A multi-unmanned aerial vehicle formation control method based on switching event triggering technology

Abstract

The application discloses a kind of multi-unmanned aerial vehicle formation control method based on switching event trigger technology, for the convergence speed and control accuracy demand of multi-four rotor unmanned aerial vehicle system under communication constraint condition, based on using local information, the fixed time distributed controller based on switching event trigger strategy is constructed, and the consistent stability of multi-four rotor unmanned aerial vehicle system is analyzed by designing Lyapunov function;Fixed time command filter effectively overcomes the problem of "computational complexity", and the fixed time error compensation mechanism designed can compensate the error of filter within fixed time;Method can guarantee that, under the condition of limited communication resources, the consistent tracking error of multi-four rotor unmanned aerial vehicle system can converge to a small enough neighborhood near the origin within fixed time;The method of the application ensures that multi-four rotor unmanned aerial vehicle system can track the desired signal quickly and effectively within fixed time under the condition of limited communication resources.

Description

TECHNICAL FIELD

[0001] The application relates to multi-quadrotor unmanned aerial vehicle formation control based on switching event-triggered technology, belongs to the technical field of quadrotor unmanned aerial vehicles, and particularly relates to a fixed-time formation control method for expected positions and attitudes of multi-quadrotor unmanned aerial vehicles based on switching event-triggered technology. BACKGROUND

[0002] In recent years, quadrotor unmanned aerial vehicles (QUAVs) have attracted more and more attention from the academic and industrial circles due to low cost, small size, simple structure, vertical take-off and landing and other characteristics, and the practical application scenarios of the QUAVs have gradually expanded, such as building fire fighting, aerial photography, agricultural irrigation and the like. However, the QUAV is a typical multivariable, strongly coupled and highly nonlinear under-actuated system, and is also sensitive to changes in the external environment, so it is of positive significance to design a QUAV system with robustness and fault tolerance in order to ensure flight safety and working efficiency.

[0003] With the increase of the complexity and difficulty of tasks, a single QUAV cannot meet the requirements of the tasks in time and efficiency, and the cooperative control of multiple QUAVs has extremely high research value. However, most of the research work on multiple QUAVs assumes that the QUAVs can continuously obtain the state information of the surrounding QUAVs and apply it to the update of control. This communication mode requires high communication between the QUAVs and achieves the task purpose through continuous control. In order to better utilize the computing resources and communication resources, an event-triggered communication mechanism is used to deal with the control problem of the multi-agent system. The application proposes a multi-quadrotor unmanned aerial vehicle formation control technology based on a switching event-triggered strategy, which realizes the consistent formation control of multiple QUAVs on the basis of reducing the number of triggers. In order to better improve the convergence speed of the multiple QUAVs, a fixed-time control technology is introduced to ensure that the consistency tracking error of the multiple QUAV system can converge to a given neighborhood within a fixed time. SUMMARY

[0004] The application overcomes the shortcomings of the prior art and proposes a multi-quadrotor unmanned aerial vehicle formation control method based on switching event-triggered technology, which introduces switching event-triggered technology to realize tracking control of the expected position and attitude within a fixed time.

[0005] A multi-quadrotor unmanned aerial vehicle formation control method based on switching event-triggered technology comprises the following steps.

[0006] Step one, a multi-quadrotor unmanned aerial vehicle system is defined, it is assumed that there is one leader quadrotor unmanned aerial vehicle and N follower quadrotor unmanned aerial vehicles with the same parameters in the formation, N is a positive integer greater than 1, and the position subsystem dynamics model and the attitude subsystem dynamics model of each quadrotor unmanned aerial vehicle are constructed; the dynamics model of the i-th follower quadrotor unmanned aerial vehicle is as follows:

[0007]

[0008] where i = 1, 2,..., N; x i , y i , z i denote the three position components of the ith quadrotor in the world frame; φ i , θ i , ψ i denote the roll, pitch, and yaw angles of the ith quadrotor, M i denotes the total mass of the vehicle, L i denotes the length from the center of mass to the rotor center, g denotes the gravitational acceleration, J i,x , J i,y , J i,z denote the moments of inertia of the ith quadrotor about the three axes of the world frame. G i,x , G i,y , G i,z denote the drag coefficients of the ith quadrotor about the three axes of the world frame. G i,φ , G i,θ , G i,ψ denote the drag coefficients of the ith quadrotor about the roll, pitch, and yaw axes, D i,x , D i,y , D i,z denote the external disturbances of the ith quadrotor about the three axes of the world frame, D i,φ , D i,θ , D i,ψ denote the external disturbances; τ i,F denotes the total lift, τ i,φ , τ i,θ , τ i,ψ denote the control inputs for the roll, pitch, and yaw moments; the dynamics model represented by equation (1) can be equivalently represented as:

[0009]

[0010] where

[0011] (v i,1 , v i,2 , v i,3 , v i,4 , v i,5 , v i,6 ) = (φ i , θ i , ψ i , z i , x i , y i )

[0012]

[0013] (λ i,4 ,λ i,5 ,λ i,6 )=(1 / M i ,1 / M i ,1 / M i )

[0014] (τ i,1 ,τ i,2 ,τ i,3 )=(τ i,φ ,τ i,θ ,τ i,ψ )

[0015] (τ i,4 ,τ i,5 ,τ i,6 )=(τ i,F cosφ i sinθ i -M i g i ,τ i,F (cosφ i sinθ i cosψ i +sinφ i sinψ i ),τ i,F (cosφ i sinθ i sinψ i -sinφ i cosψ i ))

[0016]

[0017]

[0018] (D i,1 ,D i,2 ,D i,3 ,D i,4 ,D i,5 ,D i,6 )=(D i,φ ,D i,θ ,D i,ψ ,D i,z ,D i,x ,D i,y ).

[0019] define x i,j,1 = v i,j , Equation (2) is further expressed as:

[0020]

[0021] Step two, setting control target: setting ideal trajectory v i,φ,d , v i,θ,d , v i,ψ,d , v i,z,d , v i,x,d , v i,y,d , ensuring that the cooperative tracking error E i,φ of the multi-four-rotor unmanned aerial vehicle system i,1 -v i,φ,d , E i,θ = v i,2 -v i,θ,d , E i,ψ = v i,3 -v i,ψ,d , E i,z = v i,4 -v i,z,d , E i,x = v i,5 -v i,x,d , E i,y = v i,y -v i,y,d can converge to the neighborhood of the origin within a fixed time;

[0022] Step three, for the position subsystem and the attitude subsystem, a fixed-time distributed controller is designed for each four-rotor unmanned aerial vehicle to ensure that the multi-four-rotor unmanned aerial vehicle system satisfies the fixed-time stability theorem, and all follower four-rotor unmanned aerial vehicles can achieve consistent tracking control with the leader four-rotor unmanned aerial vehicle under the communication resource constraint, which is specifically:

[0023] wherein the virtual control signal χ i,j,1 is designed as:

[0024]

[0025] wherein, x p,j,2 is the first-order derivative of the jth-order state quantity of the pth four-rotor unmanned aerial vehicle, k i,j,1 , a i,j,1 , b i,j,1 are design coefficients of the virtual control signal χ i,j,1 , 0 < α < 1 and β > 1;

[0026] wherein a directed graph G is used to describe the multi-four-rotor unmanned aerial vehicle system composed of one leader and N followers, and the graph G is expressed as wherein and are the vertex set and edge set of a directed graph, respectively; denotes that the ith node can obtain the information of the pth node, and is the neighborhood of the ith node; the adjacency matrix of the directed graph is defined as follows: if then a i,p = 1, otherwise, a i,p = 0; the directed graph contains a directed spanning tree if there exists at least one node to any other node in the graph there is a directed path. The leader is marked as node 0 in the directed graph, and the diagonal matrix S = diag{s1, s2, …, s N} is defined, where s i = 1 when the ith follower can obtain the information of the leader, otherwise s i = 0; The switching event trigger mechanism of the first-order subsystem is designed as:

[0027]

[0028]

[0029] where ρ i,j,2 is an intermediate variable, χ i,j,2 is the virtual control signal of the second-order subsystem, ζ i,j is a positive known continuous function, and d i,j is a positive design parameter; the event-triggering condition is set as:

[0030]

[0031] where c i,j,1 , c i,j,2 , c i,j,3 are positive constants, τ i,j is the control signal of the second-order subsystem, d i,j is a positive constant satisfying d i,j > c i,j,1 + c i,j,3 , and ρ i,j,2 (t k ) represents the value of the intermediate variable ρ i,j,2 (t) at t = t k ;

[0032] The virtual control signal χ i,j，2 of the second-order subsystem is designed as:

[0033]

[0034] ​Where k i,j,2 a i,j,2 b i,j,2 It is a virtual control signal χ i,j，2 The design parameters; as can be seen from the approximation characteristics of RBF-NN, there exists a positive constant ε. i,j ,satisfy in It is the input signal of the RBF-NN. It is the output signal of RBF-NN and δ i,j The error between the output signal and the input signal of the RBF-NN satisfies ||δ i,j ||≤ε i,j Define variable θ i，j =||W i，j || 2 , in It is θ i,j The estimated value.

[0035] The present invention has the following beneficial effects:

[0036] The fixed-time distributed controller based on switching event triggering designed in this invention can ensure that multi-quadcopter UAV systems can achieve fixed-time stability under limited communication resources.

[0037] The switching event triggering strategy designed in this invention can ensure a smooth switching between a fixed threshold strategy with little correlation to the control input and a relative threshold strategy with close correlation to the control input. Furthermore, the designed triggering mechanism can adjust tanh|τ according to the magnitude of the control input signal. i,j / c i,j,2 The range of values ​​for |.

[0038] This invention combines adaptive control and neural network approximation methods to effectively handle the height nonlinear function in the dynamics system of a quadcopter unmanned aerial vehicle. Attached Figure Description

[0039] Figure 1 It is a directed topology diagram of a quadcopter drone leader and four quadcopter drone followers;

[0040] Figure 2 This is a tracking error diagram of a quadcopter drone position subsystem containing four quadcopter drones;

[0041] Figure 3 This is a tracking error diagram of the attitude subsystem of a quadcopter drone, which includes four quadcopter drones.

[0042] Figure 4 It is the trigger interval time of the first quadcopter follower in a multi-quadcopter drone system;

[0043] Figure 5 is the trigger interval time of the 2nd follower quadrotor UAV in the multi-quadrotor UAV system;

[0044] Figure 6 is the trigger interval time of the 3rd follower quadrotor UAV in the multi-quadrotor UAV system;

[0045] Figure 7 is the trigger interval time of the 4th follower quadrotor UAV in the multi-quadrotor UAV system. DETAILED DESCRIPTION

[0046] The main idea of the research of the present application is as follows:

[0047] ① Define a multi-quadrotor UAV system consisting of a leader quadrotor UAV and N follower quadrotor UAVs, and construct the dynamics model of the ith follower quadrotor UAV (i = 1, 2, …, N).

[0048] ② Set three position desired signals v i,x,d , v i,y,d , v i,z,d of the ith follower quadrotor UAV system in the world coordinate system, and the desired signals v i,φ,d , v i,θ,d , v i,ψ,d of the roll, pitch and yaw of the ith follower quadrotor UAV, respectively. According to the UAV dynamics model, define the tracking errors E i,x = v i,5 -v i,x,d , E i,y = v i,y -v i,y,d , E i,z = v i,4 -v i,z,d of the three position components of the ith follower quadrotor UAV in the world coordinate system, and the tracking errors E i,φ = v i,1 -v i,φ,d , E i,θ = v i,2 -v i,θ,d , E i,ψ = v i,3 -v i,ψ,d of the roll, pitch and yaw of the ith follower quadrotor UAV, respectively.

[0049] ③ The present application constructs virtual control signals χ i,j,1 and χ i,j，2 , event trigger condition (10), intermediate variable p i,j,2 and fixed-time control signal τi,j To ensure that the multi quadrotor unmanned aerial vehicle system meets the fixed time stability theorem, and all follower quadrotor unmanned aerial vehicles can achieve consistent tracking control with the leader quadrotor unmanned aerial vehicle under the communication resource constraint.

[0050] The multi-quadrotor unmanned aerial vehicle fixed-time formation control based on the switching event triggering technology, the steps of the method include:

[0051] Step a), define a multi-quadrotor unmanned aerial vehicle system, assume that there is a leader quadrotor unmanned aerial vehicle and N follower quadrotor unmanned aerial vehicles with the same parameters in the formation, N is a positive integer greater than 1, and the position subsystem dynamics model and the attitude subsystem dynamics model of each quadrotor unmanned aerial vehicle are constructed; The dynamics model of the i-th follower quadrotor unmanned aerial vehicle is as follows (i=1, 2, …, N):

[0052]

[0053] Where x i , y i , z i respectively represent the three position components of the i-th quadrotor unmanned aerial vehicle in the world coordinate system; φ i , θ i , ψ i respectively represent the roll angle, pitch angle and yaw angle of the i-th quadrotor unmanned aerial vehicle, M i represents the total mass of the body, L i represents the length from the center of mass to the rotor center, g represents the acceleration of gravity, J i,x , J i,y , J i,z respectively represent the moment of inertia of the i-th quadrotor unmanned aerial vehicle around the three axes of the world coordinate system. G i,x , G i,y , G i,z respectively represent the resistance coefficients of the i-th quadrotor unmanned aerial vehicle in the world coordinate system. G i,φ , G i,θ , G i,ψ respectively represent the resistance coefficients of the i-th quadrotor unmanned aerial vehicle roll, pitch and yaw, D i,x , D i,y , D i,z respectively represent the external disturbance of the i-th quadrotor unmanned aerial vehicle in the world coordinate system, D i,φ , D i,θ , D i,ψ represent external disturbance. τ i,F represents the total lift, τ i,φ , τ i,θ , τ i,ψThe control inputs representing roll, pitch and yaw moments, respectively. For simplicity, the dynamics model represented by equation (1) can be equivalently expressed as:

[0054]

[0055] where

[0056] (v i,1 ,v i,2 ,v i,3 ,v i,4 ,v i,5 ,v i,6 )=(φ i ,θ i ,ψ i ,z i ,x i ,y i )

[0057]

[0058] (λ i,4 ,λ i,5 ,λ i,6 )=(1 / M i ,1 / M i ,1 / M i )

[0059] (τ i,1 ,τ i,2 ,τ i,3 )=(τ i,φ ,τ i,θ ,τ i,ψ )

[0060] (τ i,4 ,τ i,5 ,τ i,6 )=(τ i,F cosφ i sinθ i -M i g i ,τ i,F (cosφ i sinθ i cosψ i +sinφ i sinψ i ),τ i,F (cosφ i sinθ i sinψ i -sinφ i cosψ i ))

[0061]

[0062]

[0063] (D i,1 ,D i,2 ,D i,3 ,D i,4 ,D i,5 ,D i,6 )=(D i,φ ,D i,θ ,D i,ψ ,D i,z ,D i,x ,D i,y ).

[0064] Definition x i,j,1 =v i,j , Equation (2) can be further expressed as:

[0065]

[0066] Control objective: the present application designs a fixed time adaptive controller for multi four-rotor unmanned aerial vehicle, so that all signals of the closed loop system have fixed time limit, and the position and attitude of the i-th four-rotor unmanned aerial vehicle can track the ideal trajectory v i,φ,d , v i,θ,d , v i,ψ,d , v i,z,d , v i,x,d , v i,y,d , ensure that the cooperative tracking error E i,φ =v i,1 -v i,φ,d , E i,θ =v i,2 -v i,θ,d , E i,ψ =v i,3 -v i,ψ,d , E i,z =v i,4 -v i,z,d , E i,x =v i,5 -v i,x,d , E i,y =v i,y -v i,y,d can converge to the neighborhood near the origin in fixed time. Define the expected variable (v i,1,d , v i,2,d , v i,3,d , v i,4,d , v i,5,d , v i,6,d )=(vi,φ,d ,v i,θ,d ,v i,ψ,d ,v i,z,d ,v i,x,d ,v i,y,d ), wherein v i,z,d ,v i,x,d ,v i,y,d ,v i,ψ,d is continuous and first-order derivable. The quadrotor unmanned aerial vehicle system is a typical under-actuated system, and the yaw angle inverse solution can be obtained according to the control input of the position subsystem and wherein

[0067] Step b), in order to realize the consistency control of the multiple quadrotor unmanned aerial vehicles, the related lemma is introduced;

[0068] b1) the related lemma knowledge of the directed graph:

[0069] The present application adopts the directed graph to describe the multiple quadrotor unmanned aerial vehicle system composed of one leader and N followers, and the graph is expressed as wherein and are the vertex set and the edge set of the directed graph respectively. It is represented that the ith node can obtain the information of the pth node, and the notation is the neighborhood of the ith node. The adjacency matrix of the directed graph is defined as follows: if then a i,p =1, otherwise, a i,p =0. The Laplacian matrix L=Q-A is defined, wherein Q=diag{q i,1 ,q i,2 ,…,q i,N} represents the in-degree matrix.

[0070] If the directed graph has at least one node to any other node in the graph, there is a directed path, then the directed graph contains a directed spanning tree. The leader is marked as node 0 in the directed graph, and the diagonal matrix S=diag{s1,s2,…,s N} is defined, when the ith follower can obtain the information of the leader, s i =1, otherwise, s i =0.

[0071] The lemma b1) mainly represents the connection and communication relationship between each unmanned aerial vehicle in the multiple quadrotor unmanned aerial vehicle system.

[0072] b2) Related knowledge of Lyapunov function for fixed-time stability:

[0073] Suppose there is a continuous positive definite function H(s a ):R n →R + , if there is a system and s a (0)=s0, which satisfies then the system satisfies the condition of fixed-time convergence, where a>0, b>0, c>0, d>0, 0<α<1, β>1.

[0074] Lyapunov function b2) is used to analyze whether the multi-quadrotor unmanned aerial vehicle system satisfies the fixed-time stability condition in step c4).

[0075] b3) Related knowledge of Young's inequality:

[0076] For any there is an inequality:

[0077]

[0078] where p>0, and q>0.

[0079] Lyapunov function b3) is mainly used for the processing of inequalities in the stability analysis process in step c).

[0080] b4) Related knowledge of radial basis function neural network:

[0081] For a continuous function there is a small set Ω0, and the present invention introduces a radial basis function (RBF) neural network (NN) which satisfies where is the input vector, L0 is the input dimension of NN, the weight vector W=[W1,…,W n ] T ∈R n , the number of nodes of NN n>1, the basis function vector P(z0)=[p1(z0),…,p n (z0)] T ∈R n , p i (z0) is selected in the form of Gaussian function as follows:

[0082]

[0083] where: is the center of the receptive field, l i,a is the width of the Gaussian function, for any given ε0>0, when li,a RBF-NN can approximate any continuous function with larger values:

[0084] where δ(z0) is the tracking error and satisfies |δ(z0)|≤ε0, W is the unknown ideal weight vector defined in the analysis process.

[0085] Define the unknown constant θ i,j =||W i,j || 2 , j = 1, 2, 3, 4, 5, 6, where denotes the estimate of θ i,j .

[0086] Lemma b4) is mainly used to approximate the unknown nonlinear function term in each quadrotor UAV system in step c)

[0087] Step c), for the position subsystem and the attitude subsystem, designs a fixed-time distributed controller for each quadrotor UAV to control the position and attitude of the UAV system to the set value; the specific process of designing the distributed controller is as follows:

[0088] Considering a multi-quadrotor UAV system composed of one leader quadrotor UAV and N follower quadrotor UAVs, for the subsystem of the i-th follower quadrotor UAV, based on the directed topological graph, the tracking error of the first-order subsystem and the second-order subsystem of the i-th follower quadrotor UAV for the j-th order state quantity formula (3) is constructed:

[0089] and w i,j,2 = x i,j,2 - χ i,j,1 , where χ i,j,1 is the virtual control quantity of the first-order subsystem of formula (3), v i,j,d is the expected signal of the j-th order state quantity of the i-th quadrotor UAV, v p,j is the j-th order state quantity of the p-th quadrotor UAV, i = 1, 2, …, N, p = 1, 2, …, N, j = 1, 2, …, 6, i ≠ p.

[0090] c1) For the first-order system in the sub-formula (3), a Lyapunov function of the first-order subsystem is constructed Taking the derivative of H i,j,1 , we get:

[0091]

[0092] where x p,j,2is the first derivative of the pth quadrotor UAV jth state variable. χ i,j,1 is the virtual control signal of the subsystem of the sub-equation (3), χ i,j,1 is designed as:

[0093]

[0094] where k i,j,1 , a i,j,1 , b i,j,1 are the design coefficients of the virtual control signal χ i,j,1 , 0 < a < 1 and β > 1.

[0095] According to the designed virtual controller (7), the Lyapunov function of the first order subsystem satisfies

[0096]

[0097] For the second order subsystem in the sub-equation (3), the Lyapunov function of the second order subsystem is constructed as Taking the derivative of H i,j,2 , we have

[0098]

[0099] For the above equation, the switching event-triggering mechanism of the subsystem (3) is designed as:

[0100]

[0101] where ρ i,j,2 is the intermediate variable, χ i,j,2 is the virtual control signal of the second order subsystem of the subsystem (3), ζ i,j is a positive known continuous function, d i,j is a positive design parameter. The event-triggering condition is set as

[0102]

[0103] where c i,j,1 , c i,j,2 , c i,j,3 are positive constants, τ i,j is the control signal of the second order subsystem of the subsystem (3), d i,j is a positive constant satisfying d i,j > c i,j,1 + c i,j,3 , ρ i,j,2 (t k ) represents the value of the intermediate variable ρ i,j,2 at time t k . When t ∈ [t k , t k+1), |ρ i,j,2 (t)-τ i,j | <c i,j,1 +c i,j,3 Therefore τ i,j =ρ i,j,2 -υ i,j (c i,j,1 +c i,j,3 ),in It is continuous and |υ i,j |<1.

[0104] According to the above event triggering strategy, when the value of the subsystem's control signal is too large, tanh|τ i,j / c i,j,2 When the value of the control signal approaches a constant, the condition for event triggering is minimally affected by the subsystem's control signal, effectively reducing the number of event triggers. When the value of the subsystem's control signal is small, tanh|τ i,j / c i,j,2 |Controlled by signal τ i,j The impact is significant. At this time, the conditions for triggering the event are closely related to the control signals of the subsystem, which improves the control performance of the system while reducing the number of triggers.

[0105] Combining the event triggering strategy and the constructed subsystem Lyapunov function H analyzed above i,j,2 Design the virtual control signal χ for the second-order subsystem i,j，2 for

[0106]

[0107] Where k i,j,2 a i,j,2 b i,j,2 It is a virtual control signal χ i,j，2 The design parameters. From the approximation characteristics of RBF-NN, it can be seen that there exists a positive constant ε. i,j ,satisfy in It is the input signal of the RBF-NN. It is the output signal of RBF-NN and δ i,j The error between the output signal and the input signal of the RBF-NN satisfies ||δ i,j ||≤ε i,j Define variable θ i,j =||W i,j || 2 , in It is θ i,j The estimated value.

[0108] According to the designed control signal τ i,j, virtual control signal χ i,j，2 , intermediate variable p i,j,2 and switching event triggering mechanism, Lyapunov function H i,j,2 satisfies

[0109]

[0110] where D i,0 is a positive constant satisfying |D i,j |≤D i,0 , π1is a positive constant, ζ i,j is a positive known continuous function, and λ i,j is the parameter of the designed quadrotor UAV system.

[0111] c3) Design the Lyapunov function H of the ith quadrotor UAV, and design the adaptive law as Combining the adaptive law and formula (12), the Lyapunov function H i of the ith quadrotor UAV satisfies

[0112]

[0113] where

[0114] c4) Construct the Lyapunov function H of the multi-quadrotor UAV system (N quadrotor UAVs)

[0115]

[0116] where

[0117] At this time, it can be guaranteed that when H>0, the multi-quadrotor UAV system satisfies the condition of fixed-time stability.

[0118] The system simulation adopts Matlab2017a, and the ode45 solver is used. The simulation part designs a multi-quadrotor UAV system composed of 1 quadrotor UAV leader and 4 quadrotor UAV followers, and the directed topological structure diagram is as shown in Figure 1 The adjacency matrix A and the diagonal matrix S of the multi-quadrotor UAV system based on Figure 1 are respectively represented as

[0119]

[0120] The signal of the quadrotor UAV leader is selected as: v i,1,d= 0.65 sin(πt / 10), v i,2,d = 0.65 cos(πt / 10), v i,6,d = π / 5, v i,3,d = 3 - 0.039(t - 3) 2 Γ(t - 3), where Γ(t - 3) is a switching function, Γ(t - 3) = 1 when 0 < t < 3 s, and Γ(t - 3) = 0 when t ≥ 3 s.

[0121] The parameters of the quadrotor follower system are chosen as: M i = 2.5 kg, J i,x = J i,y = 0.041 kg·m 2 , J i,z = 0.093 kg·m 2 , g = 9.8 m / s 2 , G i,x = G i,y = G i,z = G i,φ = G i,θ = G i,ψ = 0.12, D i,x = D i,y = D i,z = D i,φ = D i,θ = D i,ψ = 0.12 sin(πt / 15), i = 1, 2, …, 4.

[0122] The initial states of the quadrotor follower system are set as:

[0123] [x1(0), y1(0), z1(0), φ1(0), θ1(0), ψ1(0)] = [-0.67, 0.16, 2.45, 0.28, -0.19, 0.028],

[0124] [x2(0), y2(0), z2(0), φ2(0), θ2(0), ψ2(0)] = [-0.58, 0.21, 2.35, -0.41, 0.32, 0.155],

[0125] [x3(0), y3(0), z3(0), φ3(0), θ3(0), ψ3(0)] = [-0.51, 0.34, 2.25, 0.5, -0.5, -0.322],

[0126] [x4(0), y4(0), z4(0), φ4(0), θ4(0), ψ4(0)] = [-0.45, 0.42, 2.15, -0.7, 0.6, -0.121].

[0127] The distributed control design parameter settings of the quadrotor UAV follower system are as follows: k i,j,1 = 4, k i,j,2 = 2, a i,j,1 = a i,j,2 = 1.2, b i,j,1 = b i,j,2 = 1.4, r i,j = 1, σ i,1 = σ i,2 = σ i,3 = 3, l i,j = 1, d i,j = 2.4, c i,j,1 = 0.2, c i,j,2 = 3, c i,j,3 = 0.6, i = 1, 2, …, 4, j = 1, 2, …, 6.

[0128] The neural network contains 11 nodes and is uniformly distributed at the center [-5, 5].

[0129] The simulation results of the fixed-time controller for the multi-quadrotor UAV system to achieve the desired trajectory tracking in a fixed time are shown in the accompanying drawings. The tracking error diagram of the position subsystem of each follower quadrotor UAV is shown in Figure 2 , and the tracking error diagram of the attitude subsystem of each follower quadrotor UAV is shown in Figure 2 . As can be seen from Figure 2 and Figure 3 , the tracking errors of the position subsystem and the attitude subsystem of each follower quadrotor UAV can converge to the neighborhood of zero point in a fixed time. Figure 4 , Figure 5 , Figure 6 and Figure 7 respectively show the trigger intervals of the four quadrotor UAV followers. The simulation signals clearly show that the follower quadrotor UAV system in the present application can quickly and efficiently track the desired signal of the leader quadrotor UAV system in a fixed time, and has good practical implementation significance.

[0130] Of course, the above description is only for the preferred embodiments of the present application, and the present application is not limited to the above-mentioned embodiments. It should be noted that any person skilled in the art, under the guidance of the present application, all equivalent substitutions, obvious modifications, fall within the scope of the present application, and should be protected by the present application.

Claims

1. A multi-UAV formation control method based on switching event triggering technology, characterized in that, include: Step 1: Define a multi-quadcopter UAV system. Assume a leader quadcopter UAV and N follower quadcopter UAVs with identical parameters in the formation, where N is a positive integer greater than 1. Construct the position subsystem dynamic model and attitude subsystem dynamic model for each quadcopter UAV. The dynamic model of the i-th follower quadcopter UAV is as follows: Where i = 1, 2, ..., N; x i y i z i φ represents the three position components of the i-th quadcopter UAV in the world coordinate system; i θ i ψ i M represents the roll angle, pitch angle, and yaw angle of the i-th quadcopter UAV, respectively. i L represents the total mass of the machine body. i J represents the length from the center of mass to the center of the rotor, g represents the acceleration due to gravity, and J represents the acceleration due to gravity. i,x J i,y J i,z Let G represent the moments of inertia of the i-th quadrotor UAV about the three axes of the world coordinate system; i,x G i,y G i,z G represents the drag coefficients of the i-th quadcopter UAV along the three axes in the world coordinate system; i,φ G i,θ G i,ψ D represents the drag coefficients for the roll, pitch, and yaw of the i-th quadcopter UAV, respectively. i,x D i,y D i,z Let D represent the external disturbances of the i-th quadcopter UAV along the three axes in the world coordinate system, respectively. i,φ D i,θ D i,ψ Indicates external disturbance; τ i,F τ represents the total lift. i,φ τ i,θ τ i,ψ Let these represent the control inputs for roll, pitch, and yaw moments, respectively; the dynamic model represented by formula (1) can be equivalently expressed as: in (v i,1 ,v i,2 ,v i,3 ,v i,4 ,v i,5 ,v i,6 )=(φ i ,θ i ,ψ i ,z i ,x i ,y i ) (l i,1 ,l i,2 ,l i,3 )=(L i / J i,x ,L i / J i,y ,L i / J i,z ) (l i,4 ,l i,5 ,l i,6 )=(1 / M i ,1 / M i ,1 / M i ) (t i,1 ,t i,2 ,t i,3 )=(τ i,φ ,t i,θ ,t i,ψ ) (t i,4 ,t i,5 ,t i,6 )=(τ i,F cosφ i sinth i -M i g i ,t i,F (cosφ i sinth i cosψ i +sinφ i sinψ i ),t i,F (cosφ i sinth i sinψ i -sinφ i cosψ i )) (D i,1 ,D i,2 ,D i,3 ,D i,4 ,D i,5 ,D i,6 )=(D i,φ ,D i,θ ,D i,ψ ,D i,z ,D i,x ,D i,y ) Define x i,j,1 =v i,j , Formula (2) can be further expressed as: Step 2: Set the control target: Set the ideal trajectory v i,φ,d v i,θ,d v i,ψ,d v i,z,d v i,x,d v i,y,d To ensure the cooperative tracking error E of the multi-quadrotor UAV system i,φ =v i,1 -v i,φ,d E i,θ =v i,2 -v i,θ,d E i,ψ =v i,3 -v i,ψ,d E i,z =v i,4 -v i,z,d E i,x =v i,5 -v i,x,d E i,y =v i,y -v i,y,d It can converge to a neighborhood near the origin within a fixed time. Step 3: For the position and attitude subsystems, design a fixed-time distributed controller for each quadcopter drone to ensure that the multi-quadcopter drone system satisfies the fixed-time stability theorem, and that all follower quadcopter drones can achieve consistent tracking control with the leader quadcopter drone under communication resource constraints. Specifically: Among them, the virtual control signal χ of the first-order subsystem i,j,1 Designed as follows: in, x p,j,2 It is the first derivative of the j-th order state variable of the p-th quadcopter UAV, k i,j,1 a i,j,1 b i,j,1 It is a virtual control signal χ i,j,1 The design coefficients are 0 < α < 1 and β > 1; Among them, directed graphs are used. To describe a multi-quadcopter unmanned aerial vehicle system consisting of one leader and N followers, see the diagram. Represented as in and These are the vertex set and edge set of a directed graph, respectively. This indicates that the i-th node can obtain information from the p-th node, denoted as […]. The neighborhood of the i-th node; a directed graph. adjacency matrix The element is defined as follows: If Then a i,p =1, otherwise, a i,p =0; if there is a directed graph A directed graph is a graph in which there exists at least one node from which there is a directed path to every other node in the graph. It contains a directed spanning tree; the leader is marked as node 0 in the directed graph, and the diagonal matrix S = diag{s1, s2, ..., s} is defined. N }, when the i-th follower can obtain information about the leader, s i =1, otherwise, s i =0; The switching event triggering mechanism of the first-order subsystem is designed as follows: Among them, w i,j,2 =x i,j,2 -χ i,j,1 ;ρ i,j,2 It is an intermediate variable, χ i,j,2 It is the virtual control signal of the second-order subsystem, ζ i,j It is a known positive continuous function, d i,j If the design parameter is positive, then the event triggering condition is set as follows: Where c i,j,1 c i,j,2 c i,j,3 It is a positive constant, τ i,j It is the control signal of the second-order subsystem, d i,j Are positive constants that satisfy d? i,j >c i,j,1 +c i,j,3 , ρ i,j,2 (t k ) represents the intermediate variable ρ i,j,2 (t) at t=t k The value at time; The virtual control signal χ of the second-order subsystem i,j，2 Designed as follows: Where k i,j,2 a i,j,2 b i,j,2 It is a virtual control signal χ i,j，2 The design parameters; as can be seen from the approximation characteristics of RBF-NN, there exists a positive constant ε. i,j ,satisfy in It is the input signal of the RBF-NN. It is the output signal of RBF-NN and δ i,j The error between the output signal and the input signal of the RBF-NN satisfies ||δ i,j ||≤ε i,j Define variable θ i，j =||W i，j || 2 , in It is θ i,j The estimated value.

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