CN113741513A - Method for optimizing formation of ground search task formation of multiple unmanned aerial vehicles under implicit communication condition - Google Patents

Method for optimizing formation of ground search task formation of multiple unmanned aerial vehicles under implicit communication condition Download PDF

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CN113741513A
CN113741513A CN202110973221.7A CN202110973221A CN113741513A CN 113741513 A CN113741513 A CN 113741513A CN 202110973221 A CN202110973221 A CN 202110973221A CN 113741513 A CN113741513 A CN 113741513A
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辛斌
张钧溪
郭苗
陈杰
王晴
蒋金强
熊楚依
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Beijing Institute of Technology BIT
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Abstract

本发明公开了一种隐式通信条件下多无人机对地搜索任务编队队形优化方法。本发明以UAV间的相对位置关系为决策变量，以拓扑性能指标和任务效率指标为目标函数，以目标区域大小、信息传递链路的连通性、传感器视野范围等为约束，建立了队形结构优化问题模型，并应用多目标优化算法进行求解，最终可得到UAV编队在搜索地面目标任务中的期望队形。本发明同时考虑了搜索任务效率和拓扑结构性能，适用于不同规模UAV编队执行对地搜索任务的情形。

Figure 202110973221

The invention discloses a formation optimization method for multiple unmanned aerial vehicles (UAVs) to search for the ground under the condition of implicit communication. The invention uses the relative positional relationship between UAVs as the decision variable, the topological performance index and the task efficiency index as the objective function, and the size of the target area, the connectivity of the information transmission link, the sensor field of view, etc. as constraints, and establishes a formation structure. After optimizing the problem model and applying the multi-objective optimization algorithm to solve it, the desired formation of the UAV formation in the task of searching for ground targets can be finally obtained. The present invention takes into account both the search task efficiency and the topological structure performance, and is suitable for situations where UAV formations of different scales perform ground search tasks.

Figure 202110973221

Description

Method for optimizing formation of ground search task formation of multiple unmanned aerial vehicles under implicit communication condition
Technical Field
The invention relates to the technical field of optimization of formation of multiple Unmanned Aerial Vehicles (UAVs), in particular to a formation optimization method of a ground search task of multiple UAVs under an implicit communication condition.
Background
With the increasing level of UAV technology, UAVs have become an important tool for search scouting of target areas. Because the environment is complex and changeable, the target maneuverability is strong, the search task executed by a single UAV is difficult, and the task efficiency can be improved by the cooperative execution of multiple UAVs to achieve advantage complementation, so that the cooperative search of multiple UAVs is also widely applied. Most literature studies multi-UAV collaborative search under explicit communication conditions, i.e., information is communicated between UAVs using a communication medium and a communication device. However, when the UAV enters a strong electromagnetic interference area, the conventional explicit communication means such as electromagnetic communication fails, and at this time, the UAV may establish an information transfer link by using implicit communication, that is, each UAV detects and transfers information through the limited-field-of-view sensor. Currently, there is less research on UAV collaborative search methods under implicit communication conditions.
In order to ensure the connectivity of a UAV information transmission link under the implicit communication condition, the UAVs can cooperatively search a ground target in a formation mode, and because the implicit communication cannot transmit the structure information of the formation, the formation of the UAV formation needs to be optimized off line, and the target formation information is loaded into the UAVs before the tasks are executed. The optimization of the formation structure is mainly divided into two types of geometric structure optimization and information transfer topological structure optimization, most documents separately study the optimization of the two structures, but a mapping relation exists between the geometric structure and the topological structure, and the changes of the two structures can influence each other, so that the two structures are combined for analysis, and the analysis is more practical.
Disclosure of Invention
In view of the above, the invention provides a method for optimizing formation shapes of ground search tasks of multiple unmanned aerial vehicles under an implicit communication condition, and simultaneously, geometric structure optimization and information transfer topological structure optimization of the formation shapes are ensured, so that more optimal formation shapes can be obtained.
The technical scheme for realizing the invention is as follows:
step 1: determining decision variables of the formation optimization model, wherein the decision variables comprise Euclidean distances between the UAVs and relative sight angles, and the relative sight angles are included angles between connecting lines of the two UAVs and the positive direction of a transverse axis of a geodetic coordinate system.
Step 2: determining a constraint condition of a formation optimization model, wherein the constraint condition specifically comprises three constraints:
(1) and (3) target area constraint: each UAV is required to perform a task within a target area.
(2) Constraint of shortest distance between UAVs: in order to avoid collision between UAVs, and considering that the close distance between UAVs has a large influence on the movement of each other, the distance between UAVs should not be less than the set minimum distance.
(3) Connectivity constraint of information transfer topology: a sufficient condition for reaching consistency when the UAV cluster is moving forward is that the topology structure diagrams of the cluster's information transfer are connected.
And step 3: determining an evaluation function of the formation optimization model, wherein the evaluation function specifically comprises two evaluation indexes:
(1) information transfer topology survivability: the survivability of the information transfer topological structure means that after a plurality of agents in a cluster are damaged or fail, the rest agents can still keep the communication of the information transfer topological graph. The invention adopts natural connectivity to evaluate the survivability of the information transfer topological structure, and the natural connectivity physically describes the number of closed-loop paths (paths which can still return to a node after passing through a plurality of nodes from the node) with different step lengths in the network. The larger the natural connectivity is, the more the number of closed-loop paths is, the more redundant alternative paths between nodes are, and the stronger the survivability of the topological structure is.
(2) Efficiency of search tasks: the invention applies the lateral search coverage width of the UAV formation to evaluate the efficiency of the search task. The larger the transverse coverage width is, the larger the area searched by walking the designated path is, and the area coverage rate can be improved.
And 4, step 4: and (4) synthesizing the contents of the steps 1-3 to obtain a formation optimization problem model.
And 5, solving the problems by applying a multi-objective optimization algorithm to obtain the optimal formation form. The multi-objective optimization algorithm can adopt NSGA-II-differential evolution joint algorithm, decomposition-based multi-objective optimization algorithm (MOEA/D), multi-objective particle swarm optimization algorithm (MOPSO) and other algorithms.
Preferably, the NSGA-II algorithm and the differential evolution algorithm are combined to solve the problems.
Preferably, the solution method combining the NSGA-II algorithm and the differential evolution algorithm is as follows:
s1, firstly, determining the encoding form of the solution, initializing a population P, and setting the number of the solutions in the population, the maximum iteration times, the maximum distance between nodes and the minimum distance;
s2, operating the population P by using crossover and mutation operators of a differential evolution algorithm to obtain a new population Q, wherein the solution quantity in Q is the same as that of P;
s3, decoding the solutions in the population P and the population Q to obtain the geometric structure and the information transmission topological structure of the formation; judging whether the constraint condition is a feasible solution or not based on the constraint condition, and if the constraint condition is the feasible solution, calculating a corresponding evaluation function value; if the solution is not feasible, calculating the constraint violation quantity;
and S4, merging the population P and the population Q into a new population T, and performing non-dominated sorting on the feasible solution in the population T.
S5, for feasible solutions having the same non-dominant rank, the congestion degree of each solution is calculated.
S6, selecting a specified number of solutions from the population T, and updating the population P by using the solutions; firstly, sequentially adding feasible solutions in a population T into a new population P ' according to the sequence of non-dominance levels from small to large, sequentially adding feasible solutions with the same non-dominance levels into the population P ' according to the sequence of congestion degrees from large to small, and sequentially adding infeasible solutions in the population T into the population P ' according to the sequence of constraint violation amounts from small to large; the scale of the population P 'is equal to that of the population P, and the new population P' is updated into the population P;
repeating S2-S6, stopping after reaching the maximum iteration times, and obtaining a Parato solution set of the optimization problem;
and S7, in order to ensure the survivability of formation under the implicit communication condition, selecting the solution with the highest survivability evaluation function value in the Parato solution set as the final solution.
Preferably, in S3, the method for acquiring the formation geometry is as follows:
any two unmanned planes v except the general piloting unmanned planeiAnd vjFrom v obtained in the de-encoded contentiAnd vjWith general piloting unmanned plane v1The Euclidean distance and the relative sight angle between them, so as to obtain the position vector
Figure BDA0003226699240000041
And
Figure BDA0003226699240000042
then obtaining the vector by vector subtraction
Figure BDA0003226699240000043
Thereby obtaining viAnd vjHas a Euclidean distance l betweenijAnd relative line of sight angle
Figure BDA0003226699240000044
Preferably, the connectivity constraint of the information transfer topology of the unmanned aerial vehicle is as follows: the adjacency matrix a of the unmanned aerial vehicle information transfer topological structure directed graph D only contains 1 full 0 column, and the full zero column corresponds to the total piloting unmanned aerial vehicle.
Preferably, the natural connectivity
Figure BDA0003226699240000045
The calculation formula of (a) is as follows:
Figure BDA0003226699240000046
s is the total number of closed loop paths in an undirected graph of an unmanned aerial vehicle information transfer topological structure; n is the total number of unmanned aerial vehicles, lambdaiAnd (4) characteristic values of the adjacency matrix of the topological structure undirected graph G are transferred for the unmanned aerial vehicle information.
Better, efficiency evaluation function f of search tasks of unmanned aerial vehicle formation2Comprises the following steps:
Figure BDA0003226699240000047
wherein d israngeThe horizontal search for formation of drones covers the width,
Figure BDA0003226699240000048
n is the total number of the unmanned aerial vehicles, and R is the search range to the ground of the unmanned aerial vehicles.
Has the advantages that:
(1) according to the method, the Euclidean distance and the relative sight angle between UAVs are used as decision variables, the limited detection range of an unmanned aerial vehicle sensor, the size of a target area, the shortest distance (collision prevention) between UAVs, the connectivity of an information transfer topological graph and the like are used as constraint conditions, a formation optimization model is established by taking the information transfer topological performance index and the search task efficiency of formation as objective functions, the model considers the geometrical structure optimization and the information transfer topological structure optimization of formation at the same time, and the search task efficiency and the topological structure performance are considered at the same time, so that the method is suitable for the situation that UAV formations of different scales execute the ground search task; the formation optimization model can be obtained by solving through a multi-objective optimization algorithm, and has universality.
(2) The method is used for solving the formation optimization model of the ground search task formation of the multiple unmanned aerial vehicles based on the NSGA-II-differential evolution joint algorithm, the effect of solving the low-dimensional multi-target optimization problem by the algorithm is good, and the diversity of solutions in the population can be kept.
(3) The relative position relation between the agents in the formation is solved through vector calculation, so that the redundancy of coding is reduced, and the complexity of calculation is also reduced.
Drawings
Fig. 1 is a UAV sensor forward detection range.
Fig. 2 is a connected directed tree topology (N-5).
Fig. 3 is an adjacency matrix (N-5) connected with a directed tree topology.
Fig. 4 is a conversion of redundant paths in a directed graph (fig. 4(a)) to closed paths in an undirected graph (fig. 4 (b)).
Fig. 5 is a schematic diagram of the horizontal coverage width of the search task.
FIG. 6 is a flow chart of solving for the search task lateral coverage width.
FIG. 7 is a flow chart of a multi-objective optimization method based on NSGA-II algorithm.
Fig. 8 is a schematic diagram of the arrangement of evaluation function values of solutions in a certain level set.
FIG. 9 is a flow chart of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a formation optimization method for a ground search task formation of multiple unmanned aerial vehicles under an implicit communication condition, which comprises the steps of establishing a formation structure optimization problem model by taking a relative position relation among UAVs as a decision variable, taking a topological performance index and a task efficiency index as objective functions, taking the size of a target area, the connectivity of an information transfer link, the visual field range of a sensor and the like as constraints, solving by applying a multi-objective optimization algorithm, and finally obtaining an expected formation of the UAV formation in the ground search target task, wherein a flow chart is shown in figure 9.
The method comprises the steps of setting N UAVs in an unmanned aerial vehicle cluster, and assuming that all the UAVs are at the same height, considering the UAV formation in a two-dimensional plane and defining the size Xmax×Ymax(km2) The target area of (1). Fig. 1 shows the forward detection range of the UAV onboard sensor, the farthest detection distance is dis, and the forward viewing angle (the angle between the detection range boundary and the UAV orientation) is ± ang (ang ∈ (0, pi/2)). The UAV can only obtain information about other UAVs within its detection range. The detection range constraint determines that information can only be transmitted in one direction among the UAVs, so the information transmission topology of the UAV cluster is represented by a directed graph D ═ (V, E, A), wherein V ═ V1，v2，...，vNIs the set of all UAVs, E is the set of edges of the directed graph, if viV can be obtained by probingjIs (i, j ≦ N), then there is a path vjDirection viDirected edge of<vj，vi>∈E。A＝(aij)N×NIs an adjacency matrix of the directed graph D ifHaving directed edges<vj，vi>E is E, then aji1, otherwise aji＝0。
Problem modeling:
step 1: and determining a decision variable of the optimization problem.
The decision variables of the formation optimization problem comprise Euclidean distances between every two nodes and relative sight angles (included angles between connecting lines of the two nodes and the positive direction of a transverse axis of a geodetic coordinate system). v. ofiAnd vjThe Euclidean distance between (i ≠ j) is denoted as lij，vjWith respect to viThe angle of sight of is recorded as
Figure BDA0003226699240000061
The decision variables are stored in matrix L ═ Lij)N×NAnd
Figure BDA0003226699240000062
in which l isii＝0，
Figure BDA0003226699240000063
Step 2: and determining the constraint condition of the optimization problem.
(1) Target area constraints
Let the absolute position coordinate of the UAV be (X)i，Yi) N, each UAV is required to perform a task within a target area, then
0≤Xi≤Xmax，0≤Yi≤Ymax
(2) Constraint of shortest distance between UAVs
In order to avoid collision between UAVs, and considering that the close distance between UAVs has a large influence on the movement of UAVs, the distance between UAVs should not be less than the set minimum distance dminI.e. by
lij≥dmin，i≠j，i＝1，...，N，j＝1，...，N
(3) Connectivity constraints
A sufficient condition for UAV clusters to reach consistency when moving forward isThe topological structure diagram of the information transfer of the cluster is connected. Node viNode v may be obtainedjThe following conditions are satisfied: if the orientation angle (the angle between the orientation and the positive direction of the horizontal axis of the geodetic coordinate system) of all UAVs is alpha, then
lij≤dis
Figure BDA0003226699240000071
The adjacency matrix a of the information transfer topological graph (directed graph) can be obtained according to the above conditions.
The topological structure of the model is directed tree topology, as shown in fig. 2, wherein the connecting line with an arrow represents a directed edge in the information transfer topological graph D. In a, only the column corresponding to the total pilot of the cluster is the total 0 column, which indicates that the UAVs except the total pilot can detect the information of the UAVs in the cluster, and as shown in fig. 3, the adjacency matrix (N ═ 5) communicating the directed tree topology is only the 3 rd column is the total 0 column, and the corresponding UAV is the total pilot of the cluster. If other all 0 rows exist, the UAV corresponding to the row is separated from the cluster, and the topology structure diagram is not communicated. Note that a contains lea all-zero columns, then the connectivity constraint is expressed as:
lea＝1
that is, there is only one total 0 row in a, which corresponds to the total pilot of the UAV cluster, and there is only one total pilot in the formation.
And step 3: and determining an evaluation function of the optimization problem.
(1) Topological structure survivability: the topological structure survivability means that after a plurality of intelligent agents in a cluster are damaged or fail, the rest of the intelligent agents can still keep the communication of an information transmission topological graph.
The invention applies natural connectivity to evaluate the survivability of the topological structure. The natural connectivity physically describes the number of closed-loop paths with different step lengths in the network, and describes the network survivability from the perspective of redundant alternate paths. A closed loop path refers to a path that travels from a node through several nodes and then back to the node. Let nkThe number of closed-loop paths with path length k in the network is the number of closed-loop paths in the networkTotal number S of
Figure BDA0003226699240000081
The longer the closed loop path is, the greater the communication cost of the node is, and the relatively poorer the working performance is, so the pair n is introduced in the above formulakTo prevent S from diverging, the weight is designed as follows:
Figure BDA0003226699240000082
let λiIs the eigenvalue of the adjacency matrix, then
Figure BDA0003226699240000083
Figure BDA0003226699240000084
S is also larger when N is larger, so the natural connectivity can be obtained by simplifying the above formula
Figure BDA0003226699240000085
The calculation formula of (a) is as follows:
Figure BDA0003226699240000086
the topological structure considered by the model is a directed tree-shaped topological structure, the number of redundant replacement paths from the root node to the child nodes can reflect the survivability of the network, the more redundant paths are, and when nodes are destroyed between the root node and the child nodes, the child nodes can obtain the information of the root node through the redundant paths. However, the directed tree topology does not have the above-mentioned closed path, and the natural connectivity cannot be directly applied. The directed tree topology is a weak connection structure, and an undirected graph G ═ V, E ', a') can be obtained by ignoring the direction of the edge in the graph D. In graph G, multiple paths from the root node to the child nodes may constitute a closed path, as shown in fig. 4.
The more closed paths, the more redundant replacement paths from the root node to the child nodes, the better the network survivability. Therefore, the natural connectivity of the graph G can be obtained according to the eigenvalue of the adjacency matrix A' of the graph G and the natural connectivity calculation formula
Figure BDA0003226699240000087
Which is used to characterize the survivability of the information delivery topology D.
Figure BDA0003226699240000088
The larger the value of (a), the more robust the topology is.
Maximum natural connectivity when graph G is a fully connected graph
Figure BDA0003226699240000089
Obtaining a survivability evaluation function through normalization processing:
Figure BDA0003226699240000091
(2) efficiency of search tasks: search lateral coverage width d for the present invention using UAV formationrangeTo evaluate the efficiency of the search task. The larger the transverse coverage width is, the larger the area searched by walking the designated path is, and the area coverage rate can be improved. Assuming that the ground detection area of the UAV is a circular area with a radius R, the lateral coverage width of the search task is shown in fig. 5, and the calculation method is shown in fig. 6.
To drangeCarrying out normalization processing to obtain a search task efficiency evaluation function:
Figure BDA0003226699240000092
wherein
Figure BDA0003226699240000093
When the lateral width of the covered area is
Figure BDA0003226699240000094
All UAVs are arranged in a horizontal line, but the UAV cluster can not realize the horizontal line arrangement due to the forward viewing angle ang < pi/2.
And 4, step 4: and (4) integrating the contents of the steps 1-3 to obtain a formation optimization problem model.
maxf(x)＝(f1，f2)T
Figure BDA0003226699240000095
Step 5, solving the problem:
and solving the problems by applying a multi-objective optimization algorithm.
First, the following definitions are introduced:
the pareto dominate: for the above objective function value maximization problem, solve xaDominating xbIf and only if (f)1(xa)＞f1(xb))∧(f2(xa)≥f2(xb) Either (f) or (f)1(xa)≥f1(xb))∧(f2(xa)＞f2(xb)). "Λ" indicates and operation.
Pareto optimal solution: feasible solution x*Called Parato optimal solution, if and only if there is no solution that can dominate x*. The set of all the Pareto optimal solutions is called the Pareto solution set.
The flow of solving the algorithm is shown in fig. 7. Firstly, generating a new population Q on the basis of an original population P by using crossover and mutation operators of a differential evolution algorithm, and combining the two populations to obtain a new population T, wherein each solution in the T has two attributes: a non-dominant level (indicating the number of other solutions that can dominate the solution) and a congestion level (indicating the degree of density of the arrangement of evaluation function values of the solution). The solutions in T are sorted by non-dominant rank first, which ensures that the retained solutions are at a better non-dominant rank. And then, carrying out congestion degree sorting on the solutions with the same non-dominant grade, and reserving the solutions with higher congestion degree, wherein the step can ensure the diversity of the solutions in the population. And finally, selecting a reserved part to be solved into the next generation of population according to the non-dominant grade, the crowding degree and the capacity of the population.
The method specifically comprises the following substeps:
step 5.1: and initializing the population.
(1) Determining coding forms of solutions
The encoding of the solution includes euclidean distances and relative line of sight angles of UAV # 1 (total piloted drone) to the remaining UAVs as follows:
Figure BDA0003226699240000101
(2) specifying the number of solutions M, the maximum number of iterations G in a populationmaxA maximum distance dmax and a minimum distance dmin between nodes.
(3) Initializing a population P
For portion x in the solution characterizing Euclidean distances of UAV No. 1 from the remaining UAVsl＝(l12，...，l1N) The initialization is as follows, where rand1Is [0, 1 ]]Uniformly distributed random numbers.
l1i＝dmin+rand1×(dmax-dmin)，i＝2，...，N
For the portion of the solution characterizing the relative line-of-sight angles of UAV No. 1 and the remaining UAVs
Figure BDA0003226699240000102
The initialization is as follows, where rand2Are random numbers uniformly distributed in [0, 1 ].
Figure BDA0003226699240000103
Step 5.2: and for the population P, a new population Q is generated by applying a crossover and mutation operator of a differential evolution algorithm, and the number of solutions in Q is the same as that of P.
(1) Variation of
For solution x in population Pi(i.ltoreq.M) of two moieties
Figure BDA0003226699240000111
And
Figure BDA0003226699240000112
performing mutation operation respectively to obtain a mutation vector vi。
Figure BDA0003226699240000113
Figure BDA0003226699240000114
Figure BDA0003226699240000115
F is a variation factor, and F belongs to [0, 2 ]. In order to make the algorithm have good global search capability and local search capability, F is decreased with the increase of the iteration number, and the expression is as follows, wherein G is the current iteration number.
Figure BDA0003226699240000116
(2) Crossing
And performing cross operation on the solution in the population P and the variation vector obtained by variation, wherein the method comprises the following steps:
Figure BDA0003226699240000117
wherein rand is [0, 1 ]]Internal uniformly distributed random number, xi.j，vi.jX representing a solutioni，viThe j-th dimension data, CR is a cross factor, CR belongs to [0.1,0.9]the value of CR decreases with increasing number of iterations, the expression:
Figure BDA0003226699240000118
(3) correcting the newly obtained solution q
Since l is an element of [ dmin, dmax ]]，
Figure BDA0003226699240000119
The solution obtained after the mutation and the intersection is corrected as follows:
qi.j＝dmax，if qi.j＞dmax.i≤M，1≤j≤N-1
qi.j＝dmin，if qi.j＜dmin.i≤M，1≤j≤N-1
Figure BDA00032266992400001110
Figure BDA0003226699240000121
where mod (·) is the remainder calculation. The solution in the population Q is obtained by correction.
Step 5.3: and decoding the solutions in the population P and the population Q, judging whether the solutions are feasible solutions or not, and if so, calculating corresponding evaluation function values.
(1) Decoding results in formation geometry and topology
i) The geometrical structure is as follows: consider any two UAVs other than UAV # 1 (set to v)iAnd vj) V is available in the de-encoded contentiAnd vjEuclidean distance and relative sight angle between the UAV and No. 1 so as to obtain a position vector
Figure BDA0003226699240000122
And
Figure BDA0003226699240000123
obtaining vectors by vector subtraction
Figure BDA0003226699240000124
Thereby obtaining viAnd vjHas a Euclidean distance l betweenijAnd relative line of sight angle
Figure BDA0003226699240000125
The specific calculation method is shown as the following formula c
Figure BDA0003226699240000126
Figure BDA0003226699240000127
Figure BDA0003226699240000128
The matrix L, phi, the euclidean distance and the relative line of sight angle between all UAVs, can be obtained by applying the above method.
ii) topology: v. ofiAnd vjIf the following conditions are met:
lij≤dis
Figure BDA0003226699240000129
where α is the orientation angle (AUV orientation angle with respect to the positive direction of the geodetic coordinate system axis). V is thenjAt viWithin a detectable range, there is a field of information transfer topology defined by vjDirection viThe formation topological structure chart is obtained through the criterion.
(2) Feasible solution judgment
And judging whether a certain solution is a feasible solution or not according to the constraint conditions in the step 2. If the solution meets all the constraint conditions, the solution is a feasible solution, otherwise, the solution is an infeasible solution.
(3) Calculating the evaluation function value
i) For a feasible solution: and (4) calculating an evaluation function value according to the formula in the step (3).
ii) for infeasible solutions: and calculating the constraint violation amount of the solution, wherein if the solution violates m constraints, the constraint violation amount is m.
Step 5.4: and combining the population P and the population Q to obtain a new population T, and performing non-dominant sequencing on the solution in the population T.
(1) For each solution in the population T, the number of solutions that can dominate it is recorded as n, and the initial value of the non-dominated rank value for each solution is + ∞.
(2) Add the solution with rank value of + ∞andn of 0 to set Ft(initial value of t is 1) in (F)tThe rank of the medium solution is t. Let t be t + 1.
(3) Taking out the solution with the rank value not being + ∞fromthe population T, and carrying out the following operations on the rest solutions: n-1 for each solution.
(4) And (5) repeating the operations of (2) and (3) in the step 5.4 until the grade values of all the solutions are not + ∞, and obtaining the non-dominant grade sequence of all the solutions in the T.
Step 5.5: for each set with the same non-dominant rank obtained in step 5.4, the congestion degrees of all solutions in the rank set are calculated.
The arrangement of the solutions in the target space in a non-dominated level set is shown in FIG. 8, in which the horizontal axis and the vertical axis represent two evaluation functions f1And f2. The larger the crowdedness of the solution is, the more sparsely arranged the solution is in the target space, and the solution is kept to be beneficial to improving the diversity of the solutions in the population. Conversely, the less crowded the solution, the more densely populated the solution is, and not keeping such a solution helps to speed up the algorithm to get the pareto set.
If f of a solution1Or f2The maximum value of the class set is the congestion degree of the solution is + ∞, which shows that if the solution in the class set is selected to enter the next generation population, f1Or f2The solution to take the maximum value must be retained.
For solutions where the evaluation function value is not an extreme value:
(1) for a set of feasible solutions: let a certain solution be xiCorresponding to an objective function value of
Figure BDA0003226699240000131
And
Figure BDA0003226699240000132
finding two solutions x before and after each evaluation function directioni+1And xi-1Then x is solvediThe degree of crowding of (a) is:
Figure BDA0003226699240000141
wherein
Figure BDA0003226699240000142
The extreme value of the objective function value.
(2) For a set of infeasible solutions: the congestion degree is not calculated.
Step 5.6: a specified number of solutions are selected from the population T and the population P is updated with these solutions.
Adding the solutions into a new population P ' in sequence from small to large according to the non-dominant grade values of the solutions, and adding the solutions into the P ' according to the congestion degree of the solutions in a set from large to small if the set is a feasible solution set when the addition of the solutions in a certain non-dominant grade set causes the number of the solutions in the P ' to exceed the limit (namely the scale of the population P); if the solution is a set of infeasible solutions, adding the solutions into P' from small to large according to the constraint violation amount. And finally, making P equal to P'. When adding the solution to P', the feasible solution is added first, and then the infeasible solution is added.
Step 5.7: and repeating the step 5.2-5.6, and stopping when the iteration times are equal to the maximum iteration times to finally obtain a Paratoo solution set.
Step 5.8: in order to ensure the stability of formation, the solution with the highest damage resistance evaluation function value is selected as the final solution in the Parato solution set.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1.一种隐式通信条件下多无人机对地搜索任务编队队形优化方法，其特征在于，以无人机之间的欧式距离以及相对视线角度为队形优化模型的决策变量，以目标区域约束、无人机间最短距离约束、无人机信息传递拓扑结构的连通性约束为队形优化模型的约束条件，以无人机信息传递拓扑结构的抗毁性、无人机编队的搜索任务的效率为队形优化模型的评价函数，建立多无人机对地搜索任务编队队形优化模型；其中，首先将无人机信息传递拓扑结构转化为无向图，然后采用自然连通度评价无人机信息传递拓扑结构的抗毁性；采用无人机编队的横向搜索覆盖宽度评价搜索任务的效率；1. under a kind of implicit communication condition, many unmanned aerial vehicle to ground search task formation formation optimization method, it is characterized in that, with Euclidean distance between unmanned aerial vehicle and relative line of sight angle as the decision variable of formation optimization model, with The target area constraint, the shortest distance constraint between UAVs, and the connectivity constraint of the UAV information transfer topology are the constraints of the formation optimization model. The efficiency of the search task is the evaluation function of the formation optimization model, and the formation formation optimization model of the multi-UAV-to-ground search task is established; firstly, the UAV information transfer topology is converted into an undirected graph, and then the natural connectivity is adopted. Evaluate the survivability of the UAV information transfer topology; use the lateral search coverage width of the UAV formation to evaluate the efficiency of the search task; 对所述多无人机对地搜索任务编队队形优化模型进行求解，获得最优队形。The optimal formation is obtained by solving the formation optimization model of the multi-UAV ground search task. 2.如权利要求1所述的隐式通信条件下多无人机对地搜索任务编队队形优化方法，其特征在于，基于NSGA-II-差分进化联合算法、基于分解的多目标优化算法或多目标粒子群优化算法对所述多无人机对地搜索任务编队队形优化模型进行求解。2. under the condition of implicit communication as claimed in claim 1, it is characterized in that, based on the NSGA-II-differential evolution joint algorithm, the multi-objective optimization algorithm based on decomposition or The multi-objective particle swarm optimization algorithm solves the formation optimization model of the multi-UAV ground search task. 3.如权利要求2所述的隐式通信条件下多无人机对地搜索任务编队队形优化方法，其特征在于，基于NSGA-II-差分进化联合算法的求解的具体步骤如下：3. under the condition of implicit communication as claimed in claim 2, many unmanned aerial vehicle to ground search task formation formation optimization method, it is characterized in that, the concrete steps based on the solution of NSGA-II-Differential Evolution Joint Algorithm are as follows: S1，确定解的编码形式为包括总领航无人机与其余无人机的欧式距离和相对视线角度；确定种群中解的数量、最大迭代次数、无人机间的最大距离和最小距离；初始化种群P；S1, determine the encoding form of the solution to include the Euclidean distance and relative sight angle between the general pilot drone and the rest of the drones; determine the number of solutions in the population, the maximum number of iterations, and the maximum and minimum distances between drones; initialize population P; S2，采用差分进化算法的交叉和变异算子对种群P进行操作，得到新的种群Q，Q中的解数量与P相同；S2, using the crossover and mutation operator of the differential evolution algorithm to operate the population P to obtain a new population Q, the number of solutions in Q is the same as P; S3，对种群P与种群Q中的解进行解码操作，获得编队的几何结构和信息传递拓扑结构；基于所述约束条件判断该解是否为可行解，若是可行解，则计算出对应的评价函数值；若是不可行解，则计算其约束违背量；S3: Decode the solutions in the population P and the population Q to obtain the geometric structure and information transfer topology of the formation; judge whether the solution is a feasible solution based on the constraint conditions, and if it is a feasible solution, calculate the corresponding evaluation function value; if the solution is infeasible, calculate its constraint violation; S4，将种群P与种群Q合并成一个新的种群T，对种群T中的所有可行解进行非支配等级排序；S4, merge the population P and the population Q into a new population T, and sort all feasible solutions in the population T by a non-dominated level; S5，对于具有相同非支配等级的可行解，计算其拥挤度；S5, for feasible solutions with the same non-dominated level, calculate their crowding degree; S6，将种群T中的可行解按照非支配等级从小到大的顺序依次加入新的种群P′中，具有相同非支配等级的可行解按照拥挤度由大到小的顺序依次加入种群P′中；若种群T中的可行解规模小于种群P的规模，则继续将种群T中的不可行解按照约束违背量由小到大的顺序依次加入种群P′中，直到种群P′的规模与种群P相等；将新的种群P′更新为种群P，返回S2，直到迭代次数等于最大迭代次数，得到该优化问题的Parato解集；S6, the feasible solutions in the population T are added to the new population P' in the order of the non-dominated level from small to large, and the feasible solutions with the same non-dominated level are added to the population P' in the order of the crowding degree from large to small. ; If the scale of feasible solutions in population T is smaller than that of population P, continue to add infeasible solutions in population T to population P′ in order of constraint violation amount from small to large, until the size of population P′ is equal to the size of population P is equal; update the new population P' to population P, and return to S2 until the number of iterations is equal to the maximum number of iterations, and the Parato solution set of the optimization problem is obtained; S7，在Parato解集中选择抗毁性评价函数值最高的解为最终解。S7, in the Parato solution set, select the solution with the highest value of the survivability evaluation function as the final solution. 4.如权利要求3所述的隐式通信条件下多无人机对地搜索任务编队队形优化方法，其特征在于，所述S3中，所述编队的几何结构的获取方法如下：4. under the condition of implicit communication as claimed in claim 3, it is characterized in that, in described S3, the acquisition method of the geometric structure of described formation is as follows: 除总领航无人机外的任意两个无人机vi和vj，根据解编码内容中得到的vi和vj与总领航无人机v1间的欧式距离和相对视线角度，从而得到位置向量
Figure FDA0003226699230000021
和
Figure FDA0003226699230000022
然后通过向量减法得到向量
Figure FDA0003226699230000023
从而得到vi和vj之间的欧式距离lij和相对视线角度
Figure FDA0003226699230000024
Any two UAVs vi and v j except the general pilot UAV, according to the Euclidean distance and relative line of sight angle between vi and v j obtained in the decoded content and the general pilot UAV v 1 , thus get the position vector
Figure FDA0003226699230000021
and
Figure FDA0003226699230000022
Then get the vector by vector subtraction
Figure FDA0003226699230000023
Thus, the Euclidean distance l ij and the relative sight angle between v i and v j are obtained
Figure FDA0003226699230000024
 5.如权利要求1～4任意一项所述的隐式通信条件下多无人机对地搜索任务编队队形优化方法，其特征在于，无人机信息传递拓扑结构的连通性约束为：无人机信息传递拓扑结构有向图D的邻接矩阵A中仅包含1个全0列，该全零列对应总领航无人机。5. The formation optimization method for multi-UAV-to-ground search tasks under implicit communication conditions as claimed in any one of claims 1 to 4, wherein the connectivity constraints of the UAV information transfer topology are: The adjacency matrix A of the directed graph D of the UAV information transfer topology contains only one all-zero column, which corresponds to the general pilot UAV. 6.如权利要求1～4任意一项所述的隐式通信条件下多无人机对地搜索任务编队队形优化方法，其特征在于，所述自然连通度
Figure FDA0003226699230000025
的计算公式如下：6 . The formation optimization method for multi-UAV-to-ground search tasks under implicit communication conditions according to any one of claims 1 to 4, wherein the natural connectivity
Figure FDA0003226699230000025
The calculation formula is as follows:
Figure FDA0003226699230000026
Figure FDA0003226699230000026
 其中，S为无人机信息传递拓扑结构无向图中闭环路径总数；N为无人机总数，λi为无人机信息传递拓扑结构无向图G的邻接矩阵的特征值；Among them, S is the total number of closed-loop paths in the undirected graph of UAV information transfer topology; N is the total number of UAVs, and λ i is the eigenvalue of the adjacency matrix of the undirected graph G of UAV information transfer topology; 无人机信息传递拓扑结构的抗毁性评价函数f1为：The survivability evaluation function f 1 of the UAV information transfer topology is:
Figure FDA0003226699230000031
Figure FDA0003226699230000031
 其中，
Figure FDA0003226699230000032
为人机信息传递拓扑结构无向图G的最大的自然连通度。in,
Figure FDA0003226699230000032
Maximum natural connectivity of topologically structured undirected graph G for human-machine information transfer. 7.如权利要求1～4任意一项所述的隐式通信条件下多无人机对地搜索任务编队队形优化方法，其特征在于，无人机编队的搜索任务的效率评价函数f2为：7. The method for formation formation optimization of multi-UAV-to-ground search tasks under the condition of implicit communication according to any one of claims 1 to 4, wherein the efficiency evaluation function f 2 for the search task of UAV formations for:
Figure FDA0003226699230000033
Figure FDA0003226699230000033
 其中，drange为无人机编队的横向搜索覆盖宽度，
Figure FDA0003226699230000034
N为无人机总数，R为无人机的对地搜索范围。Among them, d range is the horizontal search coverage width of the UAV formation,
Figure FDA0003226699230000034
N is the total number of UAVs, and R is the ground search range of UAVs.
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