Fault-Tolerant Cooperative Control of Multiple UAVs for Forest Fire ...

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Abstract— A fault-tolerant cooperative control (FTCC) strat- egy for cooperative unmanned aerial vehicles (UAVs) used in forest monitoring, fire detection and ...
2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol) Barcelona, Spain, Sept. 7-9, 2016

Fault-Tolerant Cooperative Control of Multiple UAVs for Forest Fire Detection and Tracking Mission Khaled A. Ghamry1 and Youmin Zhang2 Abstract— A fault-tolerant cooperative control (FTCC) strategy for cooperative unmanned aerial vehicles (UAVs) used in forest monitoring, fire detection and tracking is investigated in this paper. The proposed algorithm solves the problem of monitoring and detection of forest fires, even when fault occurs to one or more UAVs. During the search stage, the UAVs team moves in a certain formation shape, a distributed sliding mode formation control is designed to keep the desired formation shape during this stage. Once a fire is detected, another distributed reconfigurable controller is designed based on sliding mode control (SMC) to evenly distribute UAVs team around the elliptical fire perimeter in fault-free case. When one or more UAVs cannot continue their mission due to a fault or leaving from formation for refueling/recharging, an FTCC strategy will be deployed to decrease the effects of the changed formation condition and the faulty/absent UAV’s tasks will be reassigned to the remaining healthy/operable ones. Therefore, the new formation will be reconfigured and the UAVs still be evenly distributed around the fire spot for best coverage of the fire site. Simulation results are used to demonstrate the effectiveness of the proposed algorithm using six degree-offreedom (DOF) quadrotor dynamic models of UAVs. Index Terms— Fault tolerant cooperative control, Forest monitoring and fire detection, Formation reconfiguration, UAVs.

I. INTRODUCTION Forests play very important roles in nature such as purifying water, storing carbon, and moderating climate, etc. which helps planet earth survival [1]. Wildfires are one of the most threats to wildlife, human life as well as countries economies. They have consumed approximately 27 million acres of land in North America during 2005-2007 [2]. Several methods can be used for forest fires early detection, providing firefighters with the necessary information for fire fighting and rescue missions. Lookouts visual observation is the main traditional method used for forest fire detection, however it lacks accuracy due to human errors. As a result, satellites and manned aerial vehicles are used for detection. However, these technologies still have some practical problems such as low reliability, high costs, etc. [3]. Manned aerial vehicles is used to provide detailed and updated information of forest fires intensity, location and *This work was financially supported in part by NSERC, NSFC #61573282 and SPNSF #2015JZ020 1 Khaled A. Ghamry is with the Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada.

k [email protected]

2 Youmin Zhang is with the Department of Information and Control Engineering, Xi’an University of Technology, Xi’an, Shaanxi 710048, China (on sabbatical leave from Concordia University). [email protected] (Corresponding Author)

978-1-5090-0658-8/16/$31.00 ©2016 IEEE

movement. However, it may cause extreme danger on human operators due to non-structured and risky environments of forest fires. Therefore, UAVs are recently used in forest monitoring, and fire detection and fighting. They can be loaded with different types of fire detection sensors to reduce false alarm rate. However, using single aerial vehicle equipped with a large array of different sensor types is limited at any time to a single viewpoint [4]. Therefore, using multiple UAVs equipped with different types of sensors is very useful in forest monitoring and fire detection application. They have been applied in fire detection, observation and localization [5], [3]. Moreover due to dynamic and random nature of forest fires, fault-tolerant cooperative control (FTCC) is required for successfully and reliably monitoring fires and determining fire perimeters even in the presence of fault(s) in one or more UAVs during the fire detection and fighting mission. FTCC has not been fully investigated, especially in forest monitoring and fire detection and fighting. Some researchers considered this problem using the rendezvous approach to collect more information while moving around a fire spot, minimizing communication latency and operational time for fuel economy as in [6], [7]. However, this method is restricted only for using even number of UAVs. Each UAV is moving individually, backward and forward, in one segment of a circular fire perimeter. On the other hand, the FTCC problem for a team of UAVs has been initially considered in [8], in which the formation recovery algorithm is proposed based on a trajectory re-planning technique. Once an actuator fault occurs, a formation supervisor commands all the UAVs to re-plan their trajectories. Based on this, an adaptive faulttolerant control algorithm for a team of UAVs was presented. In [9], fault-tolerant formation control of UAVs subject to permanent and intermittent faults has been developed. In [10], an FTCC strategy based on graph theory was designed to reduce the effect of actuator fault occurrence in the leader or one of the follower robots. Motivated by the aformentioned, the main contribution of this paper is to solve the FTCC problem in forest monitoring and fire detection, confirmation, observation and tracking of elliptical fire perimeter using multiple UAVs. Therefore, a novel decentralized formation/cooperative reconfiguration algorithm based on graph theory is designed, with another fault-free SMC formation control for a team of UAVs surrounding an elliptical fire trajectory. The proposed algorithm is able to evenly distribute any number of UAVs around the fire perimeter, which is calculated from fire spread model based on remote sensors installled on the UAVs. Moreover,

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the designed FTCC algorithm has the flexibility to add or remove any number of UAVs for refueling/recharging or due to a fault possibly occurred in one or more UAVs during the mission. Therefore, the UAVs can continue surrounding the detected fire spot according to the newly configured formation after fault occurrence, using different fire detection sensors. Consequently, increasing the overall system performance while reducing false alarm rate as well as mission cost can be achieved. The paper is hereinafter organized in the following sections. In Section II, the description of the used UAV, its dynamics, control architecture and formation control during search stage are presented. Section III presents cooperative forest monitoring and fire detection, fire spread model, formation reconfiguration and the designed FTCC strategy. Next, the simulation results are presented in Section IV, and finally, conclusions of this work are presented in Section V. II. PRELIMINARIES The problem considered in this paper is to use multiple UAVs in forest monitoring and fire detection mission in both fault-free and faulty cases by designing an FTCC strategy based on graph theory. This section presents UAVs modeling, baseline controller for each individual UAV, and formation control of multiple UAVs during search stage. A. Quadrotor UAV Dynamic Modeling The UAV considered in this work is quadrotor helicopter, where four rotors laid up symmetrically around its center as illustrated in Fig. 1. The simplified dynamic model of the quadrotor is obtained by using the Newton-Euler formulation as [11]: Uz M Uz y¨ = (sin ψ sin θ cos φ − cos ψ sin φ) M Uz z¨ = −g + (cos θ cos φ) M x ¨ = (sin ψ sin φ + cos ψ sin θ cos φ)

Uφ φ¨ = Jxx Uθ θ¨ = Jyy Uψ ψ¨ = Jzz

(1)

where φ, θ, and ψ are the Euler angles which represent roll, pitch and yaw respectively. M is the quadrotor mass. Jxx , Jyy , and Jzz are the quadrotor moment of inertia according to x, y, and z axes respectively.

Fig. 1.

Coordination system of the quadrotor UAV

B. UAV Control and Formation Control UAV control algorithm for each UAV is based on a combination of SMC and linear quadratic regulator (LQR). Moreover, a SMC is designed for the UAVs team formation in order to maintain the desired postures of followers with respect to their leader during search stage. This ensures full sensors coverage of areas under UAVs footprints. Details of this work can be found in authors’ previous work [11]. III. COOPERATIVE FOREST FIRE DETECTION FTCC scheme in forest monitoring and fire detection of a team of cooperative UAVs will be presented in this section. The following assumptions are asserted: Assumption 1: The UAVs’ searching and coverage path is already planned. Assumption 2: Each UAV has different type of fire detection sensors than other team members, to cooperatively confirm and avoid false alarms. Assumption 3: The sensor radius can cover the area assigned under each UAV foot-prints based on the existing formation shape. Assumption 4: There is no loss of communications between UAVs. To successfully achieve the required mission in forest monitoring and fire detection in fault-free and faulty cases, the following scenario presented in Fig. 2 is proposed: i. A team of N UAVs moving within a leader-follower approach will be used in forest monitoring and fire detection and tracking. ii. The UAV team takes-off and start the search and coverage mission in a certain formation shape as can be seen in stage I of Fig. 2, as illustrated in Section II-B. iii. Once a fire is detected by ith UAV, it will send a fire alarm to the remaining UAVs team members, the ground station (GS), and the manager in charge of forest fire fighting through smart phone etc. Based on the received data, the GS will re-plan the UAVs reference trajectory based on the fire spread model which will be explained in Section III-A. Next, the team will start to track the new elliptic reference trajectory as can be seen in stage II of Fig. 2. iv. The UAV team will reconfigure its formation according to the new situation surrounding the fire spot and tracking the fire perimeter, providing updated on-line information about the fire. Suddenly, a fault occurs in one of the UAVs as can be seen in stage III of Fig. 2. v. Finally, the faulty UAV breaks its communication link with other UAVs, leaving from the formation team for a safe landing. FTCC algorithm based on graph theory and SMC formation reconfiguration will detect the number of UAVs leaving formation NB and with the remaining healthy N -NB UAVs team for new formation reconfiguration, and the task will be assigned to the remaining healthy UAVs to successfully achieve the mission with reduced numbers of UAVs.

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A. Fire Spread Model Different types of empirical models are concerned with spatial behavior simulation of fire. In this paper, a simple elliptical model has been proposed as in [12]: x = ctf ire + atf ire cos β y = btf ire sin β

(2)

where 0 ≤ β ≤ 2π, tf ire is the fire spread time, the origin being the point of ignition. the parameters a and b are both linear fire spread rates. B. UAV Formation Reconfiguration in the Presence of Fire(s) UAVs team keeps certain configuration according to Section II-B during search stage. Once a fire is detected, the whole team will change its formation shape according to new data following the fire elliptic trajectory presented in Eq. (2) while maintaining the elliptic radii r, and certain separation angle γF between leading and following UAVs as shown in Fig. 3. i.e., the formation should be reconfigured from the Cartesian coordinates ld and αd [11] to polar one with coordinates rd and γd which is designed based on a SMC. More details can be found in authors’ another work [13], a brief explanation is given here for convenience. The controller’s main objective is to satisfy the required conditions as following [14]: C1) lim |ri (t) − rd | = 0

∀i ≤ N

(3)

C2) lim |γ˙ i (t) − γ˙ d | = 0

∀i ≤ N

(4)

t→∞ t→∞

C3) lim |γi+1 (t) − γi (t)| = t→∞

2π N

∀i ≤ N

r¨i = r¨d + λr (r˙d − r˙i ) γ¨i = γ¨d + λγ (γ˙ d − γ˙ i )

(6)

where λr , λγ˙ , and λγ are control gains with λr , λγ˙ , and λγ > 0. Condition (4) is not applied, as all UAVs will keep the velocity defined by the fire spread model calculated in Section III-A. C. Under Severe Fault or Refueling Coniditions Forest monitoring and fire detection using cooperative UAVs is such a risky but important application, which needs to be accomplished with high performance, fast response, timely operation, as well as high reliability. UAVs are required to fly with a safe height over the fire flames in order to assure their safety during the mission. However, height should be optimized to gather detailed information about fire and evacuation routes. Sometimes flames could

(5)

where condition C1 states that ith UAV should maintain a desired distance from the fire spot, while condition C2 states that each ith UAV should maintain a desired angular speed around the target. Finally C3 states that all UAVs have to be spread evenly in an elliptic formation around the fire spot. Clearly, these conditions have to be satisfied for all UAVs in order to ensure complete and safe flight of the UAVs team

Fig. 2.

around the fire spot(s), to increase situational awareness and gather more information to the fire brigades [15]. Furthermore, first-order SMC will be used to satisfy the formation conditions represented in Eqs. (3) and (5) for each follower as following:

Fig. 3. UAV formation configuration during confirmation and observation stages

Forest monitoring and fire detection scenario with fault

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reach UAVs, resulting in partial or full damage. Moreover, in such continuous long duration missions, one or more UAVs may leave from formation for refueling due to their limited endurance during one flight. Therefore, it is of great importance to design an FTCC algorithm, which can mitigate the negative effect of fault occurrence or refueling during mission execution, and has the flexibility of adding or removing UAVs to the formation during observation and tracking stage. Remark 1: During a mission, UAVs may face different situations which may mark one as faulty and prevent it from successfully achieving its mission. A faulty UAV will stop communicating with other UAVs and get out from the team, if it suffers from sensor, communication, or actuator faults. Moreover, UAVs may be marked as faulty if it needs to leave from team formation for refueling or recharging. Therefore, the formation should be reconfigured to successfully achieve assigned mission for ensuring full fire spot(s) coverage. The following assumptions are asserted for the FTCC algorithm: Assumption 5: Each UAV in the formation has each own fault detection and diagnosis (FDD) algorithm. So it can detect the fault. Assumption 6: Each UAV can turn off its communication link with all other UAVs, once one of the above situations in Remark 1 occurs. In order to successfully maintain continuous fire observation and monitoring, UAVs are required to evenly distributed surrounding forest fire spots, even when loosing one or more team members. According to condition (5), N should be automatically known by applying Graph Theory [16] for formation reconfiguration during fault, refueling or recharging. The UAVs formation team is described by the pair (r, H), where r describes the formation shape and H is the control graph representing the control strategy used by each UAV. According to this theory, an N × N adjacency matrix G is generated to represent the initial control graph, where N is the number of UAVs in formation. The elements of matrix G are either 0 or 1. If an element (i, j) is 1, this will represents an incoming edge from UAV i to UAV j, and 0 represents no edge between UAVs i and j which means that the motion of UAV j is independent from UAV i. Similarly, a matrix H represents the final formation shape. The appearance of a 1 in a column for any UAV defines its formation controller as [16]: ⎧ ⎪ leader ⎨0   1s= 1 follower with l − γ control ⎪ ⎩ columns 2 follower with l − l control where l − γ control means that one UAV follows another by controlling the relative distance and orientation between them (which is used in this work), and l − l control means that a UAV is maintaining a specified distance relative to two UAVs. The transition from one control graph to another is presented by a transition matrix T as follows: T =H −G

(7)

There are 3 possible values of the (i, j) elements in the matrix T as follows: ⎧ ⎪ no edge connection between i and j ⎨0 −1 the edge connection needs to be broken ⎪ ⎩ 1 new edge needs to be established. Remark 2: Eq. (7) indicates that all matrices T , H, and G must have the same dimensions. However after adding or removing one or more UAVs from the team for refueling or due to fault, the number of UAVs will change and consequently the matrix H. This matrix represents the formation configuration of the remaining healthy UAVs. So, it is assumed that during formation reconfiguration the faulty UAVs are virtually exist but with no edge connection between them and other UAVs, i.e. the columns’ elements representing the faulty UAVs will be zeros. So, the matrix T can be calculated and the remaining UAVs start reconfiguring their formation shape [10]. As can be seen in the stage 1 of Fig. 4, four UAVs are used in monitoring and observation stage with three links established between all followers and leader UAV. Once a UAV left the formation for refueling or due to fault and according to graph theory, the connection link of the faulty robot will break and (-1) will appear in the transition matrix T . Therefore, Eq. (5) can be rewritten as follows: C3F ault ) lim |γi+1 (t) − γi (t)| = t→∞

2π N + NB

(8)

where NB is the number of broken connections appeared in matrix T according to number of faulty UAVs. IV. S IMULATION R ESULTS The control strategies discussed in Section III is successfully implemented in simulations by a team of four UAVs. The objective of simulations is to show that the proposed control algorithm is able to achieve the desired objectives. Graph theory is applied to achieve the required formation after fault, the matrix G which represents the desired diamond formation, and matrix H which represents the final formation after a fault occurrence are as follows: ⎤ ⎤ ⎡ ⎡ 0 1 1 0 0 1 1 1 ⎥ ⎢ ⎢0 0 0 0⎥ ⎥ , H = ⎢0 0 0 0⎥ G=⎢ ⎣0 0 0 0⎦ ⎣0 0 0 0⎦ 0 0 0 0 0 0 0 0

Fig. 4. Communication Links and Formation Reconfiguration in Fault and Refueling

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TABLE I

So, the transition matrix T =H-G will be; ⎡ ⎤ 0 0 0 −1 ⎢0 0 0 0 ⎥ ⎥ T =⎢ ⎣0 0 0 0 ⎦ 0 0 0 0

Jxx = 0.03 kg.m2 Jzz = 0.04 kg.m2 K = 120 N

Jyy = 0.03 kg.m2 Kyaw =4 N.m ωm =15 rad/sec

M = 1.4 kg L = 0.2 m

6 Leader UAV

5

F1

UAV

F2

UAVF3

z (m)

4 3 2 1

Wind Direction

0 40

Fire Spot

30 20 10 0 −10 −20 −30 −40

−15

−20

−10

y (m)

0

−5

5

10

Formation of UAVs team

350

300

20

15

x (m)

Fig. 5.

Formation Reconfiguration

Fault Occured in Follower 3

γF1 γ

F2

γF3

250 Formation Angle (degrees)

Substituting with connection break NB =-1 in Eq. (8), the formation angle γ will change accordingly. In following simulation, the leader UAV’s initial position is q1 (0) = [17, −22, 0]T . The first follower UAV’s initial position is q2 (0) = [14, −27.5, 0]T , the second follower UAV’s initial position is q3 (0) = [20, −24, 0]T , while the third follower UAV’s initial position is q4 (0) = [17.5, −32, 0]T . The UAVs’ desired formation during search and coverage with respect to their leader is 5 m and 150◦ for the first follower UAV, 5 m and 210◦ for the second follower, and 9 m and 180◦ for the third one. All the values of the UAV controller parameters are shown in Table I. It is assumed that the first follower UAV detects a fire spot after 50 sec of the mission starting and a sensor fault occurs to the third follower UAV at t = 120 sec. Fig. 5 illustrates the formation of UAVs team during forest monitoring and fire detection mission. As can be seen, after the UAV team takes-off and starts the search mission, the first follower UAV detects a fire spot with coordinates (0, -20, 0). The GS plans new reference trajectory that the UAVs must follow according to the fire spread model presented in Eq. (2), where a = 16 m, and b = 32 m at tf ire =1 sec. The UAVs team starts to follow the elliptic trajectory with the same formation of search stage. Once the leader UAV sends the reconfiguration commands, each follower begins to calculate its new position according to the illustrated formation control in Section III-B and follow the new trajectory at the instant marked with the three (◦) magenta markers. The UAVs team surrounds the fire spot following the elliptic trajectory with formation angle γ =90◦ according to Eq. (6). At t = 120 sec the FDD system embedded on the third follower UAV detects a sensor fault, so it decides to leave the formation. Consequently, according to the graph theory and Eq. (8), the team reconfigures the formation by changing its formation angle γ from 90◦ (followers are marked at this instant with (◦) brown markers) to 120◦ which is marked with (◦) green markers. Fig. 6 and Fig. 7 show that the remaining two followers UAVs maintain their desired formation angle with respect to the leader, and their position error converges to 0 during mission execution and after fault occurance. As shown in Fig. 8 the UAVs team is keeping its diamond formation from takeoff at t = 10 to t = 50 sec, then the team begins tracking fire perimeter by maintaining the same formation. Later, at t = 70 sec the leader UAV commands the three followers to reconfigure for surrounding the fire spot with γ = 90◦ . As shown in Fig. 9, the blue triangle represents the formation at t = 120 when fault occurred in F3 . According to graph theory and SMC formation control explained in Section IIIB and III-C, the formation is reconfigured and the task is assigned to remaining healthy UAVs as shown in the magenta

UAV C ONTROLLER PARAMETERS

200

150

100

Formation Reconfiguration due to Fault

50

0

−50

−100 0

Search Stage 20

40

Fire Confirmation and Monitoring Stage 60

80

100

120

140

160

180

200

t (sec)

Fig. 6.

Formation angles between leader UAV and followers UAVs

triangle in Fig. 9. It is clear that the proposed algorithm succeeded in fault mitigation and remaining healthy UAVs can successfully continue their mission. V. CONCLUSIONS This paper investigated and provided a solution for fault-tolerant cooperative control (FTCC) using multiple UAVs for searching, detecting and tracking the propagation of forest fires. A distributed formation controller is designed for the search stage using SMC. If one of the UAVs detects a fire, it sends an alarm to all the UAVs team members, ground station, and a human manager in charge of fire fighting through smart phone etc. Then a new reference trajectory is calculated using fire spread model for generating an elliptic fire trajectory. Also, a formation reconfiguration algorithm is designed for controlling each individual UAV in the formation team to achieve complete coverage of fire perimeter using distributed sliding-mode control (SMC)

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UAV Follower 1 20 10 ex,ey,ez

Formation Reconfiguration due to Fault

Formation Reconfiguration

0 −10

Fire Confirmation and Monitoring Stage

Search Stage

−20

e

x

e

y

ez

−30 0

20

40

60

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100

120

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Simulation results show that the proposed algorithm is stable and able to achieve the desired formation configurations in case of faults/refueling. Future work will include realtime implementation of the proposed control algorithm to quadrotor team of UAVs (Qball-X4) testbed in the Concordia Networked Autonomous Laboratory (NAV-LAB).

UAV Follower 2 40

ex,ey,ez

Formation Reconfiguration due to Fault

Formation Reconfiguration

20

R EFERENCES

0 −20

Search Stage

−40

Fire Confirmation and Monitoring Stage

ex e

y

e

z

−60 0

20

40

60

80

100

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t (sec)

Fig. 7.

Position error of followers UAVs

40

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30

L

L

20

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2

F1

F

3

y (m)

10

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F

1 L

−10

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−20

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2

F

2

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−30

Search stage −40 −20

−15

−10

−5

0

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x (m)

Fig. 8.

Snapshot of the formation during search and monitoring stages

40

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Fault Occurance F

3

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y (m)

10

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0

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L

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−10

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−30

−40 −20

Formation with Fault −15

F1 −10

−5

0

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20

x (m)

Fig. 9. Snapshot of the formation with fault on F3 and formation reconfiguration after a faulty (or refueling/recharging) UAV leaving from the team

algorithm in fault-free case. However, when fault occures or refueling is required to one or more UAVs, the UAV leaves from the formation while breaking the communication link with other UAVs. The graph theory T matrix is used to represent the number of faulty/absent UAVs and the team can reconfigure its formation autonomously, and ensure a full and evenly distribution around the fire spot(s).

[1] C. Yuan, Y. M. Zhang, and Z. Liu, “A survey on technologies for automatic forest fire monitoring, detection and fighting using UAVs and remote sensing techniques,” Canadian Journal of Forest Research, vol. 45, no. 7, pp. 783–792, 2015. [2] M. Kumar, K. Cohen, and B. HomChaudhuri, “Cooperative control of multiple uninhabited aerial vehicles for monitoring and fighting wildfires,” Journal of Aerospace Computing, Information, and Communication, vol. 8, no. 1, pp. 1–16, 2011. [3] L. Merino, F. Caballero, J. R. M. de Dios, I. Maza, and A. Ollero, “Automatic forest fire monitoring and measurement using unmanned aerial vehicles,” in The VI International Conference on Forest Fire Research, 2010. [4] A. Ollero, S. Lacroix, L. Merino, J. Gancet, J. Wiklund, V. Remu, I. V. Perez, L. G. Gutirrez, D. X. Viegas, and M. A. G. Benitez, “Multiple eyes in the skies: architecture and perception issues in the COMETS unmanned air vehicles project,” IEEE Robotics & Automation Magazine, vol. 12, no. 2, pp. 46–57, 2005. [5] L. Merino, F. Caballero, J. R. M. Dios, J. Ferruz, and A. Ollero, “A cooperative perception system for multiple UAVs: Application to automatic detection of forest fires,” Journal of Field Robotics, vol. 23, no. 34, pp. 165–184, 2006. [6] D. W. Casbeer, D. B. Kingston, R. W. Beard, and T. W. McLain, “Cooperative forest fire surveillance using a team of small unmanned air vehicles,” International Journal of Systems Science, vol. 37, no. 6, pp. 351–360, 2006. [7] K. Alexis, G. Nikolakopoulos, A. Tzes, and L. Dritsas, Coordination of helicopter UAVs for aerial forest-fire surveillance, ser. Applications of intelligent control to engineering systems. Springer, 2009, pp. 169–193. [8] A. Chamseddine, Y. M. Zhang, and C. A. Rabbath, “Trajectory planning and re-planning for fault tolerant formation flight control of quadrotor unmanned aerial vehicles,” in The American Control Conference (ACC), 2012, pp. 3291–3296. [9] Q. Xu, H. Yang, B. Jiang, D. H. Zhou, and Y. M. Zhang, “Fault tolerant formations control of UAVs subject to permanent and intermittent faults,” Journal of Intelligent & Robotic Systems, vol. 73, no. 1-4, pp. 589–602, 2014. [10] M. A. Kamel, Y. M. Zhang, and X. Yu, “Fault-tolerant cooperative control of multiple wheeled mobile robots under actuator faults,” in IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes (SafeProcess), 2015, pp. 1152–1157. [11] K. A. Ghamry and Y. M. Zhang, “Formation control of multiple quadrotors based on leader-follower method,” in International Conference on Unmanned Aircraft Systems (ICUAS), 2015, pp. 1037–1042. [12] G. Perry, “Current approaches to modelling the spread of wildland fire: a review,” Progress in Physical Geography, vol. 22, no. 2, pp. 222–245, 1998. [13] K. A. Ghamry and Y. M. Zhang, “Cooperative control of multiple UAVs for forest fire monitoring and detection,” in The 12th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications (MESA), 2016. [14] A. T. Hafez, A. J. Marasco, S. N. Givigi, A. Beaulieu, and C. A. Rabbath, “Encirclement of multiple targets using model predictive control,” in The American Control Conference (ACC), 2013, pp. 3147– 3152. [15] H. Kawakami and T. Namerikawa, “Cooperative target-capturing strategy for multi-vehicle systems with dynamic network topology,” in The American Control Conference, (ACC), 2009, pp. 635–640. [16] J. P. Desai, V. Kumar, and J. P. Ostrowski, “Control of changes in formation for a team of mobile robots,” in The IEEE International Conference on Robotics and Automation (ICRA), vol. 2, 1999, pp. 1556–1561.

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