CN112733251B - Collaborative flight path planning method for multiple unmanned aerial vehicles - Google Patents
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Abstract
The invention provides a collaborative flight path planning method for a plurality of unmanned aerial vehicles, which comprises the following steps: constructing a track evaluation model, constructing a track constraint model, constructing 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 plurality of group cyclic splitting and merging strategies; a bipolar preference dominance mechanism is adopted to highlight the emphasis points of different task backgrounds on different optimization targets; designing a synergy index to improve track cooperativity among different UAVs; through the organic combination of the strategies at different stages of the method, the overall efficiency of the multi-target UAV collaborative track planning is improved.
Description
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 planes.
Background
Along with the development of artificial intelligence technology and the transition of modern war modes to intelligence, various military developed countries disputes develop a plurality of UAV cluster research projects; with the development, the need for efficient, real-time multi-UAV collaborative trajectory planning is one of the key technologies to be improved. Compared with single UAV track planning, multi-UAV collaborative track planning also needs to consider the position constraint of the UAVs with a plurality of neighbors, so that the optimization complexity is relatively high.
The excellent performance of the intelligent optimization algorithm in solving the problem of the non-deterministic polynomial makes the intelligent optimization algorithm the most common method in solving the problem of the cooperative track, such as: the patent CN111813144A 'a multi-unmanned aerial vehicle collaborative route planning method based on an improved flock algorithm' models collaborative route planning, and adopts the improved flock algorithm to solve a multi-UAV three-dimensional collaborative route; in the patent CN111024086a 'a multi-unmanned aerial vehicle track planning method based on a flocked-bird optimizing technology', curvature, flexibility, climbing angle, track length, track duration, distance between unmanned aerial vehicles and distance between each unmanned aerial vehicle and an obstacle are used as track evaluation indexes, and a track evaluation function is constructed by utilizing the relevance between indexes and the real-time property of weights, so that a flocked-bird optimizing algorithm is provided for solving the track; in a novel multi-unmanned aerial vehicle collaborative route planning method, a green head duck optimization algorithm is utilized to solve a route in a patent CN 112034880A; in the patent CN111707267A, an ant colony algorithm is utilized to solve the multi-unmanned aerial vehicle collaborative track.
The multi-unmanned aerial vehicle track planning method uses the weighted sum of a plurality of track evaluation functions as a comprehensive evaluation model when the track evaluation model is established, so that the multi-unmanned aerial vehicle track planning method belongs to the single-target track planning problem. And the defects of mutual conflict and restriction exist among the track evaluation functions in the single-target track optimization. Therefore, researchers use flight path planning as a multi-objective optimization problem, and a multi-objective optimized UAV flight path planning method is proposed, for example: the improved particle swarm algorithm is utilized to solve the multi-target collaborative track in the literature (multi-unmanned aerial vehicle multi-target collaborative reconnaissance track planning algorithm), chinese inertial technical journal, 2019, vol-27 (3) and 340-348).
However, the multi-objective track optimization method is characterized in that: as the number of track evaluation targets is large, the number of non-dominant solutions is increased, the selection capability of the algorithm on the population is poor, and the performance attenuation of the corresponding algorithm is serious; furthermore, an increase in the number of optimal non-dominant solutions means an increase in the number of alternative optimal tracks, and therefore, the real-time nature of the algorithm is correspondingly reduced.
Therefore, the multi-target intelligent optimization method obviously has the defect of being not suitable for the flight path planning required by specific tasks aiming at multi-UAV collaborative flight path planning, and the research of a new collaborative flight path planning method with corresponding emphasis points according to the characteristics of the tasks becomes one of key technologies for developing UAV application.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a multi-unmanned aerial vehicle collaborative track planning method based on an improved multi-target firefly algorithm, which comprises the following steps:
Step A: constructing a track evaluation model, namely, constructing a track distance evaluation model, a track threat evaluation model and a track concealment evaluation model;
and (B) step (B): constructing a track constraint model, namely, constructing 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;
Step C: establishing a multi-target collaborative track planning model and optimizing a track searching space, namely establishing a multi-target track planning model by combining a track evaluation model and a track constraint model, and carrying out coordinate conversion and discretization on the track searching space;
step D: and solving the optimal track, namely improving a firefly algorithm, and solving the optimal track by using the improved firefly algorithm.
Furthermore, in the step D, the firefly algorithm is improved by utilizing variable decomposition, chaotic initialization, multiple group circulation splitting and merging and diversity maintenance under the determined preference.
Further, the step a includes:
step A1: establishing a track distance evaluation model, wherein the track distance evaluation model is defined as:
wherein l st is the linear distance from the start point to the end point; l total is 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 rd is the total length of the crossing air defense detection area in the track; d ri is the diameter length of the ith air defense detection area; n r is the number of air defense detection areas;
step A3: establishing a track hidden evaluation model, wherein a track hidden evaluation function is defined as:
fh＝(have-hmin)/(hmax-hmin) (3)
wherein h ave is the average height of the whole track; h min is the minimum UAV flight altitude; h max is the UAV flight maximum altitude.
Further, the step B includes:
Step B1: establishing a UAV maximum range constraint model, wherein the maximum flight distance is L max, and the flight distance L must satisfy the following conditions:
L≤Lmax (4)
Step B2: establishing a maximum flight angle constraint model, wherein coordinates of two adjacent tracks are (x i,yi,zi) and (x i+1,yi+1,zi+1) respectively, and the maximum flight angle constraint model must satisfy the following conditions:
Wherein α max is the maximum yaw angle and β max is the maximum pitch angle;
Step B3: establishing a flight altitude constraint model, the UAV flight altitude h xy must satisfy the following constraints:
φzxy≤hxy≤hmax (6)
Wherein phi is a height increase coefficient, phi is more than 1; z xy is the terrain height at coordinates (x, y); h xy is the flying height of the UAV; h max is the maximum flying height;
Step B4: establishing a collaborative track space constraint model, wherein the interval distance between UAVs must satisfy the following conditions:
||pi-pj||≥dsafe (7)
Wherein UAVi and j are denoted as p i and p j,dsafe as the minimum safe distance between tracks at time t;
Step B5: establishing a collaborative track time constraint model, wherein the flight speed range of the UAV is v epsilon [ v min,vmax ], the flight track distance of UAVi is l totali, and the flight time range of UAVi is:
ti∈[tmini,tmaxi]＝[ltotali/vmin,ltotali/vmax] (8)
The time constraint conditions are:
Where n UAV is the number of UAVs.
Further, step C includes:
Step C1: establishing a multi-target collaborative track planning model, wherein the multi-target optimization model comprises track distance evaluation, track threat evaluation and track concealment evaluation as indexes, and the established optimization model comprises the following steps:
wherein x is a feasible track point; s.t. the maximum sailing distance, the maximum flying angle and the basic constraint condition of flying height;
Step C2: performing 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 under a new reference coordinate system, and equally dividing the straight line to select D points as the abscissa values of the search track points; the ordinate and the height of the track points are selected on D planes which are perpendicular to the connecting straight line through D points; 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 expressed as follows:
wherein θ is an included angle formed by a starting point in the original coordinate system, a connecting line of the starting point and the target point and an X axis, θ=arcsin ((y t-ys)/|st|);(xnew,ynew) is a searching coordinate value, (X s,ys) is a coordinate value of the starting point in the original coordinate system, and st is a straight line between the starting point and the target point.
Further, step D includes:
step D1: parameter initialization setting is carried out on a multi-target firefly algorithm, wherein the parameter initialization setting comprises a firefly algorithm population scale NP, a dimension N of firefly individuals in the population, a step factor alpha, an attraction value beta and a brightness absorption coefficient gamma;
Step D2: carrying out variable decomposition on the individual dimension of firefly in the population, decomposing the N-dimensional optimization variable into N UAV Ni-dimensional sub-variables, and carrying out iterative evolution on each sub-variable by one sub-population;
Step D3: tent chaotic initialization is carried out on firefly individuals in each sub population;
step D4: position updating is carried out on firefly individuals in each sub-population;
step D5: carrying out cyclic splitting and merging on various sub populations;
Step D6: carrying out diversity maintenance of the determined preference on each sub population;
step D7: judging whether the optimizing algorithm meets the iteration termination condition, and exiting if the optimizing algorithm meets the iteration termination condition; if not, the process goes to step D4.
Further, in the step C2, the ordinate and the height of the track point are selected on D planes perpendicular to the connecting straight line through the D points, discretization grid processing is performed on each plane of the D planes, and the planes are divided into equidistant grids, so that the intersection point of each grid is a feasible track point.
Further, in step D3, the improvement of firefly position initialization is performed by selecting a Tent map, which is expressed as:
Wherein x t is a chaotic variable at the time t, and x t+1 is a chaotic variable at the time t+1;
D4, each position of fireflies represents a feasible flight path solution, and the luminous brightness of the fireflies represents the superiority of the solution; fireflies with high luminous brightness have high attraction degree, and fireflies with low luminous brightness are attracted to move to the fireflies, so that the positions of the fireflies are updated, and new feasible solutions are obtained; firefly i has a higher brightness than j, and the attractive force of firefly i to j is:
Where r ij is the firefly i to j distance; beta 0 is the maximum attractive force; gamma is the light absorption coefficient;
the corresponding firefly j position update formula is:
xj＝xj+βij(xi-xj)+αε (15)
wherein α is a constant coefficient; epsilon is a random number vector;
In the step D5, sorting fireflies according to brightness, and splitting the fireflies into m populations, wherein each population has l fireflies; the population division principle is as follows: a first firefly with brightness is distributed to a population 1, a second firefly with brightness is distributed to a population 2, an mth firefly with brightness is distributed to a population m, an (m+1) th firefly with brightness is distributed to the population 1, and the like until all fireflies are distributed; dividing Fn fireflies into m sub-populations, each sub-population sharing l=fn/m fireflies; after each sub-population iteration is completed, m sub-populations are combined into a population with the number of fireflies being Fn; k p times of iterative optimization are carried out on the split sub-populations in the respective populations according to a position updating formula (15); to improve the brightness value of the worst individuals in each sub-population, the elite individuals x best with the highest brightness in the total population are taken as reference points, so that the worst individuals x worst always move towards the elite individuals, namely
xworst＝xworst+β(xbest-xworst)+αε (16)
In addition, in order to ensure that the algorithm does not fall into local optimum in the later stage of iteration, levy flying random disturbance is added in the random motion of the firefly with optimal brightness in each iteration process of the sub population, namely
Wherein i represents the number of the sub-population; representing dot product; levy represents a random vector generated by Levy flight;
When the sub-populations finish iteration, each sub-population is combined and the position is updated at the same time, and the population splitting and combining are repeatedly performed until the termination condition of the maximum iteration times is met;
in step D6, the optimal synergy track is selected according to the synergy degree sequence, wherein the synergy degree is respectively composed of a time synergy degree and a space synergy degree, and the time synergy degree cd i is expressed as:
Wherein t i is the time UAVi arrives at the destination; t min is the minimum time to reach the destination; t max is the maximum time to reach the destination;
The distance synergy cd s is:
Wherein n is the number of other UAV tracks besides each UAV itself; f i is a safe distance mark between the first track and the ith track, if the minimum safe distance is met between the first track and the ith track, f i =1; whereas f i =0;
The total synergy cd is:
cd＝cdt+cds (22)
when the track with better synergy is selected, sequencing the synergy degree, and selecting the track at the front as the optimal track.
Further, n r＝4,dr1＝17km,dr2＝10km,dr3＝9km,dr4 =10 km in step A2; h min＝100m,hmax = 2km in step A3; in step B1, L max =500 km; d safe =50m in step B4; n UAV = 3 in step B5; d=25 in step C2; in the step D1, the population size np=50, the dimension of firefly individual is n=150, the step factor α=0.25, the attraction value β=0.2, and the light absorption coefficient γ=1; n=150 in step D2, child variable N i＝50,i＝1,2,…,nUAV; α=1 in step D4; fn=50, m= 5,l =10, k p =50 in step D5; the number of iterations in step D7 is 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 plurality of group cyclic splitting and merging strategies; a bipolar preference dominance mechanism is adopted to highlight the emphasis points of different task backgrounds on different optimization targets; designing a synergy index to improve track cooperativity among different UAVs; through the organic combination of 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 conversion of track search space coordinates in the method of the present invention;
FIG. 3 is a schematic diagram of population cycle split in the method of the present invention;
FIG. 4 is a three-dimensional topographical view of an experiment in the method of the present invention;
FIG. 5 is a three-dimensional effect diagram of a UAV collaborative flight path generated by the present invention;
FIG. 6 is a graph of a two-dimensional effect of UAV collaborative flight path generated by the present invention;
FIG. 7 is a comparison of the method of the present invention and a conventional firefly algorithm.
Detailed Description
The objects, technical solutions and advantages of the present invention will be more apparent from the following detailed description of the present invention with reference to the accompanying drawings and examples.
As shown in fig. 1, the invention provides a multi-unmanned aerial vehicle collaborative track planning method based on hybrid strategy interactive evolution based on the prior art and key technical problems to be solved, which comprises the following steps:
Step A: and constructing a track evaluation model. And establishing a track distance evaluation model, a track threat evaluation model and a track concealment evaluation model according to the quality evaluation factors of the tracks in the actual flight environment.
And (B) step (B): and constructing a track constraint model. Establishing a corresponding maximum sailing distance constraint model, a maximum flight angle constraint model and a flight height constraint model according to the physical conditions, the flight performance and the like of the unmanned aerial vehicle; in addition, a space constraint model and a time constraint model of the collaborative flight path are established aiming at the problem of unmanned aerial vehicle collaborative flight path planning.
Step C: and establishing a multi-target collaborative track planning model and optimizing a track search space. And establishing a multi-target track planning model by combining a track evaluation model and a track constraint model, and carrying out coordinate conversion and discretization on a track search space.
Step D: and solving the optimal track. And improving a firefly algorithm by utilizing variable decomposition, chaotic initialization, multiple group cyclic splitting combination and diversity maintenance under determined preference, and solving an optimal track by using the improved firefly algorithm.
And A, constructing a track evaluation model. The specific implementation process is as follows:
Step A1: and establishing a track distance evaluation model. The flight path distance refers to the space distance that the UAV passes from the flight start point to the end point, the UAV is limited by self-power energy and task completion time in the flight process, and the shorter the flight distance is, the better is generally expected to be; meanwhile, the flight distance is short, the clearance time is short, and the safety of the UAV is correspondingly improved. Thus, the track distance evaluation model is defined as:
Wherein l st is the linear distance from the start point to the end point; and l total is the total length of the actual flight.
Step A2: and establishing a track threat evaluation model. The flight path threat mainly refers to the threat detected and irradiated by the air defense system, and the less 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 assessment function is defined as:
wherein l rd is the total length of the crossing air defense detection area in the track; d ri is the diameter length of the ith air defense detection area; n r is the number of empty detection zones.
In one embodiment of the invention n r＝4,dr1＝17km,dr2＝10km,dr3＝9km,dr4 = 10km.
Step A3: and establishing a track hidden evaluation model. For tasks such as UAV burst prevention, the most effective method for improving the concealment performance is to maintain low-altitude or ultra-low-altitude flight, so that the flight concealment performance can be described to a certain extent by the track height, and the track concealment evaluation function is defined as:
fh＝(have-hmin)/(hmax-hmin) (3)
wherein h ave is the average height of the whole track; h min is the minimum UAV flight altitude; h max is the UAV flight maximum altitude.
In one embodiment of the invention h min＝100m,hmax = 2km.
And B, constructing a track constraint model. The specific implementation process is as follows:
step B1: and establishing a UAV maximum range constraint model. In the flight process of the unmanned aerial vehicle, the fuel loading capacity of the unmanned aerial vehicle is limited, the corresponding flight distance is limited, the maximum flight distance is L max, and the flight distance L must satisfy the following conditions:
L≤Lmax (4)
in one embodiment of the invention L max = 500km.
Step B2: and establishing a maximum flight angle constraint model. The unmanned aerial vehicle must take into account the limitations of maximum yaw angle α max and maximum pitch angle β max during flight, subject to its own maneuvering capabilities. If the coordinates of two adjacent tracks are (x i,yi,zi) and (x i+1,yi+1,zi+1), respectively, then the following must be satisfied:
Step B3: and establishing a flight altitude constraint model. The UAV must meet certain flight height requirements during the flight, and the flight height must be higher than the ground by a certain distance, and if the flight is too low, the UAV collides with the ground. Meanwhile, if the flying height is too high, the concealment of the flying height is correspondingly poor. Therefore, UAV flight altitude h xy must meet the following constraints:
φzxy≤hxy≤hmax (6)
Wherein phi is a height increase coefficient, phi is more than 1; z xy is the terrain height at coordinates (x, y); h xy is the flying height of the UAV; h max is the maximum flying height.
Step B4: and establishing a collaborative track space constraint model. Space constraints actually refer to collision-free conditions between UAVs, i.e., the UAVs must maintain a certain safe distance at any time during flight to avoid collisions. Assuming UAVi and j are denoted p i and p j at time t, then the separation distance between the UAVs must satisfy:
||pi-pj||≥dsafe (7)
where d safe is the minimum safe distance between tracks.
In one embodiment of the invention d safe = 50m.
Step B5: and establishing a collaborative track time constraint model. Time constraints mean that UAVs are generally required to be able to reach the target task area at the same time in order to maximize the efficiency of task execution. Assuming that the UAV has a flight speed range v ε [ v min,vmax ], and UAVi has a flight path distance l totali, the UAVi flight time range is:
ti∈[tmini,tmaxi]＝[ltotali/vmin,ltotali/vmax] (8)
the time constraint then requires:
where n UAV is the number of UAVs. This indicates that the arrival times of the UAVs have an intersection to arrive at the same time.
In one embodiment of the invention n UAV = 3.
Step C: and establishing a multi-target collaborative track planning model, and carrying out coordinate conversion and discretization 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 treatment in the traditional track planning, a multi-objective optimization model taking track distance evaluation, track threat evaluation and track hidden evaluation as indexes is established, and the established optimization model is as follows:
Wherein x is a feasible track point; s.t. means the basic constraints of maximum sailing distance, maximum flying angle and flying height.
In contrast to single-objective optimization, the multi-objective optimized solution is no longer a single optimal solution, but rather a set of Pareto optimal solutions. Assuming x 1、x2 is two possible solutions, when
And l is a track distance evaluation index, an r track threat evaluation index and an h track hidden evaluation index.
Then solution x 1 Pareto dominates solution x 2; if there is no solution governing x 1, then x 1 is a Pareto optimal solution; and the set of all Pareto optimal solutions is called the Pareto optimal solution set. The Pareto optimal solution set which is actually solved by the multi-target track planning is a feasible track point solution set which meets the track requirements. Such as: the number of Pareto optimal solution sets is 10, and then 10 optimized track routes are provided.
Step C2: and performing coordinate conversion and discretization on the track search space. Taking a connecting straight line of the starting point and the target point as an abscissa under a new reference coordinate system, and equally dividing and selecting D points for the straight line as the abscissa values of the search track points; the selection of the ordinate and the altitude of the track points is actually converted into a search problem on D planes perpendicular to the connecting straight line through D points, 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 expressed as follows:
wherein θ is an included angle formed by a starting point in the original coordinate system, a connecting line of the starting point and the target point and an X axis, θ=arcsin ((y t-ys)/|st|);(xnew,ynew) is a searching coordinate value, (X s,ys) is a coordinate value of the starting point in the original coordinate system, and st is a straight line between the starting point and the target point.
Under a new coordinate system taking the straight line st as the X axis, dividing the straight line st into D equal parts, searching track point combinations on D planes, and actually converting the three-dimensional search into two-dimensional search when the X axis coordinate of the three-dimensional track point is a known value, namely searching the ordinate and the altitude value of the track point on each plane. But searching for track points on successive planes is obviously larger in search space and will reduce the real-time performance of track planning. Therefore, discretizing the grid processing is performed on each plane of the D planes, and dividing the plane into equally spaced grids, and then the intersection point of each grid is a feasible track point, as shown in fig. 2. The higher the resolution ratio adopted by the discretization grid is, the higher the precision of the track planning result is; otherwise, the resolution is low, and the accuracy of track planning is reduced.
In one embodiment of the present invention, d=25, then 25 discrete points are determined for a track, and two variables, ordinate and altitude, are determined for each discrete point, so d×2=50 variables are determined for a track; when the improved multi-target firefly algorithm is used for solving a single flight path, the above 50 variable values are solved.
Step D: and solving the optimal track by utilizing 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 population scale of the firefly algorithm is NP, the dimension of firefly individuals in the population is N, the step factor alpha, the attraction value beta and the light absorption coefficient gamma.
In one embodiment of the invention the population size np=50, the number of firefly individuals is n=n UAV × (d×2) =150, the step factor α=0.25, the attraction value β=0.2, the light absorption coefficient γ =1.
Step D2: and carrying out variable decomposition on the individual dimension of firefly in the population. When optimizing the flight path by adopting an evolutionary algorithm, the dimension of the variable in the population individuals represents the number of the flight path points; the more the number of the track points is, the higher the precision of corresponding track planning is; thus, it is generally desirable that the number of variables be as large as possible, but large-scale variables mean that the algorithm complexity increases. In addition, multi-UAV track planning makes the number of variables in a population of individuals more enormous. According to the invention, a large-scale variable decomposition strategy under a cooperation framework is adopted to decompose the variables, N-dimensional firefly individuals are decomposed into N UAV Ni-dimensional sub-variables, each sub-variable Ni represents a track point combination of a UAV, and each corresponding sub-variable is subjected to iterative evolution by a sub-population.
In one embodiment of the invention n=150, the sub-variable ni=50, i=1, 2, …, N UAV.
Step D3: and performing Tent chaotic initialization on firefly individuals in each sub population.
In the intelligent optimization algorithm, the initializing effect of the group position has a certain influence on searching the global optimal value and the convergence speed of the algorithm, and generally, the more uniform the initial position distribution is, the easier the algorithm is to quickly converge. Chaotic mapping is proved to be the most effective initialization strategy in the current intelligent optimization algorithm in a plurality of research results, and the common chaotic mapping comprises Tent mapping and Logistic mapping, but the ergodic performance of the Tent mapping is relatively good, so that the initialization of a firefly position is improved by selecting the Tent mapping, and the Tent mapping is expressed as follows:
Wherein x t is a chaotic variable at time t, and x t+1 is a chaotic variable at time t+1.
Step D4: and (5) carrying out position updating on firefly individuals in each sub-population. The updating principle is as follows: each firefly position represents a feasible track solution, and the luminous brightness of the fireflies represents the superiority of the solution; fireflies with high luminous brightness have high attraction degree, and fireflies with low luminous brightness are attracted to move to the fireflies, so that the positions of the fireflies are updated, and new feasible solutions are obtained; fireflies are continuously searched in the solution space to find the optimal solution through the brightness attraction mechanism.
Assuming that firefly i is brighter than j, the attractiveness of firefly i to j is:
Where r ij is the firefly i to j distance; beta 0 is the maximum attractive force; gamma is the light absorption coefficient.
The corresponding firefly j position update formula is:
xj＝xj+βij(xi-xj)+αε (15)
Wherein α is a constant coefficient; epsilon is a random number vector.
In one embodiment of the invention α=1.
Step D5: and (5) carrying out multiple group circulation splitting and merging on each sub-population. Based on the original firefly algorithm, sequencing fireflies according to brightness after the position of the fireflies is updated according to a formula (15) in each algorithm iteration process, and splitting the fireflies into m populations, wherein each population has l fireflies; the population division principle is as follows: the first firefly with brightness is assigned to population 1, the second firefly with brightness is assigned to population 2, the mth firefly with brightness is assigned to population m, the (m+1) th firefly with brightness is assigned to population 1, and so on until all fireflies are assigned, as shown in fig. 3.
In fig. 3, the left box indicates that Fn fireflies are shared among the sub-populations, and the right box indicates that Fn fireflies are split into m sub-populations, each of which shares l=fn/m fireflies; after each sub-population iteration is completed, the m sub-populations are combined into a population with the number of fireflies being Fn.
In one embodiment of the invention fn=50, m= 5,l =10.
And (4) carrying out k p times of iterative optimization on the split sub-populations in the respective populations according to a position updating formula (15).
In one embodiment of the invention k p =50.
Meanwhile, in order to improve the brightness value of the worst individuals in the brightness of each sub-population, the elite individual x best with the highest brightness in the total population is taken as a reference point, so that the worst individual x worst always moves towards the elite individual, namely
xworst＝xworst+β(xbest-xworst)+αε (16)
In addition, in order to ensure that the algorithm does not fall into local optimum in the later stage of iteration, levy flying random disturbance is added in the random motion of the firefly with optimal brightness in each iteration process of the sub population, namely
Wherein i represents the number of the sub-population; Representing dot product; levy represents a random vector generated by Levy flight.
After the sub-populations finish iteration, each sub-population is combined and the position is updated at the same time, and the population splitting and combining are repeatedly performed until the termination condition of the maximum iteration times is met.
In one embodiment of the present invention the maximum number of iterations is set to 500.
Step D6: and carrying out diversity maintenance of the determined preference on each sub-population.
The flight path planning under the preference means that the UAV focuses on different objective functions according to task requirements, for example, the focus on hiding preference is that the UAV flies as close as possible to reduce the flying height cost to keep the concealment on the basis of balancing threat and distance cost in the sudden flight process. Therefore, the reference point of the weight flight altitude cost can be set empirically in a plurality of Pareto non-dominant solutions, and meanwhile, the optimal track with weight concealment is selected by a bipolar preference dominant method, and the basic strategy is to calculate the mark value of the solution firstly:
Wherein g i is the reference point of the ith target; w i is any point in the ith target space; p is the target number.
The population is subjected to layered non-dominant sorting according to the flag value, and meanwhile, the relative closeness ci of each layer of solution is calculated, and the calculation method comprises the following steps:
Wherein the method comprises the steps of Is the Euclidean distance to negative g i; /(I)Is the Euclidean distance to positive g i.
And finally, cutting the non-dominant solution by comparing the relative closeness difference value between different solutions with a set threshold value so as to keep the diversity of the solutions.
In addition, for the collaborative track planning of multiple UAVs, the synergy between the UAV tracks is also an important aspect for measuring the track quality, so in order to select the optimal track from numerous non-dominant solutions, the invention proposes a synergy ranking to select the optimal collaborative track, wherein the synergy consists of a time synergy and a space synergy, and the time synergy cd t is expressed as:
wherein t i is the time UAVi arrives at the destination; t min is the minimum time to reach the destination; t max is the maximum time to reach the destination.
The distance synergy cd s is:
Wherein n is the number of other UAV tracks besides each UAV itself; f i is a safe distance mark between the first track and the ith track, if the minimum safe distance is met between the first track and the ith track, f i =1; whereas f i =0.
The total synergy cd is:
cd＝cdt+cds (22)
when the track with better synergy is selected, sequencing the synergy degree, and selecting the track at the front as the optimal track.
Step D7: judging whether the optimizing algorithm meets the iteration termination condition, namely, judging that the iteration times reach the maximum value of 500 times, and exiting if the iteration times are met; if not, the process goes to step D4.
In order to verify the effectiveness of the method for UAV three-dimensional track planning, simulation experiments are carried out on a PC machine of Intel Core (TM) i3-3240,3.4GHz and 3G memory, wherein the running environment is Windows XP, and the programming environment is MATLAB 2013. FIG. 4 is a three-dimensional mountain topography for verifying the proposed method of the present invention, the experimental area being a 100X 1km three-dimensional space, the mountain topography being selected to better verify the performance of the proposed method. Fig. 5 is a three-dimensional effect diagram of an optimal path of a UAV generated by the method of the present invention, wherein 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, a black solid line represents an optimal track of the method of the present invention, and there are 9 optimal tracks in the figure, so that it can be seen that all tracks basically avoid the air defense threat, and the concealment of the tracks is effectively improved along the topography fluctuation. FIG. 6 is a two-dimensional elevation effect diagram of an optimal path of a UAV generated by the method of the present invention. FIG. 7 is a comparison chart of an optimal track generated by the method and an optimal track generated by a standard multi-target firefly algorithm, wherein the ordinate in the chart is the comprehensive good and bad value of the track, and the abscissa in the chart is the iterative times of the algorithm; the integrated good and bad value of the track after the optimization of the method is 110, and the integrated good and bad value of the track of the standard multi-target firefly method is 210, and the integrated good and bad value of the track of the method is superior to a comparison algorithm; in addition, the method of the invention finds the optimal track basically when iterating 20 times, while the standard multi-target firefly method finds the optimal track when iterating 30 times.
The invention provides a mixed strategy firefly multi-target UAV collaborative track planning method under preference setting, which adopts a variable decomposition strategy, a Tent chaotic initialization strategy and a plurality of group cyclic splitting and merging strategies to improve the optimal solution searching capability of a firefly algorithm; a bipolar preference dominance mechanism is adopted to highlight the emphasis points of different task backgrounds on different optimization targets; and designing a synergy index to improve the track cooperativity among different UAVs; through the organic combination of the strategies at different stages of the method, the overall efficiency of the multi-target UAV collaborative track planning is improved.
Claims (6)
1. The method for planning the collaborative flight path of the unmanned aerial vehicle is characterized by comprising the following steps of:
Step A: constructing a track evaluation model, namely, constructing a track distance evaluation model, a track threat evaluation model and a track concealment evaluation model;
and (B) step (B): constructing a track constraint model, namely, constructing 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;
Step C: establishing a multi-target collaborative track planning model and optimizing a track searching space, namely establishing a multi-target track planning model by combining a track evaluation model and a track constraint model, and carrying out coordinate conversion and discretization on the track searching space;
Step D: solving an optimal track, namely improving a firefly algorithm, and solving the optimal track by using the improved firefly algorithm;
The step D comprises the following steps:
step D1: carrying out parameter initialization setting on a multi-target firefly algorithm, wherein the parameter initialization setting comprises a firefly algorithm population scale NP, a dimension N of firefly individuals in the population, a step factor a, an attraction value beta and a brightness absorption coefficient gamma;
Step D2: performing variable decomposition on the individual dimension of firefly in the population, decomposing the N-dimensional optimized variable into N UAV N i -dimensional sub-variables, and performing iterative evolution on each sub-variable by one sub-population, wherein N UAV is the number of UAVs;
Step D3: initializing a Tent chaotic map of firefly individuals in each sub population;
step D4: position updating is carried out on firefly individuals in each sub-population;
step D5: carrying out cyclic splitting and merging on various sub populations;
Step D6: carrying out diversity maintenance of the determined preference on each sub population;
step D7: judging whether the optimizing algorithm meets the iteration termination condition, and exiting if the optimizing algorithm meets the iteration termination condition; if not, the step D4 is carried out;
The step A comprises the following steps:
step A1: establishing a track distance evaluation model, wherein the track distance evaluation model is defined as:
wherein l st is the linear distance from the start point to the end point; l total is the total length of the actual flight;
Step A2: establishing a track threat evaluation model, wherein the track threat evaluation model is defined as:
Wherein l rd is the total length of the crossing air defense detection area in the track; d rg is the diameter length of the g-th air defense detection area; n r is the number of air defense detection areas;
Step A3: establishing a track hidden evaluation model, wherein the track hidden evaluation model is defined as:
fh＝(have-hmin)/(hmax-hmin) (3)
wherein h ave is the average height of the whole track; h min is the minimum UAV flight altitude; h max is the UAV flight maximum altitude.
2. A multi-unmanned aerial vehicle collaborative flight path planning method according to claim 1, wherein: and D, improving a firefly algorithm by utilizing variable decomposition, chaotic initialization, multiple group cyclic splitting and merging and diversity maintenance under determined preference.
3. A multi-unmanned aircraft collaborative trajectory planning method according to claim 2, wherein: the step B comprises the following steps:
step B1: establishing a maximum sailing distance constraint model, wherein the maximum flight distance is L max, and the flight distance L must satisfy the following conditions:
L≤Lmax (4)
step B2: establishing a maximum flight angle constraint model, wherein coordinates of two adjacent tracks are (x i,yi,zi) and (x i+1,yi+1,zi+1) respectively, and the maximum flight angle constraint model must satisfy the following conditions:
And/>
Wherein α max is the maximum yaw angle and β max is the maximum pitch angle;
Step B3: establishing a flight altitude constraint model, the UAV flight altitude h xy must satisfy the following constraints:
φzxy≤hxy≤hmax (6)
Wherein phi is a height increase coefficient, phi is more than 1; z xy is the terrain height at coordinates (x, y); h xy is the flying height of the UAV; h max is the maximum flying height;
Step B4: establishing a collaborative track space constraint model, wherein the interval distance between UAVs must satisfy the following conditions:
||pi-pj||≥dsafe (7)
Wherein UAVi and j are denoted as p i and p j,dsafe as the minimum safe distance between tracks at time t;
step B5: establishing a collaborative track time constraint model, wherein the flight speed range of the UAV is v epsilon [ v min,vmax ], the flight track distance of UAVi is l totali, and the flight time range of UAVi is:
ti∈[tmini,tmaxi]＝[ltotali/vmin,ltotali/vmax] (8)
The time constraint conditions are:
Where n UAV is the number of UAVs.
4. A multi-unmanned aircraft collaborative trajectory planning method according to claim 2, wherein: the step C comprises the following steps:
Step C1: establishing a multi-target collaborative track planning model, wherein the multi-target optimization model comprises track distance evaluation, track threat evaluation and track concealment evaluation as indexes, and the established optimization model comprises the following steps:
wherein x is a feasible track point; s.t. the maximum sailing distance, the maximum flying angle and the basic constraint condition of flying height;
Step C2: performing 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 under a new reference coordinate system, and equally dividing the straight line to select D points as the abscissa values of the search track points; the ordinate and the height of the track points are selected on D planes which are perpendicular to the connecting straight line through D points; 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 expressed as follows:
Wherein θ is an included angle formed by a starting point in the original coordinate system, a connecting line of the starting point and the target point and an X axis, θ=arcsin ((y t-ys)/|st|);(xnew,ynew) is a searching coordinate value, (X s,ys) is a coordinate value of the starting point in the original coordinate system, and st is a straight line between the starting point and the target point.
5. A multi-unmanned aerial vehicle collaborative flight path planning method according to claim 4, wherein: and C2, selecting the ordinate and the height of the track points on D planes which are perpendicular to the connecting straight line through the D points, performing discretization grid processing on each plane in the D planes, and dividing the planes into equidistant grids, wherein the intersection point of each grid is a feasible track point.
6. A multi-unmanned aerial vehicle collaborative flight path planning method according to claim 1, wherein: step D3, a Tent map is selected to improve the initialization of the firefly position, and the Tent map is expressed as:
Wherein x t is a chaotic variable at the time t, and x t+1 is a chaotic variable at the time t+1;
D4, each position of fireflies represents a feasible flight path solution, and the luminous brightness of the fireflies represents the superiority of the solution; fireflies with high luminous brightness have high attraction degree, and fireflies with low luminous brightness are attracted to move to the fireflies, so that the positions of the fireflies are updated, and new feasible solutions are obtained; the firefly i has a higher brightness than j, and the attraction value of firefly i to j is:
Where r ij is the firefly i to j distance; beta 0 is the maximum attraction value; gamma is the light absorption coefficient;
the corresponding firefly j position update formula is:
xj＝xj+βij(xi-xj)+αε (15)
wherein α is a constant coefficient; epsilon is a random number vector;
in the step D5, sorting fireflies according to brightness, and splitting the fireflies into m populations, wherein each population has l fireflies; the population division principle is as follows: a first firefly with brightness is distributed to a population 1, a second firefly with brightness is distributed to a population 2, an mth firefly with brightness is distributed to a population m, an (m+1) th firefly with brightness is distributed to the population 1, and the like until all fireflies are distributed; dividing Fn fireflies into m sub-populations, each sub-population sharing l=fn/m fireflies; after each sub-population iteration is completed, m sub-populations are combined into a population with the number of fireflies being Fn; k p times of iterative optimization are carried out on the split sub-populations in the respective populations according to a position updating formula (15); taking the elite individual x best with the highest brightness in the total group as a reference point, enabling the worst individual x worst to always move towards the elite individual, namely
xworst＝xworst+β(xbest-xworst)+αε (16)
Adding Levy flight random disturbance into the brightness optimal firefly random motion in each iteration process of the sub population;
When the sub-populations finish iteration, each sub-population is combined and the position is updated at the same time, and the population splitting and combining are repeatedly performed until the termination condition of the maximum iteration times is met;
In step D6, the optimal synergy track is selected according to the synergy degree sequence, wherein the synergy degree is respectively composed of a time synergy degree and a space synergy degree, and the time synergy degree cd t is expressed as:
Wherein t i is the time UAVi arrives at the destination; t min is the minimum time to reach the destination; t max is the maximum time to reach the destination;
The spatial co-ordination cd s is:
Wherein n is the number of other UAV tracks besides each UAV itself; f z is a safe distance sign with the z-th track, if the minimum safe distance is satisfied with the z-th track, f z =1; whereas f z =0;
The total synergy cd is:
cd＝cdt+cds (22)
when the track with better synergy is selected, sequencing the synergy degree, and selecting the track at the front as the optimal track.
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