CN109917806B - Unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization - Google Patents

Abstract

The present invention is a method for controlling UAV swarm formation based on non-inferior solution pigeon swarm optimization, and its implementation steps are as follows: Step 1: UAV swarm formation model; Step 2: UAV swarm formation state prediction; Step 3: Initialize the parameters of the non-inferior solution pigeon swarm optimization method; Step 4: Design the method based on the non-inferior solution pigeon swarm optimization; Step 5: Design the UAV swarm formation RHC controller based on the non-inferior solution pigeon swarm optimization; Step 6: None Man-machine swarm formation control method result output. The method aims to provide a real-time and online optimization method for the UAV swarm formation controller, so as to effectively improve the control level of the UAV swarm formation in the complex battlefield environment.

Description

A UAV swarm formation control method based on non-inferior solution pigeon swarm optimization

technical field

The invention relates to a research method for swarm formation control of unmanned aerial vehicles based on biological intelligence optimization, and belongs to the field of autonomous control of unmanned aerial vehicles.

Background technique

A drone is a self-powered, radio-controlled or autonomous flying unmanned aerial vehicle that can perform a variety of tasks and can be used multiple times. Since the 1990s, with the rapid development of single UAV flight technology, it has gradually been widely used in military, civil and other fields. However, as the modern battlefield environment is integrated, three-dimensional, multi-dimensional, and the competition for modern warfare is more intense, there are performance constraints in various aspects when a single machine performs various tasks, and the efficiency and accuracy of tasks will be limited. Therefore, multi-UAV swarm operations are extremely important.

The success rate of UAV swarm flight and the ability to resist emergencies are stronger than single aircraft. UAV swarm formation is an important task of UAV swarm flight. It is used in military reconnaissance, target strike, communication relay, electronic countermeasures. , battlefield assessment and harassment temptation has a relatively wide range of applications. Effective communication and coordination are required during the formation of UAV swarms to avoid collisions between UAV swarms and accidental injuries caused by enemy UAV interference. In order to realize the autonomous flight of the UAV swarm formation and complete the designated complex war tasks, the problem of UAV swarm formation control needs to be solved urgently.

UAV swarm formation control refers to the formation, maintenance and reconstruction of a certain geometric configuration of multiple UAVs in order to adapt to the battlefield environment, task situation, and meet the needs of various war missions, military and civilian targets when performing specific tasks. Control Technology. UAV swarm formation control methods are mainly divided into: leader-wingman method, virtual structure method, behavior control method. Among them, the behavior control method needs to form control instructions according to the preset information and trigger conditions, which reduces the adaptability and flexibility of the formation; the virtual structure method requires the formation flight to meet rigid motion, which greatly limits the application scope of actual flight; - The wingman method is to designate one of the drones as the lead, and the other drones as the wingman. The lead plane flies according to the preset trajectory, and the wingman follows the lead plane to fly in formation and achieve the same speed under a certain control strategy. This method is intuitive and easy to understand, and is the most common method in UAV swarm formation control.

In the process of UAV swarm formation, there is a strong coupling relationship and nonlinear characteristics between the lead plane and the wingman model. At the same time, it is constrained and influenced by various complex battlefield environments, making UAV swarm formation a real-time solution subject. Constrained optimization problems. Although the classical PID control method can realize the swarm formation control of the UAV, the process of determining the parameters is more complicated; the extreme value search method can only solve the problem of minimizing the power required by the wingman in the UAV swarm formation flight; the rolling time domain Control (Receding Horizon Control, RHC) is a control method based on on-line optimization firstly applied to industrial control. , is the appropriate choice for the UAV swarm formation leader-wingman method controller. However, in the process of UAV swarm formation, the relationship between the input of the RHC controller and the state of the UAV is difficult to determine. How to select the parameters of the RHC controller has become a difficult problem in solving the UAV swarm formation control problem.

Pigeon Inspired Optimization (PIO) is a bionic intelligent optimization algorithm that simulates the homing behavior of pigeons. The algorithm abstracts navigation tools such as the sun, magnetic field, and landmarks into map-compass operators and landmark operators. The convergence of the algorithm is achieved and the global optimal solution is obtained, but the algorithm has a slow convergence speed and is easy to fall into the local optimum. The non-inferior solution is the suspected optimal solution in the process of finding the global optimal. This operator is introduced into the original PIO algorithm to improve its performance, and then optimize the parameters of the RHC controller.

To sum up, the present invention proposes a UAV swarm formation control method based on the non-inferior solution of pigeon swarm optimization, so as to solve the problem of difficulty in online optimization of the RHC controller in the UAV swarm formation, and effectively improve the UAV swarm formation. Formation control level.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a UAV swarm formation control method based on non-inferior solution pigeon swarm optimization, and introduce a non-inferior solution operator (suspected optimal solution in the process of finding the global optimal) into the original PIO algorithm. , to improve its performance, and then optimize the parameters of the RHC controller to solve the difficult problem of online optimization of the RHC controller in the UAV swarm formation, and effectively improve the control level of the UAV swarm formation; The pigeon-swarm optimized RHC controller can adjust parameters according to the real-time state of the UAV swarm formation to achieve the optimal control effect, so as to provide a real-time and online method for optimizing the UAV swarm formation controller, thereby effectively improving the complex battlefield. The control level of the UAV swarm formation in the environment.

In order to achieve the above purpose, the technical solution adopted in the present invention is: a method for controlling the formation of unmanned aerial vehicle swarms based on non-inferior solution pigeon swarm optimization, and the specific steps of the method are as follows:

Step 1: UAV swarm formation model

The UAV swarm is modeled on the basis of the leader-wingman method. Among them, the long machine model is

The horseshoe vortex model is used to consider the aerodynamic effect of the long plane wake on the wingman. The wingman model is

是无人机实际的位置(x,y,z)的导数，ζ为z的导数，

为编队的期望距离，

为僚机速度回路的时间常数，

表示僚机航向角回路的时间常数，ψ_W,V_W,h_W分别代表僚机的实际航向角、速度和高度，

即为对应的僚机控制输入的航向角、速度和高度。类似地，ψ_L,V_L,h_L及

为长机的实际航向角、速度和高度以及控制输入的航向角、速度和高度。τ_a,τ_b为无人机在高度通道上小于0的时间常数，S表示机翼面积，m为总质量，

是侧力导数的变化在y方向的梯度，

为侧力导数的变化在z方向的梯度，

表示升力导数的变化在y方向的梯度，

为阻力导数的变化在z方向的梯度。in,

is the derivative of the actual position of the drone (x, y, z), ζ is the derivative of z,

is the expected distance of the formation,

is the time constant of the wingman speed loop,

represents the time constant of the wingman heading angle loop, ψ _W , V _W , h _W represent the actual heading angle, speed and altitude of the wingman, respectively,

That is, the heading angle, speed and altitude of the corresponding wingman control input. Similarly, ψ _L , _VL , h _L and

The actual heading angle, speed and altitude of the lead aircraft and the heading angle, speed and altitude of the control input. τ _a , τ _b are the time constants that the UAV is less than 0 on the height channel, S is the wing area, m is the total mass,

is the gradient of the variation of the lateral force derivative in the y direction,

is the gradient of the variation of the lateral force derivative in the z direction,

represents the gradient of the lift derivative change in the y direction,

is the gradient of the drag derivative change in the z direction.

Step 2: Prediction of UAV swarm formation state

According to step 1, ignoring the nonlinear part, the model of the UAV can be simplified as

表示第k时刻的控制输入量。where A and B are coefficient matrices, X=[x ₁ ,x ₂ ,…,x _k ,…,x _N ],x _k =[x,y,V _W ,ψ _W ,z,ζ] ^T is none The state of the man-machine at the kth moment. U=[u ₁ ,u ₂ ,…,u _k ,…,u _N ],

Indicates the control input at the kth time.

The state of the UAV at time k+1 can be estimated from the state at time k, and the relationship between the two states can be expressed as

x _k+1 = Ax _k +Bu _k (4)

Among them, x _k+1 is the state of the drone at the k+1th moment.

Step 3: Initialize the parameters of the non-inferior pigeon population optimization method

Assuming that the total number of pigeons is N, initialize the position X ₀ and speed V ₀ of N pigeons respectively, and the position of the i-th pigeon is expressed as X _i =[x _i1 ,x _i2 ,x _i3 ,...,x _iD ], The speed of the i-th pigeon is expressed as V _i =[v _i1 ,v _i2 ,v _i3 ,...,v _iD ], i=1,2,...N, D is the dimension of the position and speed of each pigeon, that is, to be The number of optimization parameters. The total number of cycles of the map-compass operator stage is set as T ₁ , the number of cycles of the landmark operator stage is set as T ₂ , and the total number of cycles of the two stages is represented by T=T ₁ +T ₂ .

Step 4: Method design based on non-inferior solution pigeon population optimization

1) Independent learning method based on map-compass operator

When the pigeons are far away from the destination, the pigeons rely on the map-compass information for navigation. During the homing process, the pigeons adjust their position and speed in real time with reference to the best pigeons in the current pigeons. On the basis of the original pigeon group optimization algorithm, an independent learning mechanism is added, that is, each pigeon not only refers to the best pigeon in the current pigeon group, but also refers to its own better position so far to update its position and speed. The speed update formula is formula (5). A schematic diagram of the independent learning mechanism based on the map-compass operator is shown in Figure 1.

为第i只鸽子在第t次迭代时的位置，

表示第i只鸽子在第t次迭代时的速度，R是地图-指南针算子的影响因子，r₁和r₂分别为[0,1]之间的随机数，X_gbest表示目前所有鸽子的全局最优位置，

表示第i只鸽子到t-1时刻自身的局部最优位置，c₁表示向全局最优鸽子学习的因子，c₂表示向自身局部最优鸽子学习的因子。in,

is the position of the i-th pigeon at the t-th iteration,

Indicates the speed of the i-th pigeon at the t-th iteration, R is the influence factor of the map-compass operator, r ₁ and r ₂ are random numbers between [0, 1] respectively, X _gbest represents the current speed of all pigeons the global optimal position,

Represents the local optimal position of the i-th pigeon at time t-1, c ₁ represents the factor learned from the global optimal pigeon, and c ₂ represents the factor learned from its own local optimal pigeon.

2) Suspected optimal solution (non-inferior solution) optimization method based on landmark operator

将用于其他鸽子位置更新的参考位置，位置更新方式如式(6)所示。When the pigeons approach the destination, the pigeons rely on the landmarks for homing guidance. In this stage, the landmark operator is used to update the position. During each iteration, the better-performing half of the N ^t pigeons are selected, and the other half of the pigeons that are not selected will be eliminated. The center of the selected flock

The reference position that will be used for the position update of other pigeons, and the position update method is shown in formula (6).

是第i只鸽子在第t-1次迭代时的代价函数，rand表示[0,1]之间的随机数。in,

is the cost function of the ith pigeon at the t-1th iteration, and rand represents a random number between [0, 1].

In the process of searching for the global optimal solution, the original pigeon colony optimization algorithm is easy to mistake the non-optimal solution as the global optimal solution, which makes the algorithm fall into the local optimal solution. In order to avoid the algorithm falling into local optimum, the suspected optimal solution (non-inferior solution) is introduced into the original pigeon flock optimization algorithm. The suspected optimal solution (non-inferior solution) is when the fitness value of a pigeon is close to the currently obtained global optimal value, then the position is considered as the suspected optimal solution. The way of judging the non-inferior solution is as formula (7). The schematic diagram of the non-inferior solution optimization mechanism based on the landmark operator is shown in Figure 2.

为当前所有鸽子局部最优值的平均值，ε为一个极小值，λ表示协调参数，该协调参数可用于调整非劣解的数量，通过减少非劣解的数量可以提高搜索精度。当目前全局最优解X_gbest的适应度值f_cost(X_gbest)与被判断的解

的适应度值

的差的绝对值

和目前全局最优解X_gbest的适应度值f_cost(X_gbest)与当前所有鸽子局部最优值的平均值

的差的绝对值

的比值小于λ时，被判断的解

为非劣解，否则，被判断的解

不是非劣解。协调参数定义为：in,

is the average of the local optimal values of all pigeons at present, ε is a minimum value, λ represents the coordination parameter, which can be used to adjust the number of non-inferior solutions, and the search accuracy can be improved by reducing the number of non-inferior solutions. When the fitness value f _cost (X _gbest ) of the current global optimal solution X _gbest is different from the judged solution

fitness value of

the absolute value of the difference

and the fitness value f _cost (X _gbest ) of the current global optimal solution X _gbest and the average of the current local optimal values of all pigeons

the absolute value of the difference

When the ratio of , is less than λ, the judged solution

is a non-inferior solution, otherwise, the judged solution

Not a non-inferior solution. The coordination parameters are defined as:

被确定为非劣解，则其位置更新公式为(9)，否则按式(6)中原始鸽群优化算法的位置更新方式进行鸽子位置的更新。like

If it is determined to be a non-inferior solution, its position update formula is (9), otherwise, the position update method of the original pigeon group optimization algorithm in formula (6) is used to update the position of the pigeon.

Among them, γ=[γ ₁ ,γ ₂ ,…γ _i …γ _D ],γ _i ∈[-1,1], i=1,2,…D is a range between [-1,1] D-dimensional vector, η represents the update coefficient, X _upper and X _lower are the upper and lower limits of the search space when the pigeon flock is searching for the position.

The structural block diagram of pigeon group optimization based on non-inferior solution is shown in Figure 3.

Step 5: Design of UAV swarm formation RHC controller based on non-inferior solution pigeon swarm optimization

Firstly, design the cost function of UAV swarm formation, and secondly design the RHC controller based on non-inferior solution pigeon group optimization; the design of cost function J _QP includes the state and control input of the formation system, and the purpose of optimization is to find J _QP The minimum value of , so that the RHC controller can obtain a set of optimal control parameters, and then the control effect of the UAV self-swarm formation can be optimal.

1) Design of the cost function

In order to evaluate the optimal parameters for UAV swarm formation, the design of the cost function J _QP includes the state of the formation system and the control input, which is expressed as

为预测系统的状态，其中，N为固定时间间隔，相应的控制输入为

x_k为无人机在第k时刻的状态，u_k表示无人机在第k时刻的控制输入，二者之间的关系可表示为where R and Q are both positive definite weight matrices, and

is the state of the predicted system, where N is a fixed time interval, and the corresponding control input is

x _k is the state of the UAV at the _k -th time, and uk is the control input of the UAV at the k-th time. The relationship between the two can be expressed as

where H _x =(A,A ² ,...,A ⁱ ,... A ^N ) ^T ,

The purpose of optimization is to find the minimum value of J _QP , so that the RHC controller can obtain a set of optimal control parameters, so as to optimize the control effect of the UAV self-swarm formation.

2) RHC controller design based on non-inferior solution pigeon group optimization

The structural block diagram of the RHC controller based on the non-inferior solution pigeon swarm optimization is shown in Figure 4. The implementation steps of RHC controller parameter optimization are as follows:

选取

作为RHC控制器僚机的输入，

舍弃；①Set the state of the wingman to be x ₀ at time k, and a set of optimal control inputs can be obtained based on step 5

select

As input to the RHC controller wingman,

give up;

②At time k+1, the status of the wingman is updated to x ₁ ;

③ Re-mark the current state of the wingman as x ₀ , record the current time as the kth time, and return to ① to repeat the cycle until the formation task ends.

Step 6: Result output of UAV swarm formation control method

The present invention adopts five unmanned aerial vehicles for formation control, one of which is the lead plane, and the other four are wingmen. The lead plane is set to fly at a constant speed at a certain altitude, and the four wingmen take off at different positions, and finally the five planes fly in formation at the same altitude and at the same speed.

The invention proposes an unmanned aerial vehicle swarm formation control method based on non-inferior solution pigeon swarm optimization. This method improves the original pigeon swarm optimization method by adding independent learning and suspected optimal solution mechanism, obtains the optimal parameters of the RHC controller, and then controls the UAV swarm formation. The main advantages of the invention are mainly reflected in two aspects: 1) The improved pigeon flock optimization algorithm has a faster convergence speed, and is not easy to fall into local optimum; 2) RHC control is an online optimization control method, after non-inferior The RHC controller optimized by solving pigeon swarms can adjust parameters according to the real-time state of the UAV swarm formation to achieve the optimal control effect.

Description of drawings

Figure 1 Schematic diagram of the independent learning mechanism based on the map-compass operator.

Figure 2 is a schematic diagram of a non-inferior solution optimization mechanism based on landmark operator.

Figure 3 is a block diagram of the structure of the pigeon group optimization based on the non-inferior solution.

Figure 4 is a block diagram of the structure of the RHC controller based on non-inferior solution pigeon swarm optimization.

Figure 5. Cost function value response curve.

Figure 6. The output result of the UAV formation.

The labels and symbols in the figure are explained as follows:

X _{pbest_i ——The} local optimal solution of the i-th pigeon as of the current iteration

X _{pbest_j ——The} local optimal solution of the jth pigeon as of the current iteration

X _gbest — the global optimal solution of the pigeon flock

X _center - the center position of the flock

X _{non-inferior_i} — the i-th suspected optimal solution (non-inferior solution)

X _{non-inferior_j} — the jth suspected optimal solution (non-inferior solution)

Y - yes (conditions are met)

N - No (condition not met)

t - the number of iterations

T ₁ ——The number of iterations of the independent learning process based on the map-compass operator

T ₂ ——The number of iterations of the non-inferior solution optimization process based on landmark operator

J - cost function

Detailed ways

See Figures 1 to 4 below to verify the effectiveness of the method proposed by the present invention through a specific example of a UAV swarm formation. The experimental computer is configured with Intel Core i7-4790 processor, 3.60Ghz main frequency, 4G memory, and the software is MATLAB 2014a version. The specific steps of a UAV swarm formation control method based on non-inferior solution pigeon swarm optimization are as follows:

Step 1: UAV swarm formation model

The UAV swarm is modeled on the basis of the leader-wingman method. Among them, the long machine model is as in formula (1). The horseshoe vortex model is used to consider the aerodynamic influence of the long plane wake on the wingman. The wingman model is shown in Equation (2). Assuming that the mass of each UAV is 1Kg, the speed of the UAV during the formation process is not more than 80m/s, the range of the throttle thrust is [10N, 100N], and the range of the heading angle is [-50°, 50°].

Step 2: Prediction of UAV swarm formation state

According to step 1, ignoring the nonlinear part, the model of the UAV can be simplified as shown in formula (3). The state of the UAV at time k+1 can be estimated from the state at time k, as shown in equation (4).

Step 3: Initialize the parameters of the non-inferior pigeon population optimization method

Assuming that the total number of pigeons is N=30, initialize the position X ₀ and speed V ₀ of N=30 pigeons respectively, the position of the i-th pigeon is expressed as X _i =[x _i1 ,x _i2 ,x _i3 ,..., x _iD ], the speed of the i-th pigeon is expressed as _Vi = [v _i1 ,v _i2 ,v _i3 ,...,v _iD ], i=1,2,...N, D=36 (D=3*RHC prediction Parameter*number of wingmen=3*3*4) is the dimension of the position and speed of each pigeon, that is, the number of parameters of the RHC controller to be optimized. Comparing the test results of multiple experiments, set the total number of cycles of the map-compass operator stage as T ₁ =20, the number of cycles of the landmark operator stage as T ₂ =10, and the total number of cycles of the two stages as T=T ₁ + _T2 said.

Step 4: Method design based on non-inferior solution pigeon population optimization

1) Independent learning method based on map-compass operator

When the pigeons are far away from the destination, the pigeons rely on the map-compass information for navigation. During the homing process, the pigeons adjust their position and speed in real time with reference to the best pigeons in the current pigeons. On the basis of the original pigeon group optimization algorithm, an independent learning mechanism is added, that is, each pigeon not only refers to the best pigeon in the current pigeon group, but also refers to its own better position so far to update its position and speed. The speed update formula is formula (5). A schematic diagram of the independent learning mechanism based on the map-compass operator is shown in Figure 1. According to the relevant research results of those in the field, setting R=0.3 is the influence factor of the map-compass operator, and c ₁ =c ₂ =2 represents the learning factor.

2) Non-inferior solution optimization method based on landmark operator

将用于其他鸽子位置更新的参考位置，位置更新方式如式(6)所示。When the pigeons approach the destination, the pigeons rely on the landmarks for homing guidance. In this stage, the landmark operator is used to update the position. During each iteration, the better-performing half of the N ^t pigeons are selected, and the other half of the pigeons that are not selected will be eliminated. The center of the selected flock

The reference position that will be used for the position update of other pigeons, and the position update method is shown in formula (6).

In the process of searching for the global optimal solution, the original pigeon colony optimization algorithm is easy to mistake the non-optimal solution as the global optimal solution, which makes the algorithm fall into the local optimal solution. In order to avoid the algorithm falling into local optimum, the suspected optimal solution (non-inferior solution) is introduced into the original pigeon flock optimization algorithm. The suspected optimal solution (non-inferior solution) is when the fitness value of a pigeon is close to the currently obtained global optimal value, then the position is considered as the suspected optimal solution. The way to judge the non-inferior solution is as Eq. (7). The schematic diagram of the non-inferior solution optimization mechanism based on the landmark operator is shown in Figure 2.

λ represents the coordination parameter, which can be used to adjust the number of non-inferior solutions, and the search accuracy can be improved by reducing the number of non-inferior solutions. When the absolute value of the difference between the fitness value of the current global optimal solution and the fitness value of the judged solution is the absolute value of the difference between the fitness value of the current global optimal solution and the average value of the current local optimal values of all pigeons When the ratio of , is less than λ, the judged solution is a non-inferior solution; otherwise, the judged solution is not a non-inferior solution. The definition of coordination parameters is shown in formula (8).

被确定为非劣解，则其位置更新公式为(9)，否则按式(6)进行鸽子位置的更新。对比多次实验测试结果，η＝20表示更新系数，X_upper＝1和X_lower＝0分别表示搜索空间的上下限。like

If it is determined as a non-inferior solution, its position update formula is (9), otherwise, the pigeon position is updated according to formula (6). Comparing the test results of multiple experiments, n=20 represents the update coefficient, and X _upper =1 and X _lower =0 represent the upper and lower limits of the search space, respectively.

The structural block diagram of pigeon group optimization based on non-inferior solution is shown in Figure 3.

Step 5: Design of UAV swarm formation RHC controller based on non-inferior solution pigeon swarm optimization

1) Design of the cost function

为预测系统的状态，其中，N为固定时间间隔，相应的控制输入为

x_k为k时刻的状态，

表示控制输入，k时刻的状态与控制输入量之间的关系可表示如式(11)所示。In order to evaluate the optimal parameters for UAV swarm formation, the design of the cost function J _QP shown in Eq. (10) includes the state and control input of the formation system. where R and Q are both positive definite weight matrices, and

is the state of the predicted system, where N is a fixed time interval, and the corresponding control input is

x _k is the state at time k,

Represents the control input, and the relationship between the state at time k and the control input quantity can be expressed as shown in Equation (11).

The purpose of optimization is to find the minimum value of J _QP , so that the RHC controller can obtain a set of optimal control parameters, so as to optimize the control effect of the UAV self-swarm formation.

2) RHC controller design based on non-inferior solution pigeon group optimization

The structural block diagram of the RHC controller based on the non-inferior solution pigeon swarm optimization is shown in Figure 4. The implementation steps of RHC controller parameter optimization are as follows:

选取

作为RHC控制器僚机的输入，

舍弃；①Set the state of the wingman to be x ₀ at time k, and a set of optimal control inputs can be obtained based on step 4

select

As input to the RHC controller wingman,

give up;

②At time k+1, the status of the wingman is updated to x ₁ ;

③ Re-mark the current state of the wingman as x ₀ , record the current time as the kth time, and return to ① to cycle again.

Step 6: Result output of UAV swarm formation control method

The present invention adopts five unmanned aerial vehicles for formation control, one of which is the lead plane, and the other four are wingmen. The lead plane is set to fly at a constant speed of 50m/s at an altitude of 300m, and the four wingmen take off at different positions. Finally, five UAVs fly in formation at an altitude of 300m at a speed of 50m/s.

As shown in step 1, the state of the UAV includes the values of x, y, V _W , ψ _W , z, ζ 6 variables, and the initial positions of the five UAVs are set as follows:

The initial state of the leader is [0, 0, 300, 50, 0, 0];

The initial state of wingman 1 is [300, 300, 100, 50, 0, 0];

The initial state of wingman 2 is [300, -300, 500, 50, 0, 0];

The initial state of wingman 3 is [600, 600, 400, 50, 0, 0];

The initial state of wingman 4 is [600, -600, 200, 50, 0, 0].

In order to verify the effectiveness of the method proposed by the present invention, the present invention also conducts corresponding comparative experiments, and the response curve of the cost function value is shown in FIG. 5 . The UAV formation output result based on the method of the present invention is shown in FIG. 6 .

Claims (4)

1. a kind of unmanned aerial vehicle swarm formation control method based on non-inferior solution pigeon swarm optimization is characterized in that: the method concrete steps are as follows: Step 1: UAV swarm formation model The UAV swarm is modeled on the basis of the lead plane-wingman method; among them, the lead plane model is

The horseshoe vortex model is used to consider the aerodynamic effect of the long plane wake on the wingman. The wingman model is

in,

is the derivative of the actual position of the drone (x, y, z), ζ is the derivative of z,

is the expected distance of the formation,

is the time constant of the wingman speed loop,

represents the time constant of the wingman heading angle loop, ψ _W , V _W , h _W represent the actual heading angle, speed and altitude of the wingman, respectively,

is the heading angle, speed and altitude of the corresponding wingman control input; similarly, ψ _L , _VL , h _L and

is the actual heading angle, speed and altitude of the lead aircraft and the heading angle, speed and altitude of the control input; τ _a , τ _b are the time constants of the UAV less than 0 on the altitude channel, S represents the wing area, and m is the total quality,

is the gradient of the variation of the lateral force derivative in the y direction,

is the gradient of the variation of the lateral force derivative in the z direction,

represents the gradient of the lift derivative change in the y direction,

is the gradient of the resistance derivative change in the z direction; Step 2: Prediction of UAV swarm formation state According to step 1, ignoring the nonlinear part, the model of the UAV can be simplified as

where A and B are coefficient matrices, X=[x ₁ ,x ₂ ,…,x _k ,…,x _N ],x _k =[x,y,V _W ,ψ _W ,z,ζ] ^T is none The state of the man-machine at the kth moment;

represents the control input at the kth moment; The state of the UAV at time k+1 can be estimated from the state at time k, and the relationship between the two states can be expressed as x _k+1 = Ax _k +Bu _k (4) Among them, x _k+1 is the state of the drone at the k+1th moment; Step 3: Initialize the parameters of the non-inferior pigeon population optimization method Assuming that the total number of pigeons is N, initialize the position X ₀ and speed V ₀ of N pigeons respectively, and the position of the i-th pigeon is expressed as X _i =[x _i1 ,x _i2 ,x _i3 ,...,x _iD ], The speed of the i-th pigeon is expressed as V _i =[v _i1 ,v _i2 ,v _i3 ,...,v _iD ], i=1,2,...N, D is the dimension of the position and speed of each pigeon, that is, to be The number of optimization parameters; set the total number of cycles of the map-compass operator stage to T ₁ , the number of cycles of the landmark operator stage to be T ₂ , and the total number of cycles of the two stages to be represented by T=T ₁ +T ₂ ; Step 4: Method design based on non-inferior solution pigeon population optimization 1) Independent learning method based on map-compass operator When the pigeons are far away from the destination, the pigeons rely on the map-compass information for navigation. During the homing process, the pigeons adjust their position and speed in real time with reference to the best pigeons in the current pigeons; On the basis of the group optimization algorithm, an independent learning mechanism is added, that is, each pigeon not only refers to the best pigeon in the current pigeon group, but also refers to its own better position so far to update its position and speed; 2) Suspected optimal solution based on landmark operator, namely non-inferior solution optimization method When the pigeon flock approaches the destination, the pigeon flock relies on the landmark for homing guidance. In this stage, the landmark operator is used to update the position; in each iteration process, half of the pigeons with better performance N ^t are selected, which are not The other half of the chosen pigeons will be eliminated; the center of the chosen flock

The reference position that will be used for the position update of other pigeons, and the position update method is shown in formula (6);

in,

is the cost function of the ith pigeon at the t-1th iteration, and rand represents a random number between [0,1]; The suspected optimal solution or non-inferior solution is introduced into the original pigeon group optimization algorithm. The suspected optimal solution or non-inferior solution is when the fitness value of a pigeon is close to the currently obtained global optimal value, then the position is considered as is the suspected optimal solution; Step 5: Design of UAV swarm formation RHC controller based on non-inferior solution pigeon swarm optimization Firstly, design the cost function of UAV swarm formation, and secondly design the RHC controller based on non-inferior solution pigeon group optimization; the design of cost function J _QP includes the state and control input of the formation system, and the purpose of optimization is to find J _QP The minimum value of , so that the RHC controller can obtain a set of optimal control parameters, thereby making the control effect of the UAV self-swarm formation to be optimal; Step 6: Output of the results of the UAV swarm formation control method; The way of judging the non-inferior solution in the fourth step is as formula (7):

in,

is the average value of the local optimal values of all pigeons at present, ε is a minimum value, λ represents the coordination parameter, which can be used to adjust the number of non-inferior solutions, and the search accuracy can be improved by reducing the number of non-inferior solutions; when the current The fitness value f _cost (X _gbest ) of the global optimal solution X _gbest and the judged solution

fitness value of

the absolute value of the difference

and the fitness value f _cost (X _gbest ) of the current global optimal solution X _gbest and the average of the current local optimal values of all pigeons

the absolute value of the difference

When the ratio of , is less than λ, the judged solution

is a non-inferior solution, otherwise, the judged solution

is not a non-inferior solution; the coordination parameter is defined as:

like

is determined to be a non-inferior solution, then its position update formula is (9), otherwise, the pigeon position is updated according to the position update method of the original pigeon group optimization algorithm in formula (6);

Among them, γ=[γ ₁ ,γ ₂ ,…γ _i …γ _D ],γ _i ∈[-1,1], i=1,2,…D is a range between [-1,1] D-dimensional vector, η represents the update coefficient, X _upper and X _lower are the upper and lower limits of the search space when the pigeon flock is searching for the position. 2. a kind of UAV swarm formation control method based on non-inferior solution pigeon flock optimization according to claim 1, is characterized in that: described in step 4, carry out position and speed update with reference to the position that self is better so far so far. The formula is formula (5):

in,

is the position of the i-th pigeon at the t-th iteration, V _i ^t represents the speed of the i-th pigeon at the t-th iteration, R is the influence factor of the map-compass operator, and r ₁ and r ₂ are respectively [ A random number between 0,1], X _gbest represents the current global optimal position of all pigeons,

Represents the local optimal position of the i-th pigeon at time t-1, c ₁ represents the factor learned from the global optimal pigeon, and c ₂ represents the factor learned from its own local optimal pigeon. 3. a kind of UAV swarm formation control method based on non-inferior solution pigeon flock optimization according to claim 1, is characterized in that: the design of the cost function described in step 5 is specifically as follows: In order to evaluate the optimal parameters for UAV swarm formation, the design of the cost function J _QP includes the state of the formation system and the control input, which is expressed as

where R and Q are both positive definite weight matrices, and

is the state of the predicted system, where N is a fixed time interval, and the corresponding control input is

x _k is the state of the UAV at the _k -th time, and uk is the control input of the UAV at the k-th time. The relationship between the two can be expressed as

where H _x =(A,A ² ,...,A ⁱ ,... A ^N ) ^T ,

4. a kind of UAV swarm formation control method based on non-inferior solution pigeon flock optimization according to claim 1, is characterized in that: the RHC controller design based on non-inferior solution pigeon flock optimization described in step 5, concrete Optimizing parameters for the RHC controller includes the following steps: ①Set the state of the wingman to be x ₀ at time k, and a set of optimal control inputs can be obtained based on step 5

select

As input to the RHC controller wingman,

give up; ②At time k+1, the status of the wingman is updated to x ₁ ; ③ Re-mark the current state of the wingman as x ₀ , record the current time as the kth time, and return to ① to repeat the cycle until the formation task ends.

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