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A distributed framework for surveillance missions with aerial robots including dynamic assignment of the detected intruders Jose J. Acevedo, B. C. Arrue, Ivan Maza and Anibal Ollero Abstract— A dynamic and decentralized assignment algo- rithm based on one-to-one coordination is proposed to solve the multi-target allocation problem under communication con- straints. The objective is to assign the intruders dynamically among the available aerial robots in order to keep as many intruders as possible under tracking. When an aerial robot is not tracking a target, it is patrolling the area in order to detect new intruders. The proposed distributed method has been implemented and tested both in simulation and in an indoor testbed with quadrotors in order to validate its interest in dynamic scenarios with multiple intruders and multiple aerial robots. Comparisons with centralized assignment methods are provided to show the algorithm performance. I. I NTRODUCTION AND RELATED WORK The European Project EC-SAFEMOBIL 1 includes a surveillance scenario, where the objective is to detect and track as many intruders as possible using a team of coop- erating aerial robots. A relevant issue is taking autonomous decisions about which robot should track to each detected intruder. In addition, the distributed solutions usually offer very relevant features, such as robustness and scalability. The goal of our work is to implement a distributed method to assign multiple targets among multiple aerial robots in order to maximize the number of tracked targets. Therefore, the resulting distributed and decentralized surveillance archi- tecture should have two different and complementary levels: 1) a cooperative patrolling strategy for detecting new intrud- ers and 2) an assignment algorithm to dynamically assign the robots to follow these intruders. As the conditions are dynamic and the robots have a limited communication range, both levels are solved using distributed and decentralized methods. In particular, this paper is focused on the latter level. In [1], authors presents a thorough literature review in the multi-robot target detection and tracking field. A similar problem, assuming communication constraints, but applied to fire detection and extinguishing missions is also addressed in [2] in a distributed manner. It considers aerial and ground robots and different types of tasks: surveillance, fire extin- guish, etc. This work was carried out in the framework of the EC-SAFEMOBIL (FP7-ICT-288082) EU-funded projects and the AEROMAIN (DPI2014- 59383-C2-1-R) Spanish Research project. The first author J.J. Acevedo was partially supported by the LARSyS (FCT [UID/EEA/50009/2013]). J.J. Acevedo is with Institute for Systems and Robotics, Instituto Superior ecnico, Universidade de Lisboa, Lisbon, Portugal. E-mail: [email protected] B.C. Arrue I. Maza and A. Ollero are with Grupo de Robotica, Visi´ on y Control, Universidad de Sevilla, Spain. E-mails: {barrue, imaza, aollero}@us.es 1 http://www.ec-safemobil-project.eu/ The dynamic assignment problem has become a key research topic in the field of distributed coordination. From a distributed approach, the tasks are allocated among the robots using local information and inter-robots communica- tion without the need of a central element. Many researchers have proposed the use of market-based negotiation rules to solve these problems in a distributed manner [3], [4]. They consider that each task (or set of tasks) is announced by the holder agent and expect for the bids of the rest of the agents. The holder agent decides the winner agent and com- municates the decision to the bidders. In [5], authors propose a negotiation-based task assignment to implement a multi- UAV path planning framework in dynamic environments. Some researchers considers bids by single tasks [6], others assume set of tasks [7] and others assume that each task could be better performed by using multiple robots [8]. These methods are based on the very well-known Contract Net Protocol (CNP) [9]. In any case, the market-based alloca- tion algorithms require several information interchanges and confirmations among the agents in order to perform the task allocation coherently. Other distributed coordination approaches do not require explicit communication between the robots. They are usu- ally behaviors-based algorithms with high fault tolerance and adaptability to noisy environments, where the robots actions are defined by the evolution of their own features (or variables) as the impatience [10] or task urgency [11]. Considering a minimum communication among the robots, approaches based on inhibitors [12] or tokens [13] could improve the behaviors-based approaches. If all the tasks and robots’ states were known by all of them, they all could allocate efficiently the tasks in a distributed manner. However, from a distributed manner this assumption is too strong and a consensus technique is required [14]. In [15], the authors propose a distributed assignment algorithm based on the equal-mass property to assign different workspaces to the robots of a team to construct a structure in a decentralized manner with a team of ground robots. A similar approach considers the decen- tralized coordination by using coordination variables [16]. In these cases, the robots share information about the problem with the rest of the team and use this to self-assign their tasks without explicit communication among them. This paper proposes the application of one-to-one co- ordination to perform the dynamic and distributed target assignment. It assumes that whenever two robots meet, they set out a reduced version of the problem by using just their own information. They, sequentially, will merge the

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Page 1: A distributed framework for surveillance missions with ... · (FP7-ICT-288082) EU-funded projects and the AEROMAIN (DPI2014-59383-C2-1-R) Spanish Research project. The first author

A distributed framework for surveillance missions with aerial robotsincluding dynamic assignment of the detected intruders

Jose J. Acevedo, B. C. Arrue, Ivan Maza and Anibal Ollero

Abstract— A dynamic and decentralized assignment algo-rithm based on one-to-one coordination is proposed to solvethe multi-target allocation problem under communication con-straints. The objective is to assign the intruders dynamicallyamong the available aerial robots in order to keep as manyintruders as possible under tracking. When an aerial robot isnot tracking a target, it is patrolling the area in order to detectnew intruders. The proposed distributed method has beenimplemented and tested both in simulation and in an indoortestbed with quadrotors in order to validate its interest indynamic scenarios with multiple intruders and multiple aerialrobots. Comparisons with centralized assignment methods areprovided to show the algorithm performance.

I. INTRODUCTION AND RELATED WORK

The European Project EC-SAFEMOBIL1 includes asurveillance scenario, where the objective is to detect andtrack as many intruders as possible using a team of coop-erating aerial robots. A relevant issue is taking autonomousdecisions about which robot should track to each detectedintruder. In addition, the distributed solutions usually offervery relevant features, such as robustness and scalability.

The goal of our work is to implement a distributed methodto assign multiple targets among multiple aerial robots inorder to maximize the number of tracked targets. Therefore,the resulting distributed and decentralized surveillance archi-tecture should have two different and complementary levels:1) a cooperative patrolling strategy for detecting new intrud-ers and 2) an assignment algorithm to dynamically assignthe robots to follow these intruders. As the conditions aredynamic and the robots have a limited communication range,both levels are solved using distributed and decentralizedmethods. In particular, this paper is focused on the latterlevel.

In [1], authors presents a thorough literature review inthe multi-robot target detection and tracking field. A similarproblem, assuming communication constraints, but appliedto fire detection and extinguishing missions is also addressedin [2] in a distributed manner. It considers aerial and groundrobots and different types of tasks: surveillance, fire extin-guish, etc.

This work was carried out in the framework of the EC-SAFEMOBIL(FP7-ICT-288082) EU-funded projects and the AEROMAIN (DPI2014-59383-C2-1-R) Spanish Research project. The first author J.J. Acevedo waspartially supported by the LARSyS (FCT [UID/EEA/50009/2013]).

J.J. Acevedo is with Institute for Systems and Robotics, InstitutoSuperior Tecnico, Universidade de Lisboa, Lisbon, Portugal. E-mail:[email protected]

B.C. Arrue I. Maza and A. Ollero are with Grupo de Robotica, Visiony Control, Universidad de Sevilla, Spain. E-mails: {barrue, imaza,aollero}@us.es

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

The dynamic assignment problem has become a keyresearch topic in the field of distributed coordination. Froma distributed approach, the tasks are allocated among therobots using local information and inter-robots communica-tion without the need of a central element. Many researchershave proposed the use of market-based negotiation rules tosolve these problems in a distributed manner [3], [4]. Theyconsider that each task (or set of tasks) is announced bythe holder agent and expect for the bids of the rest of theagents. The holder agent decides the winner agent and com-municates the decision to the bidders. In [5], authors proposea negotiation-based task assignment to implement a multi-UAV path planning framework in dynamic environments.Some researchers considers bids by single tasks [6], othersassume set of tasks [7] and others assume that each taskcould be better performed by using multiple robots [8]. Thesemethods are based on the very well-known Contract NetProtocol (CNP) [9]. In any case, the market-based alloca-tion algorithms require several information interchanges andconfirmations among the agents in order to perform the taskallocation coherently.

Other distributed coordination approaches do not requireexplicit communication between the robots. They are usu-ally behaviors-based algorithms with high fault toleranceand adaptability to noisy environments, where the robotsactions are defined by the evolution of their own features(or variables) as the impatience [10] or task urgency [11].Considering a minimum communication among the robots,approaches based on inhibitors [12] or tokens [13] couldimprove the behaviors-based approaches.

If all the tasks and robots’ states were known by allof them, they all could allocate efficiently the tasks ina distributed manner. However, from a distributed mannerthis assumption is too strong and a consensus techniqueis required [14]. In [15], the authors propose a distributedassignment algorithm based on the equal-mass property toassign different workspaces to the robots of a team toconstruct a structure in a decentralized manner with a teamof ground robots. A similar approach considers the decen-tralized coordination by using coordination variables [16]. Inthese cases, the robots share information about the problemwith the rest of the team and use this to self-assign theirtasks without explicit communication among them.

This paper proposes the application of one-to-one co-ordination to perform the dynamic and distributed targetassignment. It assumes that whenever two robots meet, theyset out a reduced version of the problem by using justtheir own information. They, sequentially, will merge the

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Fig. 1. A team of four aerial robots patrolling an area S to detect andfollow potential intruders. Communication constraints are modeled by acommunication range R

information from previous solutions. Finally, they will haveconsidered all the information about the problem in theirsolutions. Although this coordination technique is an anytime strategy, the solution is better as the number of iterationsincreases. The applied one-to-one technique was describedin [17] in the context of area surveillance missions.

The multi-target tracking problem is defined in Section II.A dynamic, distributed and decentralized solution based onone-to-one coordination is proposed in Section III. Somecomparisons, simulations and experimental results are pre-sented in Section IV to validate the presented approach.Finally, the conclusions in Section V close the paper.

II. MULTI-TARGET TRACKING FOR SURVEILLANCEMISSIONS

An area S has to be covered by a team of n heterogeneousaerial robots Q = {Q1, Q2, . . . , Qn} searching for a set ofm potential non-cooperating intruders I = {I1, I2, . . . , Im},see Fig. 1. The aerial robots have to detect and track as manyintruders as possible.

The intruders I are considered ground vehicles with holo-nomic kinematics that can be or not into the area and movealong it freely. At any time, the state of an intruder Ik isdefined by its position in the area rIk and its instantaneousvelocity vIk. The variables xIk indicates if the intruder Ikis into (xIk = 1) or out (xIk = 0) of the area S.

On the other hand, pi(t) defines the current position ofthe aerial robot Qi, ri(t) its projection onto the plane z = 0and vi(t) its instantaneous velocity. It is defined a maximummotion speed vmax

i for each aerial robot Qi.Moreover, considering that the aerial robots monitor the

area according to a circular pattern, the instantaneous coveredarea Ci by the robot Qi will depend on its coverage rangeci as:

Ci := {r ∈ R2 :‖ r− ri ‖< ci}. (1)

It is assumed that if Qi is detecting Ik, it knows its actualposition rIk and instantaneous velocity vIk. According to

the aerial robot description, an aerial robot Qi has detectedan intruder Ik if dik ≤ ci, where:

dik =‖ ri − rIk ‖ . (2)

Otherwise, defining a reaching range ρi smaller than thecoverage range ci to take into account the uncertainties inthe perception, it is assumed that the robot Qi has reachedthe intruder Ik if dik ≤ ρi. Then, the reaching time can bedefined as the time that Qi would take to reach to a stoppedintruder Ik and can be computed as follows:

tik =

{dik−ρivmaxi

, if dik > ρi

0, in other case .(3)

The main objective of the mission is to track as manyintruders as possible and an intruder Ik is well tracked by anaerial robot Qi if tik = 0. Then, the problem is to minimizethe cost function J , which is defined as the sum of thereaching times of all the intruders that are into the area atany time t:

J =

m∑k=1

xIkmini(tik). (4)

If m ≤ n all the intruders could be reached andmini(tik) = 0,∀k = 1..m with J → 0. But if m > n,more than one intruder could be assigned to a single robot.In this case, the aerial robot will follow only one of them. Onother hand, the problem is dynamic. It means that intruders(targets) can appear or disappear and move freely throughthe area. The robots have to detect new targets, share thisinformation and reallocate them in a distributed manner.

III. DYNAMIC TRACKING TARGET ASSIGNMENT

In the one-to-one coordination technique when two robotsmeet, they set out a reduced version of the whole problem byusing just their own information. This technique representsa good approach in dynamic scenarios and under communi-cation constraints.

A. Required local information

The proposed solution requires that each robot Qi storeslocally the following information:• A vector Xi containing information about its own status

and capabilities: identifier i, position pi, instantaneousspeed vi, maximum motion speed vmax

i , coverage rangeci and reaching range ρi.

• A list targetsi with all the targets known by the robot.Each element of the list should include:

– An unique identifier for each target.– The last known position of the target.– The last instantaneous speed of the target.– The assignment status defined by the identifier of

the robot which has allocated the task.– The monitoring time showing the last time that this

target’s information was updated.

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– The assignment time showing the last time that thistarget was reallocated to a robot.

• A plani composed by the identifiers of all the tasks thathave been allocated to the robot.

• The next way-point to visit wi.

B. Distributed algorithm

Algorithm 1 applies one-to-one coordination to implementa dynamic target assignment in a distributed manner.

Algorithm 1 Distributed algorithm for the allocation of thetargets among the robots.Require: S

Xi ← initialize(Xi,S)while !ABORT do

if plani == ∅ thenwi ← patrol(Xi,S)

elseif meet(Xj) then

targetsi ← update(targetsi,targetsj)[targetsi, plani] ← assign(targetsi,Xi,Xj)

end ifwi ← track(plani(1))

end iftarget′ ← monitor(Xi)if target′ 6∈ targetsi then

targetsi ← targetsi ∪ target′[targetsi, plani] ← assign(targetsi,Xi,∅)wi ← track(plani(1))

elsetargetsi ← update( targetsi,target′)

end ifXi ← move( Xi, wi)

end while

When two robots Qi and Qj meet, they share their infor-mation about the known targets (update), their own statesand capabilities. As both robots have the same informationabout targets and robots and the same metrics and assignmentfunctions to solve the problem, both compute the samesolution in an independent manner (assign). Therefore,each one obtains the plan for both and can execute its ownplan. This assignment function should consider the targets tobe allocated and the features of both robots.

Then, each robot controls its motion to track the firsttarget in its own plan (track function). When a robot losessight of the target which was tracking, it sets the target asunassigned in its target list, updates the assigning time, takesthis target out from its plan and recomputes its own plan,according to its new target list.

On the other hand, the robots are monitoring continuouslythe area (monitor function), updating the target status in itstarget lists, depending on the detected targets. When a robotdetects an intruder, it generates a new target′ and checks ifit is into its own target list. If it is not, it includes it into thetarget list, self-assigns it and generates a new plan taking intoaccount the new target. If the target was into its own target

list, the robot just updates its target list. So, this strategyassures that any detected target is assigned to at least oneof the robots, even without defining a meeting strategy andassuming communications constraints. Obviously, in theseconditions the actual target assignation could not be the bestone.

The robots without assigned targets perform a patrollingtask on the area to detect new targets (patrol function).This patrolling task can be also performed in a cooperative,distributed and dynamic manner by using the algorithmsdescribed in [17]–[20].

This process is repeated continuously. Then, assumingthat all the robots share their information in a direct orindirect manner, they will converge to the more efficient(and coherent) solution from a distributed manner. However,assuming a short communication range, the robots couldnot meet and the information could not be shared. Someauthors [21] propose the idea of checkpoints to guaranteethe complete shared information in a distributed frameworkwithout centralized coordination. However, this paper doesnot address this problem, because the objective is to trackcontinuously as many intruders as possible. Hence, if therobots do not meet, the system will offer a less efficient butvalid solution.

C. Sharing information

The first step in one-to-one coordination is that a pairof contacting robots share the required information to solvethe problem. In this case, they interchange their status andcapabilities vectors and their lists of targets. Then, theycombine both lists of targets to generate a new common andupdated list of targets by using an update function:

targetsout = update(targetsin1, targetsin2). (5)

The update function runs as follows. The list targetsoutis initialized as targetsin1. Then, it checks each elementfrom the list targetsin2. If the element does not belong totargetsout, it includes the element in the list targetsout. Inother case, it updates targetsout according to this element.Hence, if the monitoring time in the element of targetsin2is newer than in the one of the targetsout, it changes themonitoring time position and instantaneous speed in theelement of targetsout to the values of the targetsin2. In thesame manner, if the assigning status is newer, it changes boththe assigning time and status.

It is interesting to note the commutative property of thefunction, which assures that both robots generate the samelist of targets when they meet:

update(targetsi, targetsj) = update(targetsj, targetsi).(6)

D. Self-assigning targets

The second step in one-to-one coordination is that eachrobot obtains the solution of the problem in an independent

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manner. As both robots have the same information of thescenario, they should obtain the same solution, even withoutcommunication.

The robots use the assign function to decide whichtargets are assigned to each robot depending on their statusand capabilities vector:

[targetsout,planout] = assign(targetsin,Xin1,Xin2).(7)

The assign function checks the targetsin looking forthe targets which are currently assigned to one of the robotsor are unassigned. Then, it stores these targets identifiers inan auxiliary plan. Now, it executes a task allocation strategytaking into account 2 robots and m′ ≤ m targets. Dependingon which task allocation strategy is used, the system could bemore efficient, but the problem will be always much easierthan the whole one with m targets and n robots. It returnsa plan for the first robot Qi and another plan for contactingrobot Qj for each case. These two generated plans will becomplementary.

Any task allocation strategy will be based on a costfunction. This cost should be unique for each case, thereare no two different pairs of plans with the same cost. Thus,it chooses the lowest cost option, obtaining two plans, oncefor each robot and returns the first plan as planout.

On other hand, it initializes targetsout as targetsin. Then,according to the chosen plans, it modifies the assignmenttime and assignment status in the appropriate targets intothe list targetsout.

E. Cost function

When using the approach described above, two robotssolve a reduced version of the whole problem.

Given two plans for two contacting robots, the whole costis defined as the sum of the costs associated to each robot:

Cij = cost(plani,Xi) + cost(planj,Xj). (8)

The cost associated to a robot could be defined as thetime that it takes to reach the first target in its plan tiplan(1).However, with this cost, the system could converge to a sub-optimal solution. For instance, in Fig. III-E, three targets haveto be tracked by two robots. According to the cost (8) andassuming that the robots can move at the same speed, the tworobots go to the nearest targets (see Fig. III-E). Nevertheless,the two tracked targets are so close that could be reached bya single robot. Thus, the best solution would be one wherethese nearby targets are reached by a single robot, while theother reaches the other target, as it is shown in Fig. III-E.

Therefore, the cost associated for a robot Qi to run a planof size m′ (number of targets) is defined as the sum of threeterms:

cost(plan,X) = Ftime + Ftargets + Fbusy, (9)

where the terms are as follow.

Fig. 2. Targets tracking allocation depending on the cost function. Theblack crossing represents aerial robots, the dashed circle defines the reachedarea and the gray squares represent the targets. The white rectangle definesthe covered area. This figure shows: (top) initial robots’ status, (mid) sub-optimal solution obtained using the sum of reaching times as cost function,and (bottom) best solution obtained using a suitable cost function

• A term that depends on the time that the robot wouldtake to reach the first target in its own plan, Ftime. Itis related to the cost function defined in the problemstatement:

Ftime(plan,Xi) = Ctimetiplan(1), (10)

where Ctime is a constant value and tiplan(1) is thereaching time from the aerial robot to the first targetincluded in its plan.

• A term related to the rest of the targets in its plan ifthe size (m′) of the plan is greater than one, Ftargets.This term depends on the estimated distance and thedifference of instantaneous speeds between the targets inthe plan. Too distant targets, depending on each robot’sreaching range, are heavily penalized. It favors thattargets moving together are tracked by a single robot:

Ftargets(plan,Xi) =

m′∑k=2

(Cdistdiplan(k) + Cvel ‖ vIplan(1) − vIplan(k) ‖),

(11)where Cdist and Cvel are constant values, diplan(k)is the estimated distance from the aerial robot afterreaching the fist target to the k-th target included inits plan and vIplan(k) is the instantaneous velocity of thek-th target included in its plan.

• An extra term if and only if its associated plan isnot empty, Fbusy. Therefore, a robot with an emptyplan will have an associated cost equal to zero. Thisgives advantage to the case in which there are robotsperforming the patrolling tasks:

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TABLE IONE-TO-ONE METHOD PERFORMANCE DEPENDING ON THE NUMBER OF

ROBOTS (n) AND TARGETS (m). THE OPTIMAL PERFORMANCE IS EQUAL

TO 1

HHHHmn 2 3 4 5 6 7

1 1 1 1 1 1 12 1 0.9966 0.9835 0.9826 0.9890 0.98983 1 0.9887 0.9780 0.9782 0.9563 0.97584 1 0.9865 0.9585 0.9483 0.9450 0.94995 1 0.9758 0.9532 0.9459 0.9325 0.93226 1 0.9746 0.9435 0.9399 0.9126 0.91187 1 0.9692 0.9412 0.9307 0.9081 0.9021

Fbusy(plan,Xi) = Cbusymin(1,m′). (12)

where Cbusy is a constant value and m′ is the numberof targets included in its plan.

IV. VALIDATION RESULTS

A. Performance analysis

A large set of scenarios has been analyzed to comparethe one-to-one coordination method performance against acentralized method, depending on the number of robots andthe number of targets. The performance is defined as the ratebetween the cost computed using the one-to-one method andthe cost computed for the optimal solution obtained usingthe centralized method. For this analysis, the cost is definedas the maximum time to get all the targets. The centralizedmethod checks the cost for all possible combinations andpermutations to distribute the targets between the robots.Then, it can obtain the optimal plan for each robot.

The scenarios consist of a 20 × 20 m2 area with nrobots and m targets. Each scenario has been tested 300times, assuming that robots and targets location and robotscapabilities (maximum motion speed, reaching range) aredefined randomly (standard uniform distribution) for eachtest. For this performance analysis, it will be assumed thatthe first robot knows initially the targets. It should be noticedthat this is not a requirement for the method, where the robotscan start without knowing the targets and have to detect themduring the mission, as it will be shown in the subsections IV-B and IV-C.

Table I shows the average performance computed duringthe tests depending on the number of robots and the numberof targets. Therefore, if the computed assignment is theoptimal one, the performance will be 1.

Table II shows the average value for the rate betweenthe number of checks that the one-to-one method needs toconverge and the number of checks that uses the centralizedmethod. The number of checks computed for the one-to-onemethod is defined as the average number of checks computedfor each robot, assuming that each robot meets at most twiceeach other robot.

These results show that as the number of targets increases,the performance of the one-to-one based allocation methodslightly decreases. However, they also evidence a very high

TABLE IIRATE BETWEEN NUMBER OF CHECKS FOR THE ONE-TO-ONE AND THE

CENTRALIZED METHODS DEPENDING ON THE NUMBER OF ROBOTS (n)AND TARGETS (m)

HHHHmn 2 3 4 5 6 7

1 0.5 0.2173 0.1487 0.1028 0.0750 0.05072 0.5 0.2143 0.1158 0.0617 0.0371 0.02443 0.5 0.1684 0.0637 0.0277 0.0150 0.00794 0.5 0.1271 0.0354 0.0126 0.0051 0.00245 0.5 0.0978 0.0223 0.0062 0.0023 0.00086 0.5 0.0819 0.0152 0.0035 0.0011 0.00047 0.5 0.0646 0.0105 0.0025 0.0004 0.0002

TABLE IIIROBOTS’ IDENTIFIER, COLOR (IN THE VIDEO FROM THE SIMULATION)AND SPEED FOR THE MULTI-INTRUDER TRACKING SIMULATION TEST

Robot id 1 2 3 4color red magenta blue green

speed (m/s) 1 0.8 2 1.5

performance for the one-to-one method for any number ofrobots and targets. There is not a clear relation betweenthe performance of the one-to-one based allocation methodand the number of robots, which is coherent because themethod always considers allocation processes between pairof robots. On the other hand, the number of checks (andhence the computational cost) needed strongly increases withthe number of robots and targets for the centralized methodwith respect to the proposed one-to-one distributed method.

Therefore, the one-to-one method seems to be an usefulallocation technique for multi-target-tracking applicationsthat need on-line targets re-assignations because the prob-lem conditions changes continuously. It is also a scalablesolution, where the whole number of robots does not impactin each allocation process.

B. Dynamic case scenario

A multi-target tracking scenario with 4 robots and 3intruders that can move and stop together or separatelythrough the area is posed to test the proposed method indynamic conditions. Robots have to patrol the area and trackthe intruders. A video from this simulation can be viewed inhttp://www.youtube.com/watch?v=gXCL3ffvbeM.

Intruders move along the area with a maximum speed of1 m/s. Reaching range ρi = 3 m and covering range ci =15 m are defined equal for all the robots. Communicationrange is limited to R =20 m. The rest of robots features andcapabilities are summarized in Table III.

The test is executed during 360 s. At time t = 100 s twointruders go to position (10,10) m and stop there until timet = 130 s. From 200 s to 260 s, the three robots move togetherthrough the area. Finally, at time t = 300 s the three robotsgo to position (5,10) m and stop there.

The distributed and dynamic target assignment processbased on the one-to-one coordination technique is used.

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0 50 100 150 200 250 300 3500

1

2

3

4

5

6

time (s)

J (s

)

Fig. 3. Cost function J (as it is defined in expression (4)) computed duringthe test at any time. The optimal minimal value would be zero at any timeduring the test

0 50 100 150 200 250 300 35001234

robot 1

0 50 100 150 200 250 300 35001234

assi

gned

targ

ets robot 2

0 50 100 150 200 250 300 35001234

robot 3

0 50 100 150 200 250 300 35001234

time (s)

robot 4

Fig. 4. Number of targets assigned to each robot during the simulationtest

When the robots are performing the patrolling task, they runa path partitioning strategy along a common path using thedistributed algorithm presented in [18]. The objective is tominimize the optimization function (4) at any time, maxi-mizing the number of reached intruders while the number ofrobots patrolling the area is maximized. Figure 3 shows theoptimization function value computed during the test.

In Fig. 4, the target assignment status is shown at any timeduring the test. Robots without assigned targets perform thepatrolling task searching for new undetected targets. Figure 5shows the number of reached targets and the number ofrobots performing the patrolling task.

0 50 100 150 200 250 300 3500

1

2

3

4

time (s)

robo

ts p

erfo

rmin

g pa

trol

ling

task

0 50 100 150 200 250 300 3500

1

2

3

4

reac

hed

targ

ets

Fig. 5. Plot above shows the amount of reached targets at any time duringthe test. Plot below show the number of robots performing the patrollingtask at any time during the test

Fig. 6. Snapshot from experiments carried out in an indoor testbed withtwo aerial robots and three intruders. A video from this simulation can beviewed in https://www.youtube.com/watch?v=fo1ZMyb13g0

Results show that robots re-assign dynamically the targets,according to robots and intruders status and robots capa-bilities, to keep the maximum number of targets reachedpermanently and a cost function near to zero. As there arefour robots and three intruders, always at least one robot isperforming the patrolling task. Note that when two or threeintruders are together (moving or stopped), they are assignedto one robot and the rest can perform the patrolling task. Onother hand, when intruders get back to separate (times around130 s and 260 s), the cost function is increasing until they arereached again (it means that the intruders are reassigned todifferent robots that have to abandon their task and reachtheir assigned intruder). The results show the interest of themethod in dynamic scenarios, where targets move and stop,and robots reassign them in a distributed manner obtaininga near-optimal solution.

C. Experimental test

The proposed system has also been tested experimentallywith two aerial robots (Hummingbird quad-rotors by Ascend-ing Technologies) and three intruders (one RC car and twoline trackers ground robots), see Fig. 6. The tests have beenperformed in a 9×9 m2 indoor testbed of the Spanish Centerfor Advanced Aerospace Technologies (CATEC) in Seville.The localization system is based on 20 VICON camerasand offers millimeter accuracy in the quad-rotors and carpositions.

A large enough communications range R is assumed, suchthat both robots can communicate whatever their positionsinto the area. On the other hand, both robots are consideredhomogeneous with a maximum speed of vmax

i = 0.5 m2, acoverage range of ci = 3 m and a reaching range of ρi =1 m.

First, the two robots are patrolling the area and twointruders appear. The robots detect the targets and, basedon the proposed distributed assignment process, each onechooses and tracks a different intruder. About 60 s later, bothintruders go to nearby positions and stop. Then, they bothare assigned to a single robot and the other robot obtains anempty plan and starts to perform the patrolling task searchingfor new targets. About 40 s later, a new intruder appears in

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the area. When the robots detect it, the patrolling robot self-assigns it and start tracking it. Finally, between t = 150 s andt = 210 s, the third intruder is moving close to the other twostopped intruders, such that all of them could be tracked by asingle quad-rotor. Figure 7 shows the optimization functionvalue computed during the experiments.

0 20 40 60 80 100 120 140 160 180 200 2200

2

4

6

8

10

12

14

16

18

20

time (s)

J(s)

Fig. 7. Cost function J (as it is defined in expression (4)) computed duringthe experiment. The optimal minimal value would be zero at any time.

The experiment shows the interest of the proposed dis-tributed system in real-time applications obtaining the besttargets assignment to maximize the number of tracked in-truders.

V. CONCLUSIONS

A team of aerial robots is in charge to secure a definedarea against a set of intruders. The aerial robots have todetect and track as many intruders as possible. The problemis addressed as a dynamic target assignment problem wherethe robots that are not tracking intruders, remain executinga patrolling task to detect new intruders.

One-to-one coordination is proposed here to design thetarget assignment method. The solution is totally distributedand decentralized, the robots get a common and coherentsolution from local decisions and asynchronous communica-tion. It is scalable because its complexity does not dependon the number of robot in the problem and obtains a close tooptimal performance with a lower computational cost thanother centralized methods as it has been shown.

Simulation and experimental tests show how the intrudersare dynamically assigned (and reassigned) among the aerialrobots, maximizing the number of tracked intruders whilekeeping the maximum number of robots performing thepatrolling tasks. They evidence a robust and dynamic methodthat can adapt to changes in the conditions.

ACKNOWLEDGMENTS

We would also like to thank Miguel Angel Trujillo,Yamnia Rodrıguez and Irene Alejo for their support withthe experiments.

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