Resource manager for an autonomous coordinated team of UAVs

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1 Resouce manage fo an autonomous coodinated team of UAVs James F. Smith III, ThanhVu H. Nguyen Naval Reseach Laboatoy, Code 574, Washington, D.C., ABSTRACT A ecently developed fuzzy logic esouce allocation algoithm that enables a collection of unmanned ai vehicles (UAVs) to automatically coopeate as they make meteoological measuements 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, 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, changes the points that will be sampled when obseving inteesting phenomena, o to teminate the mission and etun to base. The contol algoithm allows thee types of coopeation between UAVs. The undelying optimization pocedues including the fuzzy logic based cost function, the fuzzy logic decision ule fo UAV path assignment, the fuzzy algoithm that detemines when a UAV should alte its mission to help anothe UAV and the undelying appoach to quantifying isks ae discussed. Significant simulation esults will show the planning algoithm s effectiveness in initially selecting UAVs and detemining UAV outes. Likewise, simulation shows the ability of the contol algoithm to allow UAVs to effectively coopeate to incease the UAV team s likelihood of success. Keywods: esouce management, fuzzy logic, planning algoithms, decision suppot algoithms, coopeative behavio. 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 ai vehicles (UAVs) and an intefeomete platfom (IP) 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 pe-planned, and coopeate with othe UAVs. Section 2 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 descibes 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 4 descibes the contol algoithm that endes the UAVs autonomous. Section 4 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 pesents 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. Coespondence: jfsmith@dsews.nl.navy.mil Signal Pocessing, Senso Fusion, and Taget Recognition XV, edited by Ivan Kada, Poc. of SPIE Vol. 6235, 62350C, (2006) X/06/$5 doi: 0.7/ Poc. of SPIE Vol C-

2 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 geo-location ; detemination of the pesence and extent of such phenomena as adio holes and ducts, which may intefee with communications; tacking atmospheic contaminants 2 ; 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 4. The fist type of coopeation that the UAVs may exhibit is to suppot each othe if thee is evidence that an inteesting physical phenomenon has been discoveed. If one UAV seems to have discoveed a adio hole, it can equest that anothe UAV o UAVs help detemine the extent of the adio hole so the IP can fly aound it. Simila coopeation can be caied out if a UAV may have discoveed othe elevated extended weathe systems. The second type of coopeation that the UAVs can exhibit though thei contol algoithm is when a UAV is malfunctioning o may be malfunctioning. If a UAV s intenal diagnostics indicate a possible malfunction, then it will send out an omni-diectional equest to the othe UAVs fo help. Each UAV will calculate its pioity fo poviding help using a fuzzy logic pocedue descibed below. The UAVs send thei pioity fo poviding help message back to the equesting UAV. The equeste subsequently sends out a message infoming the goup of the ID of the highest pioity UAV. The high pioity UAV then poceeds to aid the equeste. The suppot povided by the helping UAV can take on diffeent foms. If the equeste suspects a malfunction in its sensos, the helpe may measue some of the same points oiginally measued by the UAV in doubt. This will help establish the condition of the equeste s sensos. If additional sampling indicates the equeste is malfunctioning, and epesents a liability to the goup it will etun to base. In this case the suppote may take ove the mission of the equeste, whethe o not the suppote samples all the emaining sample points of the equeste; subsequently, abandoning its oiginal points depends on the sample points pioities. A fuzzy logic based pocedue fo detemining sample point pioities is discussed below. If it is established that the equeste is not malfunctioning o the equeste can still contibute to the mission s success it may emain in the field to complete its cuent mission. 3. MEASUREMENT SPACE, THE PLANNING ALGORITHM, 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 subsection Planning algoithm The planning algoithm allows the detemination of the minimum numbe of UAVs needed fo the mission subject to fuel constaints, isk, UAV cost, UAV speed, and impotance of vaious points fo sampling. Risk efes to tubulent egions o egions undesiable fo othe easons, e.g., the pesence of enemy obseves o physical obstuctions. Risk may also be incued if the UAV s populsion o senso systems ae consideed uneliable. The planning algoithm automatically establishes the ode in which to send the UAVs taking into account the UAV s value; speed; onboad Poc. of SPIE Vol C-2

3 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 3 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. If fo that egion of the measuement space, the spatial vaiation of the index of efaction is slow, the degee of desiability may assume its maximum value of unity fo a ball of adius measued in miles. Fo egions of space whee the index of efaction s spatial vaiation is geate, the degee of desiability may fall off much moe apidly, appoaching the minimum value of zeo afte just a mile o two. The desiable egion need not have spheical geomety. Rotational symmety may be boken by a vaiety of pocesses, e.g., an elevated duct, a adio hole, etc. 3.2 UAV isk and the fuzzy isk tee 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. A method of quantifying isk and incopoating it into the path assignment algoithm is pesented that offes conceptual impovements ove an appoach peviously developed. This section uses fuzzy logic to quantify how much isk a given neighbohood poses fo a UAV. This quantitative isk is then incopoated into the UAV s cost fo taveling though the neighbohood as descibed in subsection 3.3. Once the cost is established an optimization algoithm is used to detemine the best path fo the UAV to each its goal. 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 allow a UAV to pass though a taboo point. The concept of isk is based on human expetise and employs ules each of which cay a degee of uncetainty. This uncetainty is bon of linguistic impecision 4, the inability of human expets to specify a cisp assignment fo isk. Owing to this uncetainty it is vey effective to specify isk in tems of fuzzy logic. Risk is epesented as a fuzzy decision tee 5-0. The isk subtee defined below is a subtee of the lage isk 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), Poc. of SPIE Vol C-3

4 µ oot _ concept q taboo (, x), if = 0 3 4, if 0 < l = 2, if l < 2 l, if 2 l < 3 l 4 0, if > 3 l = x, q taboo q taboo = position of taboo point. () (2) (3) whee taboo point is the point at which the isk phenomenon has been obseved. The oot concepts used on the isk subtee ae given in (4). Root_concept RC={Mountains, High Tension Wies, Buildings, Tees, Smoke Plumes, Suspended Sand, Bids/Insects, Othe UAVs, Ai Polution, Civilian, Own Militay, Allied Militay, Neutal Militay, Cold, Heat, Icing, Rain, Fog, Sleet, Snow, Hail, Ai Pocket, Wind, Wind Shea, Hostile Action/Obsevation} (4) 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 µ isk ( q,x) µ ( q,x) taboo = max, (5) α RC with the Undesiable Neighbohood defined as follows: ntaboo Undesiabl e Neighbohood = x µ isk ( ti,x) τ i. (6) i= α taboo The paamete, τ i, of the i th UAV, UAV(i) is defined such that it is pefeed that UAV(i) not fly though the undesiable neighbohood given in (6). Instead it is pefeed that UAV(i) should only fly though points within an Acceptable Neighbohood as defined in (7), the complement of the set defined in (6). ntaboo Acceptable Neighbohood = x 0 < µ isk ( ti,x) < τ i. (7) i= 3.3 Cost matix The best path algoithm is actually an optimization algoithm that attempts to minimize a 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 Poc. of SPIE Vol C-4

5 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 _ cos t (, ) A B d ntaboo (, ) + β µ ( t, ) A B i= = v (, ) A B isk i B. (8) whee ntaboo is the numbe of taboo points, i.e., columns in the taboo point matix Taboo [ t,t, K, ] 2 tn taboo (9) and ti,i =,2, K, ntaboo ae the taboo points detemined to exists in the measuement space when path _ cost( A, B ) is path _ cost A, B is an effective time. When n taboo β µ t, is zeo, then path _ cost(, ) is the actual tavel time. When isk is calculated. The quantity, β, is an expet assigned paamete. Note that ( ) isk is not pesent, i.e., ( ) i= isk i B 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 (0), then the total path cost is defined to be Path i [,, K, ] 2 n A B =, (0) total _ cost( n Pathi ) path _ cost( j,j+ ). j= () Detemining the optimal path fo the the i th UAV consists of minimizing the total path cost given by () 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 section Decision ule fo UAV path assignment The planning algoithm must assign UAVs to the flight paths detemined by the optimization pocedue descibed in section 3.3. 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, Path = [ P,P2, K,Pn, P ] path (2) Poc. of SPIE Vol C-5

6 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 (9). Let the degee of undesiability of the neighbohood associated with taboo points, ti,i =,2, K, ntaboo be denoted µ isk ( ti, Pj ) fo the oute points Pj, j =,2, K, n path. The definition of the mission isk is mission _ isk n taboo npath ( Path) ( t, P ) i= j= Within the path specified by (2), let thee be the following sample points to be measued, function pio assign pioities to the sample points, i.e, pio( S j ) pio( S j ) µ isk i j (3) S, j =,2, K, n. Let the is the pioity of the j th sample point. The values that can take ae positive integes with one epesenting the highest pioity, two the next highest pioity, etc. The mission pioity fo Path is defined to be n sp mission _ pio( Path). (4) i= pio Futhemoe, let the T ( UAV () i,path) 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 µ 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, µ 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 = to. Let UAV(i) s fuzzy gade of membeship in the fuzzy concept isk toleance be denoted as isk tol ( UAV ( i) ) quantity, ( UAV () i ) isk tol ( ) S i j sp µ. The µ, 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 isk toleance 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 of each UAV that can be assigned to the mission in the fuzzy concept Value is defined as ( ( i) ) { Value( UAV ( j) )} Value UAV µ V ( UAV () i ) max (5) The max opeation in (5) is taken ove the set of all possible UAVs that can be assigned to the mission. j 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. Poc. of SPIE Vol C-6

7 The final concept and elated fuzzy membeship function that will 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: ( UAV ( i),path) { T ( UAV ( j),path)} T µ slow( UAV () i,path) (6) max j A slow UAV expeiences a highe elative 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: facto facto 2 ( ) ( UAV () i,path) fuel( UAV ( i),t ) + ε T ( UAV ( i),path) χ, (7) o fuel ( UAV () i,path) min [ µ s ( UAV ( i) ), µ ns ( UAV ( i) )] mission _ pio( Path) denom( UAV () i,path), (8) denom UAV + min ( () i,path) [ µ ( UAV () i ), µ ( UAV ( i) )] ( UAV () i,path) mission _ isk( Path), isk tol V µ slow (9) num( UAV () i,path) facto ( UAV ( i),path) facto2 ( UAV ( i),path). (20) The Heaviside step function denoted as χ in (7) 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 ( ( i),path) ( ( j),path) num UAV µ AUP ( UAV () i,path), (2) max num UAV j whee the max opeation in the denominato of (2) is taken ove the set of all UAVs that can be assigned to the path. Given the fuzzy gade of membeship it is necessay to defuzzify, i.e., make definite UAV-path assignments. Simply assigning the UAV with the highest fuzzy gade of membeship fo a paticula path to that path can give less than desiable esults. Anothe appoach to defuzzification is as follows: assume that the following matix has been detemined µ AUP ( UAV () i,path j );i =,2, K,nUAV ; j =,2, K,npath; whee nuav and n path ae the numbe of UAVs and paths, espectively. Futhe assume that n n. Thee must be an assignment of a one UAV to each path. The numbe of ways of doing this is UAV path n n UAV P n n UAV path path n path th p assignment of UAVs to paths be denoted by the set of odeed pais Pem ( p) ( index( j, p), j) =!. Let the set of paths be denoted as Path _ set. Let the { j =,2, K,n }, p =,2, K, P path nuav npath. (22) Poc. of SPIE Vol C-7

8 whee index( j, p ) is defined to be a function that gives the UAV index as a function of path index j =,2, K,npath, and pemutation index p,2, K, P npath nuav =. Let Pem _ set Pem( p) { n p =,2, K path,p } The appoach to defuzzification cuently used is to select the pemutation p such that the following cost function is maximized nuav Cost AUP ( p,path _ set ) = n path k= AUP ( UAV ( index( index( k, p) )),Path ), p Pem _ set µ. (23) If the numbe of paths exceeds the numbe of UAVs a simila pocedue is taken whee all possible pemutations of path assignment to UAVs ae consideed and the assignment that is made is the one that maximizes a cost function analogous to (23). 4. 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 pe-flight stage. As in the case of the planning algoithm the contol algoithm uses an A-sta algoithm to do the best path calculation, employs fuzzy logic and solves a constained optimization poblem. This has poven successful fo eal-time application. 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 emegence of new o elimination of old 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 messages can esult in inteactions between the UAVs based on tansmission of the esults of pioity calculations fo endeing 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 k Poc. of SPIE Vol C-8

9 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) equests 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 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}. (24) The fuzzy pioity fo helping denoted as µ PH takes the fom PH ( UAV () i,uav ( j) ) = w UAV ( j) µ α µ α α UAV _ pop ( ). (25) The quantities w α and µ α, fo α UAV _ pop ae expet defined weights and fuzzy membeship functions, espectively. The fuzzy membeship functions ae defined in (26-29) and given below, help _time ( () ( )) ( UAV ( j) ) help _ time UAV i,uav j max { help _time( UAV ( k) )} k help( i,t ) µ = +, (26) ( UAV ( j) ) { fuel( UAV ( k) )} fuel µ fuel ( UAV () i,uav ( j) ) =, max k help( i,t ) (27) mission _ pio ( () ( )) ( UAV ( j) ) mission _ pio UAV i,uav j max { mission _ pio( UAV ( k) )} k help( i,t ) µ = +, (28) Value ( () ( )) ( UAV ( j) ) µ pice UAV i,uav j = + max { Value( UAV ( k) )} k help( i,t ). (29) It is assumed that all evaluations ae pocessed at time, t, so time dependence is suppessed in (25-29) 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 one o two UAVs ae discussed. UAV expeiments using only one UAV demonstate how the planning and contol algoithm, while avoiding taboo points, will detemine the oute the UAV flies so that it is successful in making measuements at sample points in space. 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. Poc. of SPIE Vol C-9

10 Figues -4 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 nsp sample points th and the 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 -4. 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 cicula egions 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 2 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, the UAV flies into the taboo points undesiable neighbohood as indicated in Figue 2. 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 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(2), 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(2) 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 4 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 Poc. of SPIE Vol C-0

11 a malfunction. UAV() s eal-time contol algoithm subsequently sends out a help equest infoming the only othe UAV in the field, UAV(2) of the malfunction. UAV(2) s contol algoithm detemines a new path fo UAV(2) to fly so that the pioity one points, labeled (3,) and (4,), that UAV() was not able to sample ae subsequently measued. Afte UAV(2) measues sample point five, its new flight path allows it to measue sample points thee and fou. UAV(2) 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(2), UAV(2) did not have enough fuel to measue sample points seven and eight which wee of pioity two. UAV(2) s eal-time 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(2) diect both UAVs to alte thei etun flight 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 isk toleance to detemine how close each UAV may appoach a taboo point. PLANNING PHASE CONTROL PHASE ALTITUDE (miles) (,) (2,) (3,) (4,) (5,2) UAV path Base Taboo pt Sample pt (a,b) Index, pioity degee (6,3) ALTITUDE (miles) (2,) UAV samples neighbo (,) egion (3,) Taboo Region moved diectly ove sampling aea (4,) (5,2) UAV path Base Taboo pt Sample pt (a,b) Index, pioity degee (6,3) 4 (7,3) 4 (7,3) 2 2 new UAV changes path to avoid taboo egions RANGE (miles) Figue : One UAV tajectoy as detemined by the planning algoithm RANGE (miles) Figue 2: One UAV tajectoy as detemined by the eal-time contol algoithm. ALTITUDE (miles) UAV path UAV 2 path Base Taboo pt Sample pt (a,b) Index, pioity degee PLANNING PHASE (7,2) (8,2) (6,2) (9,2) (5,2) (4,) ALTITUDE (miles) UAV path UAV 2 path Base Taboo pt Sample pt (a,b) Index, pioity degee Old taboo egions new CONTROL PHASE (7,2) UAV 2 esponses to (8,2) help equest. (9,2) (6,2) new Less dangeous taboo egion theefoe able to fly nea (5,2) (4,) 4 (3,) 4 (3,) 2 (,) (2,) 2 (,) (2,) UAV malfunctions, equests fo help RANGE (miles) Figue 3: Tajectoy of two UAVs as detemined by the planning algoithm RANGE (miles) Figue 4: Duing flight, updates about envionmental changes cause the eal-time contol algoithms on the two UAVs to change thei tajectoies. Poc. of SPIE Vol C-

12 6. SUMMARY Fuzzy logic based planning and contol algoithms that allow a team of coopeating unmanned ai 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 examined. ACKNOWLEDGEMENTS This wok was sponsoed by the Office of Naval Reseach. The authos would also like to acknowledge M. Alan Schultz, D. Lawence Schuette, D. Jeffey Heye, D. Fancis Klemm, D. Gegoy Cowat, and D. Peston Gounds. REFERENCES. James F. Smith, III and ThanhVu H. Nguyen Distibuted autonomous systems: esouce management, planning, and contol algoithms, Signal Pocessing, Senso Fusion, and Taget Recognition XIV, I. Kada, Vol. 5809, pp , SPIE Poceedings, Olando, Diana Speas and Dimiti Zazhitsky, Multi-Robot Chemical Plume Tacing, Multi-Robot Systems: Fom Swams to Intelligent Automata, L. Pake, Vol. III, pp. 2-22, Spinge, New Yok, L.V. Blake, Rada Range-Pefomance Analysis, Atech House, Boston, L.H. Tsoukalas and R.E. Uhig, Fuzzy and Neual Appoaches in Engineeing, Chapte 5, John Wiley and Sons, New Yok, James F. Smith, III, Fuzzy logic esouce manage: eal-time adaptation and self oganization, Signal Pocessing, Senso Fusion, and Taget Recognition XIII, I. Kada, Vol. 5429, pp , SPIE Poceedings, Olando, S. Blackman and R. Popoli, Design and Analysis of Moden Tacking Systems, Chapte, Atech House, Boston, James F. Smith, III, Fuzzy logic esouce manage: decision tee topology, combined admissible egions and the selfmophing popety, Signal Pocessing, Senso Fusion, and Taget Recognition XII, I. Kada, Vol. 5096, pp. 04-4, SPIE Poceedings, Olando, James F. Smith, III, Co-evolutionay Data Mining to Discove Rules fo Fuzzy Resouce Management, Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, H. Yin, pp. 9-24, Spinge- Velag, Mancheste, J.F. Smith III; Genetic Pogam Based Data Mining fo Fuzzy Decision Tees, Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, Z.R. Yang, R. Eveson, H. Yin, pp , Spinge-Velag, Exete, James F. Smith, III, Data Mining fo Fuzzy Decision Tee Stuctue with a Genetic Pogam, Poceedings of the Intenational Confeence fo Intelligent Data Engineeing and Automated Leaning, H. Yin, N. Allinson, R. Feeman, J. Keane, S. Hubbad, pp. 3-8, Spinge-Velag, Mancheste, S.J. Russel and P. Novig, Atificial Intelligence: A Moden Appoach (2nd Edition), Pentice-Hall, Englewood Cliffs, Poc. of SPIE Vol C-2

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