CN109917806B - Unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization - Google Patents
Unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization Download PDFInfo
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Abstract
The invention relates to an unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization, which comprises the following implementation steps: the method comprises the following steps: unmanned aerial vehicle cluster formation model; step two: predicting the formation state of the unmanned aerial vehicle cluster; step three: initializing parameters of a non-inferior solution pigeon group optimization method; step four: designing based on a non-inferior solution pigeon group optimization method; step five: designing an unmanned aerial vehicle cluster formation RHC controller based on non-inferior solution pigeon swarm optimization; step six: and outputting the result of the unmanned aerial vehicle cluster formation control method. The method aims to provide a method for optimizing the unmanned aerial vehicle cluster formation controller on line in real time, so that the control level of unmanned aerial vehicle cluster formation in a complex battlefield environment is effectively improved.
Description
Technical Field
The invention discloses an unmanned aerial vehicle cluster formation control research method based on biological intelligent optimization, and belongs to the field of unmanned aerial vehicle autonomous control.
Background
The unmanned aerial vehicle is an unmanned aerial vehicle which is self-powered, remotely controlled by radio or autonomously flies, can perform various tasks and can be used for multiple times. The 20 th century 90 s began, and with the rapid development of the flight technology of a single unmanned aerial vehicle, the unmanned aerial vehicle gradually has very wide application in the fields of military, civil use and the like. However, as the modern battlefield environment becomes more comprehensive, three-dimensional, multidimensional and modern war, the single machine has performance constraints in various aspects when executing various tasks, and the efficiency and accuracy of executing the tasks are limited. Therefore, the cluster battle of multiple unmanned aerial vehicles is very important.
The success rate and the emergency resistance of unmanned aerial vehicle cluster flight are stronger than those of a single machine, unmanned aerial vehicle cluster formation is an important task of unmanned aerial vehicle cluster flight, and the unmanned aerial vehicle cluster formation is widely applied to aspects of military reconnaissance, target striking, communication relay, electronic countermeasure, battlefield evaluation, disturbance temptation and the like. The unmanned aerial vehicle cluster formation process needs effective communication and coordination, and mutual collision among the unmanned aerial vehicle clusters and accidental injury caused by interference of enemy unmanned aerial vehicles are avoided. In order to realize autonomous flight of unmanned aerial vehicle cluster formation and complete specified complex war tasks, the problem of unmanned aerial vehicle cluster formation control needs to be solved urgently.
The unmanned aerial vehicle cluster formation control refers to a control technology with a certain geometric configuration, which is formed, maintained and reconstructed in order to adapt to battlefield environments and task situations and meet the requirements of various war tasks, military and civil targets when a plurality of unmanned aerial vehicles execute specific tasks. The unmanned aerial vehicle cluster formation control method mainly comprises the following steps: a Changji-Liaoji law, a virtual structure law, a behavior control law. The behavior control method needs to form a control instruction according to preset information and a trigger condition, so that the adaptability and flexibility of formation are reduced; the virtual structure method requires formation flying to meet rigid motion, and greatly limits the application range of actual flying; a director-bureaucratic law designates one of the drones as a director and the other drones as bureaucratic laws. The paraplane flies according to a preset track, and the wing planes fly in formation along with the paraplane under a certain control strategy to reach consistent speed.
In the process of forming unmanned aerial vehicle clusters, strong coupling relation and nonlinear characteristics exist between long plane-wing plane models, and meanwhile, the unmanned aerial vehicle clusters are restrained and influenced by various complex battlefield environments, so that the unmanned aerial vehicle clusters become an optimization problem which is solved in real time and restrained. Although the classical PID control method can realize cluster formation control of the unmanned aerial vehicle, the process of determining parameters is complex; the extremum search method can only solve the problem of minimizing the power required by the wing plane in the formation flight of the unmanned aerial vehicle cluster; the Rolling Horizon Control (RHC) is a Control method based on online optimization and applied to industrial Control at the earliest, has the advantages that cost functions can integrate multiple Control targets, can adapt to condition changes, can handle Control input constraints and system state constraints, and the like, and is a proper choice for a leader-bureau law controller of a cluster formation of unmanned aerial vehicles. However, in the unmanned aerial vehicle cluster formation process, the relationship between the input quantity of the RHC controller and the state of the unmanned aerial vehicle is difficult to determine, and the problem of how to select the parameters of the RHC controller becomes a difficult point in solving the unmanned aerial vehicle cluster formation control problem.
A Pigeon Instrumented Optimization (PIO) is a bionic intelligent Optimization algorithm for simulating homing behavior of a Pigeon flock, and navigation tools such as sun, magnetic field, landmarks and the like are abstracted into a map-compass operator and a landmark operator to realize convergence of the algorithm and obtain a global optimal solution, but the convergence speed of the algorithm is low and the algorithm is easy to fall into local optimal. The non-inferior solution is a suspected optimal solution in the process of finding the global optimal solution, and the operator is introduced into the original PIO algorithm to improve the performance of the operator, so that the RHC controller parameters are optimized.
In conclusion, the invention provides the unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization, so as to solve the problem that the RHC controller in the unmanned aerial vehicle cluster formation is difficult to optimize on line, and effectively improve the unmanned aerial vehicle cluster formation control level.
Disclosure of Invention
The invention aims to provide an unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization, wherein a non-inferior solution operator (suspected optimal solution in the process of searching global optimal solution) is introduced into an original PIO algorithm to realize the improvement of the performance of the unmanned aerial vehicle cluster formation control method, so that the optimization of the RHC controller parameters is realized, the problem that the RHC controller in the unmanned aerial vehicle cluster formation is difficult to optimize on line is solved, and the unmanned aerial vehicle cluster formation control level is effectively improved; meanwhile, the RHC controller optimized by the non-inferior solution pigeon swarm can adjust parameters according to the real-time state of the unmanned aerial vehicle cluster formation to achieve the optimal control effect, so that a method for optimizing the unmanned aerial vehicle cluster formation controller on line in real time is provided, and the control level of the unmanned aerial vehicle cluster formation in the complex battlefield environment is effectively improved.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: an unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization comprises the following specific steps:
the method comprises the following steps: unmanned aerial vehicle cluster formation model
And modeling the unmanned aerial vehicle cluster on the basis of adopting a Changplane-Liao plane method. Wherein the long machine model is
The pneumatic influence of the wake flow of the long plane on the wing plane is considered by utilizing the horseshoe vortex model, and the wing plane model is
Wherein the content of the first and second substances,
is the derivative of the actual position (x, y, z) of the drone, ζ is the derivative of z,
in order to be the desired distance for the formation,
as the time constant of the bureau-like motor speed circuit,
time constant, ψ, representing a wing aircraft course angle loopW,VW,hWRespectively representing the actual course angle, speed and altitude of a wing plane,
i.e. the heading angle, speed and altitude of the corresponding wing plane control input. Similarly,. psiL,VL,hLAnd
the actual heading angle, speed and altitude of the longplane and the heading angle, speed and altitude of the control input. Tau isa,τbIs the time constant of the unmanned plane on the height channel less than 0, S represents the wing area, m is the total mass,
is the gradient of the change in the derivative of the lateral force in the y-direction,
is the gradient of the change in the lateral force derivative in the z direction,
representing the gradient in the y-direction of the change in the derivative of the lift force,
is the gradient of the change in the derivative of the resistance in the z direction.
Step two: unmanned aerial vehicle cluster formation state prediction
According to step one, ignoring the non-linear part, the model of the drone can be simplified to
Where A and B are coefficient matrices, X ═ X1,x2,…,xk,…,xN],xk＝[x,y,VW,ψW,z,ζ]TThe state of the unmanned plane at the kth moment. U ═ U1,u2,…,uk,…,uN],
Indicating the control input at time k.
The state of the unmanned aerial vehicle at the k +1 th moment can be estimated from the state at the k +1 th moment, and the relation between the two states can be expressed as
xk+1＝Axk+Buk(4)
Wherein x isk+1The state of the unmanned plane at the k +1 th moment.
Step three: parameter for initializing optimization method of non-inferior solution pigeon group
Assuming that the total number of the pigeon groups is N, respectively initializing the positions X of N pigeons0And velocity V0The position of the ith pigeon is represented by Xi＝[xi1,xi2,xi3,…,xiD]The velocity of the ith pigeon is denoted Vi＝[vi1,vi2,vi3,…,viD]I-1, 2, … N, D is the dimension of the position and speed of each pigeon, i.e. the number of parameters to be optimized. Setting the total cycle number of the map-compass operator stage to be T1The number of cycles of the landmark operator phase is T2The total number of cycles of the two stages is T ═ T1+T2And (4) showing.
Step four: method design based on optimization of non-inferior solution pigeon group
1) Independent learning method based on map-compass operator
When the pigeon group is far away from the destination, the pigeon group navigates by means of the map-compass information, and the position and the speed of the pigeon group are adjusted in real time by referring to the optimal pigeon in the current pigeon group in the homing process. An independent learning mechanism is added on the basis of an original pigeon group optimization algorithm, namely, each pigeon not only refers to the optimal pigeon in the current pigeon group, but also refers to the superior position of the pigeon so far to update the position and the speed, and the position and speed updating formula is shown as an expression (5). A schematic diagram of an independent learning mechanism based on map-compass operators is shown in fig. 1.
Wherein the content of the first and second substances,
for the position of the ith pigeon at the t-th iteration,
representing the velocity of the ith pigeon at the t-th iteration, R being the influence factor of the map-compass operator, R1And r2Are respectively [0,1]Random number between, XgbestRepresents the global optimal position of all pigeons at present,
represents the local optimum position of the ith pigeon to the t-1 moment, c1Factor representing learning towards globally optimal pigeon, c2Representing a factor for learning towards the own locally optimal pigeon.
2) Suspected optimal solution (non-inferior solution) optimization method based on landmark operator
When the pigeon group approaches to the destination, the pigeon group is guided to home by the landmark, and the position of the pigeon group is updated by adopting a landmark operator at the stage. In each iteration process, the number N of half of the better performancetThe pigeons are selected, and the other half pigeons which are not selected are eliminated. The central position of the selected pigeon group
And (3) updating the reference position for updating the positions of other pigeons in a manner shown in the formula (6).
Wherein the content of the first and second substances,
is the cost function of ith pigeon in t-1 iteration, and rand represents [0,1]A random number in between.
In the process of searching the global optimal solution, the original pigeon swarm optimization algorithm is easy to mistake the non-optimal solution as the global optimal solution, so that the algorithm is trapped in local optimization. To avoid the algorithm from falling into local optima, a suspected optimal solution (non-inferior solution) is introduced into the original pigeon flock optimization algorithm. The suspected optimal solution (non-inferior solution) is that when the fitness value of a certain pigeon is close to the currently obtained global optimal value, the position is regarded as the suspected optimal solution. The non-inferior solution is judged according to the formula (7). A schematic diagram of a landmark operator based non-inferiority solution optimization mechanism is shown in fig. 2.
Wherein the content of the first and second substances,
the average value of the local optimal values of all the pigeons is a minimum value, lambda represents a coordination parameter which can be used for adjusting the number of non-inferior solutions, and the searching precision can be improved by reducing the number of the non-inferior solutions. When the current global optimum solution XgbestIs a fitness value fcost(Xgbest) And the determined solution
Fitness value of
Absolute value of the difference of
And the current global optimum solution XgbestIs a fitness value fcost(Xgbest) Average value of local optimum values of all current pigeons
Absolute value of the difference of
When the ratio of (A) is less than λ, the solution is judged
Is a non-inferior solution, otherwise, is a solution judged
Is not a non-inferior solution. The coordination parameters are defined as:
if it is
If the pigeon is determined to be a non-inferior solution, the position updating formula is (9), otherwise, the pigeon position is updated according to the position updating mode of the original pigeon swarm optimization algorithm in the formula (6).
Wherein γ ═ γ1,γ2,…γi…γD],γi∈[-1,1]I-1, 2, … D is a range of [ -1,1]D-dimensional vector between, η denotes update coefficient, XupperAnd XlowerThe upper limit and the lower limit of the search space when the pigeon group searches the position are respectively.
A structural block diagram based on non-inferior solution pigeon flock optimization is shown in figure 3.
Step five: unmanned aerial vehicle cluster formation RHC controller design based on non-inferior solution pigeon swarm optimization
Firstly, designing an unmanned aerial vehicle cluster formation cost function, and secondly, designing an RHC controller based on non-inferior solution pigeon group optimization; cost function JQPThe design of (1) comprises the state of the formation system and the control input quantity, optimizedThe purpose is to find JQPThe RHC controller obtains a group of optimal control parameters, and the control effect on the self-cluster formation of the unmanned aerial vehicles is optimal.
1) Design of cost function
Cost function J for evaluating optimization parameters for unmanned aerial vehicle cluster formationQPThe design of (A) includes the state of the formation system and the control input quantity, expressed as
Wherein R and Q are both positive definite weight matrices, an
To predict the state of the system, where N is a fixed time interval and the corresponding control input is
xkFor the state of the drone at the kth moment, ukRepresents the control input of the unmanned plane at the k-th moment, and the relation between the two can be expressed as
Wherein Hx＝(A,A2,…,Ai,…AN)T，
The purpose of the optimization is to find JQPThe RHC controller obtains a group of optimal control parameters, and the control effect on the self-cluster formation of the unmanned aerial vehicles is optimal.
2) RHC controller design based on optimization of non-inferior solution pigeon flock
The structural block diagram of the RHC controller based on the optimization of the non-inferior solution pigeon flock is shown in figure 4. The RHC controller parameter optimization is implemented by the following steps:
① when k is set, the state of a wing plane is x0Based on step five, a group of optimal control input quantities can be obtained
Selecting
As input of the RHC controller bureaucratic,
discarding;
② k +1 time point, the state of wing plane is updated to x1；
③ re-marking the bureaucratic aircraft at this time as x0And recording the current time as the kth time, returning to ① to cycle again until the queuing task is finished.
Step six: unmanned aerial vehicle cluster formation control method result output
The invention adopts 5 unmanned planes to form a formation control, wherein one unmanned plane is a leader plane, and the other four unmanned planes are bureaucratic planes. If a pilot plane flies at a uniform speed at a certain altitude, 4 wing planes take off at different positions, and finally 5 planes fly in formation at the same speed at the same altitude.
The invention provides an unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization. The method is characterized in that an original pigeon group optimization method is improved by adding an independent learning and suspected optimal solution mechanism, optimal parameters of an RHC controller are obtained, and unmanned aerial vehicle cluster formation is controlled. The main advantages of the invention are mainly reflected in 2 aspects: 1) the improved pigeon group optimization algorithm has higher convergence speed and is not easy to fall into local optimum; 2) the RHC control is an online optimization control method, and the RHC controller optimized by the non-inferior solution pigeon swarm can adjust parameters according to the real-time state of the unmanned aerial vehicle cluster formation to achieve the optimal control effect.
Drawings
Fig. 1 is a schematic diagram of an independent learning mechanism based on a map-compass operator.
FIG. 2 is a schematic diagram of a landmark operator based non-inferiority solution optimization mechanism.
Fig. 3 is a structural block diagram based on optimization of a non-inferior solution pigeon flock.
Fig. 4 is a structural block diagram of an RHC controller based on non-inferior solution pigeon flock optimization.
Figure 5 cost function value response curve.
Fig. 6 is a diagram of the unmanned aerial vehicle formation output result.
The reference numbers and symbols in the figures are as follows:
Xpbest_i-local optimal solution for down to ith pigeon of current iteration number
Xpbest_j-local optimal solution for j pigeons up to the current number of iterations
Xgbest-global optimal solution of a pigeon flock
XcenterCentral position of the Pigeon group
Xnon-inferior_iThe ith suspected optimal solution (non-inferior solution)
Xnon-inferior_j-the jth suspected optimal solution (non-inferior solution)
Y-is (satisfies the condition)
N-No (unsatisfied with condition)
t-number of iterations
T1-number of iterations of independent learning process based on map-compass operator
T2-number of iterations of landmark operator based non-inferiority solution optimization procedure
J-cost function
Detailed Description
The validity of the proposed method is verified by a specific drone cluster formation example, see fig. 1 to 4. The experimental computer is configured with an Intel Core i7-4790 processor, 3.60Ghz dominant frequency, 4G memory, and software as MATLAB 2014a version. An unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization specifically comprises the following steps:
the method comprises the following steps: unmanned aerial vehicle cluster formation model
And modeling the unmanned aerial vehicle cluster on the basis of adopting a Changplane-Liao plane method. Wherein, the long machine model is shown as formula (1). The pneumatic influence of the wake of a long plane on a wing plane is considered by utilizing a horseshoe vortex model, and the wing plane model is as a formula (2). Assuming that the mass of each unmanned aerial vehicle is 1Kg, the speed of the unmanned aerial vehicle in the formation process is not more than 80m/s, the range of throttle thrust is 10N,100N, and the range of course angles is [ -50 degrees, 50 degrees ].
Step two: unmanned aerial vehicle cluster formation state prediction
According to the first step, ignoring the non-linear part, the model of the drone can be simplified as shown in equation (3). The state of the drone at the k +1 th moment can be estimated from the state at the k th moment, as shown in equation (4).
Step three: parameter for initializing optimization method of non-inferior solution pigeon group
Assuming that the total number of pigeons is N-30, respectively initializing the positions X of the N-30 pigeons0And velocity V0The position of the ith pigeon is represented by Xi＝[xi1,xi2,xi3,…,xiD]The velocity of the ith pigeon is denoted Vi＝[vi1,vi2,vi3,…,viD]I-1, 2, … N, D-36 (D-3-RHC prediction parameter 3-4) is the dimension of the position and speed of each pigeon, i.e. the number of parameters of the RHC controller to be optimized. Comparing the test results of multiple experiments, and setting the total cycle number of the map-compass operator stage as T 120, the number of cycles of the landmark operator phase is T210, T is the total number of cycles of the two phases1+T2And (4) showing.
Step four: method design based on optimization of non-inferior solution pigeon group
1) Independent learning method based on map-compass operator
When the pigeon group is far away from the destination, the pigeon group navigates by means of the map-compass information, and the position of the pigeon group and the optimal pigeon in the current pigeon group are adjusted in real time in the homing process of the pigeon groupSpeed. An independent learning mechanism is added on the basis of an original pigeon group optimization algorithm, namely, each pigeon not only refers to the optimal pigeon in the current pigeon group, but also refers to the superior position of the pigeon so far to update the position and the speed, and the position and speed updating formula is shown as an expression (5). A schematic diagram of an independent learning mechanism based on map-compass operators is shown in fig. 1. According to the relevant research results of those skilled in the art, setting R to 0.3 is an influence factor of a map-compass operator, c1＝c 22 denotes a learning factor.
2) Non-inferior solution optimizing method based on landmark operator
When the pigeon group approaches to the destination, the pigeon group is guided to home by the landmark, and the position of the pigeon group is updated by adopting a landmark operator at the stage. In each iteration process, the number N of half of the better performancetThe pigeons are selected, and the other half pigeons which are not selected are eliminated. The central position of the selected pigeon group
And (3) updating the reference position for updating the positions of other pigeons in a manner shown in the formula (6).
In the process of searching the global optimal solution, the original pigeon swarm optimization algorithm is easy to mistake the non-optimal solution as the global optimal solution, so that the algorithm is trapped in local optimization. To avoid the algorithm from falling into local optima, a suspected optimal solution (non-inferior solution) is introduced into the original pigeon flock optimization algorithm. The suspected optimal solution (non-inferior solution) is that when the fitness value of a certain pigeon is close to the currently obtained global optimal value, the position is regarded as the suspected optimal solution. The non-inferior solution is judged according to the formula (7). A schematic diagram of a landmark operator based non-inferiority solution optimization mechanism is shown in fig. 2.
λ represents a coordination parameter that can be used to adjust the number of non-inferior solutions, which can improve the search accuracy by reducing the number of non-inferior solutions. And when the ratio of the absolute value of the difference between the fitness value of the current global optimal solution and the fitness value of the judged solution to the absolute value of the difference between the fitness value of the current global optimal solution and the average value of the local optimal values of all the pigeons is smaller than lambda, judging the judged solution to be a non-inferior solution, otherwise, judging the judged solution not to be the non-inferior solution. The coordination parameter is defined as shown in equation (8).
If it is
If the pigeon position is determined to be a non-inferior solution, the position updating formula is (9), otherwise, the pigeon position is updated according to the formula (6), comparing the test results of multiple experiments, η -20 represents an updating coefficient, and X represents an updating coefficient upper1 and X lower0 denotes the upper and lower limits of the search space, respectively.
A structural block diagram based on non-inferior solution pigeon flock optimization is shown in figure 3.
Step five: unmanned aerial vehicle cluster formation RHC controller design based on non-inferior solution pigeon swarm optimization
1) Design of cost function
In order to evaluate the optimization parameters for the formation of unmanned aerial vehicle clusters, a cost function J shown in formula (10) is usedQPThe design of (a) includes the state of the formation system and the control inputs. Wherein R and Q are both positive definite weight matrices, an
To predict the state of the system, where N is a fixed time interval and the corresponding control input is
xkThe state at the time point k is set,
representing the control input, the relationship between the state at time k and the control input amount can be represented as shown in equation (11).
The purpose of the optimization is to find JQPThe RHC controller obtains a group of optimal control parameters, and the control effect on the self-cluster formation of the unmanned aerial vehicles is optimal.
2) RHC controller design based on optimization of non-inferior solution pigeon flock
The structural block diagram of the RHC controller based on the optimization of the non-inferior solution pigeon flock is shown in figure 4. The RHC controller parameter optimization is implemented by the following steps:
① when k is set, the state of a wing plane is x0Based on step four, a group of optimal control input quantity can be obtained
Selecting
As input of the RHC controller bureaucratic,
discarding;
② k +1 time point, the state of wing plane is updated to x1；
③ re-marking the bureaucratic aircraft at this time as x0The current time is set to the kth time, and the process returns to ① to perform the loop again.
Step six: unmanned aerial vehicle cluster formation control method result output
The invention adopts 5 unmanned planes to form a formation control, wherein one unmanned plane is a leader plane, and the other four unmanned planes are bureaucratic planes. The designed planes fly at a constant speed of 50m/s at the height of 300m, 4 wing planes take off at different positions, and finally 5 unmanned planes fly in formation at a speed of 50m/s at the height of 300 m.
As shown in step one, the state of the drone includes x, y, VW,ψWZ, values of 6 variables, the initial position of 5 drones is set as follows:
the initial state of the long machine is [0, 0, 300, 50, 0, 0 ];
the initial state of a bureaucratic 1 is [300, 300, 100, 50, 0, 0 ];
the initial state of a bureaucratic 2 is [300, -300, 500, 50, 0, 0 ];
the initial state of a wing-machine 3 is [600, 600, 400, 50, 0, 0 ];
the initial state of a wing-machine 4 is [600, -600, 200, 50, 0, 0 ].
In order to verify the effectiveness of the method provided by the invention, the invention also carries out corresponding comparison experiments, and the response curve of the cost function value is shown in figure 5. The unmanned aerial vehicle formation output result based on the method of the invention is shown in fig. 6.
Claims (4)
1. An unmanned aerial vehicle cluster formation control method based on non-inferior solution pigeon swarm optimization is characterized in that: the method comprises the following specific steps:
the method comprises the following steps: unmanned aerial vehicle cluster formation model
Modeling an unmanned aerial vehicle cluster on the basis of a Changplane-Liao plane method; wherein the long machine model is
The pneumatic influence of the wake flow of the long plane on the wing plane is considered by utilizing the horseshoe vortex model, and the wing plane model is
Wherein the content of the first and second substances,
is the derivative of the actual position (x, y, z) of the drone, ζ is the derivative of z,
in order to be the desired distance for the formation,
as the time constant of the bureau-like motor speed circuit,
time constant, ψ, representing a wing aircraft course angle loopW,VW,hWRespectively representing the actual course angle, speed and altitude of a wing plane,
namely the corresponding bureaucratic controlMaking an input course angle, speed and height; similarly,. psiL,VL,hLAnd
the actual course angle, speed and height of the long machine and the course angle, speed and height of the control input are obtained; tau isa,τbIs the time constant of the unmanned plane on the height channel less than 0, S represents the wing area, m is the total mass,
is the gradient of the change in the derivative of the lateral force in the y-direction,
is the gradient of the change in the lateral force derivative in the z direction,
representing the gradient in the y-direction of the change in the derivative of the lift force,
is the gradient of the change in the resistance derivative in the z direction;
step two: unmanned aerial vehicle cluster formation state prediction
According to step one, ignoring the non-linear part, the model of the drone can be simplified to
Where A and B are coefficient matrices, X ═ X1,x2,…,xk,…,xN],xk＝[x,y,VW,ψW,z,ζ]TThe state of the unmanned plane at the kth moment is shown;
indicating a control input amount at the k-th time;
the state of the unmanned aerial vehicle at the k +1 th moment can be estimated from the state at the k +1 th moment, and the relation between the two states can be expressed as
xk+1＝Axk+Buk(4)
Wherein x isk+1The state of the unmanned plane at the (k + 1) th moment is shown;
step three: parameter for initializing optimization method of non-inferior solution pigeon group
Assuming that the total number of the pigeon groups is N, respectively initializing the positions X of N pigeons0And velocity V0The position of the ith pigeon is represented by Xi＝[xi1,xi2,xi3,…,xiD]The velocity of the ith pigeon is denoted Vi＝[vi1,vi2,vi3,…,viD]D is the dimension of the position and speed of each pigeon, i is 1,2, … N, i is the number of parameters to be optimized; setting the total cycle number of the map-compass operator stage to be T1The number of cycles of the landmark operator phase is T2The total number of cycles of the two stages is T ═ T1+T2Represents;
step four: method design based on optimization of non-inferior solution pigeon group
1) Independent learning method based on map-compass operator
When the pigeon group is far away from the destination, the pigeon group navigates by means of map-compass information, and the position and speed of the pigeon group are adjusted in real time by referring to the optimal pigeon in the current pigeon group in the homing process; an independent learning mechanism is further added on the basis of an original pigeon group optimization algorithm, namely, each pigeon not only refers to the optimal pigeon in the current pigeon group, but also refers to the superior position of the pigeon so far to update the position and the speed;
2) suspected optimal solution, namely non-inferior solution optimizing method based on landmark operator
When the pigeon group approaches to the destination, the pigeon group is guided to home by the landmark, and the position of the pigeon group is updated by adopting a landmark operator at the stage; in each iteration process, the number N of half of the better performancetThe pigeons are selected, and the other half pigeons which are not selected are eliminated; selected byCentral position of pigeon in the middle
Updating the reference positions for updating the positions of other pigeons in a position updating mode shown as a formula (6);
wherein the content of the first and second substances,
is the cost function of ith pigeon in t-1 iteration, and rand represents [0,1]A random number in between;
introducing a suspected optimal solution, namely a non-inferior solution, into an original pigeon group optimization algorithm, wherein the suspected optimal solution, namely the non-inferior solution is regarded as the suspected optimal solution when the fitness value of a certain pigeon is close to the currently obtained global optimal value;
step five: unmanned aerial vehicle cluster formation RHC controller design based on non-inferior solution pigeon swarm optimization
Firstly, designing an unmanned aerial vehicle cluster formation cost function, and secondly, designing an RHC controller based on non-inferior solution pigeon group optimization; cost function JQPThe design of (1) comprises the state of the formation system and the control input quantity, and the optimization aims to find JQPThe RHC controller obtains a group of optimal control parameters, and the control effect on the self-cluster formation of the unmanned aerial vehicles is optimal;
step six: outputting the result of the unmanned aerial vehicle cluster formation control method;
the mode of judging non-inferior solutions in the fourth step is as shown in formula (7):
wherein the content of the first and second substances,
is as followsThe average value of the local optimal values of all the pigeons is a minimum value, lambda represents a coordination parameter which can be used for adjusting the number of non-inferior solutions, and the search precision can be improved by reducing the number of the non-inferior solutions; when the current global optimum solution XgbestIs a fitness value fcost(Xgbest) And the determined solution
Fitness value of
Absolute value of the difference of
And the current global optimum solution XgbestIs a fitness value fcost(Xgbest) Average value of local optimum values of all current pigeons
Absolute value of the difference of
When the ratio of (A) is less than λ, the solution is judged
Is a non-inferior solution, otherwise, is a solution judged
Not a non-inferior solution; the coordination parameters are defined as:
if it is
If the solution is determined to be a non-inferior solution, the position update formula is (9), otherwise, the formula is pressed(6) Updating the positions of the pigeons in a position updating mode of a medium-original pigeon group optimization algorithm;
wherein γ ═ γ1,γ2,…γi…γD],γi∈[-1,1]I-1, 2, … D is a range of [ -1,1]D-dimensional vector between, η denotes update coefficient, XupperAnd XlowerThe upper limit and the lower limit of the search space when the pigeon group searches the position are respectively.
2. The unmanned aerial vehicle cluster formation control method based on non-inferiority solution pigeon crowd optimization according to claim 1, characterized in that: in step four, the formula for updating the position and the speed with reference to the best position so far is expressed as formula (5):
wherein the content of the first and second substances,
for the position of the ith pigeon at the t-th iteration, Vi tRepresenting the velocity of the ith pigeon at the t-th iteration, R being the influence factor of the map-compass operator, R1And r2Are respectively [0,1]Random number between, XgbestRepresents the global optimal position of all pigeons at present,
represents the local optimum position of the ith pigeon to the t-1 moment, c1Factor representing learning towards globally optimal pigeon, c2Representing a factor for learning towards the own locally optimal pigeon.
3. The unmanned aerial vehicle cluster formation control method based on non-inferiority solution pigeon crowd optimization according to claim 1, characterized in that: the design of the cost function described in the step five is specifically as follows:
cost function J for evaluating optimization parameters for unmanned aerial vehicle cluster formationQPThe design of (A) includes the state of the formation system and the control input quantity, expressed as
Wherein R and Q are both positive definite weight matrices, an
To predict the state of the system, where N is a fixed time interval and the corresponding control input is
xkFor the state of the drone at the kth moment, ukRepresents the control input of the unmanned plane at the k-th moment, and the relation between the two can be expressed as
Wherein Hx＝(A,A2,…,Ai,…AN)T，
4. The unmanned aerial vehicle cluster formation control method based on non-inferiority solution pigeon crowd optimization according to claim 1, characterized in that: the design of the RHC controller based on the optimization of the non-inferior solution pigeon flock, specifically the parameter optimization of the RHC controller, comprises the following steps:
① when k is set, the state of a wing plane isx0Based on step five, a group of optimal control input quantities can be obtained
Selecting
As input of the RHC controller bureaucratic,
discarding;
② k +1 time point, the state of wing plane is updated to x1；
③ re-marking the bureaucratic aircraft at this time as x0And recording the current time as the kth time, returning to ① to cycle again until the queuing task is finished.
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