Cooperative Control for UAV Formation FlightBased on Decentralized Consensus Algorithm*Yaohong Qu1, Xu Zhu1, and Youmin M. Zhang21 School of Automation, Northwestern Polytechnical University, Xi’an, 710129, China2 Department of Mechanical and Industrial Engineering,Concordia University, Montreal, H3G 2W1, CanadaAbstract. Decentralized consensus algorithm is suggested to maintain aspecified formation configuration of multiple Unmanned Aerial Vehicles(UAVs). As no explicit leader exists in the team, only the localneighbor-to-neighbor information between vehicles is needed for the proposedcontrol strategy. Position of the virtual leader and attitude of each UAV is theconvergence state variable chosen for the algorithm. Communication limits andmeasurement errors are also considered to improve robustness. Besides, themotion synchronization technology is incorporated to achieve coordinatedcontrol of the UAVs, such that coupled relative position errors are used tocalculate the trajectory modification. Finally, conclusion is conducted based onthe testing results with simulation examples.Keywords: Unmanned Aerial Vehicle (UAV), formation control, decentralizedconsensus, synchronization technology.1IntroductionFormation flight control of multiple Unmanned Aerial Vehicles has been an active topic in recent years[1-5] since it promises many practical applications, such as reconnaissance, surveillance, atmospheric study, communication relaying and search and rescue. Some of these tasks may be dangerous and will not be recommended for human pilots, thus making them ideal for autonomous unmanned vehicles.Recently, there are many research methods suggested on multiple UAVs control, such as leader following[6], behavior based approach[7], virtual leader[8] and artificial potential function[9]. In these methods, virtual leader is much reliable in modern war. Comparing with the traditional real leader, the virtual one can be never destroyed in physics. Moreover, there is a big problem in formation control that how to make full use of neighbor-to-neighbor information communication. Because using the information could improve synchronization of the entire formation. In the virtual leader approach used in this paper, decentralized consensus is induced to the entire formation is treated as a single entity. It can evolve as a rigid body in a given direction with some*T his work is supported by the National Natural Sciences Foundation (NNSF) of China under Grant 60974146.C.-Y. Su, S. Rakheja, H. Liu (Eds.): ICIRA 2012, Part I, LNAI 7506, pp. 357–366, 2012.© Springer-Verlag Berlin Heidelberg 2012358 Y. Qu, X. Zhu, and Y.M. Zhanggiven orientation and maintain the geometric relationship among multiple vehicles base on a reference point in the virtual leader structure. For more specific formation flight problem of aircraft, a consensus is that the vehicles should be able to achieve tracking for given velocity, heading, and altitude commands[9,10] in order for a formation controller to be developed for the aircraft. An autopilot model that provides tracking capabilities for the three commands and the method of trajectory command modifications based on relative position errors is used as part of the control algorithm in this note. This method is coupled with the virtual leader approach to achieve formation flights for research.This paper is outlined as follows. In Section 2, the virtual leader structure is defined followed by distributed consensus formation algorithm. In Section 3, communication limits is analyzed and the synchronization technology is incorporated into the controller to suppress measurement errors. Simulation results on formation control of multiple flying wings are given in Section 4. At last, Section 5 offers conclusions and future research possibilities.2 Formation Control for UAVSConsider the formation of n identical UAVS, and each is denoted by i U . They constitute of a graph },{E V G =, where },,2,1{n V = is the set of nodes.V V E ×⊆ is the set of edges, and an edge of the graph G is denoted by ),(j i e ij =,i.e., ij e is a directed edge from i to j . The set of neighbors for node i is denoted by }),(:{E j i V j N i ∈∈=. i U does not send information to i N j ∈. Therefore i N is endowed with a neighboring unidirectional relation. That is, when i N j ∈, a directed edge ),(i j exists such that i j →, which means that sensory data comprised of position and velocity for j flowing from j to i .Fig. 1. Virtual leader structureFormation stabilization obtained with the controller presented in the next section is guaranteed under the assumption that G is a connected digraph. The formation geometry is defined by prescribed line-of-sight angle and relative distance between iCooperative Control for UAV Formation Flight359and j that are communicated from one node to another according to the graph. For brevity, morphing of the formation is not considered here; that is, relative distances are assumed time invariant. Finally, the formation comprises a virtual leader vehicle, which tracks a certain reference trajectory xyz I .Assumption 1. UAV formation is kept in a fixed geometry during the whole flight envelope, and each team member does not change its relative position in formation with time.Vehicle positions are attained with respect to an inertial frame xyz I . Each agent UAV isa rigid body with inertial position i ρ, which is constructed by three dimensions.T i i i i z y x ),,(=ρ(1)Velocity and heading angle of i U can be represented as i V and i ψ, respectively.Fig. 2. Virtual leader generated by i UThe virtual leader is defined as F U with initial position iF ρ, which is generated byeach UAV. In the autonomous cooperation, virtual leader is generated by each UAV. d iF ρ is desired distance from i U to the virtual leader. If each desired distance is given, the team geometry is identified to keep formation maneuvering. Figure 2 shows therelation of ∈+−+−=iNj d jFj d iFi ij xi x x x x a e )]()[(**, iF ρ and d iF ρ considered in this study.diF i iF ρρρ+=(2)Relative distance between UAVS is denoted by i ij N j ∈,ρ.Assume that the formation maintains fixed geometry during flight, and similarly relative desired distancei d ij N j ∈,ρ between UAVS is fixed. The control objective of the team is that d ij ij ρρ→as ∞→t . Navigation equations for each UAV are selected asi i i i i i i i i i i V zV yV xμμμϕμsin sin cos cos cos === (3)360 Y. Qu, X. Zhu, and Y.M. Zhangwhere i μ and i ϕ are flight path angle and azimuth track angle, respectively. If i U obtains information from j U , then kinematics equations is represented as followsi i j j ij i i i j j j ij i i i j j j ij V V zV V yV V xμμϕμϕμϕμϕμsin sin sin cos sin cos cos cos cos cos +−=−=−= (4)It can be easily seen that the position T i i i i z y x ],,[=ρ is adjusted by trajectory commands T i i i i V T ],,[μϕ=. In order to control the distance between UAVs, thecontrol law of i i i V μϕ,, is designed to realize cooperation.2.1Distributed Consensus Formation Control AlgorithmDistributed consensus algorithm is a new control method with complete autonomy, which casts off dependence of ground station and all team members take participation in decision-making. Consensus algorithm needs common variables to achieve synchronization. F ρ is the common variable. In the consensus algorithm, iF ρ represents the position of virtual leader generated by each UAV, which is different at the beginning. As time going on, consensus algorithm makes jF iF ρρ→ as ∞→t . Specific control laws are designed as follows.∑∑∑∈∈∈−+−+−=−+−+−=−+−+−=ii iN j ij d jFj d iF i ij zi N j ij d jFj d iF i ij yi N j ij d jF j d iF i ij xi z z z z z a V y y y y y a V x x x x x a V ])()[(])()[(])()[( γγγ (5)where γ is a positive constant, and ij a is determined by the Laplacian graph. Letd iF i iF x x x +=, d iF i iF y y y += and diF i iF z z z +=, where T iF iF iF iF z y x ),,(=ρ. Therefore,the control algorithm of i Vis obtained thatxi xi yi yi zi ziiiV V V V V V V V ++′== (6)where i V is a second consensus algorithm consists of both position information and velocity information. In the design of attitude control, first consensus is capable ofsynchronization.∑∈−−=iN j j i ij i a )(ϕϕϕ(7)∑∈−−=iN j j i ij i a )(μμμ(8)Cooperative Control for UAV Formation Flight361The objective of consensus algorithm is to guarantee that j i V V →, j i ϕϕ→,j i ϕϕ→, as ∞→t , which means that the formation fight can be realized. The Laplace matrix of digraph G is defined asj i a l and a l l L ij ij N j ij ii ij i≠∀−===∑∈,],[(9)and Lis a positive definite matrix. Let TnF F F F x x x X ],,,[21 =, T nF F F F y y y Y ],,,[21 =,TnF F F F z z z Z ],,,[21 =,Tn V V V V ],,,[21 =,T n ],,,[21ϕϕϕϕ =, and T n ],,,[21μμμμ =.Then, the control algorithm (5), (7) and (8) change into();();()x F y F z FV L X X V L Y Y V L Z Z γγγ=−+=−+=−+ (10)ϕϕL −= (11)μμL −= (12)(10), (11) and (12) are matrix forms of the distributed consensus algorithm.2.2Flight Path ControlFlight path control is designed to control the trajectory of formation. The desired flightpath angle is defined as d ϕ. All UAVs in the formation aim to follow d ϕ. Such that the control law of i ϕ is modified, which will not only realize synchronization for formation maneuver, but also complete trajectory planning.d ϕ is considered as a reference state in the consensus algorithm, which is the terminal convergence value for all i ϕ. Then, new control law for i ϕ is generated with reference state.)()(d i N j j i ij i ia ϕϕϕϕϕ−−−−=∑∈ (13)2.3 Consensus StabilityEquation (6) is a second-order consensus algorithm, though equation (7) and (8) areboth first-order consensus algorithms. In literature [11], first-order consensus algorithm achieving convergence only needs a directed spanning tree in communication graph. However, if second-order consensus algorithm reach consensus, a directed spanning tree is just a precondition, where γ should be properly chosen as well. Now, γ should be chosen properly such that the control algorithm can reach convergence. It can’t be too small in order to avoid positive poles arising in the system[11]. According to our previous work [12], a sufficient condition is given that the polynomial with362 Y. Qu, X. Zhu, and Y.M. Zhangcoefficient T ]1[γ should be Hurwitz. When communication topology has a directed spanning tree and 1>γ, xi V , yi V and zi V could achieve convergence.It is assured that xj xi V V →, yj yi V V → and zj zi V V → as ∞→t . In another word, 0→xi V , 0→yi V and 0→zi V as ∞→t . Submitting them into (6), it is easy to concluded that 0→iV as ∞→t . Consequently, control algorithm (6) can also achieve convergence at finite time.3Robustness of Control Algorithm3.1Communication TopologyConsidering the measurements from sensors with limited fields of views or random communication data loss, a unidirectional or bidirectional information flow topology can be considered. On account of low cost for miniature UAVs and a spot of airborne communication equipment, bidirectional ring communication topology is chosen to overcome these limits. Figure 3 depicts this communication topology.If there are communication faults between certain UAVs such as bidirectional communication changing into directional one, a directed spanning tree still exists in the topology. Only when bidirectional information flow is both invalid, consensus stability is completely destroyed.Fig. 3. Bidirectional ring communication topology3.2 Synchronization TechnologyAnother objective in this project is to incorporate the motion synchronization technology to achieve coordinated control of the UAVs. Thus, the next step is to apply this technology in the controller.On the influence of navigation and range finding, position data ρ contains measurement errors.***;;i i i i i i i i i x x xy y yz z z =+=+=+ (14)Such that the measurement values ***,,i i i z y x are used to replace the values i i i z y x ,,,where iiiz y x ~,~,~are measurement errors. Substitute (14) into (5) to get thatCooperative Control for UAV Formation Flight363∑∑∑∈∈∈−+−+−=−+−+−=−+−+−=iiiN j ij d jFj d iF i ij zi N j ij d jFj d iF i ij yi N j ij d jFj d iF i ij xi z z z z z a V y y y y y a V x x x x x a V ])()[(])()[(])()[(****** γγγ (15)For simplicity, x channel is chosen to analysis the control algorithm. The strategyuses the cross coupling concept to synchronize the relative position tracking motion ofthe aircraft. It utilizes synchronization errors ∑∈+−+−=iN j d jF j diF i ij xi x x x x a e )]()[(**, which incorporates error information from different UAVs in the system, to identify the performance of synchronization. The cross coupled error *xi e then couples the errori x ~ and synchronization error xi e through a positive synchronization gain i β.xi xi i xi e x e β+=~*(16)The objective of the synchronization strategy is to drive*xi e of each UAV in (16) to 0by choosing the proper gain values, implying that both ix ~and xie are driven to 0 as well. In another word, the team uses information from each other to eliminate theerrors synchronously.The coupled relative position errors from (16) are used to calculate the trajectorymodification *xiV Δ and the new modified trajectory command that will be passed to the controller of the UAVs is *xi xi xi V V V Δ+=, where *xiV Δ is a PID controller. ′++=Δ⎰*0***xi Dx t xiIx xi Px xi e k dt e k e k V (17)where ,,Px Ix Dx k k k are proportional, integral and differential coefficients. The controllers for ,y z channel are designed in the same way. Then, the control law fori V is concludedizi zi yi yi xi xi i V V V V V V V V *++==(18)4 Simulation EvaluationsThe formation flight control system’s response to the virtual leader maneuvers is simulated using nonlinear models of UAVs. Six aircrafts are taken for our simulation, where all UAVs are considered similar. Flight path commands are decided by the virtual leader and performance of the whole formation UAVs are analyzed. Figure 4 shows a communication network which has a directed spanning tree, which consists of six UAVs. An edge from UAV j to UAV i means that UAV i can receive information from UAV j .364 Y. Qu, X. Zhu, and Y.M. ZhangFig. 4. Communication topologySimulations are performed on a maneuver followed by straight line travel for UAVs in a flight formation. An autopilot model developed for a MAGICC lab flying- wing UAV is used in the simulations. All the UAVs have to maintain an equilateral triangular formation, where every three adjacent UAVs constitute a small equilateral triangular with side length of m 4. Besides, they do not fly at an identical altitude. 2Uand 3U maneuver m 4lower than 1U , while 4U , 5U and 6U are m 8lower than 1U . The virtual leader is in the front of 1U with the distance of m 4. However, the team does not start at the desired positions at the beginning of the flight. No collision avoidance algorithm is implemented.The initial position of each UAV are T ]1200,20,30[1=ρ, T ]1195,10,20[2=ρ,T ]1190,0,10[3=ρ, T ]1185,10,0[4−=ρ, T ]1180,20,10[5−−=ρ andT ]1175,30,20[6−−=ρ. Initial flight path angle and azimuth track angle are selected as T ]5,10,5,5,0,5[ −−−=μ and T ]40,20,75,65,0,45[ =ϕ, respectively. There are white Gaussian noises in the measurement of position with mean value of 0 and variance of .5m 0.Formation control is then implemented for the UAVs based on virtual leader approach and trajectory modifications as proposed in Section 3. The setup for the simulation is the same as before and the gains used for the trajectory PID controllers are given in Table 1.Table 1. Control Gains of PID ControllerParameter Value Parameter Value Parameter ValuePx K 5 Ix K 0.5 Dx K0.3 Py K0.005 IyK 0.0005 DyK 0.0003 Pz K 1Iz K 0.005Dz K0.003The synchronization technology in Section 3 is incorporated in the controller. Thesynchronization gains xi β, yi β and zi β for these vehicles are being set to 1. Applying the suggested control law, Figs. 5-7 illustrate the flight path angle, the azimuth track angle and the velocity of the team, which show that each information variable achieves consensus quickly for the bidirectional ring structure.Cooperative Control for UAV Formation Flight365Times (s)u i (d e g )Times (s)ψi (d e g )Fig. 5. Flight path angle of UAVs Fig. 6.Azimuth track angle of UAVsTimes (s)V i (m /s )Fig. 7. Velocity of UAVsTimes (s)x i F (m )Times (s)y i F(m )Fig. 8.x position for F U Fig. 9. y position for F UTimes (s)z i F (m )x (m)z (m )Fig. 10.z position for F U Fig. 11. Trajectory responses of UAVs366 Y. Qu, X. Zhu, and Y.M. Zhangρ states in the first seconds. At the beginning, the virtual leader Figs. 8-10 areiFgenerated by each UAV is at different position. As time goes on, the positions coincide. It can also be seen that disturbances in the measurement of position information can be depressed by the synchronization strategy. Distributed consensus algorithm is still effective with disturbances. The trajectory of the team is depicted as Fig. 11.5ConclusionsA distributed consensus formation control strategy is proposed for multiple UAVs in this paper. In the proposed strategy, neighbor-to-neighbor information communication affects maneuvers of each UAV. To improve the robustness of communication, bidirectional ring topology is chosen to suppress communication limits. Moreover, a synchronized PID controller is suggested to deal with measurement errors. Our future work will focus on formation control with time-varying geometry.References[1]Giulietti, F., Pollini, L., Innocenti, M.: Autonomous formation flight. IEEE ControlSystems Magazine 20(6), 34–44 (2006)[2]Pachter, M., D’Azzo, J.J., Proud, A.W.: Tight formation flight control. 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