CN112733251A

CN112733251A - Multi-unmanned aerial vehicle collaborative track planning method

Info

Publication number: CN112733251A
Application number: CN202011547277.8A
Authority: CN
Inventors: 来磊; 邹鲲; 吴德伟; 杨宾锋; 李海林; 李保中
Original assignee: Air Force Engineering University of PLA
Current assignee: Air Force Engineering University of PLA
Priority date: 2020-12-24
Filing date: 2020-12-24
Publication date: 2021-04-30
Anticipated expiration: 2040-12-24

Abstract

The invention provides a multi-unmanned aerial vehicle collaborative flight path planning method, which comprises the following steps: constructing a track evaluation model, constructing a track constraint model, establishing a multi-target collaborative track planning model, optimizing a track search space, and solving an optimal track; the optimal solution searching capability of the firefly algorithm is improved by adopting a variable decomposition strategy, a Tent chaotic initialization strategy and a multi-population cyclic division combining strategy; highlighting the emphasis points of different task backgrounds on different optimization targets by adopting a bipolar preference dominance mechanism; the design cooperation degree index improves the track cooperativity among different UAVs; by organically combining the strategies at different stages of the method, the overall efficiency of the multi-target UAV collaborative track planning is improved.

Description

Multi-unmanned aerial vehicle collaborative track planning method

Technical Field

The invention belongs to the technical field of aircraft track planning, and particularly relates to a track planning method under the condition of multiple unmanned aerial vehicles.

Background

With the development of artificial intelligence technology and the intelligent conversion of modern war mode, a plurality of UAV cluster research projects are made in each developed military country; with the development, efficient and real-time multi-UAV collaborative track planning becomes one of the key technologies to be urgently promoted. Compared with single-UAV flight path planning, multi-UAV collaborative flight path planning also needs to consider position constraints with numerous neighbor UAVs, so that the optimization complexity is relatively high.

The intelligent optimization algorithm has excellent performance in solving the nondeterministic polynomial problem, so that the intelligent optimization algorithm becomes the most common method for solving the collaborative flight path problem, such as: in patent CN111813144A, "a multi-UAV collaborative route planning method based on improved herd algorithm", modeling collaborative route planning, and solving multi-UAV three-dimensional collaborative flight path by adopting improved herd algorithm; in patent CN111024086A, "a multi-unmanned aerial vehicle flight path planning method based on crowd bird optimization technology", curvature, deflection, climbing angle, flight path length, flight path duration, distance between unmanned aerial vehicles, and distance between unmanned aerial vehicles and an obstacle are used as flight path evaluation indexes, and a flight path evaluation function is constructed by using relevance between indexes and real-time property of weight, so that a crowd bird optimization algorithm is proposed to solve a flight path; in patent CN112034880A, "a novel multi-unmanned aerial vehicle collaborative route planning method", a green-headed duck optimization algorithm is used to solve the route; in patent CN111707267A, "a multi-unmanned aerial vehicle collaborative flight path planning method", the ant colony algorithm is used to solve the multi-unmanned aerial vehicle collaborative flight path.

When the multi-unmanned aerial vehicle track planning method is used for establishing a track evaluation model, the weighted sum of a plurality of track evaluation functions is used as a comprehensive evaluation model, so that the method belongs to the single-target track planning problem. And the defects of mutual conflict and restriction usually exist among all track evaluation functions in the single-target track optimization. Therefore, researchers take the flight path planning as a multi-objective optimization problem, and propose a multi-objective optimization UAV flight path planning method, such as: the multi-target cooperative reconnaissance track planning algorithm of multiple unmanned aerial vehicles, Chinese inertial technology bulletin, 2019, Vol-27(3) and 340-supplement 348, wherein the multi-target cooperative reconnaissance track planning algorithm is used for solving the multi-target cooperative track by using an improved particle swarm algorithm.

However, the multi-target track optimization method has the following defects: along with the large number of the track evaluation targets, the number of non-dominated solutions is increased, the selection capability of the algorithm to the population is poor, and the performance attenuation of the corresponding algorithm is serious; in addition, the increase of the number of optimal non-dominated solutions means that the number of alternative optimal tracks is increased, and therefore, the real-time performance of the algorithm is correspondingly reduced.

Therefore, the multi-objective intelligent optimization method obviously has defects aiming at multi-UAV collaborative track planning, is not suitable for track planning required by a specific task, and is one of key technologies for developing UAV application by researching a new collaborative track planning method with corresponding emphasis points according to task characteristics.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a multi-unmanned aerial vehicle collaborative flight path planning method based on an improved multi-target firefly algorithm, which comprises the following steps:

step A: constructing a track evaluation model, namely establishing a track distance evaluation model, a track threat evaluation model and a track hiding evaluation model;

and B: constructing a track constraint model, namely establishing a maximum navigation distance constraint model, a maximum flight angle constraint model and a flight height constraint model; establishing a space constraint model and a time constraint model of the collaborative flight path;

and C: establishing a multi-target collaborative track planning model and optimizing a track search space, namely establishing a multi-target track planning model combining a track evaluation model and a track constraint model, and performing coordinate conversion and discretization processing on the track search space;

step D: and solving the optimal flight path, namely improving the firefly algorithm and solving the optimal flight path by using the improved firefly algorithm.

And further, in the step D, the firefly algorithm is improved by utilizing variable decomposition, chaotic initialization, multi-population cyclic splitting and merging and diversity maintenance under the determined preference.

Further, step a comprises:

step A1: establishing a track distance evaluation model, wherein the track distance evaluation model is defined as:

wherein l_stIs the linear distance from the starting point to the end point; l_totalIs the total length of the actual flight;

step A2: establishing a track threat evaluation model, wherein a track threat evaluation function is defined as:

wherein l_rdThe total length of the crossing air defense detection area in the flight path; d_riThe diameter length of the ith air defense detection area; n is_rThe number of the air defense detection areas;

step A3: establishing a track hiding evaluation model, wherein a track hiding evaluation function is defined as:

f_h＝(h_ave-h_min)/(h_max-h_min) (3)

in the formula h_aveAverage height of the overall track; h is_minA UAV flight minimum altitude; h is_maxThe UAV flight maximum altitude.

Further, step B includes:

step B1: establishing a maximum flight distance constraint model of the UAV, wherein the maximum flight distance is L_maxThen the flight distance L must satisfy:

L≤L_max (4)

step B2: establishing a maximum flight angle constraint model, wherein the coordinates of two adjacent tracks are respectively (x)_i，y_i，z_i) And (x)_i+1，y_i+1，z_i+1) It must satisfy:

wherein alpha is_maxIs the maximum yaw angle, beta_maxIs the maximum pitch angle;

step B3: establishing a flight altitude constraint model, namely UAV flight altitude h_xyThe following constraints must be satisfied:

φ_zxy≤h_xy≤h_max (6)

wherein phi is a height increasing coefficient, and phi is more than 1; z is a radical of_xyIs the terrain height at coordinate (x, y); h is_xyIs the altitude of the UAV; h is_maxIs the maximum flying height;

step B4: establishing a collaborative track space constraint model, wherein the spacing distance between the UAVs must satisfy the following conditions:

||p_i-p_j||≥d_safe (7)

where UAVi and j are denoted as p at time t_iAnd p_j，d_safeThe minimum safe distance between tracks;

step B5: establishing a collaborative track time constraint model, wherein the flight speed range of the UAV is v ∈ [ v [ ]_min，v_max]UAVi has a flight path distance of l_totaliThen the time-of-flight range of UAVi is:

t_i∈[t_mini，t_maxi]＝[l_totali/v_min，l_totali/v_max] (8)

the time constraint conditions are as follows:

wherein n is_UAVIs the number of UAVs.

Further, step C includes:

step C1: establishing a multi-target collaborative track planning model, which comprises a multi-target optimization model taking track distance evaluation, track threat evaluation and track hiding evaluation as indexes, wherein the established optimization model is as follows:

wherein x is a feasible track point; s.t. refers to the basic constraint conditions of maximum sailing distance, maximum flight angle and flight height;

step C2: carrying out coordinate conversion and discretization processing on the track searching space, taking a connecting straight line of the starting point and the target point as an abscissa in a new reference coordinate system, and equally selecting D points as the abscissa of the track searching point; the longitudinal coordinate and the height of the track point are selected on D planes which pass through the D points and are vertical to the connecting straight line; after the track point search is completed, converting the track point under the new coordinate system into a point under the original coordinate system, wherein the conversion formula is as follows:

wherein theta is an included angle formed by a connecting line of the starting point and the target point in the original coordinate system and the X axis, and theta is arcsin ((y)_t-y_s)/|st|)；(x_new，y_new) Is a search coordinate value; (x)_s，y_s) Is the coordinate value of the starting point under the original coordinate system; st is a straight line between the start point and the target point.

Further, step D includes:

step D1: initializing and setting parameters of a multi-target firefly algorithm, wherein the parameters comprise a firefly algorithm population scale NP, a dimension N of a firefly individual in the population, a step factor alpha, an attraction value beta and a bright absorption coefficient gamma;

step D2: carrying out variable decomposition on the dimension of the firefly individual in the population, and decomposing the N-dimensional optimized variable into N_UAVEach sub-variable is subjected to iterative evolution by a sub-population;

step D3: carrying out Tent chaos initialization on firefly individuals in each sub population;

step D4: updating the positions of the firefly individuals in each sub-population;

step D5: performing multi-population circulating division and combination on each sub-population;

step D6: performing preferential diversity maintenance on each sub-population;

step D7: judging whether the optimization algorithm meets the iteration termination condition, and quitting if the optimization algorithm meets the iteration termination condition; if not, go to step D4.

Further, in the step C2, the longitudinal coordinate and the height of the track point are selected on D planes passing through the D points and perpendicular to the connecting straight line, discretization grid processing is performed on each plane in the D planes, the planes are divided into grids at equal intervals, and then the intersection point of each grid is a feasible track point.

Further, selecting Tent map in step D3 to improve the firefly location initialization, where Tent map is expressed as:

wherein x_tIs a chaotic variable at time t, x_t+1Is a chaotic variable at the moment of t + 1;

in the step D4, the position of each firefly represents a feasible flight path solution, and the luminance of the firefly represents the superiority of the solution; the firefly with high luminance has high attraction degree, and can attract the firefly with low luminance to move to the self, so that the self position is updated, and a new feasible solution is obtained; the luminance of firefly i is higher than j, then the attraction of firefly i to j is:

wherein r is_ijDistance from firefly i to j; beta is a₀Is the maximum attractive force; gamma is the light absorption coefficient;

the corresponding firefly j position update formula is as follows:

x_j＝x_j+β_ij(x_i-x_j)+αε (15)

wherein α is a constant coefficient; epsilon is a random number vector;

d5, sequencing the fireflies according to the brightness, and dividing the fireflies into m populations, wherein each population contains l fireflies; the population splitting principle is as follows: the first firefly with the brightness is distributed to the population 1, the second firefly with the brightness is distributed to the population 2, the mth firefly with the brightness is distributed to the population m, the (m + 1) firefly with the brightness is distributed to the population 1, and so on until all the fireflies are distributed; dividing Fn fireflies into m sub-populations, wherein l is Fn/m fireflies in each sub-population; after each sub-population is iterated, combining the m sub-populations into a population with the firefly number Fn; k is carried out on the split sub-populations in respective populations according to a position updating formula (15)_pOptimizing by iteration; in order to improve the brightness value of the individual with the worst brightness in each sub-population, the elite individual x with the highest brightness in the total population is used_bestAs a reference point, let the worst individual x_worstMove towards the elite body all the time, i.e.

x_worst＝x_worst+β(x_best-x_worst)+αε (16)

In addition, in order to ensure that the algorithm does not fall into local optimum in the later period of iteration, Levy flight random disturbance is added to the random motion of the firefly with the optimum brightness in each iteration process of the sub-population, namely

Wherein i represents the number of the sub-population;

represents a dot product; levy represents a random vector generated by Levy flight;

after the sub-populations complete iteration, combining the sub-populations and updating the positions, splitting and combining the populations repeatedly until a termination condition of the maximum iteration times is met;

d6, selecting the optimal collaborative flight path by the collaborative degree sequence, wherein the collaborative degrees are respectively the time collaboratorsA degree of identity and a degree of spatial co-ordination, wherein the degree of temporal co-ordination cd_iExpressed as:

wherein t is_iThe time of arrival of UAVi at the destination; t is t_minIs the minimum time to reach the destination; t is t_maxIs the maximum time to reach the destination;

distance co-ordination degree cd_sComprises the following steps:

where n is the number of UAV trajectories except for each UAV itself; f. of_iIs a safety distance mark between the ith track, if the minimum safety distance between the ith track and the safety distance mark is met, f _i1 is ═ 1; otherwise f_i＝0；

The total synergy cd is then:

cd＝cd_t+cd_s (22)

and when selecting a path with better cooperativity, sequencing the cooperativity, and selecting a front path as an optimal path.

Further, n in step A2_r＝4，d_r1＝17km，d_r2＝10km，d_r3＝9km，d _r410 km; h in step A3_min＝100m，h _max2 km; l in step B1 _max500 km; step B4 d_safe50 m; n in step B5 _UAV3; d-25 in step C2; in step D1, the population size NP is 50, the dimension of the firefly individual is 150, the step factor α is 0.25, the attraction value β is 0.2, and the light absorption coefficient γ is 1; in step D2, N is 150, and the submariable N_i＝50，i＝1，2，…，n_UAV(ii) a α is 1 in step D4; in step D5, Fn is 50, m is 5, l is 10, k _p50; the number of iterations in step D7 was 500.

The optimal solution searching capability of the firefly algorithm is improved by adopting a variable decomposition strategy, a Tent chaotic initialization strategy and a multi-population cyclic division combining strategy; highlighting the emphasis points of different task backgrounds on different optimization targets by adopting a bipolar preference dominance mechanism; the design cooperation degree index improves the track cooperativity among different UAVs; by organically combining the strategies at different stages of the method, the overall efficiency of the multi-target UAV collaborative track planning is improved.

Drawings

FIG. 1 is a flow chart of the method of the present invention;

FIG. 2 is a schematic diagram of the track search space coordinate transformation in the method of the present invention;

FIG. 3 is a schematic diagram of population cycle splitting in the method of the present invention;

FIG. 4 is a three-dimensional topographical view for use in the experiments of the method of the present invention;

FIG. 5 is a diagram of the three-dimensional effect of the UAV collaborative track generated by the present invention;

FIG. 6 is a two-dimensional effect plot of UAV collaborative flight path generated by the present invention;

FIG. 7 is a graph comparing the method of the present invention with a conventional firefly algorithm.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the following describes the present invention in further detail with reference to the accompanying drawings and examples.

As shown in fig. 1, the present invention provides a multi-unmanned aerial vehicle collaborative track planning method based on mixed strategy interactive evolution based on the prior art and key technical problems to be solved, which includes:

step A: and constructing a track evaluation model. And establishing a track distance evaluation model, a track threat evaluation model and a track hiding evaluation model according to the quality evaluation factors of the track in the actual flight environment.

And B: and constructing a track constraint model. Establishing a corresponding maximum navigation distance constraint model, a maximum flight angle constraint model and a flight height constraint model according to the self physical conditions, flight performance and the like of the unmanned aerial vehicle; in addition, aiming at the problem of unmanned aerial vehicle collaborative track planning, a space constraint model and a time constraint model of the collaborative track are established.

And C: and establishing a multi-target collaborative track planning model and optimizing a track search space. And establishing a multi-target track planning model combining a track evaluation model and a track constraint model, and performing coordinate conversion and discretization processing on a track search space.

Step D: and solving the optimal track. And improving the firefly algorithm by utilizing variable decomposition, chaotic initialization, multi-population cyclic splitting and merging and diversity maintenance under the determined preference, and solving the optimal flight path by using the improved firefly algorithm.

And B, constructing a track evaluation model in the step A. The specific implementation process is as follows:

step A1: and establishing a track distance evaluation model. The flight path distance refers to the spatial distance that the UAV passes from a flight starting point to a flight terminal point, the UAV is limited by self-power energy and task completion time in the flight process, and the shorter the flight path distance is, the better the flight path distance is generally expected to be; meanwhile, the flight distance is short, the air-leaving time is short, and the safety of the UAV is correspondingly improved. Therefore, the track distance evaluation model is defined as:

wherein l_stIs the linear distance from the starting point to the end point; l_totalThe total length of the actual flight.

Step A2: and establishing a track threat evaluation model. For the flight path threat mainly refers to the threat detected and irradiated by the air defense system, the more the flight path is far away from or passes through the air defense detection area, the smaller the flight path threat is; conversely, the greater the track threat. The track threat valuation function is defined as:

wherein l_rdThe total length of the crossing air defense detection area in the flight path; d_riThe diameter length of the ith air defense detection area; n is_rFor air defenseThe number of detection zones.

In a particular embodiment of the invention n_r＝4，d_r1＝17km，d_r2＝10km，d_r3＝9km，d_r4＝10km。

Step A3: and establishing a track concealed evaluation model. For the tasks such as UAV (unmanned aerial vehicle) defense outburst, the most effective method for improving the concealment of the UAV is to keep low-altitude or ultra-low-altitude flight, so the flight path height can explain the flight concealment of the UAV to a certain extent, and a flight path concealment evaluation function is defined as follows:

f_h＝(h_ave-h_min)/(h_max-h_min) (3)

In a particular embodiment of the invention h_min＝100m，h_max＝2km。

And step B, constructing a track constraint model. The specific implementation process is as follows:

step B1: and establishing a UAV maximum range constraint model. When the unmanned aerial vehicle flies, the fuel oil loading capacity is limited, the corresponding flying distance is limited, and the maximum flying distance is L_maxThen the flight distance L must satisfy:

L≤L_max (4)

in one embodiment of the invention L_max＝500km。

Step B2: and establishing a maximum flight angle constraint model. Influenced by self maneuvering capability, the maximum yaw angle alpha of the unmanned aerial vehicle during flight must be considered_maxAnd a maximum pitch angle beta_maxThe limit of (2). If the coordinates of two adjacent tracks are respectively (x)_i，y_i，z_i) And (x)_i+1，y_i+1，z_i+1) Then, it must satisfy:

step B3: and establishing a flight height constraint model. The UAV has to meet a certain flight altitude requirement in the flight process, the flight altitude of the UAV has to be higher than the ground by a certain distance, and the UAV collides with the ground if the UAV flies too low. Meanwhile, if the flying height is too high, the concealment performance is correspondingly deteriorated. Thus, UAV flight altitude h_xyThe following constraints must be satisfied:

φz_xy≤h_xy≤h_max (6)

wherein phi is a height increasing coefficient, and phi is more than 1; z is a radical of_xyIs the terrain height at coordinate (x, y); h is_xyIs the altitude of the UAV; h is_maxIs the maximum flying height.

Step B4: and establishing a collaborative track space constraint model. The space constraint actually refers to a collision-free condition between UAVs, that is, a certain safety distance must be kept between UAVs at any time during the flight of the UAVs to avoid collision. Assume that UAVi and j are denoted as p at time t_iAnd p_jThen, at this time, the spacing distance between UAVs must satisfy:

||p_i-p_j||≥d_safe (7)

wherein d is_safeIs the minimum safe distance between tracks.

In a particular embodiment of the invention d_safe＝50m。

Step B5: and establishing a collaborative track time constraint model. Time constraints refer to UAVs that generally require each UAV to be able to reach the target mission area at the same time in order to maximize the efficiency of performance of the mission. Assuming that the flight speed range of the UAV is v ∈ [ v ]_min，v_max]UAVi has a flight path distance of l_totaliThen the time-of-flight range of UAVi is:

t_i∈[t_mini，t_maxi]＝[l_totali/v_min，l_totali/v_max] (8)

the time constraint then requires:

wherein n is_UAVIs the number of UAVs. This equation indicates that the UAVs arrive at the same time with an intersection.

In a particular embodiment of the invention n_UAV＝3。

And C: and establishing a multi-target collaborative track planning model, and carrying out coordinate conversion and discretization processing on a track search space. The specific implementation process is as follows:

step C1: and establishing a multi-target collaborative track planning model. Aiming at the defect that each evaluation function is subjected to simple weighted summation in the traditional track planning, the invention establishes a multi-target optimization model taking track distance evaluation, track threat evaluation and track hiding evaluation as indexes, wherein the established optimization model is as follows:

wherein x is a feasible track point; and s.t. refers to basic constraint conditions of maximum sailing distance, maximum flight angle and flight height.

Compared with single-target optimization, the solution of multi-target optimization is not a single optimal solution, but a group of Pareto optimal solution sets. Let x be₁、x₂For two feasible solutions, when

Wherein l is a track distance evaluation index, r is a track threat evaluation index, and h is a track concealment evaluation index.

Then x is solved₁Pareto dominate solution x₂(ii) a If there is no dominance x₁Solution of (1), then x₁The Pareto optimal solution is obtained; and the set of all Pareto optimal solutions is called a Pareto optimal solution set. The Pareto optimal solution set actually solved by the multi-target track planning is a feasible track point solution set meeting the track requirement. Such as: and if the number of Pareto optimal solution sets is 10, 10 optimized flight path routes are provided.

Step C2: and carrying out coordinate conversion and discretization processing on the track search space. Taking a connecting straight line of the starting point and the target point as an abscissa in a new reference coordinate system, and equally selecting D points of the straight line as the abscissa value of the track searching point; and for the selection of the longitudinal coordinate and the height of the track point, the problem of searching on D planes which pass through the D points and are vertical to the connecting straight line is actually converted, as shown in fig. 2.

After the track point search is completed, converting the track point under the new coordinate system into a point under the original coordinate system, wherein the conversion formula is as follows:

Under a new coordinate system taking a straight line st as an X axis, dividing the straight line st into D equal parts, searching track point combinations on D planes, and actually, converting the search of the track points from three-dimensional search to two-dimensional search, namely, searching the longitudinal coordinates and the height values of the track points on each plane, wherein the X axis coordinate of the three-dimensional track points is a known value. However, it is obvious that the search space for searching the track points on the continuous plane is large, and the real-time performance of track planning is reduced. Therefore, discretization grid processing is performed on each plane in the D planes, the planes are divided into grids at equal intervals, and then intersection points of each grid are feasible track points, as shown in fig. 2. The higher the resolution adopted by the discretized grid is, the higher the precision of the track planning result is; conversely, the resolution is low and the accuracy of the track planning is reduced.

In one embodiment of the present invention, D is 25, 25 discrete points required for determining a flight path, and two variables of ordinate and height are required for determining each discrete point, so that D × 2 is 50 variables required for determining a flight path; when the improved multi-target firefly algorithm is used for solving a single track, the above 50 variable values are solved.

Step D: and solving the optimal flight path by using an improved multi-target firefly algorithm. The specific implementation process is as follows:

step D1: and carrying out parameter initialization setting on the multi-target firefly algorithm. The firefly algorithm has a population size NP, dimensions of firefly individuals in the population N, a step factor alpha, an attraction value beta and a brightness absorption coefficient gamma.

In one embodiment of the invention, the population size NP is 50 and the dimension of the firefly individual is N N_UAVX (D × 2) 150, step factor α 0.25, attraction value β 0.2, and light absorption coefficient_γ＝1。

Step D2: and carrying out variable decomposition on the dimension of the firefly individual in the population. When the flight path is optimized by adopting an evolutionary algorithm, the number of flight path points is represented by the dimension of a variable in a population individual; the more the number of track points is, the higher the accuracy of corresponding track planning is; therefore, it is generally desirable to have as many variables as possible, but large-scale variables mean increased algorithm complexity. In addition, multiple UAV trajectory planning makes the number of variables in a population of individuals more voluminous. The invention adopts a large-scale variable decomposition strategy under a cooperative framework to decompose the variables and decompose the N-dimensional firefly individuals into N_UAVAnd each sub-variable Ni represents a track point combination of the UAV, and each corresponding sub-variable is iteratively evolved by a sub-population.

In one embodiment of the present invention, N is 150, the submariate Ni is 50, i is 1, 2, …, N_UAV。

Step D3: tent chaotic initialization is carried out on firefly individuals in each sub population.

In the intelligent optimization algorithm, the initialization effect of the group positions has certain influence on searching a global optimum value and the convergence speed of the algorithm, and generally, the more uniform the initial position distribution is, the more rapid the algorithm is to converge. Chaotic mapping has been proved to be the most effective initialization strategy in the current intelligent optimization algorithm in a plurality of research results, the commonly used chaotic mapping comprises Tent mapping and Logistic mapping, but the ergodicity of the Tent mapping is relatively good, so the Tent mapping is selected to improve the firefly position initialization, and the Tent mapping is expressed as:

wherein x_tIs a chaotic variable at time t, x_t+1Is the chaos variable at the moment of t + 1.

Step D4: and (4) updating the positions of the firefly individuals in each sub-population. The updating principle is as follows: the position of each firefly represents a feasible flight path solution, and the luminance of the firefly represents the superiority of the solution; the firefly with high luminance has high attraction degree, and can attract the firefly with low luminance to move to the self, so that the self position is updated, and a new feasible solution is obtained; the firefly continuously searches for the optimal solution in the solution space through the brightness attraction mechanism.

Assuming that firefly i is brighter than j, the attraction of firefly i to j is:

wherein r is_ijDistance from firefly i to j; beta is a₀Is the maximum attractive force; gamma is a light absorption coefficient.

The corresponding firefly j position update formula is as follows:

x_j＝x_j+β_ij(x_i-x_j)+αε (15)

wherein α is a constant coefficient; ε is the random number vector.

In one specific embodiment of the present invention α ═ 1.

Step D5: and performing multi-population cycle division and combination on each sub population. On the basis of the original firefly algorithm, in each algorithm iteration process, after the firefly carries out position updating according to the formula (15), the firefly is sequenced according to the brightness, and is split into m populations, wherein each population has l fireflies; the population splitting principle is as follows: the first firefly of luminance is assigned to population 1, the second firefly of luminance is assigned to population 2, the mth firefly of luminance is assigned to population m, the (m + 1) th firefly of luminance is assigned to population 1, so on until all the fireflies are assigned, as shown in fig. 3.

In fig. 3, the left box indicates a total of Fn fireflies in the sub-population, and the right box indicates the division of Fn fireflies into m sub-populations, each of which has a total of l ═ Fn/m fireflies; and after each sub-population is iterated, combining the m sub-populations into a population with the firefly number Fn.

In one embodiment of the present invention Fn is 50, m is 5 and l is 10.

K is carried out on the split sub-populations in respective populations according to a position updating formula (15)_pAnd optimizing by the secondary iteration.

In a specific embodiment of the invention k_p＝50。

Meanwhile, in order to improve the brightness value of the individual with the worst brightness in each sub-population, the elite individual x with the highest brightness in the total population is used_bestAs a reference point, let the worst individual x_worstMove towards the elite body all the time, i.e.

x_worst＝x_worst+β(x_best-x_worst)+αε (16)

Wherein i represents the number of the sub-population;

represents a dot product; levy represents the random vector generated by Levy flight.

And after the sub-populations complete iteration, merging the sub-populations and updating the positions, and splitting and merging the populations repeatedly until a termination condition of the maximum iteration number is met.

In one embodiment of the present invention the maximum number of iterations is set to 500.

Step D6: and performing diversity maintenance for determining preference on each sub-population.

The route planning under the preference means that the UAV emphasizes different objective functions according to task needs, for example, the emphasis concealment preference actually means that the UAV flies close to the ground to reduce the flying height cost to keep concealment on the basis of balancing threats and distance cost in the process of penetration flight. Therefore, a reference point of the side-emphasis flight altitude cost can be set according to experience in a plurality of Pareto non-dominated solutions, and meanwhile, the optimum flight path of the side-emphasis concealment is selected by a bipolar preference dominance method, and the basic strategy firstly calculates the mark value of the solution:

wherein g is_iA reference point for the ith target; w is a_iIs any point in the ith target space; p is the number of targets.

According to the flag value, carrying out layering non-dominated sorting on the population, and simultaneously calculating the relative closeness ci of each layer solution, wherein the calculation method comprises the following steps:

wherein

To a negative g_iThe Euclidean distance of (c);

is up to positive g_iThe euclidean distance of (c).

And finally, cutting the non-dominated solution by comparing the relative closeness difference value between different solutions with a set threshold value so as to keep the diversity of the solution.

In addition, for the collaborative flight path planning of multiple UAVs, the cooperativity among the flight paths of the UAVs is also an important aspect for measuring the quality of the flight paths, so in order to select the optimal flight path from a plurality of non-dominated solutions, the invention provides the synergy ranking so as to select the optimal collaborative flight path, wherein the synergy respectively consists of time synergy and space synergy, and the time synergy cd_tExpressed as:

wherein t is_iThe time of arrival of UAVi at the destination; t is t_minIs the minimum time to reach the destination; t is t_maxThe maximum time to reach the destination.

Distance co-ordination degree cd_sComprises the following steps:

where n is the number of UAV trajectories except for each UAV itself; f. of_iIs a safety distance mark between the ith track, if the minimum safety distance between the ith track and the safety distance mark is met, f _i1 is ═ 1; otherwise f_i＝0。

The total synergy cd is then:

cd＝cd_t+cd_s (22)

Step D7: judging whether the optimization algorithm meets an iteration termination condition, namely the iteration frequency reaches the maximum value of 500 times, and quitting if the iteration frequency meets the maximum value; if not, go to step D4.

In order to verify the effectiveness of the method in UAV three-dimensional track planning, simulation experiments are carried out on a PC (personal computer) with an Intel Core (TM) i3-3240, 3.4GHz and 3G memory, the running environment is Windows XP, and the programming environment is MATLAB 2013. Fig. 4 is a three-dimensional mountain terrain map for verifying the method of the present invention, and the experimental area is a three-dimensional space of 100 × 100 × 1km, and the performance of the method of the present invention can be better verified by selecting mountain terrain. Fig. 5 is a three-dimensional effect graph of an optimal path of the UAV generated by the method of the present invention, where a black spherical area represents a ground air defense threat area, the unmanned aerial vehicle should avoid the air defense threat area as much as possible when planning an optimal track, and a black solid line represents a track optimized by the method of the present invention, and there are 9 optimized tracks in the graph, it can be seen that all tracks basically avoid the air defense threat, and the concealment of the track is effectively improved along the relief of the terrain. FIG. 6 is a two-dimensional elevation effect diagram of an optimal path for a UAV generated by the method of the present invention. FIG. 7 is a comparison graph of the optimal flight path generated by the method of the present invention and the optimal flight path generated by a standard multi-target firefly algorithm, wherein the ordinate in the graph is the comprehensive quality value of the flight path and the abscissa in the graph is the number of iterations of the algorithm; the comprehensive good and bad value of the flight path optimized by the method is 110, the comprehensive good and bad value of the flight path of the standard multi-target firefly method is 210, and the comprehensive good and bad value of the flight path of the method is superior to that of a comparison algorithm; in addition, the method basically finds the optimal track when the iteration is performed for 20 times, and the standard multi-target firefly method finds the optimal track when the iteration is performed for 30 times.

The invention provides a firefly multi-target UAV (unmanned aerial vehicle) collaborative flight path planning method adopting a mixed strategy under preference setting, wherein the method adopts a variable decomposition strategy, a Tent chaotic initialization strategy and a multi-population cyclic division combining strategy to improve the optimal solution searching capability of a firefly algorithm; highlighting the emphasis points of different task backgrounds on different optimization targets by adopting a bipolar preference dominance mechanism; designing a degree of cooperation index to improve the track cooperativity among different UAVs; by organically combining the strategies at different stages of the method, the overall efficiency of the multi-target UAV collaborative track planning is improved.

Claims

1. A multi-unmanned aerial vehicle collaborative flight path planning method comprises the following steps:

2. The method for planning the collaborative flight path of the multiple unmanned aerial vehicles according to claim 1, wherein the method comprises the following steps: and D, improving the firefly algorithm by utilizing variable decomposition, chaotic initialization, multi-population cyclic splitting and merging and diversity maintenance under the determined preference.

3. The method for planning the collaborative flight path of the multiple unmanned aerial vehicles according to claim 2, wherein the method comprises the following steps: the step A comprises the following steps:

f_h＝(h_ave-h_min)/(h_max-h_min) (3)

4. The method for planning the collaborative flight path of the multiple unmanned aerial vehicles according to claim 2, wherein the method comprises the following steps: the step B comprises the following steps:

L≤L_max (4)

φz_xy≤h_xy≤h_max (6)

||p_i-p_j||≥d_safe (7)

t_i∈[t_mini，t_maxi]＝[l_totali/v_min，l_totali/v_max] (8)

the time constraint conditions are as follows:

wherein n is_UAVIs the number of UAVs.

5. The method for planning the collaborative flight path of the multiple unmanned aerial vehicles according to claim 2, wherein the method comprises the following steps: the step C comprises the following steps:

6. The method for planning the collaborative flight path of the multiple unmanned aerial vehicles according to claim 2, wherein the method comprises the following steps: the step D comprises the following steps:

step D2: carrying out variable decomposition on the dimension of the firefly individual in the population, and decomposing the N-dimensional optimized variable into N_UAVN is_iDimensional sub-variables, each sub-variable being iteratively evolved by a sub-population;

step D6: performing preferential diversity maintenance on each sub-population;

7. The method for planning the collaborative flight path of the multiple unmanned aerial vehicles according to claim 5, wherein the method comprises the following steps: and C2, selecting the longitudinal coordinate and height of the track point on D planes which pass through the D points and are perpendicular to the connecting straight line, performing discretization grid processing on each plane in the D planes, dividing the planes into grids at equal intervals, and enabling the intersection point of each grid to be a feasible track point.

8. The method for planning the collaborative flight path of the multiple unmanned aerial vehicles according to claim 6, wherein the method comprises the following steps: selecting a Tent map in step D3 to improve the firefly position initialization, wherein the Tent map is expressed as:

the corresponding firefly j position update formula is as follows:

x_j＝x_j+β_ij(x_i-x_j)+αε (15)

wherein α is a constant coefficient; epsilon is a random number vector;

d5, sequencing the fireflies according to the brightness, and dividing the fireflies into m populations, wherein each population contains l fireflies; the population splitting principle is as follows: luminance first firefly to population 1 and luminance second firefly to populationThe population 2, the luminance mth firefly is distributed to the population m, the luminance mth +1 firefly is distributed to the population 1, and the rest is done until all the fireflies are distributed; dividing Fn fireflies into m sub-populations, wherein l is Fn/m fireflies in each sub-population; after each sub-population is iterated, combining the m sub-populations into a population with the firefly number Fn; k is carried out on the split sub-populations in respective populations according to a position updating formula (15)_pOptimizing by iteration; the elite individual x with the highest brightness in the total population_bestAs a reference point, let the worst individual x_worstMove towards the elite body all the time, i.e.

x_worst＝x_worst+β(x_best-x_worst)+αε (16)

In each iteration process of the sub-population, Levy flight random disturbance is added in the random movement of the firefly with optimal brightness, namely

Wherein i represents the number of the sub-population;

d6, selecting the optimal collaborative flight path by the collaborative degree sequence, wherein the collaborative degrees respectively consist of time collaborative degrees and space collaborative degrees, and the time collaborative degrees cd_tExpressed as:

wherein t is_iThe time of arrival of UAVi at the destination; t is t_minTo a minimum time to reach a destinationA (c) is added; t is t_maxIs the maximum time to reach the destination;

distance co-ordination degree cd_sComprises the following steps:

where n is the number of UAV trajectories except for each UAV itself; f. of_iIs a safety distance mark between the ith track, if the minimum safety distance between the ith track and the safety distance mark is met, f_i1 is ═ 1; otherwise f_i＝0；

The total synergy cd is then:

cd＝cd_t+cd_s (22)

9. The method for planning the collaborative flight path of multiple unmanned aerial vehicles according to any one of claims 1 to 8, wherein: n in step A2_r＝4，d_r1＝17km，d_r2＝10km，d_r3＝9km，d_r410 km; h in step A3_min＝100m，h_max2 km; l in step B1_max500 km; step B4 d_safe50 m; n in step B5_UAV3; d-25 in step C2; in step D1, the population size NP is 50, the dimension of the firefly individual is 150, the step factor α is 0.25, the attraction value β is 0.2, and the light absorption coefficient γ is 1; in step D2, N is 150, and the submariable N_i＝50，i＝1，2，…，n_UAV(ii) a α is 1 in step D4; in step D5, Fn is 50, m is 5, l is 10, k_p50; the number of iterations in step D7 was 500.