Base 85.0 Base 85.0 (, NS (6, NS (,3 NS (, S (7, S 55. (,3 S 5.0 (3, S 5.66 (8, S (3,3 S (, S.7809 (9, S (,3 S (5, S (0, S.08 Base NS 6.57 Base NS 6.73 Base NS.785

9 PLANNING PHASE CONTROL PHASE ALTITUDE (miles (, (, (3, (, (5, UAV path Base Taboo pt Sample pt (a,b Index, pioity degee (6,3 ALTITUDE (miles (, UAV samples neighbo (, egion (3, Taboo Region moved diectly ove sampling aea (, (5, UAV path Base Taboo pt Sample pt (a,b Index, pioity degee (6,3 (7,3 (7,3 new UAV changes path to avoid taboo egions RANGE (miles Figue : One UAV tajectoy as detemined by the planning algoithm RANGE (miles Figue : One UAV tajectoy as detemined by the eal-time contol algoithm. ALTITUDE (miles UAV path UAV path Base Taboo pt Sample pt (a,b Index, pioity degee PLANNING PHASE (7, (8, (6, (9, (5, (, ALTITUDE (miles UAV path UAV path Base Taboo pt Sample pt (a,b Index, pioity degee Old taboo egions new CONTROL PHASE (7, UAV esponses to (8, help equest. (9, (6, new Less dangeous taboo egion theefoe able to fly nea (5, (, (3, (3, (, (, (, (, UAV malfunctions, equests fo help RANGE (miles Figue 3: Tajectoy of two UAVs as detemined by the planning algoithm. 35 PLAN PHASE RANGE (miles Figue : Duing flight, updates about envionmental changes cause the eal-time contol algoithms on the two UAVs to change thei tajectoies., 5, 30 3,,3 3,3,3 5,,3 X Plane 0, 5 6, 0 8, 7, UAV path UAV path 5 0, 9, UAV 3 path Base Taboo Region Sample pt (a,b Index, pioity degee Y Plane Figue 5: Thee UAV mission descibed in Table, an example of the AUP decision tee s assignments.

10 Figue 5 povides an example of the AUP decision tee s assignment of thee UAVs to thee paths. The highest pioity locations ae assigned to UAV( as it has the geatest fuel capacity, i.e., 90 minutes. UAV( howeve does not have enough fuel to handle the high pioity points located at positions six and seven and theefoe UAV( is assigned these points along with the second degee high pioity locations. Table povides numeical details of the tasks depicted in Figue 5. The column labels have the following intepetation: Location, the UAV coodinates on the map; Fly mode, whethe the UAV sampled fom its pevious location to its cuent position. If the UAV sampled then a S was enteed. NS was enteed if sampling did not occu. Fuel Time efes to how much fuel emained by the time the UAV eached the associated location. 6 SUMMARY Fuzzy logic based planning and contol algoithms that allow a team of coopeating unmanned aeial vehicles (UAVs to make meteoological measuements have been developed. The planning algoithm including the fuzzy logic based optimization algoithm fo flight path detemination and the UAV path assignment algoithm ae discussed. The contol algoithm also uses these fuzzy logic algoithms, but also allows thee types of automatic coopeation between UAVs. The fuzzy logic algoithm fo automatic coopeation is examined in detail. Methods of incopoating envionmental isk measues as well as expet measues of UAV eliability ae discussed as they elate to both the planning and contol algoithms. Expeimental esults ae povided. The expeiments show the algoithms effectiveness. Smith, J. F., 00a. Co-evolutionay Data Mining to Discove Rules fo Fuzzy Resouce Management, In: H. Yin, ed., Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, August, 00, Mancheste, Spinge-Velag, 9-. Smith, J. F., 00b. Data Mining fo Fuzzy Decision Tee Stuctue with a Genetic Pogam, In: H. Yin, ed., Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, August 00, Mancheste, Spinge-Velag, 3-8. Smith, J. F., 003. Fuzzy logic esouce manage: decision tee topology, combined admissible egions and the self-mophing popety, In: I. Kada ed., Signal Pocessing, Senso Fusion, and Taget Recognition XII, Vol. 5096, Apil 003, Olando, SPIE Poceedings, 0-. Smith, J. F., 00a. Fuzzy logic esouce manage: ealtime adaptation and self oganization, 00, In: I. Kada, ed., Signal Pocessing, Senso Fusion, and Taget Recognition XIII, Vol. 59. Apil 00, Olando, SPIE Poceedings, Smith, J. F., 00b. Genetic Pogam Based Data Mining fo Fuzzy Decision Tees, In: H. Yin, ed., Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, August 00, Exete, Spinge-Velag, Smith, J. F., Nguyen, T. H., 005. Distibuted autonomous systems: esouce management, planning, and contol algoithms, In: I. Kada ed., Signal Pocessing, Senso Fusion, and Taget Recognition XIV, Vol. 5809, Apil, 005, Olando, SPIE Poceedings, Speas, D. and Zazhitsky, 005. D., Multi-Robot Chemical Plume Tacing. In: A. Schultz, ed. Multi- Robot Systems: Fom Swams to Intelligent Automata, Vol. III, May, 005, New Yok, Spinge, -. Tsoukalas, L., H. and Uhig, R., E Fuzzy and Neual Appoaches in Engineeing, New Yok, John Wiley and Sons, Chapte 5. REFERENCES Blake, L.V Rada Range-Pefomance Analysis. Boston. Atech House. Blackman, S. and Popoli, R Design and Analysis of Moden Tacking Systems, Boston, Atech House, Chapte. Russel, S.J. and Novig, P. 00. Atificial Intelligence: A Moden Appoach (nd Edition, Englewood Cliffs, Pentice-Hall.

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