CN113625767A - Fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on preferred pheromone gray wolf algorithm - Google Patents

Fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on preferred pheromone gray wolf algorithm Download PDF

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CN113625767A
CN113625767A CN202111027993.8A CN202111027993A CN113625767A CN 113625767 A CN113625767 A CN 113625767A CN 202111027993 A CN202111027993 A CN 202111027993A CN 113625767 A CN113625767 A CN 113625767A
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pheromone
unmanned aerial
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刘中常
杨川龙
岳伟
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Dalian Maritime University
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Abstract

The invention provides a fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on an optimal pheromone gray wolf algorithm. The method comprises the following steps: s1, establishing a three-dimensional map containing M threat sources; s2, establishing a cluster track planning cost function; and S3, planning the flight paths of all fixed-wing unmanned aerial vehicle clusters by adopting a gray wolf algorithm based on the preferred pheromone. The method adopts an optimal pheromone gray wolf algorithm to solve the collaborative track planning problem of the fixed-wing unmanned aerial vehicle cluster in the three-dimensional scene, and selects a plurality of optimal gray wolfs to update pheromones on track points based on a wolf cluster grade system in the algorithm; the exploration phase of each wolf is guided by pheromone to improve the convergence rate and the solving stability of the algorithm, and the corner constraint of the unmanned aerial vehicle and the collision avoidance constraint between the unmanned aerial vehicles are met. The technical scheme of the invention solves the problem of fixed wing unmanned cluster collaborative path planning in high-dimensional and multi-constraint complex scenes.

Description

Fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on preferred pheromone gray wolf algorithm
Technical Field
The invention relates to the technical field of unmanned aerial vehicle cluster collaborative path planning and flight path planning, in particular to a fixed wing unmanned aerial vehicle cluster collaborative path planning method based on an optimal pheromone gray wolf algorithm.
Background
In the face of modern air environment which is increasingly complex, working efficiency and task success rate can be improved by utilizing cooperative work of unmanned aerial vehicle clusters. Meanwhile, the fixed-wing unmanned aerial vehicle has the characteristics of long endurance time, high flying speed and large load capacity, and is widely applied to the fields of geological exploration, disaster rescue, military reconnaissance, attack and the like. Collaborative flight path planning is a key technology for ensuring effective work of fixed-wing unmanned aerial vehicle clusters, and multiple flight paths enabling each unmanned aerial vehicle to finally reach respective target points from an initial point according to a better flight path need to be searched in a specific task scene, and the flight paths meet the physical constraints of the fixed-wing unmanned aerial vehicles, so that collision among the unmanned aerial vehicles is avoided, and meanwhile, obstacles and threats are safely avoided. In addition, in order to meet the requirement of the maneuverability of the unmanned aerial vehicle, the planning algorithm needs to have higher solving speed and solving stability.
Traditional path planning methods (e.g., a-algorithm, Dijkstra, etc.) are computationally intensive, inefficient, and difficult to handle scenarios with motion constraints. The swarm intelligent algorithm is widely applied to solving various path planning problems in recent years due to the characteristics of easy implementation, simple structure and the like, wherein the gray wolf algorithm carries out optimization by simulating a rank system and collective predation behavior of a wolf swarm, and compared with swarm intelligent optimization algorithms such as a particle swarm algorithm and an ant swarm algorithm, the swarm intelligent algorithm has the advantages of strong optimization capability, high convergence speed, good result stability and the like when solving a complex optimization problem. However, in the basic gray wolf algorithm, the cooperation capability between gray wolfs is not strong, each iteration lacks correlation, the convergence speed of the algorithm in the subsequent stage is slow, and the algorithm is easy to fall into local optimum when solving a complex problem. The gray wolves living in nature cooperate closely, for example, pheromone factors such as smell are left in the process of chasing the prey, and the wolves approach the prey as soon as possible.
Disclosure of Invention
According to the scheme, the problem of how to solve the fixed-wing unmanned cluster collaborative path planning of the high-dimensionality and multi-constraint complex scene is solved, and the fixed-wing unmanned cluster collaborative path planning method based on the preferred pheromone gray wolf algorithm is provided. The method adopts an optimal pheromone gray wolf algorithm to solve the collaborative track planning problem of the fixed-wing unmanned aerial vehicle cluster in the three-dimensional scene, and selects a plurality of optimal gray wolfs to update pheromones on track points based on a wolf cluster grade system in the algorithm; the exploration phase of each wolf is guided by pheromone to improve the convergence rate and the solving stability of the algorithm, and the corner constraint of the unmanned aerial vehicle and the collision avoidance constraint between the unmanned aerial vehicles are met.
The technical means adopted by the invention are as follows:
a fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on an optimal pheromone Grey wolf algorithm comprises the following steps:
s1, establishing a three-dimensional map containing M threat sources;
s2, establishing a cluster track planning cost function;
and S3, planning the flight paths of all fixed-wing unmanned aerial vehicle clusters by adopting a gray wolf algorithm based on the preferred pheromone.
Further, the specific implementation process of step S1 is as follows:
determining a starting point and a target point of each unmanned aerial vehicle, equally dividing a connecting line of the starting point and the target point of each unmanned aerial vehicle into D +1 parts, namely, the track of each unmanned aerial vehicle comprises D track points.
Further, the step S2 includes:
s21, constructing fuel cost J of each unmanned aerial vehicle N E {1,2n,fuel：
Figure BDA0003244237570000021
Wherein, wi→i+1,fuelThe fuel cost from each track point i to i +1 is in direct proportion to the length of the range;
s22, constructing potential threat cost J of all threat sources to unmanned aerial vehicle nn,threat：
Figure BDA0003244237570000022
Wherein, Jthreat,i→i+1The threat cost of the track between two adjacent track points i and i +1 is obtained;
s23, calculating the sum of the threat function values on 5 equipartition points on the track, namely:
Figure BDA0003244237570000031
wherein, wthreat,kIs the threat function value at the k-th equipartition point, and the calculation formula is as follows:
Figure BDA0003244237570000032
wherein, constant CmCoefficient, R, representing the threat magnitude of the mth threat sourcemIs the radius of the mth threat source, di,m,kRepresenting the distance from the center of the mth threat source to the kth child node on the connection line of the points i and i + 1;
s24, establishing a cluster track planning cost function J:
Figure BDA0003244237570000033
wherein λ ∈ [0,1] represents a weight coefficient.
Further, the specific implementation process of step S3 is as follows:
s31, initializing gray wolf algorithm parameters and pheromones of all the alternative track points, wherein the gray wolf algorithm parameters comprise the number POP of gray wolfs, the maximum iteration number T and the pheromone concentration tau (0) on all the alternative tracks;
s32, each time of iteration t, projecting the three-dimensional scene to a two-dimensional XY plane to reduce the calculated amount, generating a POP group of feasible alternative track points meeting constraint conditions for each unmanned aerial vehicle on the two-dimensional XY plane, namely generating POP wolfs, wherein each wolf represents a group of feasible two-dimensional track points { (x)n,i(t),yn,i(t)),i＝1,2,...,D}；
S33, generating a height value meeting the pitch angle constraint;
s34, calculating the cost of each group of feasible alternative three-dimensional track points according to the cluster track planning cost function established in the step S2, and selecting the optimal three groups of track points as alpha, beta and delta wolfs;
s35, updating the position of each wolf according to the wolf algorithm
Figure BDA0003244237570000034
S36, selecting the optimal flight path represented by the three wolfs alpha, beta and delta, and updating pheromones on the flight path;
and S37, circularly executing the steps S32 to S36 for each unmanned aerial vehicle until the maximum iteration number T is met, and outputting the optimal flight paths of all the unmanned aerial vehicles.
Further, the POP grayish generated in the step S32 follows the following principle:
principle one, satisfying the yaw angle constraint:
Figure BDA0003244237570000041
i.e. the yaw angle of each drone
Figure BDA0003244237570000042
Not greater than maximum yaw angle
Figure BDA0003244237570000043
And a second principle is to satisfy collision avoidance constraints:
Figure BDA0003244237570000044
wherein D issafeExpressed as the minimum safe distance between drones;
principle three, probability of each possible alternative track point being selected:
Figure BDA0003244237570000045
h (i) is a set of a first and a second principle when the next track point is selected on the ith track point, and hiRepresenting any feasible point in the set; γ and ξ are normal numbers;
Figure BDA0003244237570000046
representing waypoints i to h in the t iterationiPheromone concentration in between;
Figure BDA0003244237570000047
is a heuristic factor, which indicates that the wolf is at the step i to the next selectable point hiTo a desired degree of (c), the values thereof with i and hiLinear distance between two points
Figure BDA0003244237570000048
In inverse proportion, i.e.
Figure BDA0003244237570000049
Further, the step S33 generates a height value satisfying the pitch angle constraint, including:
on the premise of meeting the horizontal XY direction collision avoidance constraint, selecting a height value meeting the pitch angle constraint in the height Z direction to form a feasible alternative three-dimensional track point
Figure BDA00032442375700000410
The height between every two adjacent track points satisfies the following constraint:
|φn|≤φmax
wherein phi isnIs the pitch angle.
Further, the step S35 updates the position of each wolf according to the wolf algorithm
Figure BDA00032442375700000411
The update formula is as follows:
Figure BDA0003244237570000051
Figure BDA0003244237570000052
wherein,
Figure BDA0003244237570000053
respectively representing the current positions of alpha, beta and delta wolf,
Figure BDA0003244237570000054
respectively represent the distances between alpha, beta, delta wolf and other individuals, and the calculation formula is as follows:
Figure BDA0003244237570000055
Figure BDA0003244237570000056
and
Figure BDA0003244237570000057
the update rule of (2) is as follows:
Figure BDA0003244237570000058
Figure BDA0003244237570000059
wherein,
Figure BDA00032442375700000510
is a convergence factor, which decreases linearly as the number of iterations decreases from 2 to 0,
Figure BDA00032442375700000511
and
Figure BDA00032442375700000512
is taken as [0,1]]A random number in between.
Further, the step S36 includes:
s361, updating pheromones on the flight path represented by the three wolfs alpha, beta and delta, and updating the formula as follows:
τi,i+1(t+1)＝(1-ρ)·τi,i+1(t)+Δτi,i+1(t)
where ρ ≦ 0 ≦ 1 denotes the attenuation factor of the pheromone, Δ τi,i+1(t) represents newly-left pheromone increment of the paths of the three wolfs of alpha, beta and delta from the i to the i +1 during the t iteration;
s362, calculating newly-left pheromone increment delta tau of the alpha, beta and delta three wolfs on the waypoints i to i +1 during the t iterationi,i+1(t), the calculation formula is as follows:
Figure BDA00032442375700000513
wherein Q ispP ∈ { α, β, δ } is a normal number, and Qα>Qβ>QδThe pheromone increment left by the three best wolfs is different, di,i+1The length of the track point i to i +1, namely the concentration of the newly left pheromone on each route is inversely proportional to the length of the route.
Compared with the prior art, the invention has the following advantages:
1. according to the fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on the preferred pheromone gray wolf algorithm, aiming at the collaborative path planning problem of the fixed-wing unmanned aerial vehicle cluster in the three-dimensional scene, the solving efficiency is accelerated by performing dimensionality reduction decomposition on the three-dimensional scene and adopting measures such as an improved gray wolf algorithm and the like;
2. according to the fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on the optimal pheromone gray wolf algorithm, the convergence speed of the algorithm and the solving stability are enhanced by introducing the pheromone and the optimal method into the traditional gray wolf algorithm, so that the optimizing capability of the gray wolf algorithm in solving the optimal track point is improved;
3. according to the fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on the preferred pheromone gray wolf algorithm, the planned route takes the corner constraint and the mutual collision avoidance constraint of the unmanned aerial vehicle into consideration, and the actual requirement of the unmanned aerial vehicle cluster route can be effectively met.
Based on the reason, the method can be widely popularized in the fields of unmanned aerial vehicle cluster collaborative track planning and the like.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of a three-dimensional track planning result of the scene 1 according to the embodiment of the present invention.
Fig. 3 is a two-dimensional track planning result diagram of the scene 1 according to the embodiment of the present invention.
Fig. 4 is a diagram of a three-dimensional track planning result of the scene 2 according to the embodiment of the present invention.
Fig. 5 is a two-dimensional track planning result diagram of the scene 2 according to the embodiment of the present invention.
Fig. 6 is a diagram of a three-dimensional track planning result of the scene 3 according to the embodiment of the present invention.
Fig. 7 is a diagram of a two-dimensional track planning result of the scene 3 according to the embodiment of the present invention.
Fig. 8 is a comparison graph of the average cost convergence curves for the scenario 3 under different planning algorithms provided in the embodiment of the present invention.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
As shown in fig. 1, the invention provides a fixed-wing drone cluster collaborative path planning method based on a preferred pheromone grayish wolf algorithm, which includes the following steps:
s1, establishing a three-dimensional map containing M threat sources;
in specific implementation, as a preferred embodiment of the present invention, the specific implementation process of step S1 is as follows:
determining a starting point and a target point of each unmanned aerial vehicle, equally dividing a connecting line of the starting point and the target point of each unmanned aerial vehicle into D +1 parts, namely, the track of each unmanned aerial vehicle comprises D track points.
S2, establishing a cluster track planning cost function;
in a specific implementation manner, as a preferred embodiment of the present invention, the step S2 includes:
s21, constructing fuel cost J of each unmanned aerial vehicle N E {1,2n,fuel：
Figure BDA0003244237570000071
Wherein, wi→i+1,fuelThe fuel cost from each track point i to i +1 is in direct proportion to the length of the range;
s22, constructing potential threat cost J of all threat sources to unmanned aerial vehicle nn,threat：
Figure BDA0003244237570000081
Wherein, Jthreat,i→i+1The threat cost of the track between two adjacent track points i and i +1 is obtained;
s23, calculating the sum of the threat function values on 5 equipartition points on the track, namely:
Figure BDA0003244237570000082
wherein, wthreat，kIs the threat function value at the k-th equipartition point, and the calculation formula is as follows:
Figure BDA0003244237570000083
wherein, constant CmCoefficient, R, representing the threat magnitude of the mth threat sourcemIs the radius of the mth threat source, di,m,kRepresenting the distance from the center of the mth threat source to the kth child node on the connection line of the points i and i + 1;
s24, establishing a cluster track planning cost function J:
Figure BDA0003244237570000084
wherein λ ∈ [0,1] represents a weight coefficient.
And S3, planning the flight paths of all fixed-wing unmanned aerial vehicle clusters by adopting a gray wolf algorithm based on the preferred pheromone.
In specific implementation, as a preferred embodiment of the present invention, the specific implementation process of step S3 is as follows:
s31, initializing gray wolf algorithm parameters and pheromones of all the alternative track points, wherein the gray wolf algorithm parameters comprise the number POP of gray wolfs, the maximum iteration number T and the pheromone concentration tau (0) on all the alternative tracks;
s32, each time of iteration t, projecting the three-dimensional scene to a two-dimensional XY plane to reduce the calculated amount, generating a POP group of feasible alternative track points meeting constraint conditions for each unmanned aerial vehicle on the two-dimensional XY plane, namely generating POP wolfs, wherein each wolf represents a group of feasible two-dimensional track points { (x)n,i(t),yn,i(t)),i＝1,2,...,D}；
The POP grayish wolf generated in the step S32 follows the following principle:
principle one, satisfying the yaw angle constraint:
Figure BDA0003244237570000091
i.e. the yaw angle of each drone
Figure BDA0003244237570000092
Not greater than maximum yaw angle
Figure BDA0003244237570000093
And a second principle is to satisfy collision avoidance constraints:
Figure BDA0003244237570000094
wherein D issafeExpressed as the minimum safe distance between drones;
principle three, probability of each possible alternative track point being selected:
Figure BDA0003244237570000095
h (i) is a set of a first and a second principle when the next track point is selected on the ith track point, and hiRepresenting any feasible point in the set; γ and ξ are normal numbers;
Figure BDA0003244237570000096
representing waypoints i to h in the t iterationiPheromone concentration in between;
Figure BDA0003244237570000097
is a heuristic factor, which indicates that the wolf is at the step i to the next selectable point hiTo a desired degree of (c), the values thereof with i and hiLinear distance between two points
Figure BDA0003244237570000098
In inverse proportion, i.e.
Figure BDA0003244237570000099
S33, generating a height value meeting the pitch angle constraint, comprising:
on the premise of meeting the horizontal XY direction collision avoidance constraint, selecting a height value meeting the pitch angle constraint in the height Z direction to form a feasible alternative three-dimensional track point
Figure BDA00032442375700000910
The height between every two adjacent track points satisfies the following constraint:
|φn|≤φmax
wherein phi isnIs the pitch angle.
S34, calculating the cost of each group of feasible alternative three-dimensional track points according to the cluster track planning cost function established in the step S2, and selecting the optimal three groups of track points as alpha, beta and delta wolfs;
s35, updating the position of each wolf according to the wolf algorithm
Figure BDA00032442375700000911
The update formula is as follows:
Figure BDA0003244237570000101
Figure BDA0003244237570000102
wherein,
Figure BDA0003244237570000103
respectively representing the current positions of alpha, beta and delta wolf,
Figure BDA0003244237570000104
respectively represent the distances between alpha, beta, delta wolf and other individuals, and the calculation formula is as follows:
Figure BDA0003244237570000105
Figure BDA0003244237570000106
and
Figure BDA0003244237570000107
the update rule of (2) is as follows:
Figure BDA0003244237570000108
Figure BDA0003244237570000109
wherein,
Figure BDA00032442375700001010
is a convergence factor, which decreases linearly as the number of iterations decreases from 2 to 0,
Figure BDA00032442375700001011
and
Figure BDA00032442375700001012
is taken as [0,1]]A random number in between.
S36, selecting the optimal flight path represented by the three wolfs alpha, beta and delta, and updating pheromones on the flight path;
the step S36 includes:
s361, updating pheromones on the flight path represented by the three wolfs alpha, beta and delta, and updating the formula as follows:
τi,i+1(t+1)＝(1-ρ)·τi,i+1(t)+Δτi,i+1(t)
where ρ ≦ 0 ≦ 1 denotes the attenuation factor of the pheromone, Δ τi,i+1(t) represents newly-left pheromone increment of the paths of the three wolfs of alpha, beta and delta from the i to the i +1 during the t iteration;
s362, calculating newly-left pheromone increment delta tau of the alpha, beta and delta three wolfs on the waypoints i to i +1 during the t iterationi,i+1(t), the calculation formula is as follows:
Figure BDA00032442375700001013
wherein Q ispP ∈ { α, β, δ } is a normal number, and Qα>Qβ>QδThe pheromone increment left by the three best wolfs is different, di,i+1The length of the track point i to i +1, namely the concentration of the newly left pheromone on each route is inversely proportional to the length of the route.
And S37, circularly executing the steps S32 to S36 for each unmanned aerial vehicle until the maximum iteration number T is met, and outputting the optimal flight paths of all the unmanned aerial vehicles.
Examples
A simulation experiment is carried out on a Windows10 operating system, an algorithm running platform is MATLAB2016B, and the size of a planning space is 75km multiplied by 15 km. The method is implemented in three scenes with different complexity aiming at an N-5 fixed wing unmanned aerial vehicle cluster, and the implementation steps of each scene are as follows:
step 1: establishing a three-dimensional map containing 5 threat sources, and determining a starting point and a target point of each unmanned aerial vehicle, wherein the information of the threat sources is shown in table 1, and the starting point target points of the unmanned aerial vehicles are shown in table 2. And equally dividing a connecting line ST between the starting point S and the target point T of each unmanned aerial vehicle into 11 parts, namely, the track of each unmanned aerial vehicle comprises 10 track points.
TABLE 1 threat Source information
Figure BDA0003244237570000111
Table 2 starting point information of unmanned aerial vehicle
Figure BDA0003244237570000112
Figure BDA0003244237570000121
Step 2: establishing a cluster track planning cost function;
constructing fuel cost J of each unmanned aerial vehicle N E {1,2n,fuel：
Figure BDA0003244237570000122
Wherein, wi→i+1,fuelThe fuel cost from each track point i to i +1 is in direct proportion to the length of the range;
constructing potential threat cost J of all threat sources to unmanned aerial vehicle nn,threat：
Figure BDA0003244237570000123
Wherein, Jthreat,i→i+1Is a track between two adjacent track points i and i +1The threat cost of;
calculating the sum of the threat function values on 5 equipartition points on the flight path, namely:
Figure BDA0003244237570000124
wherein, wthreat，kIs the threat function value at the k-th equipartition point, and the calculation formula is as follows:
Figure BDA0003244237570000125
wherein, constant CmCoefficient, R, representing the threat magnitude of the mth threat sourcemIs the radius of the mth threat source, di,m,kRepresenting the distance from the center of the mth threat source to the kth child node on the connection line of the points i and i + 1;
establishing a cluster track planning cost function J:
Figure BDA0003244237570000126
wherein λ ∈ [0,1] represents a weight coefficient. In this embodiment, the weight coefficient λ is 0.1.
And step 3: the method for planning the flight paths of all fixed-wing unmanned aerial vehicle clusters by adopting the gray wolf algorithm based on the preferred pheromone specifically comprises the following steps:
step 301: initialization algorithm parameters
Figure BDA0003244237570000131
And
Figure BDA0003244237570000132
setting the number POP of wolfs as 50, the maximum iteration number T as 25 and the initial concentration value tau (0) of the pheromones on all the alternative tracks as zero;
step 302: each iteration t, the three-dimensional scene is firstly projected to a two-dimensional XY plane to reduce the calculated amount, and each unmanned aerial vehicle is generated on the two-dimensional XY plane to meet the constraintAnd (3) generating POP gray wolfs which are feasible alternative track points of the POP group of conditions, wherein each gray wolf represents a feasible two-dimensional track point { (x)n,i(t),yn,i(t)), i ═ 1,2,. and D }; wherein the minimum safe distance D between dronessafeMaximum yaw angle of 0.1km
Figure BDA0003244237570000133
In the formula of principle three, let γ be 5, ξ be 5;
the generated POP gray wolves follow the following principle:
principle one, satisfying the yaw angle constraint:
Figure BDA0003244237570000134
i.e. the yaw angle of each drone
Figure BDA0003244237570000135
Not greater than maximum yaw angle
Figure BDA0003244237570000136
And a second principle is to satisfy collision avoidance constraints:
Figure BDA0003244237570000137
wherein D issafeExpressed as the minimum safe distance between drones;
principle three, probability of each possible alternative track point being selected:
Figure BDA0003244237570000138
h (i) is a set of a first and a second principle when the next track point is selected on the ith track point, and hiRepresenting any feasible point in the set; γ and ξ are normal numbers;
Figure BDA0003244237570000139
representing waypoints i to h in the t iterationiPheromone concentration in between;
Figure BDA00032442375700001310
is a heuristic factor, which indicates that the wolf is at the step i to the next selectable point hiTo a desired degree of (c), the values thereof with i and hiLinear distance between two points
Figure BDA00032442375700001311
In inverse proportion, i.e.
Figure BDA00032442375700001312
Step 303: generating a height value that satisfies a pitch angle constraint, comprising:
on the premise of meeting the horizontal XY direction collision avoidance constraint, selecting a height value meeting the pitch angle constraint in the height Z direction, and setting a maximum pitch angle phimax45 degrees to form a feasible alternative three-dimensional track point
Figure BDA0003244237570000141
The height between every two adjacent track points satisfies the following constraint:
|φn|≤φmax
wherein phi isnIs the pitch angle.
Step 304: calculating the cost of each group of feasible alternative three-dimensional track points according to the established cluster track planning cost function, and selecting the optimal three groups of track points as alpha, beta and delta wolfs;
step 305: updating the position of each wolf according to the Grey wolf algorithm
Figure BDA0003244237570000142
The update formula is as follows:
Figure BDA0003244237570000143
Figure BDA0003244237570000144
wherein,
Figure BDA0003244237570000145
respectively representing the current positions of alpha, beta and delta wolf,
Figure BDA0003244237570000146
respectively represent the distances between alpha, beta, delta wolf and other individuals, and the calculation formula is as follows:
Figure BDA0003244237570000147
Figure BDA0003244237570000148
and
Figure BDA0003244237570000149
the update rule of (2) is as follows:
Figure BDA00032442375700001410
Figure BDA00032442375700001411
wherein,
Figure BDA00032442375700001412
is a convergence factor, which decreases linearly as the number of iterations decreases from 2 to 0,
Figure BDA00032442375700001413
and
Figure BDA00032442375700001414
is taken as [0,1]]A random number in between.
Step 306: selecting the optimal flight path represented by the three wolfs alpha, beta and delta, and updating pheromones on the flight path;
updating pheromones on the tracks represented by the three wolfs alpha, beta and delta, wherein the updating formula is as follows:
τi,i+1(t+1)＝(1-ρ)·τi,i+1(t)+Δτi,i+1(t)
where ρ ≦ 0 ≦ 1 represents the attenuation factor of the pheromone, and in the present embodiment, ρ ≦ 0.25; delta taui,i+1(t) represents newly-left pheromone increment of the paths of the three wolfs of alpha, beta and delta from the i to the i +1 during the t iteration;
calculating newly-left pheromone increment delta tau on the flight points i to i +1 of alpha, beta and delta during the t-th iterationi,i+1(t), the calculation formula is as follows:
Figure BDA0003244237570000151
wherein Q ispP ∈ { α, β, δ } is a normal number, and Qα>Qβ>QδThe pheromone increment representing the three best wolves is different, in the embodiment, the pheromone increment coefficient proportion of alpha, beta and delta wolves is Qα:Qβ:Qδ＝1:0.5:0.3。di,i+1The length of the track point i to i +1, namely the concentration of the newly left pheromone on each route is inversely proportional to the length of the route.
Step 307: and circularly executing the steps 302 to 306 for each unmanned aerial vehicle until the maximum iteration number T is met, and outputting the optimal flight path of all the unmanned aerial vehicles.
The planned flight path according to the above steps is shown in fig. 2-4. In the embodiment, the improved grey wolf algorithm is compared and analyzed with the original grey wolf algorithm, the ant colony algorithm and the particle swarm algorithm, and the comparison results are shown in tables 3, 4 and 5. In a scene 1, a threat area is sparse, and the improved gray wolf algorithm is close to the cost value obtained by the original gray wolf algorithm and superior to the ant colony algorithm and the particle swarm algorithm. In the scenes 2 and 3, the number of threat areas is large and dense, and the improved grayish wolf algorithm is superior to other algorithms in average cost, total track length and minimum maximum value of a cost function. In scenario 3, the number of threat areas is the largest and the most dense, and at this time, the average cost of the improved grayling algorithm is reduced by 13.3%, 19.0% and 15.8% respectively compared with the average cost of the grayling algorithm, the ant colony algorithm and the particle swarm algorithm, and the average calculation time is only 1.5% longer than that of the shortest grayling algorithm. It can be seen from this example that the improved gray wolf algorithm has better performance in more complex scenes.
For the scene 3, the convergence conditions of different algorithms are compared, and as a result, as shown in fig. 5, it can be seen that the convergence speed of the improved grayling algorithm is faster than that of each compared algorithm, so that the improved grayling algorithm can improve the calculation efficiency of performing collaborative flight path planning on the unmanned aerial vehicle cluster.
Table 3 improved gray wolf algorithm compared to other algorithms (scene 1, population number POP 50, iteration number T25)
Figure BDA0003244237570000161
Table 4 improved gray wolf algorithm compared to other algorithms (scene 2, population number POP 50, iteration number T25)
Figure BDA0003244237570000162
Table 5 improved gray wolf algorithm compared to other algorithms (scene 3, population number POP 50, iteration number T25)
Figure BDA0003244237570000163
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (8)

1. A fixed-wing unmanned aerial vehicle cluster collaborative path planning method based on an optimal pheromone Grey wolf algorithm is characterized by comprising the following steps:
s1, establishing a three-dimensional map containing M threat sources;
s2, establishing a cluster track planning cost function;
and S3, planning the flight paths of all fixed-wing unmanned aerial vehicle clusters by adopting a gray wolf algorithm based on the preferred pheromone.
2. The fixed-wing drone cluster collaborative path planning method based on the preferred pheromone grayling algorithm according to claim 1, wherein the specific implementation process of the step S1 is as follows:
determining a starting point and a target point of each unmanned aerial vehicle, equally dividing a connecting line of the starting point and the target point of each unmanned aerial vehicle into D +1 parts, namely, the track of each unmanned aerial vehicle comprises D track points.
3. The method for fixed-wing drone cluster collaborative path planning based on the preferred pheromone grayling algorithm of claim 1, wherein the step S2 includes:
s21, constructing fuel cost J of each unmanned aerial vehicle N E {1,2n,fuel：
Figure FDA0003244237560000011
Wherein, wi→i+1,fuelThe fuel cost from each track point i to i +1 is in direct proportion to the length of the range;
s22, constructing potential threat cost J of all threat sources to unmanned aerial vehicle nn,threat：
Figure FDA0003244237560000012
Wherein, Jthreat,i→i+1The threat cost of the track between two adjacent track points i and i +1 is obtained;
s23, calculating the sum of the threat function values on 5 equipartition points on the track, namely:
Figure FDA0003244237560000013
wherein, wthreatkIs the threat function value at the k-th equipartition point, and the calculation formula is as follows:
Figure FDA0003244237560000014
wherein, constant CmCoefficient, R, representing the threat magnitude of the mth threat sourcemIs the radius of the mth threat source, di,m,kRepresenting the distance from the center of the mth threat source to the kth child node on the connection line of the points i and i + 1;
s24, establishing a cluster track planning cost function J:
Figure FDA0003244237560000021
wherein λ ∈ [0,1] represents a weight coefficient.
4. The fixed-wing drone cluster collaborative path planning method based on the preferred pheromone grayling algorithm according to claim 1, wherein the specific implementation process of the step S3 is as follows:
s31, initializing gray wolf algorithm parameters and pheromones of all the alternative track points, wherein the gray wolf algorithm parameters comprise the number POP of gray wolfs, the maximum iteration number T and the pheromone concentration tau (0) on all the alternative tracks;
s32, each time of iteration t, projecting the three-dimensional scene to a two-dimensional XY plane to reduce the calculated amount, generating a POP group of feasible alternative track points meeting constraint conditions for each unmanned aerial vehicle on the two-dimensional XY plane, namely generating POP wolfs, wherein each wolf represents a group of feasible two-dimensional track points { (x)n,i(t),yn,i(t)),i＝1,2,...,D}；
S33, generating a height value meeting the pitch angle constraint;
s34, calculating the cost of each group of feasible alternative three-dimensional track points according to the cluster track planning cost function established in the step S2, and selecting the optimal three groups of track points as alpha, beta and delta wolfs;
s35, updating the position of each wolf according to the wolf algorithm
Figure FDA0003244237560000022
S36, selecting the optimal flight path represented by the three wolfs alpha, beta and delta, and updating pheromones on the flight path;
and S37, circularly executing the steps S32 to S36 for each unmanned aerial vehicle until the maximum iteration number T is met, and outputting the optimal flight paths of all the unmanned aerial vehicles.
5. The fixed-wing drone cluster collaborative path planning method based on the preferred pheromone grayling algorithm of claim 4, wherein the POP grayling generated in the step S32 follows the following principle:
principle one, satisfying the yaw angle constraint:
Figure FDA0003244237560000023
i.e. the yaw angle of each drone
Figure FDA0003244237560000024
Is not bigAt maximum yaw angle
Figure FDA0003244237560000025
And a second principle is to satisfy collision avoidance constraints:
Figure FDA0003244237560000031
wherein D issafeExpressed as the minimum safe distance between drones;
principle three, probability of each possible alternative track point being selected:
Figure FDA0003244237560000032
h (i) is a set of a first and a second principle when the next track point is selected on the ith track point, and hiRepresenting any feasible point in the set; γ and ξ are normal numbers;
Figure FDA0003244237560000033
representing waypoints i to h in the t iterationiPheromone concentration in between;
Figure FDA0003244237560000034
is a heuristic factor, which indicates that the wolf is at the step i to the next selectable point hiTo a desired degree of (c), the values thereof with i and hiLinear distance between two points
Figure FDA0003244237560000035
In inverse proportion, i.e.
Figure FDA0003244237560000036
6. The method for fixed-wing drone cluster collaborative path planning based on the preferred pheromone grayish wolf algorithm of claim 4, wherein the step S33 generates altitude values satisfying the pitch angle constraint, comprising:
on the premise of meeting the horizontal XY direction collision avoidance constraint, selecting a height value meeting the pitch angle constraint in the height Z direction to form a feasible alternative three-dimensional track point
Figure FDA0003244237560000037
The height between every two adjacent track points satisfies the following constraint:
|φn|≤φmax
wherein phi isnIs the pitch angle.
7. The method for fixed-wing drone cluster collaborative path planning based on the preferred pheromone grayling algorithm of claim 4, wherein the step S35 updates the position of each wolf according to the grayling algorithm
Figure FDA0003244237560000038
The update formula is as follows:
Figure FDA0003244237560000041
Figure FDA0003244237560000042
wherein,
Figure FDA0003244237560000043
respectively representing the current positions of alpha, beta and delta wolf,
Figure FDA0003244237560000044
respectively represent the distances between alpha, beta, delta wolf and other individuals, and the calculation formula is as follows:
Figure FDA0003244237560000045
Figure FDA0003244237560000046
and
Figure FDA0003244237560000047
the update rule of (2) is as follows:
Figure FDA0003244237560000048
Figure FDA0003244237560000049
wherein,
Figure FDA00032442375600000410
is a convergence factor, which decreases linearly as the number of iterations decreases from 2 to 0,
Figure FDA00032442375600000411
and
Figure FDA00032442375600000412
is taken as [0,1]]A random number in between.
8. The method for fixed-wing drone cluster collaborative path planning based on the preferred pheromone grayling algorithm according to claim 4, wherein the step S36 includes:
s361, updating pheromones on the flight path represented by the three wolfs alpha, beta and delta, and updating the formula as follows:
τi,i+1(t+1)＝(1-ρ)·τi,i+1(t)+Δτi,i+1(t)
where ρ ≦ 0 ≦ 1 denotes the attenuation factor of the pheromone, Δ τi,i+1(t) represents newly-left pheromone increment of the paths of the three wolfs of alpha, beta and delta from the i to the i +1 during the t iteration;
s362, calculating newly-left pheromone increment delta tau of the alpha, beta and delta three wolfs on the waypoints i to i +1 during the t iterationi,i+1(t), the calculation formula is as follows:
Figure FDA00032442375600000413
wherein Q ispP ∈ { α, β, δ } is a normal number, and Qα>Qβ>QδThe pheromone increment left by the three best wolfs is different, di,i+1The length of the track point i to i +1, namely the concentration of the newly left pheromone on each route is inversely proportional to the length of the route.
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