The control design for formation flight about multiple Unmanned Aerial Vehicles.docx

1、The control design for formation flight about multiple Unmanned Aerial VehiclesAbstract: The control design for formation flight about multiple Unmanned Aerial Vehicles (UAVs) is a highly complex question because of the harsh requirements imposed by many kinds of tasks. The problem is about to desig

2、n a formation-hold autopilot for the follower UAVs ,as a result the positions between the leader and the followers can be designed close to the desired value. In this paper, we first give a Receding Horizon Control (RHC) scheme which makes the UAVs formation problem to a sequence of online optimizat

3、ion problems over a planning horizon. We next raised a novel Chemical Reaction Optimization (CRO) approach to seek optimal control inputs for the follower UAVs to keep coordinated flight with the minimum input cost in all of the planning horizons. Several experimental comparison results are given to

4、 show the feasibility and effectiveness of our proposed control method.Keywords: Unmanned Aerial Vehicles (UAVs); Formation Flight;Chemical Reaction OptimizationI. IntroductionModeling and control of formation flight of multiple UAVs is an growing topic of research in the aerospace field, and has a

5、number of applications in military missions such as reconnaissance and surveillance, task allocation and target data acquisition, radio jamming, and the suppressions of enemy air defense as well as in civilian missions such as crop monitoring, area search and rescue . The multiple UAVs formation fli

6、ght problem aims to achieve desired geometries by controlling the overall behavior of the group. Accurate maintenance of the formation can often accomplish objectives impossible for a single UAV and lead to certain advantages such as a reduction in the formations induced drag and energy saving from

7、vortex force created by the lead aircraft . Development of formation control problems and numerous approaches for UAVs formation control design have been well demonstrated. In Ref, R. Sattigeri et al. proposed a decentralized adaptive output feedback approach which allowed the vehicles to maintain t

8、he formation while considering obstacles. In Ref , W. Ren et al. developed a leaderless formation control scheme based on consensus algorithms which overcome a single point of failure for the formation. In Ref, D. Galzi et al. proposed High Order Sliding Mode (HOSM) controller for a swarm of UAVs to

9、 achieve leader/followers collision-free formation in the presence of unknown disturbances. In Ref , Masayuki Suzuki et al. designed a three-dimensional formation control scheme using the new approach of bifurcating artificial potential fields. In Ref, Yunfei Zou and Prabhakar R. Pagilla used the th

10、eory of constraint forces to determine the total force required on every aircraft to build a formation from arbitrary initial conditions for UAVs. But these methods may not be able to deal with the constraints easily, such as the acceleration of velocity and angular turn rate constraints, and contro

11、l input saturation constraints . Optimization-based approaches can solve the constraints of UAV formation control systems appropriately and have been proved to a successful way to the multiple UAVs formation problems. Among the most popular optimization-based methods is RHC method.II. Problem Formul

12、ation 2.1 Model of UAV flight dynamics and control systemsThe equations of motion describing UAV flight dynamics are given as follows 23,24:Force equations: (1)Kinematic equations: (2)Moment equations: (3)Navigation equations: (4)In this paper, we reduced the complex model to a simpler model for the

13、 purpose of guidance law design. Accordingly, first-order systems are adopted to represent two control channels including the UAV flight dynamics as follows: (speed control channel) (5) (heading angle control channel) (6)Where are the time constants and are the control command input of each control

14、loop. 2.2 Receding Horizon Control Receding horizon control (RHC), also known as model predictive control (MPC), is a feedback control scheme in which a finite horizon open-loop optimization problem is solved at each sampling instant 25, 26.The RHC procedure works as shown in Fig. 1. At time t, we c

15、onsider a time interval extending p steps into the future, t, t+1, , t+p. We then carry out the following steps:(1) Replace all the uncertain quantities over the prediction horizon p with their estimates using the information available at time t to predict the future dynamic behavior of the system.(

16、2) Optimize a predetermined performance objective function subject to the estimated dynamics and constraints. The optimization result is a plan of action for the next p steps.(3) Determine the input over a control horizon m using the plan of action. At the next time step, the process is repeated, wi

17、th the updated estimates of the current state and future quantities.Fig. 1 Procedure of Receding Horizon Control2.3 Leader-follower formation flight modelIn this paper, we mainly focus on multiple UAVs formation problem on a horizontal plane. The horizontal formation geometric parameters are the for

18、ward clearance and the lateral clearance, as defined in Fig.2. The reference position for the follower UAV can be calculated using the following relationship: (7)where represent the followers desired position, and represent the position and the heading angle of the leader UAV.and are expressed as: (

19、8) (9)Fig. 2 Horizontal Formation Geometry We formulate a receding horizon control scheme based on the cost function. At time k, the controller predicts a control sequence from time k to time (k+p), which can be represented by, , . Using this control sequence and the current state of the system, the

20、 state at time k+1, k+p, which are represented by, , can be obtained. The fitness function at time k can be defined as: (10)subject to (11)where Q and R are positive-definite weighted matrices. is reference state of follower UAVs at time k. is the state of follower UAVs at time k+j over the predicti

21、on horizon. is the sampling time. Fig. 3 Receding Horizon Control Scheme Minimizing this fitness function yields an optimal control sequence, then the first m control actions in this sequence is applied to the formation flight system. At time k+m, repeat sampling, predicting, optimization and implem

22、enting. This procedure can be described as Fig.3.III. Principles of the basic CRO algorithmChemical Reaction Optimization (CRO) is a recently established metaheuristics for optimization, inspired by the nature of chemical reactions. In microscopic view, a chemical reaction starts with some unstable

23、molecules with excessive energy. The molecules interact with each other thro- ugh a sequence of elementary reactions. At the end, they are converted to those with minimum energy to support their existence. This property is embedded in CRO to solve optimization problems.In general, the principles of

24、chemical reactions are governed by the first two laws of thermodynamics. The first law (conservation of energy) says that energy cannot be created or destroyed; energy can transform from one form to another and transfer from one entity to another. The second law says that the entropy of a system ten

25、ds to increase, where entropy is the measure of the degree of disorder. Potential energy is the energy stored in a molecule with respect to its molecular configuration. When it is converted to other forms, the system becomes more disordered. All reacting systems tend to reach the state of equilibriu

26、m , whose potential energy drops to a minimum. In CRO, we capture the phenomenon by converting potential energy to kinetic energy and by gradually losing the energy of the chemical molecules to the surroundings. 3.1 The manipulated agent CRO is a multi-agent algorithm and the manipulated agents are

27、molecules. Each molecule has several attributes, some of which are essential to the basic operations of CRO. The essential attributes include: the molecular structure (); the potential energy (PE); the kinetic energy (KE); the number of hits (NumHit); the minimum structure (Min-Struct); the minimum

28、PE (MinPE); and the minimum hit number (MinHit).3.2 Elementary reactionsA chemical change of a molecule is triggered by a collision. There are two types of collisions: uni-molecular and inter-molecular collisions. We consider four kinds of elementary reactions: on-wall ineffective collision , decomp

29、osition, inter-molecular ineffective collision, and synthesis. The two ineffective collisions implement local search(intensification) while decomposition and synthesis give the effect of diversification. An appropriate mixture of intensification and diversification makes an effective search of the g

30、lobal minimum in the solution space.3.2.1 On-wall Ineffective Collision An on-wall ineffective collision occurs when a molecule hits the wall and then bounces back. Some molecular attributes change in this collision, and thus, the molecular structure varies accordingly. As the collision is not so vi

31、gorous, the resultant molecular structure should not be too different from the original one. Suppose the current molecular structure is .The molecule intends to obtain a new structure = Neighbor() in its neighborhood on the PES in this collision. The change is allowed only ifPE + KE PEWe getKE= (PE

32、+ KE PE) qwhere q KELossRate ,1, and (1 q) represents the fraction of KE lost to the environment when it hits the wall. KELossRate is a system parameter which limits the maximum percentage of KE lost at a time. The lost energy is stored in the central energy buffer. The stored energy can be used to support decomposition. If it does not hold, the change is prohibited and the molecule retains its original , PE and KE.3.2.2 Decomposition Decomposition r