typical fault estimation and dynamic analysis of a leader ...system. based on the fault-tolerant...

Research ArticleTypical Fault Estimation and Dynamic Analysis of a Leader-Follower Unmanned Aerial Vehicle Formation

Jian Shen ,1 Qingyu Zhu,2 Xiaoguang Wang,3 and Pengyun Chen 1

1College of Mechatronics Engineering, North University of China, Tai Yuan 030051, China2AVIC China Aero-Polytechnology Establishment, Beijing 100028, China3Department of Smart Ammunition, Norinco Group Aviation Ammunition Research Institute, Harbin 150030, China

Correspondence should be addressed to Jian Shen; [email protected]

Received 7 October 2020; Revised 3 March 2021; Accepted 9 March 2021; Published 26 March 2021

Academic Editor: Giovanni Palmerini

Copyright © 2021 Jian Shen et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In this paper, the typical fault estimation and dynamic analysis are presented for a leader-follower unmanned aerial vehicle (UAV)formation system with external disturbances. Firstly, a dynamic model with proportional navigation guidance (PNG) control of theUAV formation is built. Then, an intermediate observer design method is adopted to estimate the system states and faultssimultaneously. Based on the graph theory, the topology relationship between each node in the UAV formation has been alsoanalyzed. The estimator and the system error have been created. Moreover, the typical faults, including the components failure,airframe damage, communication failure, formation collision, and environmental impact, are also discussed for the UAVsystem. Based on the fault-tolerant strategy, five familiar fault models are proposed from the perspectives of fault estimation,dynamical disturbances, and formation cooperative control. With an analysis of the results of states and faults estimation, theactuator faults can be estimated precisely with component failure and wind disturbances. Furthermore, the basic dynamiccharacteristics of the UAV formation are discussed. Besides, a comparison of two cases related to the wind disturbance has beenaccomplished to verify the performance of the fault estimator and controller. The results illustrate the credibility andapplicability of the fault estimation and dynamic control strategies for the UAV system which are proposed in this paper.Finally, an extension about the UAV formation prognostic health management system is expounded from the point of view ofthe fault-tolerant control, dynamic modeling, and multifault estimation.

1. Introduction

In most developed fields of unmanned aerial vehicle (UAV),formation flight is one of the most important techs in swarmcooperative work. Multiple UAVs in a formation are moreefficient than a single one during the process of mission com-pletion. The swarm cooperative flight technology has beenpaid a lot of attention in the UAV field. However, it juststarts, and there are many significant problems needed tobe solved. For example, assuming that the formation config-uration is stable, one crucial question is how to maintain thereliability and stability of the UAV system. Tomake the UAVformation flying safer, fault diagnosis and fault-tolerant con-trol will be the key solutions. When faults appear during theformation flight, they should be detected, localized, and cor-rected in a short time. Otherwise, the mission will fail. With

the help of accurate and in-time fault diagnosis and reliablefault-tolerant control, the formation will be reconfigured,and communication between each other will be optimized.As a result, the UAV formation will fly in a safe and stablestatus. There are many different kinds of faults that aroseand coupled in real flight. According to the different degreesof faults, they can be divided into an intermittent fault, sud-den fault, and slow fault. If classified by different fault parts,they include the actuators, sensors, and communication fail-ures which may cause the whole formation to work in chaos.

Due to the complex coupled relationships between differ-ent stages in formation, the fault diagnosis will be affected byparameter perturbation, external disturbance, and noses. Theformation controller has no ideal robustness performance,and the control accuracy declines [1]. In the fault diagnosisfield, an observer-based method is usually used. In the

HindawiInternational Journal of Aerospace EngineeringVolume 2021, Article ID 6656422, 16 pageshttps://doi.org/10.1155/2021/6656422

https://orcid.org/0000-0002-9999-2999

https://orcid.org/0000-0003-2157-281X

https://creativecommons.org/licenses/by/4.0/

https://creativecommons.org/licenses/by/4.0/

https://doi.org/10.1155/2021/6656422

process of observer design, disturbance decoupling should beconsidered carefully. Consequently, the uncertainties in faultdiagnosis can be eliminated, and the formation control willbe more robust. Separating the disturbances and faults helpsfault diagnosis efficiency and reduces the rate of false faultjudgment.

In engineering applications, there are several typical faultdiagnosis methods for UAV formation, for instance, distrib-uted fault detection, sliding mode observer, robust unknowninput observer, fuzzy sliding mode observer, and neural net-work. In these methods, the observer-based is one of the mostused for linear systems with perturbations [2–4] and nonlin-ear systems [5]. The thought of the observer-based fault diag-nosis method is using the measurable input and output valueof the UAV formation system to design the system stateobserver and measure the status. With the residual signalobservation of the estimate and the actual value, the approx-imation of system fault can be estimated, and fault diagnosiswill be accomplished. For the observer-based fault diagnosismethod appliance in the UAV field, Negash illustrated a bankof unknown input observer- (UIO-) based distributed faultdetection scheme to detect and identify the compromisedUAV in the formation. A rule based on the residuals gener-ated using the bank of UIO has been used to detect attacks.Moreover, an algorithm was developed to remove the faultyUAV from the network once an attack has been detectedand the compromised UAV isolated while maintaining theformation flight with a missing UAV node. A numerical casestudy has demonstrated that the residual generated at themonitoring node UAV can successfully detect and isolatethe cyberattack. And the faulty UAV removal algorithm hasbeen shown to effectively remove the compromised UAV tomaintain the formation accordingly [6]. Reference [7] intro-duced a sliding mode observer which is designed to recon-struct the actuator faults and then eliminate the influence ofthe actuator faults in the UAV formation fault-tolerant con-trol. Simulation results verified that the active fault diagnosisand fault-tolerant control scheme proposed for the UAV for-mation system with actuator faults were effective. In [8], anUIO-based scheme was used for icing detection in overactu-ated unmanned aerial vehicles. Decision algorithms had beenproposed to correctly identify possibly unexpected effects inthe system dynamics. Moreover, the icing accommodationtask was addressed, using a fault-tolerant control allocationscheme and exploiting input redundancy in the case of con-trol surface failures, or by using an automated deicing subsys-tem in the case of ice accretion on airfoils. Rotondo et al.proposed a discrete-time linear parameter varying (LPV)UIO for the diagnosis of actuator faults and ice accretion inthe UAV system. The proposed approach, which was suitedfor an implementation onboard, exploited a complete 6-degrees of THE freedom (DOF) UAVmodel, which includedthe coupled longitudinal/lateral dynamics and the impact oficing. The LPV formulation had the advantage of allowingthe icing diagnosis scheme to be consistent with a wide rangeof operating conditions. The developed theory was supportedby simulations illustrating the diagnosis of actuator faultsand icing in a small UAV. The obtained results validate theeffectiveness of the proposed approach [9]. Reference [10]

stated that a new online detection strategy was developed todetect faults in sensors and actuators of the UAV systems.In this design, the weighting parameters of the neural net-work (NN) were updated by using the extended Kalman fil-ter (EKF). Online weighting parameter adaptation helped todetect abrupt, intermittent, and incipient faults accurately.There had been applied the proposed fault detection systemto a nonlinear dynamic model of the WVU YF-22unmanned aircraft for its evaluation. The simulation resultsshow that the new method has better performance in com-parison with conventional recurrent neural network-basedfault detection strategies [10]. A 3D leader–follower forma-tion control problem was discussed in [11]. A novel controllaw and an adaptive disturbance observer have beenexplored for the swarms of fixed-wing UAVs with motionconstraints and disturbances. The simulation results showedthat the proposed method was effective whether there weredisturbances existing. In [12], a novel distributed slidingmode control law has been investigated for the leader-follower UAV formation. Numerical simulations verifiedthat the adjustable range of the followers’ linear velocitywas not required to be larger than that of the leaders, whichwas of significance in the leader-follower formation flight fora large scale of UAVs.

However, in the traditional observer-based fault diagno-sis method, the observer matching conditions must besatisfied [13]. This goal usually could not be meet in realengineering applications. Under the condition that thesystem satisfies the strict positive realness conditions, in[14, 15], a self-adaptive fault estimation method was stated.With a comparison of the observer matching conditions,the strict positive realness conditions were more conserva-tive. To solve these problems, an intermediate observer-based method was presented in [16]. An intermediatevariable was built, and the fault estimation observer wasdesigned. The estimated value of the built intermediatevariable was used to calculate the fault value. The mostadvantage was that the observer matching conditions andthe strict positive realness conditions would not be neededto be satisfied for the systems. It was desirable for the faultestimation in the UAV formation system. In [17], theauthor adopted this kind of intermediate observer into anetwork of dynamical systems with external disturbances.A distributed intermediate estimator was constructed foreach node based on local output measurements. Exceptfor the built intermediate fault estimator, the intercon-nected relationship between UAVs should be considered.Additionally, the dimension of the linear matrix inequality(LMI) would increase with the growth of UAV number.These problems ought to be thought seriously when design-ing the UAV formation’s fault estimator.

In [13], a new intermediate estimator was introduced toestimate the fault in a multiagent system. It could be usedin a system which could not meet the observer matchingconditions. Also, in the estimation of intermediate variables,the feedback effect of the output error was taken intoaccount. In consequence, the estimation performance couldbe improved. Finally, the dimension of linear matrix inequal-ity (LMI) will not enhance with the increase of UAV number.

2 International Journal of Aerospace Engineering

In this paper, the typical fault modeling and simulationfor a leader-follower UAV formation system, like the compo-nents failure, airframe damage, communication failure,formation collision, and environmental impact, will be themain focuses through the research process of fault estimationand dynamic analysis. A kinematic model of the leader andfollower UAV is built, and the relative relationship will bemaintained with the PNG control method in Section 2. Toestimate the system states and faults, an intermediateobserver design method is adopted in Section 3. The commu-nication topology between each node in the UAV formationis built based on the graph theory. The estimator and estima-tion error model are also shown in this part. Furthermore,the typical faults are also discussed and modeled in Section4. Then, the fault estimation and the dynamic analysis willbe shown in the simulation and discussion part. With theanalysis of the results, the future research extensions aboutthe UAV formation fault diagnosis and cooperative controlare concluded in the final part.

2. Dynamic Model of the UAV Formation

During the flight of the UAV formation, each member has arelative relationship of motion. According to different forma-tion configurations, the definitions of the coordinate systemsare not the same. In this section, a leader-follower scheme hasbeen adopted to set up the formation [1]. Assuming that nUAVs are flying in the two-dimensional plane, consideringthe kinematics and dynamics of the leader and follower, therelative position relationship between them is shown inFigure 1.

In Figure 1, L is the leader, and Fi is the ith follower in theUAV system. The velocities for leader and follower are VLand VFi

, respectively. XLand YL are the coordinates of theinertial system of leader, respectively. XFi and YFi are thecoordinates of the inertial system of follower, respectively.ψL and ψFi are the pitch angles of leader and follower. RLand RFi are the radius vectors of leader and follower.

According to the relative position relationship shown inFigure 1, the kinematic equations of leader and follower canbe illustrated as [18]

_XL =VL cos ψL

_YL =VL sin ψL

_ψL = ωL

_XFi= VFi

cos ψFi

_YFi= VFi

sin ψFi

_ψFi= ωFi

eFi =XL − XFi

YL − YFi

" #

8>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>:

i = 1, 2,⋯, n, ð1Þ

where ωL and ωFi are the pitch angle velocities of leader andfollower. eFi is the leader-follower relative distance error.

Under the inertial system, the second-order derivative ofeFi

is the function of control input and the control inputswhich can be shown as

€eFi= f uFið Þ,

uL =NVL2 sin ψLð Þ/RL,

uFi =NVFi2 sin ψFið Þ/RFi,

8>><>>: ð2Þ

where uL and uFi are the UAV formation system controlinputs for leader and follower which are based on the propor-tional navigation guidance (PNG) method. N is the scalefactor of PNG.

A linearized and topology distributed UAV formationmodel is shown as

_xi tð Þ = Axi tð Þ + Bui tð Þ + Ff i tð Þ + Edi tð Þyi tð Þ = Cxi tð Þ,

(, ð3Þ

where xiðtÞ = ½Xi Yi ωi ψi�T contains the states of the ith nodein the UAV formation (including leader). The system controloutput is yiðtÞ. f iðtÞ denotes the fault of UAV. diðtÞ repre-sents the system disturbance. A, B, C, E, and F are the coeffi-cient matrixes.

2.1. Intermediate Observer-Based Fault Estimator of the UAVFormation. In the process of intermediate observer design,the centralized and distributed output estimation errors areconsidered at the same time. For the UAV formation withoriented topology connection, a low order LMI can be solvedto calculate the observer gain matrix which is based on Schurmatrix decomposition theory. The dimension of LMI is thesame as the one which is related to the solved LMI dimensionin fault estimation for a single UAV. As a result, for the inter-mediate fault estimator in [13], the amount of computationwill not increase even more UAVs joined in the formation.In addition, for the UAV formation with unoriented topol-ogy, due to the symmetry of the Laplacian matrix, the strictpositive realness conditions are less conservative.

2.1.1. Graph Theory. If there are n UAVs connected in oneformation, the connection relationship based on graph the-ory can be proposed as

VFi

RL

ΨL

ΨFi

VL

XLXFi

YFi

YL

RFi

O

Y

Follower i

Leader

X

Figure 1: Relative position relationship between leader and followerin the UAV formation.

3International Journal of Aerospace Engineering

ς = ν, ε, Γð Þ, ð4Þ

where ν = fν1, ν2,⋯, νng represents the member set of theUAV formation, and the ith node is νiði = 1, 2,⋯, nÞ. Theedge set is ε = fðνi, νjÞ: νi, νj ∈ νg ⊂ ν × ν. The adjacencymatrix of graphs is Γ = ½Γij� ∈ Rn×n, which can be shown as

Γij =0, i = j

1, νi, νj

� �∈ ε

0, other

8>><>>: : ð5Þ

Assuming that νiand νj are two connected nodes in theUAV formation, for one formation with unoriented topologyconnection, ðνi, νjÞ ∈ ε and ðνj, νiÞ ∈ ε are all established. Butfor the one with oriented topology connection, ðνi, νjÞ ∈ ε orðνj, νiÞ ∈ ε is founded.

The symmetric Laplacian matrix L = ½Lij� ∈ Rn×n of thegraph is

Lij =〠N

j=1Γij, i = j

−Γij, i ≠ j

8>><>>: : ð6Þ

As mentioned above, the observer matching conditionsor the strict positive realness conditions must be satisfiedfor the system fault estimator design. It means that CF in(3) is a matrix with a full rank column. But for the interme-diate observer-based estimator, the above conditions arenot needed to meet. The derivation process is shown in [13].

2.1.2. Intermediate Observer. The intermediate variable isdefined as

ηi tð Þ = f i tð Þ − Sxi tð Þ, ð7Þ

where S is a matrix which needed to be designed. The deriva-tion of ηiðtÞ is

_ηi tð Þ = _f i tð Þ − S _xi tð Þ = _f i tð Þ − SA + SFSð Þxi tð Þ − SBui tð Þ− SFηi tð Þ − SEdi tð Þ:

ð8Þ

Combining (3) and (8), the intermediate estimator can beshown as

_xi tð Þ = Axi tð Þ + Bui tð Þ + F f i tð Þ + ρ1K1ζ1i tð Þ + ρ2K2ζ2i tð Þ,_bη i tð Þ = −SFbη i tð Þ − SA + SFSð Þxi tð Þ − SBui tð Þ + ρ1K3ζ1i tð Þ + ρ2K4ζ2i tð Þf i tð Þ = bη i tð Þ + Sxi tð Þ,

8>><>>: ,

ð9Þ

where xiðtÞ and bη iðtÞ are the estimations of the system statesand the intermediate variable. f iðtÞis the estimated value offaults. The centralized output estimation error and distrib-

uted output estimation error are ζ1iðtÞ and ζ2iðtÞ. ρ1 and ρ2are the weights of ζ1iðtÞ and ζ2iðtÞ, respectively. K1, K2, K3,and K4 are the gain matrixes of the observer. ρ1 and ρ2 areall positive, and the sum of them equals one.

ζ1iðtÞ and ζ2iðtÞ can be defined as

ζ1i tð Þ = yi tð Þ − yi tð Þ,

ζ2i tð Þ = 〠N

j=1Aij yi tð Þ − yi tð Þð Þ − yj tð Þ − y j tð Þ

� �h i,

8>><>>:ð10Þ

where yiðtÞ = CxiðtÞ is the output estimation of the i’th node.

2.1.3. System Error. In order to evaluate the estimation errors,the sets of equality are adopted as

~xi tð Þ = xi tð Þ − xi tð Þ,~ηi tð Þ = ηi tð Þ − bη i tð Þ~f i tð Þ = f i tð Þ − f i tð Þ:

8>><>>: , ð11Þ

The derivations of the estimation errors ~xiðtÞ and ~ηiðtÞare proposed as

_~xi tð Þ = _xi tð Þ − _xi tð Þ =A~xi tð Þ + F~f i tð Þ + Edi tð Þ − ρ1K1ζ1i tð Þ − ρ2K2ζ2i tð Þ,_~ηi tð Þ = _ηi tð Þ − _bη i tð Þ = −SF~ηi tð Þ − SA + SFSð Þ~xi tð Þ − SEdi tð Þ + _f i tð Þ − ρ1K3ζ1i tð Þ − ρ2K4ζ2i tð Þ:

(

ð12Þ

In [16, 17], the designed matrix S is

S = μFT : ð13Þ

If the value of the empirically selected parameter μ islarger, the convergence rate is faster, and the overshoot is big-ger [19]. With derivation, the estimation errors of the UAVformation can be illustrated as

_ξ tð Þ = IN ⊗ A1 − ρ1 �K1C1� �

ξ tð Þ − L ⊗ ρ2 �K2C1ξ tð Þ + IN ⊗ E1ω tð Þ,Y tð Þ = IN ⊗ �Cξ tð Þ,

(ð14Þ

Actuatorfailure

Figure 2: Component failure (e.g., actuator fault) in the UAVformation.


where

ξ tð Þ = ξT1 tð Þ, ξT2 tð Þ,⋯, ξTN tð Þh i

,

ω tð Þ = ωT1 tð Þ, ωT

2 tð Þ,⋯, ωTN tð Þ� �

,

Y tð Þ = YT1 tð Þ, YT

2 tð Þ,⋯, YTN tð Þ� �

:

ð15Þ

And the matrixes in (14) are

A1 =A + μFFT F

−μFT A + μFFT� �−μFT F

" #,

E1 =E On×nf

−μFTE Inf

" #,

�K1 =K1

K3

" #, �K2 =

K2

K4

" #,

C1 = C Ony×nf� �

, ω tð Þ =di tð Þ_f i tð Þ

" #,

ð16Þ

where n, nf and ny are the dimensions of nodes number,faults, and outputs.

In [13], the different forms of (14) for the UAV formationwith oriented and unoriented topology connection were alsoderived. Moreover, the stability of system error (14) wasalready proved in this reference. It will not be repeated here.

2.2. Typical Fault Models of the UAV Formation

2.2.1. Typical Fault Introduction. During the flight of theUAV formation, the vehicles may be affected by manyfactors, such as the actuator jam, airframe damage, commu-nication failure, collisions, or environmental impact. Thesefactors, regarded as the typical faults of the UAV formation,may occur at the same time, or one thing happening causesthe other to happen. To maintain the safety and reliabilityof the UAV formation flight, a fault-tolerant health manage-ment system must be designed to handle these faults [20].The descriptions and responses of the typical faults are illus-trated as follows.

(1) The Component Failure of UAV. Failures of the onboardactuators, sensors, control systems, flight computers, powersystems, and other components are collectively referred to

the component level failure [21–24]. An example of the actu-ator fault in the UAV formation is shown in Figure 2.

For component failures of the UAV formation, the healthmanagement system can monitor fault signals online in real-time and reduce the impact of measurement deviation andsignal drift on system performance through algorithm opti-mization and other measures [25].

(2) Airframe Damage. Failures of the UAV formation, such ascollision with neighboring members or obstacles, may causedamage to the airframe. These failures, as shown inFigure 3, belong to the components level faults. The impactof components or UAV body damage on formation perfor-mance is determined by the effectiveness of the health man-agement system [26].

When the components are damaged, the health manage-ment system provides the control system with a controlscheme adapted to the current situation through online iden-tification and adaptive technology [27].

(3) Communication Failure. Temporary or permanent loss ofcommunication signals between connected members inFigure 4 is caused by interference or communication devicefailure [28].

When information flow failure occurs in formation, thehealth management system should make up for the lostinformation in time to accomplish the tasks [29].

(4) Formation Collision. When UAV deviates from theplanned track or the expected motion state, it is consideredthat the formation is abnormal. This increases the risk of col-lision with obstacles or neighboring aircrafts [30, 31] likewhat is shown in Figure 5.

If the formation of UAVs is abnormal and colliding, themonitoring system quickly acquires abnormal information

Figure 3: Airframe damage of UAV.

Follower 1

Follower 3

Follower 2communication failure

Information flow Leader

Figure 4: Information flow failure in the UAV formation.


and notices each member. The health management systemadopts control decision optimization to adjust the configura-tion of the formation and the relative movement relationshipof nodes in real-time [32, 33].

(4) Environmental Impact. Severe weather (Figure 6) or envi-ronmental factors cause performance degradation or failureof the UAV communication system, control system, andactuator [34].

The health management system can monitor the charac-teristics and signals of the working environment and meteo-rological conditions and adjust the formation according toreal-time feedback.

2.2.2. Modeling of the Typical Faults

(1) Actuator Failure (AF). Typical actuator failures includelock-in place, harder over fault, and floating. During theflight of the UAV formation, any member’s normal controlinput uinðtÞ has been taken by a faulty control signal �uiðtÞwhich is corresponding to the actuator failure [35]. If theactuator fault of UAV happens at time t f , the control inputin (3) can be shown as

ui tð Þ = uin tð Þ + σAi ui tð Þ − uin tð Þ½ �: ð17Þ

The unit step function σAi is expressed as

σAi =1, t ≥ t f

0, t < t f

(, ð18Þ

(2) UAV Component Damage (UCD). The damages of UAV’scomponents will lead to the change of the formation dynam-ics. These faults can be regarded as disturbance dDiðtÞ whichbelongs to a finite norm L2½0, +∞Þ [17]. dDiðtÞ can be pro-posed as [16]

dDi tð Þk k < Lg xi tð Þ − xi tð Þk k, ð19Þ

where Lg is the Lipschitz constant.

(3) Communication Failure (COMF). Take the leader-follower formation model as an example, the leader movesindependently under the requirements of the planned task.Other followers just go after the leader and receive the stateinformation from the leader periodically. The informationflow among the formation nodes constitutes a communica-tion topology, and every node modulates its own state basedon the information. Time delay always exists in the commu-nication process which may causes collision during themaneuvering of formation. As a result, the feedback strategymust be adopted in the communication topology to maintainthe stability of the UAV formation [36, 37].

The communication failures include transmitter,receiver, and transceiver failures [28]. If the transmitter failson any node, it may not communicate with other nodesaccording to the information received from the linked UAVs.Once the failure happened on the receiver, the faulty nodewill broadcast its decision to others, and the leader will makea new decision on the assignment of the targets for theformation again. In order to make the formation task achiev-able, the node, which has a partial or complete communica-tion failure, will leave the formation safely and heads to theground station following a prescribed escape maneuver.Meanwhile, the transceiver of this faulty node must be shut

Figure 6: UAV formation fly in extreme weather.

Collision

Figure 5: Collision occurred in the UAV formation.


down immediately to prevent its influence on the reconfi-gured communication topology.

For the communication topology reconfiguration, UAVconnected adjacency matrix and the Laplacian matrix needto be reset. Figure 4 shows a connected formation configu-ration. If there is no communication failure exists, theconnection adjacency matrix and the Laplacian matrix areproposed as

Γ =

0 1 1 01 0 1 01 1 0 10 0 1 0

2666664

3777775, L =2 −1 −1 0−1 2 −1 0−1 −1 3 −10 0 −1 1

2666664

3777775: ð20Þ

If follower 2 has communication failure, it leaves theformation, and follower 3 links to follower 1. The index offollower 3 changes to 2. The connection adjacency matrixand the Laplacian matrix are shown as

ΓCOMF =0 1 01 0 10 1 0

26643775, LCOMF =

1 −1 0−1 2 −10 −1 1

26643775: ð21Þ

(4) Collision Failure (COLF). With the need for configura-tion maintenance, every node in the formation ought tohold a safe distance from its neighbors. If UAVs are tooclose to each other, the collision may happen. And if thedistance is very long, the time delay of communicationmay cause other failures [38].

According to the desired safe distance rdesire sent by theleader, a scheme of collision avoidance is shown inFigure 7. Every node will get a reward value from the leaderdepending on the distance to its neighbors. Members in theformation will adjust their states based on these rewardvalues.

The reward value is defined as

rewardi =

−1, rij < rmin

−1, 0ð Þ, rijdesiremin

0, rij = rdesire

0, 1ð Þ, rdesire < rij ≤ rmax

1, rij > rmax

8>>>>>>>><>>>>>>>>:, ð22Þ

where rmin and rmax are the minimum and maximum dis-tance between two connected nodes, respectively. Once colli-sions occur during the flight, the leader must affirm thatwhether the collided nodes are still in the topology. If thatis the case, these nodes quit the formation and fly back tothe base station following the leaving strategy as same asthe communication failure.

(5) Extreme Environment (EE). If the UAV formation flies ina real environment, such as desert, forest, valley, and ocean,many factors will affect the system’s dynamic stability. Forexample, the low temperature in the polar region may freezethe wings of the actuator. Or if a UAV is struck by a thunder-bolt, the internal communication equipment will be dam-aged, and the information cannot be transformed in timeamong the formation nodes. These baneful influences willlead to the failures of onboard actuators, sensors, and controlsystems. Except for the fault models that have been alreadymentioned in this section, a wind model is needed to be con-sidered. The perturbation of wind is the main factor thatcauses flight failure though the design of the aircraft whichis relatively perfect [39].

The influence of wind can be regarded as a part of the sys-tem disturbance diðtÞ. There are static and dynamic parts in awind model. The speed of static wind can be proposed as

Vs tð Þ =Vconst +Va tð Þ, ð23Þ

where Vconst is the constant wind speed. VaðtÞ represents thetime-varying part and can be illustrated as

Va tð Þ =

0 , t ∈ 0, t0½ � ∪ t2,+∞ð Þvs max t − t0ð Þt1 − t0

, t ∈ t0, t1ð �

vs max t − t1ð Þt1 − t2

, t t1, t2ð �

8>>>>>><>>>>>>:, ð24Þ

where Vs max is the maximum value of the static wind. t0, t1,and t2 are the time-varying wind speed increase, decrease,and disappear time.

The speed of the dynamic wind is complex and changesrandomly over time. In engineering application, a simplifiedmodel has been set up as

Vd tð Þ =Vd maxrand −1, 1ð Þ sin 2πt +U −π, πð Þ, ð25Þ

where Vd max is the maximum value of the dynamicwind.Uð−π, πÞ is a uniform distribution between −π and π.

Node j

Node irij

rmin

rdesire

rmax

j

Noder jijj

in

Figure 7: UAV formation collision avoidance scheme.


Asmentioned above, the part which relates to the wind insystem disturbance diðtÞ can be shown as

dwi tð Þ =Vs tð Þ +Vd tð Þ: ð26Þ

The total system disturbance can be illustrated as

di tð Þ = dDi tð Þ + dwi tð Þ: ð27Þ

In this paper, the fault estimation will be the main con-tents which will be discussed in the next section. The basicmodels of typical faults are just derived in this section.Among these faults models mentioned above, COMF andCOLF are relevant to the specific control model of the UAVformation. More simulation, verification and analysis aboutthese two faults will be proposed in future research which willnot be included in this paper.

3. Results and Discussion

A four-UAV formation is taken as an instance to analyze thedynamics and estimate different types of faults in this part.The both-way communication topology for the UAV forma-tion is shown in Figure 8.

The connection adjacency matrix and the Laplacianmatrix are shown as

Γ =

0 1 1 01 0 1 11 1 0 10 1 1 0

2666664

3777775, L =2 −1 −1 0−1 3 −1 −1−1 −1 3 −10 −1 −1 2

2666664

3777775: ð28Þ

The coefficient matrixes in (3) are illustrated as

A =

‐3:5 7:0 0:0 ‐3:5

3:5 ‐7:0 3:5 0:0

0:0 3:5 ‐3:5 0:0

3:5 0:0 3:5 ‐3:5

26666664

37777775, C =

7:0 3:5 0:0 ‐7:0

3:5 1:75 0:0 3:5

0:0 0:0 0:0 3:5

2666437775,

E =

3:5

3:5

3:5

3:5

26666664

37777775, F =

3:5

‐7:0

3:5

0:0

26666664

37777775, B =

0:0

3:5

3:5

3:5

26666664

37777775:

ð29Þ

The gain matrixes for the intermediate observer, whichare calculated by the LMI solver, can be shown as

K1 =

‐11:9224 5:4709 19:508051:1084 38:2448 ‐53:4466‐17:5233 71:1116 ‐29:4173‐8:3095 20:6574 4:8709

2666664

3777775,

K2 =

‐1:4625 2:9249 ‐5:84993:8633 ‐7:7266 15:45320:3167 ‐0:6337 1:2671‐0:3082 0:6163 ‐1:2326

2666664

3777775,

K3 = 73:3798 ‐3:6015 ‐50:7336½ �,K4 = 4:7801 ‐9:5604 19:1207½ �: ð30Þ

Fault simulation conditions are shown in Table 1.The components’ damages are assumed as a disturbance

for the nodes in the formation. And formation UCD can beproposed as

dDL tð Þ = dDFi tð Þ = 0:5e−3/trand −2, 2½ �, i = 1, 2, 3: ð31Þ

Table 1: Fault injected strategy.

Fault type AF UCD EE

Leader f L =0, t ∈ 0, 20½ Þ0:5 cos t, t ∈ 20,+∞½ Þ

(dDL tð Þ dwL tð Þ

Follower 1 f F1 =0, t ∈ 0, 10½ Þ2:0, t ∈ 10,+∞½ Þ

(dDF1 tð Þ dwF1 tð Þ

Follower 2 No faults dDF2 tð Þ dwF1 tð Þ

Follower 3 f F3 =0, t ∈ 0, 20½ Þ−2e ‐0:2tð Þ, t ∈ 20,+∞½ Þ

(dDF3 tð Þ dwF1 tð Þ

Table 2: Basic parameters.

Parameters Unit Value

Constant wind speed m/s Vconst = rand −2, 2½ �Maximum static wind m/s Vs max = rand −5, 5½ �Maximum dynamic wind m/s Vd max = rand −15, 15½ �Wind speed increase time s t0 = 5Wind speed decrease time s t1 = 30Wind speed disappear time s t2 = 400Scale factor of PNG — N = 3:0Estimation error weight — ρ1 = 0:5, ρ2 = 0:5Observer parameter — μ = 1:2

Follower 2

Follower 1 Leader

Follower 3

Figure 8: UAV formation both-way communication topology.


500 100 150 200 250 300 350 400

Flight time (s)

–0.6

–0.3

0

0.3

0.6

Long

itudi

nal v

eloc

ity (m

/s)

Leader

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–5

–4

–3

–2

–1

0

1

Long

itudi

nal v

eloc

ity (m

/s)

Follower 1

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.5

–0.25

0

0.25

0.5

Long

itudi

nal v

eloc

ity (m

/s)

Follower 2

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–4

–3

–2

–1

0

1

Long

itudi

nal v

eloc

ity (m

/s)

Follower 3

StateEstimation

Figure 10: The system longitudinal velocity and estimation.

500 500100 150 200 250 300 350 400

Flight time (s)

–0.6

–0.4

–0.2

0

0.2

0.4

0.6H

oriz

onta

l vel

ocity

(m/s

)Leader

StateEstimation

100 150 200 250 300 350 400

Flight time (s)

–3

–2.5

–2

–1.5

–1

–0.5

0

0.5

Hor

izon

tal v

eloc

ity (m

/s)

Follower 1

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.3

–0.2

–0.1

0

0.1

0.2

0.3

Hor

izon

tal v

eloc

ity (m

/s)

Follower 2

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–2

–1.5

–1

–0.5

0

0.5

Hor

izon

tal v

eloc

ity (m

/s)

Follower 3

StateEstimation

Figure 9: The system horizontal velocity and estimation.


500 100 150 200 250 300 350 400

Flight time (s)

–0.6

–0.4

–0.2

0

0.2

0.4

0.6Pi

tch

angl

e vel

ocity

(rad

/s)

Leader

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–2

–1.5

–1

–0.5

0

0.5

1

Pitc

h an

gle v

eloc

ity (r

ad/s

)

Follower 1

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.4

–0.2

0

0.2

0.4

Pitc

h an

gle v

eloc

ity (r

ad/s

)

Follower 2

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–2

–1.5

–1

–0.5

0

0.5

1

Pitc

h an

gle v

eloc

ity (r

ad/s

)

Follower 3

StateEstimation

Figure 11: The system pitch angle velocity and estimation.

500 100 150 200 250 300 350 400

Flight time (s)

–1

–0.5

0

0.5

1

Pitc

h an

gle (

rad)

Leader

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–5

–4

–3

–2

–1

0

1

Pitc

h an

gle (

rad)

Follower 1

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.5

–0.25

0

0.25

0.5

Pitc

h an

gle (

rad)

Follower 2

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–4

–3

–2

–1

0

1

Pitc

h an

gle (

rad)

Follower 3

StateEstimation

Figure 12: The system pitch angle and estimation.


500 100 150 200 250 300 350 400

Flight time (s)

–30

–20

–10

0

10

20

30

40D

istur

banc

es

Disturbances without windDisturbances with wind

Figure 13: The disturbance comparison for the situations with or without wind.

500 100 150 200 250 300 350 400

Flight time (s)

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

Faul

t (–)

Leader

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.5

0

0.5

1

1.5

2

2.5

Faul

t (–)

Follower 1

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.06

–0.04

–0.02

0

0.02

0.04

0.06

Faul

t (–)

Follower 2

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.5

0

0.5

1

1.5

2

Faul

t (–)

Follower 3

StateEstimation

Figure 14: The faults and estimations for the UAV formation (without wind).


500 100 150 200 250 300 350 400

Flight time (s)

–1.5

–1

–0.5

0

0.5

1

1.5Fa

ult (

–)

Leader

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.5

0

0.5

1

1.5

2

2.5

Faul

t (–)

Follower 1

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

Faul

t (–)

Follower 2

StateEstimation

500 100 150 200 250 300 350 400

Flight time (s)

–0.5

0

0.5

1

1.5

2

2.5

Faul

t (–)

Follower 3

StateEstimation

Figure 15: The faults and estimations for the UAV formation (with wind).

500 100 150 200 250 300 350 400

Flight time (s)

–1

–0.5

0

0.5

1

Faul

t esti

mat

ion

erro

r

Leader

Without windWith wind

500 100 150 200 250 300 350 400

Flight time (s)

–0.5

0

0.5

1

1.5

2

Faul

t esti

mat

ion

erro

r

Follower 1


500 100 150 200 250 300 350 400

Flight time (s)

–0.6

–0.4

–0.2

0

0.2

0.4

0.6

Faul

t esti

mat

ion

erro

r

Follower 2


500 100 150 200 250 300 350 400

Flight time (s)

–1

–0.5

0

0.5

1

1.5

Faul

t esti

mat

ion

erro

r

Follower 3


Figure 16: The fault estimation error comparison for the situations with or without wind.


500 100 150 200 250 300 350 400

Flight time (s)

–7

–6

–5

–4

–3

–2

–1

0

1

2Co

ntro

l inp

ut (m

/s2 )

LeaderFollower 1

Follower 2Follower 3

Figure 17: The control inputs for the UAV formation (without wind).

500 100 150 200 250 300 350 400

Flight time (s)

–14

–12

–10

–8

–6

–4

–2

0

2

4

6

Cont

rol i

nput

(m/s

2 )

LeaderFollower 1

Follower 2Follower 3

Figure 18: The control inputs for the UAV formation (with wind).


The wind disturbance model is

dwL tð Þ = dwFi tð Þ =Vs tð Þ + Vd tð Þ, i = 1, 2, 3: ð32Þ

The basic parameters for the simulation are illustrated inTable 2.

Figures 9–12 (without wind disturbance) illustrate thesystem states and estimations for leaders and followers 1-3,respectively. As shown in these Figures, the states changedramatically after the faults appearing. For the leader, theactuator fault arises at t = 20 s, and the states change matcheswith the cosine curve basically. This fulfills the set of the AFfault model in Table 1. For the followers 1 and 3, the curvesof states and estimation also meet the fault injected strategy.There is no AF fault that happened to follower 2, and thestates and estimations results are just affected by thedisturbances.

Figure 13 proposes the value comparison of disturbancesfor the EE fault situation (wind consideration). The ampli-tude ratio between with and without wind situations is upto a maximum of 60.99. In order to verify the influences ofwind disturbances, the results of fault estimation are com-pared in Figures 14 and 15. In contrast to Figure 14, it showsobvious estimation errors increase in Figure 15. As the curvesshown in Figure 16, take follower 1 as an example, the max-imum average fault estimation errors of the system rise from0.26% (without wind) to 0.51% (with wind).

From the comparison between Figures 17 and 18, it pro-poses that the wind disturbance aggravates the control inputsof the UAV formation. In Figure 17, the control inputs changegently, and the maximum amplitude is below 7m/s2. Due tothe injected fault, leader and followers 1 and 3 need the PNGcontroller to be acting more to make the system stabler. Oncethe wind disturbance has been added into the system simula-tion, a rapid and high-frequency control signal emerged aswhat is shown in Figure 18. With the linear superposition offaults and disturbances, the maximum amplitude of controlinput exceeds 12m/s2, and it costs a longer time (nearly 150second) for the controller convergence.

4. Conclusions

The fault estimation and dynamic analysis for the leader-follower UAV formation with typical faults were discussedin this paper. The kinematic model of leader and followerwas built, and the PNG control model was adopted. Mean-while, the linearized form of the system state equations wasalso represented in Section 2. To estimate the system statesand faults, an intermediate observer-based estimator hadbeen adopted for the UAV formation in Section 3. In thispart, the connection relationship based on graph theorywas proposed as the adjacency matrix of graphs and a sym-metric Laplacian matrix. Next, it illustrated the intermediateestimator model and the estimation errors. In Section 4, thetypical faults models were proposed with the basic concept,normal solution, and physical model. With the institutionof the fault-tolerant strategy, five familiar faults models werediscussed and derived according to the considerations offault estimation, disturbances, control strategy, and dynami-

cal analysis. According to the simulation results, the maintypical fault estimation and dynamic characteristics of theUAV formation were accomplished. Moreover, it inspectedthe performance of the estimator and controller with two sit-uations related to the wind disturbance. And the resultsshowed that the fault estimation and dynamic control modelwere applicable for the UAV formation system.

In the real flight environment, faults and disturbance fac-tors may arise at any time. As a result, the typical fault toler-ance should be considered seriously in the fault-tolerantcontrol design for the UAV formation. Additionally, for thesake of meeting the dynamic analysis needs, the model uncer-tainty, control output perturbation, time-lags effect, and non-linear model ought to be thought during the modeling of theformation coordinated control strategy. Finally, multifaultcoupling, mixed estimation method, and multiestimators willbe the important works in the UAV formation prognosticand health management field.

Data Availability

Hindawi research data policy request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China [grant numbers 62003314, 51909245],Aeronautical Science Foundation of China [grant number2019020U0002], Shanxi Province Applied Basic ResearchProject [grant numbers 201901D211244, 201801D221039],Scientific and Technological Innovation Programs of HigherEducation Institutions in Shanxi [grant number 2019L0570],Youth Science and Technology Research Fund, and ScienceFoundation of North University of China [grant numberXJJ201813].

References

[1] Y. Dong, Research on Fault Diagnosis for UAVs formation Sys-tems Based on Observer [M.S. thesis], Colg. Auto. Eng., NanjingUniv., of Aero., Astro., ], 2018.

[2] X. Lin and X. Yao, “Improved disturbance-observer-basedfault-tolerant control for the linear system subject to unknownactuator faults and multiple disturbances,” International Jour-nal of Control, vol. 93, no. 10, pp. 1–11, 2020.

[3] T. H. Lee, C. P. Lim, S. Nahavandi, and R. G. Roberts,“Observer-based H∞ fault-tolerant control for linear systemswith sensor and actuator faults,” IEEE Systems Journal,vol. 13, no. 2, pp. 1981–1990, 2019.

[4] C. Liu, B. Jiang, and K. Zhang, “Sliding mode observer-basedactuator fault detection for a class of linear uncertain systems,”in Proceedings of 2014 IEEE Chinese Guidance, Navigation andControl Conference, pp. 230–234, Yantai, China, 2014.

[5] A. N. Hanafi, M. M. Seron, and J. A. De Doná, “Observer–based fault tolerant control for a class of lure nonlinear sys-tems,” in 2019 IEEE International Conference on Automatic


Control and Intelligent Systems (I2CACIS), pp. 179–184,Selangor, Malaysia, 2019.

[6] L. Negash, S. Kim, and H. Choi, “Distributed observes forcyberattack detection and isolation in formation-flyingunmanned aerial vehicles,” Journal of Aerospace InformationSystems, vol. 14, no. 10, pp. 551–565, 2017.

[7] L. Yin, J. Liu, P. Yang, and J. Shi, “Sliding mode observer-basedactive fault tolerant control for UAVs formation,” IOP Confer-ence Series: Materials Science and Engineering, vol. 452, 2018.

[8] A. Cristofaro and T. A. Johansen, “An unknown inputobserver based control allocation scheme for icing diagnosisand accommodation in overactuated UAVs,” in 2016 Euro-pean Control Conference (ECC), pp. 2171–2178, Aalborg, Den-mark, 2016.

[9] D. Rotondo, A. Cristofaro, T. Johansen, F. Nejjari, and V. Puig,“Diagnosis of icing and actuator faults in UAVs using LPVunknown input observers,” Journal of Intelligent & RoboticSystems, vol. 91, no. 3-4, pp. 651–665, 2018.

[10] A. Abbaspour, P. Aboutalebi, K. K. Yen, and A. Sargolzaei,“Neural adaptive observer-based sensor and actuator faultdetection in nonlinear systems: application in UAV,” ISATransactions, vol. 67, pp. 317–329, 2017.

[11] Y. Liang, Q. Dong, and Y. Zhao, “Adaptive leader-followerformation control for swarms of unmanned aerial vehicleswith motion constraints and unknown disturbances,” Chi-nese Journal of Aeronautics, vol. 33, no. 11, pp. 2972–2988,2020.

[12] X. Wang, Y. Yu, and Z. Li, “Distributed sliding mode controlfor leader-follower formation flight of fixed-wing unmannedaerial vehicles subject to velocity constraints,” InternationalJournal of Robust and Nonlinear Control, vol. 31, no. 6,pp. 2110–2125, 2021.

[13] X. Liu, J. Han, and X. Wei, “Intermediate observer based dis-tributed fault estimation for multi-agent systems,” Acta Auto-matica Sinica, vol. 46, no. 1, pp. 142–152, 2020.

[14] B. Jiang, P. Shi, and K. Zhang, “Fast fault estimation andaccommodation for dynamical systems,” IET Control Theory& Applications, vol. 3, no. 2, pp. 189–199, 2009.

[15] K. Zhang, B. Jiang, and A. Shumsky, “A new criterion of faultestimation for neutral delay systems using adaptive observer,”Acta Automatica Sinica, vol. 35, no. 1, pp. 85–91, 2009.

[16] J. Zhu, G. Yang, H.Wang, and F. Wang, “Fault estimation for aclass of nonlinear systems based on intermediate estimator,”IEEE Transactions on Automatic Control, vol. 61, no. 9,pp. 2518–2524, 2016.

[17] J. Zhu and G. Yang, “Robust distributed fault estimation for anetwork of dynamical systems,” IEEE Transactions on Controlof Network Systems, vol. 5, no. 1, pp. 14–22, 2018.

[18] J. Shen, X.Wang, Q. Liu, J. Yu, G. Chen, and X. Tian, “Analysisof time coordinated guidance control for leader-follower smartammunition formation,” in 2020 3rd International Conferenceon Unmanned Systems (ICUS), pp. 214–219, Harbin, China,2020.

[19] J. Zhang, A. K. Swain, and S. K. Nguang, “Robust sensor faultestimation scheme for satellite attitude control systems,” Jour-nal of the Franklin Institute, vol. 350, no. 9, pp. 2581–2604,2013.

[20] C. A. Rabbath and N. Léchevin, Safety and Reliability in Coop-erating Unmmaned Aerial Systems, World Scientific Publish-ing Co. Pte. Ltd., Singapore, 2010.

[21] M. Guiatni, H. Saidani, and Y. Bouzid, “Fault tolerant controldesign for actuator loss of effectiveness in quadrotor Uavs,” in2019 International Russian Automation Conference (RusAuto-Con), pp. 1–7, Sochi, Russia, 2019.

[22] M. I. Momtaz and A. Chatterjee, “Hierarchical state spacechecks for errors in sensors, actuators and control of nonlinearsystems: diagnosis and compensation,” in 2019 IEEE 28thAsian Test Symposium (ATS), pp. 141–1415, Kolkata, India,2019.

[23] O. Prakash, A. K. Samantaray, and R. Bhattacharyya, “Model-based diagnosis of multiple faults in hybrid dynamical systemswith dynamically updated parameters,” IEEE Transactions onSystems, Man, and Cybernetics: Systems, vol. 49, no. 6,pp. 1053–1072, 2019.

[24] M. Qian, B. Jiang, and H. H. Liu, “Dynamic surface active faulttolerant control design for the attitude control systems of UAVwith actuator fault,” International Journal of Control, Automa-tion and Systems, vol. 14, no. 3, pp. 723–732, 2016.

[25] Z. Yu, Y. Qu, and Y. Zhang, “Distributed fault-tolerant cooper-ative control for multi-UAVs under actuator fault and inputsaturation,” IEEE Transactions on Control Systems Technology,vol. 27, no. 6, pp. 2417–2429, 2019.

[26] Y. Xiao, Y. Fu, C. Wu, and P. Shao, “Modified model referenceadaptive control of UAV with wing damage,” in 2016 2ndInternational Conference on Control, Automation and Robotics(ICCAR), pp. 189–193, Hong Kong, China, 2016.

[27] B. Fan, X. Zhang, B. Tian, and L. Guo, “Fault-tolerant controlfor unmanned aerial vehicle with wing damaged,” in IECON2017-43rd Annual Conference of the IEEE Industrial Electron-ics Society, pp. 3191–3196, Beijing, China, 2017.

[28] P. B. Sujit and J. B. Sousa, “Multi-UAV task allocation withcommunication faults,” in 2012 American Control Conference(ACC), pp. 3724–3729, Montreal, QC, Canada, 2012.

[29] M. Labbadi and M. Cherkaoui, “Robust integral terminal slid-ing mode control for quadrotor UAV with external distur-bances,” International Journal of Aerospace Engineering,vol. 2019, Article ID 2016416, 10 pages, 2019.

[30] F. F. Khan, T. Samira, A. Jana, and K. N. E. Alam Siddiquee,“Performance of agro-sensors: Assessment of optimality inrouting protocols of MANET in wireless sensor networks,” in2016 International Conference on Intelligent Control Powerand Instrumentation (ICICPI), pp. 98–102, Kolkata, 2016.

[31] H. Kim and J. Ben-Othman, “A collision-free surveillance sys-tem using smart UAVs in multi domain IoT,” IEEE Communi-cations Letters, vol. 22, no. 12, pp. 2587–2590, 2018.

[32] J. Ghommam, L. F. Luque-Vega, andM. Saad, “Distance-basedformation control for quadrotors with collision avoidance viaLyapunov barrier functions,” International Journal of Aero-space Engineering, vol. 2020, Article ID 2069631, 17 pages,2020.

[33] D. Wang, T. Fan, T. Han, and J. Pan, “A two-stage reinforce-ment learning approach for multi-UAV collision avoidanceunder imperfect sensing,” IEEE Robotics and Automation Let-ters, vol. 5, no. 2, pp. 3098–3105, 2020.

[34] H. Tanner and D. Christodoulakis, “Decentralized cooperativecontrol of heterogeneous vehicle groups,” Robotics and Auton-omous Systems, vol. 55, no. 11, pp. 811–823, 2007.

[35] G. Ducard and H. P. Geering, “Efficient nonlinear actuatorfault detection and isolation system for unmanned aerial vehi-cles,” Journal of Guidance, Control, and Dynamics, vol. 31,no. 1, pp. 225–237, 2008.


[36] X. Cheng, C. Dong, G. H. Chen, W. J. Wang, and H. P. Dai,“Communication and networking techniques for formationcontrol in UAV ad hoc networks,” Computer Science, vol. 45,no. 11, pp. 1–12, 2018.

[37] R. Abdallah, R. Kouta, C. Sarraf, J. Gaber, and M.Wack, “Faulttree analysis for the communication of a fleet formation flightof UAVs,” in 2017 2nd International Conference on SystemReliability and Safety (ICSRS), pp. 202–206, Milan, Italy, 2017.

[38] J. Longting, W. Ruixuan, Z. Qirui, and W. Dong, “Anti-colli-sion control of UAVs based on swarm intelligence mecha-nism,” Acta Aeronautica et Astronautica Sinica, vol. 41,article 724291, Supplement 2, 2020.

[39] M. Khalid, “Crosswise wind shear represented as a rampedvelocity profile impacting a forward-moving aircraft,” Interna-tional Journal of Aerospace Engineering, vol. 2019, Article ID7594737, 18 pages, 2019.


typical fault estimation and dynamic analysis of a leader ...system. based on the fault-tolerant...

Documents