The block-sharing strategy for area monitoring missions using adecentralized multi-UAV system*

L.E. Caraballo J.J. Acevedo J.M. Dıaz-Banez B.C. Arrue I. Maza A. Ollero

Abstract— In monitoring missions, using a cooperative teamof Unmanned Aerial Vehicles (UAVs), the goal is to minimizethe elapsed time between two consecutive observations of anypoint in the area. Techniques based in area partitioning achievethe goal when the sub-area assigned to each UAV is accordingto its capabilities.

In previous work of the authors [1] it was presented theone-to-one strategy to obtain in a decentralized way a nearoptimal partition from any initial grid partition. In this papera generalization of that strategy called the block-sharing tech-nique is presented. The goal in this work is to accelerate theconvergence to an optimal partition with respect to previouswork.

I. INTRODUCTION AND RELATED WORK

The European Project EC-SAFEMOBIL1 is devoted tothe development of sufficiently accurate common motionestimation and control methods and technologies in order toreach levels of reliability and safety to facilitate unmannedvehicle deployment in a broad range of applications. One ofthe applications of the project includes the distributed safereliable cooperation and coordination of many high mobilityentities. The aim is to precisely control hundreds of entitiesefficiently and reliably and to certify developed techniquesto support the exploitation of unmanned platforms in non-restricted areas. Two scenarios have been chosen for the vali-dation of the developments: industrial warehousing involvinga large number of autonomous vehicles and surveillance alsoinvolving many mobile entities. This paper is focused on thelatter scenario.

Surveillance and monitoring missions with unmannedaerial vehicles (UAVs) have been widely studied in differ-ent contexts [2]: military applications, automated inspec-tion, search and rescue missions, etc. The application ofdistributed multi-UAV systems allows to accomplish themwith robustness against failures and dynamism, in a waythat each UAV can quickly self-adapt its sub-area, higherspatial coverage and an efficient deployment [3], [4], [5].Therefore, the system can perform the mission, even ifthe communication link with the control station is broken.

*This work has been developed in the framework of the the EC-SAFEMOBIL (FP7-ICT-2011-288082), the PLANET (INFSO-ICT-257649)and the CLEAR (DPI2011-28937-C02-01) projects.

Luis Evaristo Caraballo is with Departamento de Computacion, Universi-dad de La Habana, Cuba. E-mail: luis.caraballo@iris.uh.cu

Jose Miguel Diaz-Banez is with Dpto. de Matematica Aplicada II,Universidad de Sevilla, Spain. E-mail: dbanez@us.es

Jose Joaquin Acevedo, Begona Arrue, Ivan Maza and Anibal Olleroare with Grupo de Robotica, Vision y Control, Universidad deSevilla, Spain. E-mails: jacevedo@us.es, barrue@us.es,imaza@us.es, aollero@us.es

1http://www.ec-safemobil-project.eu/

This paper addresses, in a distributed manner, a surveillancescenario using a large-scale team of aerial robots.

Surveillance tasks are solved from frequency-based ap-proach, where the objective implies to optimize the refreshtime or elapsed time between two consecutive visits toany position. The objectives are to minimize the maximalfrequency as in [6] or to guarantee an uniform frequencyof visits as in [7] and the solution is deterministic. Otherauthors, as in [8], address the patrolling problem in adver-sarial settings applying a probabilistic approach and con-sidering intelligent intruders that could learn the strategy.In [9], different partitioning and cyclic patrolling strategiesare defined and compared from a frequency-based approach.Authors of [10] also analyze the refresh time in area coverageproblems with multiple robots using different approaches. Apartitioning method is proposed in [11] to monitor a set ofpositions with different priorities.

Regarding distributed coordination, in [12] and [13] meth-ods based on the coordination variables are proposed toperform a perimeter monitoring mission in a cooperativemanner with multiple UAVs. However, the selection of thesevariables can be difficult for complex problems as the areamonitoring. Then in [4], a rectangular area is monitoredwith a team of UAVs applying the one-to-one coordination.This technique implies that each pair of UAVs solves acoordination problem including only their own information.A similar technique is proposed in [14] to coordinate a teamof video-cameras in surveillance missions. These techniquesallows the system to obtain the whole coordination fromlocal decisions and information. The resulting system isscalable, because each UAV only needs information fromnearby neighbors.

In previous work of the authors [1], one-to-one coordina-tion allowed convergence in a distributed and decentralizedmanner to an area partition where each UAV has an area tomonitor according to its capabilities. However, in this paper itis shown how to accelerate the convergence in more generalscenarios where the previous one-to-one strategy is time-consuming and slow. A new distributed method called blocksharing is described and proposed as a generalization ofthe previous scheme. In the previous algorithm, the UAVsperformed an area division every time they communicatewith a neighbor. However, with the proposed block-sharingstrategy, the UAVs wait until they get information from aset of UAVs before performing the area division. This delayin the area partitioning allows to execute fewer operationsof sub-area allocation, reconstruction of boundaries andsynchronization maintenance.

2014 International Conference on Unmanned Aircraft Systems (ICUAS)May 27-30, 2014. Orlando, FL, USA

978-1-4799-2376-2/14/$31.00 ©2014 IEEE 602

The paper is organized as follows. In Sect. II the pre-viously presented one-to-one strategy is revisited whereasSection III describes the new block-sharing strategy con-sidering both the one-dimensional and two-dimensional gridpartitions. The details of the distributed algorithm and thearea division protocol are provided in Sect. IV. Section Vshows different simulations that have been performed in or-der to validate the new technique. Comparisons with the pre-vious one-to-one coordination technique are also presented.Finally, Section VI closes the paper with the conclusions.

II. THE ONE-TO-ONE STRATEGY REVISITED

Given a system of multiple UAVs Q = {Q1, Q2, . . . , QN}and an irregular area S with surface A, the so-called one-to-one strategy to monitoring the area S with a distributedalgorithm has been proposed in [1]. The area is divided inN non-overlapped sub-areas Si according to robots’s sensingcapabilities in a decentralized manner and the area distribu-tion converges to an optimal partitioning where all aerialrobots spend the same time to complete its surveillance.

In order to be self-contained, we borrow here the for-mulation of the problem given in [1]. The aerial vehiclesflies at the same altitude and its sensing capabilities aredefined by its maximum coverage speed amax

i dependingon its maximum motion speed vmax

i and its coverage rangeci (these values as assumed constants). Thus, the coveragespeed amax

i is stated as the area covered per second and canbe approximated by

amaxi = 2civ

maxi . (1)

Therefore, a sub-area Si which surface Ai is assigned toeach aerial robot Qi according to the following formula:

Ai = amaxi

A∑Nj=1 a

maxj

,∀i = 1, ..., n . (2)

The one-to-one technique is based on the following areapartitioning paradigm: the whole area is divided into disjointsub-areas resulting a grid partition in which each cell ismonitored by an aerial robot in a synchronized system. Whentwo neighboring UAVs are closer that the communicationrange ci they share information and they spread over thearea according to their capabilities. An effective approach toensure synchronization is proposed in [1] by scheduling thestarting point of every aerial robot.

As a consequence, several issues have to be addressedin the strategy: the sub-areas allocation problem, the recon-struction of the boundaries and synchronization maintenance.Although the one-to-one technique ensures convergence tothe optimal partition (in which all the aerial robots spendthe same time to cover its own cell). In this paper a gener-alization of the one-to-one strategy is proposed in order toaccelerate convergence by reducing the number of operationsinvolved in the de-centralized approach. The key idea is toperform both the sub-areas and boundaries assignment on aset of UAVs instead of just two neighbors. This strategy willbe called the block sharing strategy in the following.

III. THE BLOCK SHARING STRATEGY

Let us assume an irregular area S to monitor for whichonly the latitudinally and longitudinally bounds are known.Moreover, the area may contain geographical accidents orholes that should be avoided in the surveillance mission. LetQ = {Q1, Q2, . . . , QN} be a set of N UAVs to monitorthe area. In the one-to-one coordination technique [1] aninitial simple grid division of the area S is given for whicheach robot can generate its own coverage path. In thisapproach when two robots are close enough to establish acommunication, they exchange the information and executethe share & divide operation, in which the robots join thetwo areas and divide it according to their capabilities usingnew vertical or horizontal lines maintaining synchronization.The convergence to the optimal partition has been testedexperimentally [1].

Let us suppose that the area is partitioned by parallel stripssuch that at the beginning, the strips are assigned to differentUAVs (see Fig. 1).

S1

S2

S3

S4S5

Fig. 1: Unknown irregular area with holes. Si is the area tobe covered by the aerial robot Qi.

Each UAV Qi has the established initial link position withits neighbors, and after a first recognition pass the UAVknows the area Si to cover in its strip and then can generateits own coverage path. However, due to the irregularity of thearea and the different capabilities of each robot, that initialdivision can not be efficient. Using the strategy one-to-one[1] the robots can achieve a near optimal area distributionaccording to their maximum capabilities. But this process canbe slow in many cases, for example if there is a distributionwhere adjacent areas are very similar. Figure 2 shows aninitial partition in which each operation of the one-to-onestrategy brings little headway.

Fig. 2: An initial partition where the one-to-one process isslow.

A strategy to accelerate the redistribution area process isintroduced in the following. It is based in the one-to-oneprinciple, that is, when two robots are located within thecommunication link they share all the area information intheir memories. However, instead of doing the share &divide operation at this time, they expect to have enoughinformation to assign areas to all elements in a block. In thispaper, a block is a set of robots forming a grid and we denote

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by (g, h)-block a block of robots in a grid configuration withg rows and h columns. Note that if we use blocks of tworobots this approach reduces to the one-to-one strategy.

As we started above, the one-to-one strategy involvestwo issues to be solved after the area allocation. First, theboundaries of the new sub-areas have to be redefined andafter that, the communication links must be established tomaintain synchronization. In this section, we focus on thearea allocation task. Other issues will be treated in sectionIV.

A. The one-dimensional grid partition

In this section we elaborate on the block sharing strategywhen the initial partition is given by an one-dimensionalgrid as in Figure 1. Let robots in odd positions to haveclockwise motion and counter-clockwise motion in othercase, see Figure 3. Initially robots Qi and Qj only knowthe areas Si and Sj , respectively. After a contact betweenthem, Qi and Qj know Si ∪ Sj . After that, if Qi contactto Qk (it has information about Sk ∪ Sl) then Qi and Qk

know Si ∪ Sj ∪ Sk ∪ Sl. Now Qi can allocate the new sub-areas and a new area division between Qi, Qj , Qk and Ql

is performed.Of course, if each robot wait until knowing all information

in the fleet then all of them can make an exact area division.The upper bound for the time to share all information inthe fleet with m× n grid configuration is Ts ≤ 5T

4 + (n+m−4)T2 where T is the period of the tour [15]. In many realapplications it is not convenient to wait until the aerial robotsknow all the information about the area; robots could alsohave limited capacities of computing and memory, preventingto operate with a lot of information, even more in case ofpossible loss of vehicles.

In this scenario we have a trade-off situation and a suitablevalue for the time before doing the area allocation has to bedecided. For a case study, we propose to work with groups(blocks) of four robots. At the first contact, the pairs of robots< Q1, Q2 > and < Q3, Q4 > share information, Figure3a. After a half of period, the pair of robots < Q2, Q3 >share information, Figure 3b, and in that moment Q2 andQ3 can make an area division between Q1, Q2, Q3 and Q4.However, Q1 and Q4 do not know yet the area assigned tothem. In the next contact, Figure 3c, the first area divisionis completed. The process between Q5, . . . , Q8 is similar.The next area division will be processed between the robotsQ3, . . . , Q6, starting just when the areas of pairs < Q3, Q4 >and < Q5, Q6 > are equal, after a half of period the pair< Q4, Q5 > share information, Figure 3d and they know thearea to cover by robots Q3, . . . , Q6 and the area division isprocessed. In the next contact they will complete the areadivision for the block, see Figure 3e. Notice that, for thiscase, the area division is performed at the odd contacts.Generalizing the idea, the robots make an area divisionaccording to a (1, 4)-block alternating groups starting in theposition 4k + 1 and groups starting in the position 4k + 3,see Figure 4.

. . .Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q98.0 2.0 5.0 1.0 7.0 3.0 8.0 4.0 6.5

(a) Initial state, first contact.

. . .Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q98.0 2.0 5.0 1.0 7.0 3.0 8.0 4.0 6.5

(b) Half period, second contact.

. . .Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q94.0 4.0 4.0 4.0 5.5 5.5 5.5 5.5 3.0

(c) A period, third contact.

. . .Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q94.0 4.0 4.0 4.0 5.5 5.5 5.5 5.5 3.0

(d) Half period, fourth contact.

. . .Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q94.0 4.0 4.75 4.75 4.75 4.75 4.0 4.0 4.0

(e) A period, fifth contact.

Fig. 3: Block-sharing strategy in the one-dimensional gridpartition. Robots in light strip have clockwise motion, robotsin dark strip have counter-clockwise motion. The numbersinside the cells are the allocated sub-areas.

. . .Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9

Fig. 4: Blue groups start in robots located at the 4k + 1position and the red ones in robots located at the 4k + 3position.

B. The two-dimensional grid partition

Now, let suppose we have a big area and, instead astrip initial division, we start by using a grid shape as inFigure 5. Color the grid like a chessboard, and let supposecounter-clockwise motion for the robots located at dark cellsand clockwise motion in other case. In this scenario, inorder to generalize the one-dimensional case, we use groupsof sixteen robots, that is, (4, 4)-blocks. The coordinationprocess is similar to the one in the strip partition, alternatingdivisions between blue groups and red groups as shown inFigure 6. Notice that, in the first step of the strategy, thefirst time for sub-area allocation is performed by means ofthe (4, 4)-blocks starting at the corner (blue groups in Figure6). Now, the first division spends 1.25 periods, and after that,the following divisions can be completed one per period.

C. Computational results

We have implemented the block sharing strategy, using(1, 4)− blocks and (4, 4)− blocks for strip and grid shapeconfigurations respectively, and we show here some testscomparing this strategy versus one-to-one. In this sectionwe are not counting the time required for the location of

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Fig. 5: Grid shape initial division in an unknown irregulararea with holes.

Q1,1 Q1,2 Q1,3 Q1,4 Q1,5 Q1,6 Q1,7

Q2,1 Q2,2 Q2,3 Q2,4 Q2,5 Q2,6 Q2,7

Q3,1 Q3,2 Q3,3 Q3,4 Q3,5 Q3,6 Q3,7

Q4,1 Q4,2 Q4,3 Q4,4 Q4,5 Q4,6 Q4,7

Q5,1 Q5,2 Q5,3 Q5,4 Q5,5 Q5,6 Q5,7

Q6,1 Q6,2 Q6,3 Q6,4 Q6,5 Q6,6 Q6,7

Q7,1 Q7,2 Q7,3 Q7,4 Q7,5 Q7,6 Q7,7

Fig. 6: Groups of sixteen robots (4x4 blocks), blue groupswith top-left corner in cells (4k+1, 4q+1) and red groupswith top-left corner in cells (4k + 3, 4q + 3).

new boundaries nor for the synchronization of the system.(Notice that for the one-to-one strategy these issues have tobe computed more times than for the block-sharing strategy).The test consists in the generation of 100 random cases ofsize n in strip division or n× n in grid shape division. Weapplied the strategies until the maximum difference betweentwo values become less than or equal 0.1. The diagramsin figures 7 and 8 show a comparison between the averagecount of needed periods for each strategy when the numberof aerial robots (size of the grid) increases. Note that block-sharing achieves the goal using approximatively half ofperiods required by the one-to-one process.

IV. SYSTEM IMPLEMENTATION

This section describes the methods and algorithms de-signed to implement, over the distributed system of multipleaerial robots defined in Sect. II, the block sharing strategyexplained in Sect. III. Section III defines how each aerialrobot can compute its assigned area size in a distributedmanner from an initial unsuitable area division and knowing

Fig. 7: This graphic shows a comparison between bothstrategies in a strip division, size is the length of the strip.

Fig. 8: This graphic shows a comparison between bothstrategies in a grid shape division, size is the length sideof a square grid.

no information about the rest of UAVs. However, if we wantto implement it in practical area surveillance scenarios, therobots need to decide consistently not just the area size butalso the area shape. On other hand, the UAVs should be ableto keep their communications links while this is running.

A. Definitions

Given an area S divided as a m × n grid of sub-areaswith N = m ∗ n, we can identify each UAV using a coupleof indexes to define the row and the column of its sub-areainto the matrix. If indi = (indi.x, indi.y) is an index, wedefine indi.x as the row component and indi.y as the columncomponent.

On the other hand, we define 4 link positions for eachsub-area where the owner UAV can contact with anotherone. This link positions are numbered from 1 to 4 startingfrom the top in counter-clockwise. We say that an UAV Qj

is neighbor of Qi if both share a common link position.Now, Qj is the k-neighbor of Qi if Qi meet Qj in the linkposition numbered as k. Applying the block sharing strategy,the UAVs are divided into groups or blocks. The UAVs inblock of Qi are the rest of UAVs that belong to its sameblock.

605

For instance, in Figure 9, a 4×4 grid is shown and dividedin (2, 2)-blocks. Here, the neighbors of Q11 are Q7, Q10,Q15 and Q12, its index is (2, 3) and its UAVs in block areQ12, Q15 and Q16.

Fig. 9: On the left a rectangular area divided as a 4× 4 gridis shown. Each cell is drawn by dotted lines. The dashedlines delimit the (2, 2)-blocks. The black points indicate thelink positions. On the right, the cell assigned to UAV Q11 isdetailed. Next to the black points into the cell is indicatedthe number of link position

B. Required local information

The multi-robot system behaves in a totally distributedmanner. All the robots execute the same algorithms, but usingtheir own local information. Each robot Qi just needs to storethe following information.

• The actual area Si that the robot has to patrol, definedas the boundary polygon (ordered list of vertexes).

• The list of the link positions LPi. The link positionnumber k can be accessed using LPi(k).

• The list of neighbors UAVs LNi, ordered according totheir link positions. A link position without associatedneighbor is identified in the list with a −1. The k-neighbor is defined as LNi(k).

• The actual path Pi to cover its assigned area defined asa ordered list of way-points.

• The list of link positions where there is an UAV in blockBLPi

• A list of the indexes of the UAVs in block BIi. Theelement k of this list can be accessed as BIi(k), and therow and column components as BIi(k).x and BIi(k).y,respectively.

• The list of the maximum area coverage of the UAVsin block BCi, ordered according to the list of indexes.This list is initialized setting all the elements to −1. Theelement k of this list is accessed using the expressionBCi(k).

• The list of the areas of the UAVs in block BSi, definedas the boundary polygons. The elements of this list areinitialized as empty sets. The area k of this list can beaccessed as BSi(k)

• And, finally, a vector Xi which contains informationabout its actual status and capabilities: identifier i, grid

index indi, maximum motion speed vmaxi , coverage

range ci, maximum coverage speed amaxi , direction di

in which the robot has to travel its path, next way-pointto visit, next link position to visit li, a variable bi toindicate the present block considered (with availablevalues: 1 or −1), actual position pi and instantaneousvelocity vi.

So, the required information that each UAV needs to storesdepends on the size of the block but not on the size of thegrid (it means, the total amount of UAVs). Therefore, it isan scalable system.

C. Distributed algorithm

Given the area S to be covered by the UAVs, and using asimple initial division as is shown in Figure 5 and proposedin [1], each UAV Qi is initialized with an initial assignedsub-area Si, an initial list of link positions LPi, a list ofneighbors LNi, its direction di, its index indi and the firstlink position to visit li. Direction and first link position arealternated between 1 and −1, and 1 and 3 respectively, suchas neighbors UAVs have always different values for bothparameters. The first way-point to be visited is initialized tothe first link position LPi(li).

Then, each UAV can execute the algorithm 1 in a dis-tributed manner.

The process is as follows. First, each UAV Qi plans aclosed path Pi to cover its initial assigned area Si usingthe plan function and according to the initial list of linkpositions LPi. This function generates a pseudo-symmetricpath such as is defined in [1]. The UAV decides the indexesBIi and the list of the link positions BLPi of the UAVs inblock using to block function, see subsection IV-E. Then,the UAVs initialize the list of areas BSi and list of sensingcapabilities BCi of UAVs in block using the initializefunction. All the areas less its own area are initialized toempty sets. And all the capabilities less its own are initializedto −1.

Then, the robots start moving (move function) followingthe path Pi depending on their direction di while monitor thearea looking for area changes and informations of interestusing the monitor function. If an UAV reaches a linkposition but it is not in its block, it updates (next function)its next link to visit li according to its own direction di andcontinues moving.

If the reached link position is in its list of link positions inblock and there it should meet a neighbor, but the UAV cannot contact with anyone, it stop and wait until the neighborreaches using the stop function.

However, in case that the link position has not neighboror has a null neighbor, the UAV updates the lists of areasand sensing capabilities using empty sets and 0 respectivelyin the proper positions with the share function. And, whenthe UAV reaches a link position and meet its neighbor Qj ,it receive from the neighbor all the information that it hasabout its UAVs in block (areas BSj and sensing capabilitiesBCj, using the share function. In both cases, they updatesthe next link to visit li with the next function.

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Algorithm 1 Distributed algorithm to generate the area topatrol according to the block sharing strategy.

Require: Si,LPi,LNi,Xi

Pi ← plan(ci,Si,LPi)bi ← 1[BIi,BLPi] ← block(bi,indi,LPi)[BCi,BSi] ← initialize()while !ABORT do

if wi ∈ BLPi thenif meet(Qi,Qj)==true then

[BSi,BCi] ← share(BSj,BCj)if −1 6∈ BCi then

[Si,LPi] ← divide(BSi,BCi,indi,BIi,LPi)Pi ← plan(ci,Si,LPi)bi ← −bi[BIi,BLPi] ← block(bi,indi,LPi)[BCi,BSi] ← initialize()

end ifli ← next(li,di)Xi ← move(Xi)

elseif LNi(li)==-1 then

[BSi,BCi] ← share(∅,0)if −1 6∈ BCi then

[Si,LPi] ← divide(BSi,BCi,indi,BIi,LPi)Pi ← plan(ci,Si,LPi)bi ← −bi[BIi,BLPi] ← block(bi,indi,LPi)[BCi,BSi] ← initialize()

end ifli ← next(li,di)Xi ← move(Xi,Pi)

elseXi ← stop(Xi)

end ifend if

elseif wi ∈ LPi then

li ← next(li,di)end ifXi ← move(Xi,Pi)

end if[Xi,Si] ← monitor(wi,Xi)

end while

When an UAV has all the necessary information aboutits block (areas BSi and sensing capabilities BCi), it usesthe divide function to compute the new area to patrolSi, according to the sensing capabilities BCi and the list oflink positions LPi. More details about the divide functioncan be found in subsection IV-D. Then, it generates theclosed pseudo-symmetric path to cover Pi with the planfunction, changes the variable bi and uses the block func-tion to decide its new block (indexes BIi and link positionsBLPi) initializing the list of areas and sensing capabilities(initialize function).

D. Area division protocol

An area division protocol has to be defined for all theUAVs, such that they can divide the area and choose theirassigned sub-area in a coherent manner. It means, there arenot regions without being assigned to any UAV or regionsassigned to more than one UAV.

According to the algorithm 1, when an UAV has all theinformation about its actual block, it decide its new sub-area.We propose a general method to decide in a distributed butcoherent manner which sub-area to choose according to theinformation about the block. The issue is to join the areas ofall the UAVs in the block and divide it depending on UAVssensing capabilities and UAV index with straight and parallellines.

Therefore, the divide function runs as follows. A newarea Sblock is generated joining all the areas included in thelist of areas BSi and, then, the whole surface of this areaAblock can be calculated.

Given the index of the UAV indi, let aleft be the sum ofall the elements of the sensing capabilities list BCi whichhas a column component in the list of indexes BIi lessthan indi.y. Now, let amiddle be the sum of elements whichcolumn components are equal than indi.y and, finally, definearight as the sum of the rest of elements. Then, we caneasily compute (4) the surface of area Amiddle that shouldbe assigned to all the UAVs which column component isindi.y.

Aleft =aleft

aleft + amiddle + arightAblock (3)

Amiddle =amiddle

aleft + amiddle + arightAblock (4)

Aright =aright

aleft + amiddle + arightAblock (5)

Using two vertical straight lines, the whole area Sblock

is divided in three parts which surfaces are from left toright (3), (4) and (5), respectively, see Figure 10a. We defineSmiddle as the area between the two lines.

A similar process but depending on the row componentsof the indexes BIi and indi.x is used to obtain the as-signed area Si from the area obtained in the previous stepSmiddle. Parameter aabove, abelow and ai are defined asthe sum of the elements of the sensing capabilities whichcolumn component is indi.y and which row component isless, greater or equal, respectively, than indi.x. Using theweighted average (7), we compute the surface Ai than shouldbe assigned to the UAV Qi from the surface Amiddle.

Aabove =aabove

aabove + ai + abelowAmiddle (6)

Ai =ai

aabove + ai + abelowAmiddle (7)

Abellow =abellow

aabove + ai + abelowAmiddle (8)

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Finally, using two horizontal straight lines, the area Smiddle

is divided in three parts which surfaces are from above tobellow (6), (7) and (8), respectively, see Figure 10b. Wedefine Si as the area between the lines. All the links positionsof the list LPmiddle which associated neighbors belong to thepresent block are updated, obtaining a common position foreach pair of neighbors.

(a) (b)

Fig. 10: This figure shows the process to generate the areaSi from Sblock.

E. Deciding blocks

A relevant issue for each UAV to apply the block strategyis deciding which others UAVs belong to its own block at anytime. According to the block strategy described in Sect. IIIany UAV should change its block when it has received all theinformation about its old block and has calculated its newarea. Then, UAVs can mix the areas obtained from differentblocks enabling to converge to a global solution.

The block function allows each UAV Qi to decide whichindexes include in the list BIi according to a parameter bi.Therefore, the list BLPi is also updated. Obviously, thisfunction depends on the size of the blocks. However, ingeneral, this function can decide two different blocks foreach UAV. The process is as follows.

Given a m × n grid, (g, h)-blocks and assuming that gand h are even, the grid can be divided in sub-blocks ofsize g

2 ×h2 starting from the index (1, 1). Each sub-block

has 4 adjacent sub-blocks. Now, the adjacent sub-blocks arejoined starting from the index (1, 1) and forming (g, h)-blocks. These will be the blocks when bi = 1. On otherhand, joining each sub-block with its adjacent sub-blocksthat are not joined previously, it obtained the (g, h) blocksfor bi = −1. Figure 11 summarizes both options.

V. VALIDATION RESULTS

As a case of study (2, 2)-blocks sharing strategy has beenimplemented using MATLAB as is described in Sect. IV.The simulations have been executed using parallel objects totest the decentralized and distributed issues. In these cases,rotary wing UAVs are considered.

A. Comparisons with the one-to-one technique

A large set of more than 60 scenarios has been executedwith team of UAVs of different sizes and different areas. Acommunications range of 3 meters has been considered. The

(a) Blocks for bi = 1. (b) Blocks for bi = −1.

Fig. 11: This figure shows as a 16×16 grid should be dividedin (4, 4)-blocks depending on the variable bi. Sub-areas, sub-blocks and blocks are delimited by dotted, dashed and thicksolid lines, respectively.

coverage range is of 3 meters for all the UAVs. However,the maximum speeds are randomly chosen for each UAVusing an standard uniform distribution between 0.5 and 1meters. Each scenario has been executed using both: theproposed (2, 2)-blocks sharing strategy and the one-to-onestrategy described in previous work [1]. It is assumed that asystem converges when the maximum difference between theactual areas and the desired ones is less than 1%. Figure 12summarizes the results obtained.

2x2 3x2 3x3 4x3 4x4 5x40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

grid size (row x column)

Tc (

one−

to−

one)

/Tc(2

x2bl

ock)

Fig. 12: This figure shows the average relation between theconvergence times using the one-to-one and a (2, 2)-blockssharing strategy (± its standard deviation) depending on thesize of the grid.

It shows as the block sharing strategy using (2, 2)-blocksconverges about a 30% quicker than the one-to-one strategyfor grid size larger than (3, 2)-blocks. When the size of thegrid is equal to the size of the block ((2, 2)-blocks), theresults are even more advantageous.

B. An irregular area with heterogeneous UAVs

In this case, an irregular area and 16 rotary wing UAVswith different sensing capabilities and a communicationsrange of 3 meters are considered. Figure 13a shows thescenario and the initial unsuitable area division and the table Idescribes the UAVs sensing capabilities and its sub-areasassigned indexes.

608

0 10 20 30 40 50 60 70 80

0

10

20

30

40

50

60

70

80

X (meters)

Y (

met

ers)

(1,1) (1,2) (1,3) (1,4)

(2,1)

(3,1)

(4,1)

(2,2)

(3,2)

(4,2) (4,3) (4,4)

(3,4)

(2,3) (2,4)

(3,3)

(a) Initial area division

0 10 20 30 40 50 60 70 80

0

10

20

30

40

50

60

70

80

X (meters)

Y (

met

ers)

(b) One-to-one strategy.

0 10 20 30 40 50 60 70 80

0

10

20

30

40

50

60

70

80

X (meters)

Y (

met

ers)

(c) (2, 2) Block-sharing strategy.

Fig. 13: Scenario with an irregular area and 16 UAVs. (a)simulation initial state, (b) and (c) correspond to the areadivision obtained during the test at time t = 600s. Pairsof number between brackets are the sub-areas indexes, solidblack lines indicate the irregular area, red dashed lines theinitially assigned sub-areas, the blue dashed lines the cover-ing paths and the black circles the different coverage ranges.A video from the test using the block sharing strategy can beviewed in http://www.youtube.com/watch?v=-oKOcEirQq8.

Figure 14 shows the maximum relative difference (%)between the actual surface assigned to each UAV and thedesired one (according to expression (2)) computed duringthe tests (for both strategies). In Figure 13 the final areadivisions (at time t = 600 s) obtained for both strategiesis drawn. From these results can be deducted that the blocksharing converges quicker and steeper than the one-to-onestrategy and obtains less concave sub-area shapes.

i indi vmaxi m/s ci m

1 (1,1) 0.77 4.282 (1,2) 0.75 3.583 (1,3) 0.79 3.004 (1,4) 0.61 5.205 (2,1) 0.88 4.286 (2,2) 0.66 3.587 (2,3) 0.65 3.008 (2,4) 0.95 5.209 (3,1) 0.61 4.28

10 (3,2) 0.98 3.5811 (3,3) 0.97 3.0012 (3,4) 0.70 5.2013 (4,1) 0.95 4.2814 (4,2) 0.83 3.5815 (4,3) 0.66 3.0016 (4,4) 0.68 5.20

TABLE I: UAVs sensing capabilities.

0 100 200 300 400 500 6000

10

20

30

40

50

60

70

80

time (s)

max

dif

fere

nce

actu

al a

nd d

esir

ed a

reas

(%

)

one to oneblock sharing

Fig. 14: This figure shows how the maximum relative dif-ference between the actual area assigned to each UAV andthe optimal one changes during the test using both the one-to-one (dashed red line) and the (2, 2)-blocks sharing (solidblue line) strategies.

0 100 200 300 400 500 6000

50

100

150

200

250

num

ber

of d

ivis

ions

com

pute

d

time (s)

block sharingone to one

Fig. 15: This figure shows how many divisions operationsperformed by the UAVs is increasing during the test usingboth the one-to-one (dashed red line) and the (2, 2)-blockssharing (solid blue line) strategies.

Finally, Figure 15 shows the total sum of divisions per-formed by the UAVs at any time during the tests. Note thatthe block sharing strategy needs many fewer operations thanthe one-to-one strategy to obtain a near-optimal area division.

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VI. CONCLUSIONS

The one-to-one strategy was described in [1] to allowa team of multiple UAVs to converge in a distributed anddecentralized way to an area partition where each robot hasan area to monitoring according to it’s capabilities. However,in the present paper, it is shown how to accelerate theconvergence in more general scenarios where of the one-to-one strategy is time-consuming and slow.

Therefore, a new distributed strategy called block sharingstrategy is described and proposed as one-to-one generaliza-tion to obtain a quicker convergence. While with the one-to-one strategy the UAVs perform an area division always theymeet a neighbor, with the proposed block-sharing strategy theUAVs wait until getting information about a block of UAVsand then perform the area division. This delay in the areapartitioning allows to execute fewer operations of sub-areaallocation, reconstruction of boundaries and synchronizationmaintenance.

Validation results show how a (2, 2)-block sharing strategycan be successfully implemented in a distributed manner inmutli-UAV systems, assuming communications constraintsand rotary wings UAVs with different sensing capabilities.In Section V are shown some diagrams that illustrate theimprovements obtained in simulations. The block-sharingstrategy is 30% faster than the one-to-one approach. More-over, the fact of avoiding to recalculate the boundaries ineach meeting leads to nicer boundaries and reduces the num-ber of needed operations to achieve the optimal solution inthe decentralized system. These improvements are increasedwith the size of the blocks, as is shown in subsection. III-C.

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