CN106705970A - Multi-UAV(Unmanned Aerial Vehicle) cooperation path planning method based on ant colony algorithm - Google Patents

Multi-UAV(Unmanned Aerial Vehicle) cooperation path planning method based on ant colony algorithm Download PDF

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CN106705970A
CN106705970A CN201611023386.3A CN201611023386A CN106705970A CN 106705970 A CN106705970 A CN 106705970A CN 201611023386 A CN201611023386 A CN 201611023386A CN 106705970 A CN106705970 A CN 106705970A
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unmanned plane
path
cost
paths
plane
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CN106705970B (en
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康敏旸
熊智勇
屈鸿
黄利伟
李�浩
刘昕彤
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China Aeronautical Radio Electronics Research Institute
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20Instruments for performing navigational calculations

Abstract

The invention discloses a multi-UAV (Unmanned Aerial Vehicle) cooperation path planning method based on an ant colony algorithm. The method comprises the following steps of (1) analyzing a UAV flight environment, and building environment modeling based on a Voronoi diagram; (2) calculating consideration of an edge in the environment modeling based on the Voronoi diagram; (3) utilizing the ant colony algorithm to plan an initial path for a UAV; (4) smoothing the initial path of each UAV to judge whether cooperation is achieved or not, and carrying out corresponding operation according to the results. According to the multi-UAV cooperation path planning method based on the ant colony algorithm provided by the invention, multiple different kinds of unmanned aerial vehicles are mutually cooperated, intelligently and autonomously adapt to complicated and changeable war environment factors, and dynamically adjust self-strategies so as to cooperatively accomplish the combat mission.

Description

A kind of multiple no-manned plane collaboration paths planning method based on ant group algorithm
Technical field:
This method is applied to UAV Flight Control, obstacle avoidance, shortest path search, path smooth treatment and load balancing Deng field, and in particular to the setting of the structure and side right value of voronoi figures, ant group algorithm searches for shortest path and by track Smooth and reach association's equivalent technology.
Background technology:
Unmanned air vehicle technique is a hot research field of military civil aircraft in recent years, battle reconnaissance and monitoring, Positioning school penetrate, injure assessment etc. military use, such as border patrol, environment detection, photography of taking photo by plane, exploration resource, the condition of a disaster monitor, The civilian uses such as security monitoring, logistics transportation are all widely used.Compared with manned aircraft, unmanned plane is able to carry out low energy The low-latitude flying of degree of opinion, low clouds layer, so as to dramatically increase the time that can fly daily, accelerate job scheduling, additionally it is possible to perform height in real time Precision high resolution remote sensing flight etc..Military affairs unmanned plane is due to the speed advantage of itself, and mobility itself waits well spy Point is used to perform some highly difficult tasks, even needs multiple UAVs to go to perform one or more tasks sometimes, we It is accomplished by providing suitable Task Assigned Policy under online or line, and the path planning scheme of high security arranges unmanned plane (group) goes execution task.
For the difference of flight environment of vehicle, it is reasonable to which choosing has suitable Antagonistic Environment to go to simulating actual combat battlefield.These environment moulds Type has the three-dimensional space environment based on B-Spline curves, and the two-dimentional non-directed graph based on probability waypoint figure, voronoi figures Deng.Voronoi diagram is a kind of classical polygon diagram based on plane zoning, and it is by the generation point of unequal number amount and generation The perpendicular bisector of point line is constituted, and each generation o'clock is by a specific polygon around the point in these polygons is to originally The distance of point is generated always less than the distance to other generation points.Using the side of voronoi figures as unmanned plane can overlap, can be by Threat suffered by aircraft is preferably minimized.Ant group algorithm is a kind of intelligent algorithm for simulating Biology seed coating, with very strong robust Property and solvability, add side right value heuristic information the solution of algorithm can be made to tend to optimal.
In view of the flying property of unmanned plane, the angle of flight is unlikely to be sharp angle flight, aircraft turn when Needs are waited to be smoothed so that aircraft is turned with circular arc, and the anglec of rotation of unmanned plane can not be more than the maximum anglec of rotation. By smooth trajectory so that path length slightly changes, this smooth flexibility can be used to carry out the collaboration of multiple no-manned plane. Because single unmanned plane performance is single, load capacity is limited, and a group of planes for comprehensive multiple no-manned plane must have certain in the task of execution Precedence reach and perform task, the problem of the collaboration of multiple no-manned plane causes extensive concern.It is effective to utilize whole The research of the paths planning method of team's capacity and ability of aircraft unit, efficient distributed sensing and synthesis is whole association With the main contents of control.Collaboration between unmanned plane is flown by different requirement definitions for different contents, but mainly It is that the distribution task and path planning of each unmanned plane complete its Cooperative Security with whole task as target.Additionally, collaboration path Planning needs the factor considered except the kinematical constraint of itself is limited, in addition it is also necessary to dynamic hedging other side's obstacle, reduces flight The risk that device bumps against, adapts to the factors such as enemy's threatening environment change.
Unmanned plane cooperates with path planning, realizes that multiple no-manned plane performs the feasibility of task, can also detect for current nothing The man-machine possibility that whether can realize collaboration flight, for the unmanned plane that can not realize collaboration flight, by change of flight state Or weight-normality is drawn and causes that multiple UAVs realize collaboration flight.
The content of the invention
Part provides a kind of multiple no-manned plane collaboration path based on ant group algorithm to the present invention in view of the shortcomings of the prior art Planing method, solves the difficult point of cooperation in existing multiple no-manned plane flight course, if desired for multiple UAVs simultaneously from respective Starting point is set out, and reaches respective objects point simultaneously, to complete a certain task jointly.In addition, reality of the demand to algorithm The requirement of when property is also higher, and calculating speed will can get caught up in the flying speed of unmanned plane, just it can so preferably be applied to many Unmanned plane cooperation.
To achieve these goals, the technical solution adopted by the present invention is:
A kind of multiple no-manned plane collaboration paths planning method based on ant group algorithm, comprises the steps of:
Step (1) is analyzed to unmanned plane during flying environment, sets up the environmental modeling based on Voronoi diagram;
Step (2) calculates the cost on side in the environmental modeling based on Voronoi diagram;
Step (3) is that unmanned plane plans initial path using ant group algorithm;
Can step (4) be smoothed to judge reach collaboration by the initial path to each unmanned plane, and according to result Perform corresponding operating.
Preferably, the step (1) comprises the following steps:
(1-1) determines the flying height of unmanned plane, intercepts the two dimensional surface terrain information of the flying height, and by ground prestige The side of body projects to the two dimensional surface terrain information, obtains ground based threats plane landform;
(1-2) by ground based threats plane landform and other to threaten sources abstract be to threaten point set { xi};
The coordinate-system that (1-3) is established in plane, obtains the coordinate set { (x in threat sourcei, yi), and generate Voronoi diagram.
The starting point and terminal of (1-4) input unmanned plane, the environmental modeling of Voronoi diagram are completed.
Preferably, the step (2) comprises the following steps:
(2-1) calculates the cost that orographic factor threatens opposite side:
Wherein,Fixed threat source j is represented to i-th cost on side;K is the threat level of threat source j;K is that people is for about Determine coefficient;rijIt is threat source j to i-th distance on side;
(2-2) calculates the cost for having investigation ability but the threat opposite side without attacking ability:
Wherein,It is radar j to i-th cost on side;LiIt is the length of side i;d1/8,i,jBe at i-th the 1/8 of side extremely The distance of radar j;QjIt is the transmission power of radar j, QjComputing formula is as follows:
Wherein, P is the transmission power of radar;PtIt is transmitter power;G is wireless gain;AeIt is the significant surface of emitter Product, δ is the area of section of radar;R is the length apart from radar;
(2-3) calculates the cost that existing investigation ability has the threat opposite side of attacking ability again:
Wherein,Threat for guided missile j to the i-th paths;B is the attacking ability of guided missile;(1- α) is Hitting Accuracy of Missile; pijFor the probability that unmanned plane is detected on i-th side;
(2-4) calculates the length cost on side:
Pi-L=λ Li
Wherein, Pi-LIt is the cost of length opposite side i;λ is a coefficient;LiIt is i-th length on side.
The cost computing formula on (2-5) total side:
Wherein a, b, c, d are constant, meet a+b+c+d=1;M is fixed obstacle number, and n is radar number, and r is to lead Play number.
Preferably, ant group algorithm is described in the step (3):
(3-1) ant is by start node, according to transition probability formula
One transfering node of selection, and start node is added into taboo list, wherein
ηij(t):Heuristic information when representing t on < i, j > paths;
It is the inverse of cost;
τij(t):Represent the pheromones on t < i, j > paths;
α, β represent τ respectivelyij(t)、ηijThe weight coefficient of (t);
The abutment points of the i positions that expression was not accessed;
ηir(t):Represent t<i,j>Heuristic information on path;
τir(t):Represent t<i,j>Pheromone concentration on path;
(3-2) ant selects transfering node according to transition probability, and selected transfering node is added into taboo list;Judge Whether transfering node reaches home, if not reaching home, constantly (3-2) is repeated, until reaching home;If reaching home Go to (3-3);
Whether (3-3) iterations reaches fixed value, and (3-4) fresh information element is gone to if fixed value is not reaching to, if Iterations reaches fixed value and then goes to (3-5) fresh information element;
(3-4) updates the path of this circulation according to Pheromone update formula, and iterations+1 goes to (3-6)
(3-5) updates the path in circulating several times recently according to Pheromone update formula, and iterations+1 goes to (3-6);
(3-6), if iterations is more than maximum algebraically, search is completed, and obtains shortest path, is otherwise gone to (3-1);Wherein, Pheromone update formula is as follows:
ρ:Represent pheromones volatility coefficient;
Q:Represent the constant of pheromone concentration;
Lk:Ant k paths traversed total lengths in this circulation.
Preferably, the step (4) comprises the following steps:
(4-1) is unsatisfactory for the angle of certain predetermined angle to initial path turning and carries out the path length after being smoothed It is interval;
(4-2) takes the maximum of each unmanned plane respective paths length of interval lower limit, is designated as A, takes each unmanned plane respective paths The minimum value of the length of interval upper limit, is designated as B;
(4-3) judges the value of A-B;
(4-4) completes collaboration if A-B≤0;
(4-5) is if A-B > 0, it is impossible to complete collaboration.
Compared with prior art, the advantage of the invention is that:
1) environmental modeling is carried out by Voronoi diagram, using Voronoi diagram aufbauprinciple path planning it is initial most Limits ensure the flight safety of unmanned plane;
2) factor that can be impacted to the total cost of unmanned plane during flying in research environment, increased radar detection probability, leads Bullet attacks the related new factor such as probability, detection probability of enemy plane, rather than only consideration fixed obstacle to unmanned plane during flying Influence and unmanned plane during flying total path so that environmental modeling is more nearly reality;
3) optimize ant group algorithm, heuristic function is optimized in enlightening ant group algorithm, increase pheromones Maximum and minimum value preventing the precocity of algorithm, and two kinds of different Pheromone update mechanism from accelerating algorithmic statements speed Degree;
4) smooth trajectory is carried out for the angle that unmanned plane during flying constraint is not met in the path cooked up for the first time, and is limited Determine to need the scope of Smoothing angle, save computing resource;
5) collaboration of multiple no-manned plane is completed using smooth trajectory, unmanned plane path is obtained by initial path smooth Length of interval, goes to reach collaboration by interval operation, rather than the purpose that collaboration is reached by changing the speed of unmanned plane, and The demand while arriving at can be met.
Brief description of the drawings
Fig. 1 Structure and Process schematic diagrams of the invention;
Fig. 2 overall flow schematic diagrams of the invention;
Fig. 3 Voronoi environmental modelings schematic diagrames of the invention;
Fig. 4 initial path flow charts based on ant group algorithm of the invention;
Fig. 5 cooperation flow figures of the invention.
Specific embodiment
Below in conjunction with drawings and Examples, the invention will be further described.
Unmanned plane confidentiality is high, error is small, implementation capacity is strong, in the process of implementation efficiency high, low cost, can be substituted for war Scholar completes some tasks larger to life threat, and the study hotspot technology in military field has been turned into recent years.The whole world is each State tries to be the first a large amount of human and material resources of input and financial resources launch comprehensive research and deployment to it.A large amount of different type, different performances Unmanned plane be developed and delivered to battlefield and performed various combat duties.However, during some complex tasks are performed (as investigation strike integration), single rack unmanned plane it is limited in one's ability, be not enough to completion task.It is different types of that this is accomplished by multi rack Cooperated between unmanned plane, intelligently, independently adapt to war environment factor complicated and changeable, dynamically adjust itself strategy, Cooperation completes combat duty.The present invention utilizes computational intelligence correlation theory, the problems such as research and solve multiple no-manned plane path planning, be Following unmanned plane confrontation provides technical support.
Refering to Fig. 1, at the beginning of algorithm is designed, it is necessary first to consider that what unmanned plane may be subject in flight environment of vehicle threatens, Voronoi models are set up according to threatening, influence of the full spectrum of threats to side in figure is then calculated, then by classical ant group algorithm It is improved to find initial path, the corresponding path length interval of unmanned plane is then obtained according to smooth principle, and sentence with this Can disconnected collaboration be reached, if can reach, each unmanned plane is cooperateed with, if can not reach, each unmanned plane can not meet appoints Business demand.As shown in Fig. 2 its specific design process is as follows:
A kind of to cooperate with paths planning method based on the multiple no-manned plane for improving ant group algorithm, step is as follows:
(1) unmanned plane during flying environment is analyzed, the process for setting up the environmental model based on Voronoi diagram is as follows:
(1-1) determines the flying height of unmanned plane, intercepts the two dimensional surface terrain information of the height, and ground based threats are thrown Shadow obtains ground based threats plane landform to the elevation plane;
(1-2) by ground based threats plane landform and other to threaten sources abstract be to threaten point set { xi};
The coordinate-system that (1-3) is established in plane, obtains the coordinate set { (x in threat sourcei, yi), and generate Voronoi diagram.
The starting point and terminal of (1-4) input unmanned plane, the environmental modeling of Voronoi diagram are completed, as shown in Figure 3.Wherein, Starting point is represented by triangular representation, impact point by star.R represents enemy radar, and M represents enemy missile, and O represents terrain obstruction Thing.Each summit label successively in the Voronoi diagram of generation, facilitates the table of the shortest path that follow-up path planning algorithm obtains Show.
(2) comprising the following steps that for weights is assigned to the side in the Voronoi diagram that establishes:
The influential main consideration following four factor of cost of (2-1) opposite side:The orographic factors such as massif are threatened (fixed), radar (Radar) etc. had had investigation ability but the threat source without attacking ability, guided missile (Guided missile) etc. both Have investigation ability has the threat source of attacking ability, and side length (Length) cost in itself again;
The orographic factors such as (2-2) massif threaten (fixed):
Wherein,Fixed threat source j is represented to i-th cost on side;K is the threat level of threat source j;K is that people is for about Determine coefficient;rijIt is threat source j to i-th distance on side.For the ease of calculating, threat source j to i-th midpoint on side is taken as Wire length;
(2-3) radar (Radar) etc. has investigation ability but the threat without attacking ability:
Wherein,It is radar j to i-th cost on side;LiIt is the length of side i;QjIt is the transmission power of radar j;
QjComputing formula is as follows:
Wherein, P is the transmission power of radar;PtIt is transmitter power;G is wireless gain;AeIt is the significant surface of emitter Product, δ is the area of section of radar;R is the length apart from radar, it is assumed that R≤Rmax(RmaxIt is the maximum investigation radius of radar);
The existing investigation abilities such as (2-4) guided missile (Guided missile) have the threat of attacking ability again:
Wherein,Threat for guided missile j to the i-th paths;B is the attacking ability of guided missile;(1- α) is Hitting Accuracy of Missile; pijFor the probability that unmanned plane is detected on i-th side.
Length (Length) cost on (2-5) side:Pi-L=λ Li
Wherein, Pi-LIt is the cost of length opposite side i;λ is a coefficient;LiIt is i-th length on side.
(2-6) total cost computing formula:
Wherein a, b, c, d are constant, meet a+b+c+d=1.M is fixed obstacle number, and n is radar number, and r is to lead Play number.
(3) using ant group algorithm is improved for the flow chart of unmanned plane planning initial path refers to Fig. 4, its specific steps is such as Under:
(3-1) ant is by start node, according to transition probability formula
One transfering node of selection, and start node is added into taboo list, wherein
ηij(t):Heuristic information when representing t on < i, j > paths;
It is the inverse of cost;
τij(t):Represent the pheromones on t < i, j > paths;
α, β represent τ respectivelyij(t)、ηijThe weight coefficient of (t);
The abutment points of the i positions that expression was not accessed;
ηir(t):Represent t<i,j>Heuristic information on path;
τir(t):Represent t<i,j>Pheromone concentration on path;
(3-2) ant selects transfering node according to transition probability, and selected transfering node is added into taboo list;Judge Whether transfering node reaches home, if not reaching home, constantly (3-2) is repeated, until reaching home;If reaching home Go to (3-3);
Whether (3-3) iterations reaches fixed value, and (3-4) fresh information element is gone to if fixed value is not reaching to, if Iterations reaches fixed value and then goes to (3-5) fresh information element;
(3-4) updates the path of this circulation according to Pheromone update formula, and iterations+1 goes to (3-6)
(3-5) updates the path in circulating several times recently according to Pheromone update formula, and iterations+1 goes to (3-6);
(3-6), if iterations is more than maximum algebraically, search is completed, and obtains shortest path, is otherwise gone to (3-1);Wherein, Pheromone update formula is as follows:
ρ:Represent pheromones volatility coefficient;
Q:Represent the constant of pheromone concentration;
Lk:Ant k paths traversed total lengths in this circulation.
(4) judge that collaboration can be reached by smoothing each unmanned plane path, and corresponding behaviour is performed according to result Make, cooperation flow figure is as shown in figure 5, it is comprised the following steps that:
(4-1) is unsatisfactory for the angle of certain predetermined angle to initial path turning and carries out the path length after being smoothed It is interval;
(4-2) takes the maximum of each unmanned plane respective paths length of interval lower limit, is designated as A, takes each unmanned plane respective paths The minimum value of the length of interval upper limit, is designated as B;
(4-3) judges the value of A-B;
(4-4) can complete collaboration if A-B≤0;
After completing collaboration, arbitrary value can be taken as unmanned plane path length in the interval common factor of each unmanned plane path length Benchmark;Each unmanned plane calculates its difference with original path value according to this benchmark;According to path length difference, calculated using greed Method calculates each angle in requisition for the length for increasing or decreasing, and root determines therefrom that the position of inscribed circle, until meet requiring.
(4-5) is if A-B > 0, it is impossible to complete collaboration.
The present invention is illustrated by above-described embodiment, but it is to be understood that, above-described embodiment is only intended to Citing and descriptive purpose, and be not intended to limit the invention in described scope of embodiments.In addition people in the art Member is it is understood that the invention is not limited in above-described embodiment, teaching of the invention can also be made more kinds of Variants and modifications, these variants and modifications are all fallen within scope of the present invention.Protection scope of the present invention by The appended claims and its equivalent scope are defined.

Claims (5)

1. a kind of multiple no-manned plane collaboration paths planning method based on ant group algorithm, comprises the steps of:
Step (1) is analyzed to unmanned plane during flying environment, sets up the environmental modeling based on Voronoi diagram;
Step (2) calculates the cost on side in the environmental modeling based on Voronoi diagram;
Step (3) is that unmanned plane plans initial path using ant group algorithm;
Can step (4) be smoothed to judge reach collaboration by the initial path to each unmanned plane, and is performed according to result Corresponding operating.
2. a kind of multiple no-manned plane based on ant group algorithm cooperates with paths planning method, it is characterised in that the step (1) is comprising such as Lower step:
(1-1) determines the flying height of unmanned plane, intercepts the two dimensional surface terrain information of the flying height, and ground based threats are thrown Shadow obtains ground based threats plane landform to the two dimensional surface terrain information;
(1-2) by ground based threats plane landform and other to threaten sources abstract be to threaten point set { xi};
The coordinate-system that (1-3) is established in plane, obtains the coordinate set { (x in threat sourcei, yi), and generate Voronoi diagram.
The starting point and terminal of (1-4) input unmanned plane, the environmental modeling of Voronoi diagram are completed.
3. a kind of multiple no-manned plane based on ant group algorithm cooperates with paths planning method, it is characterised in that the step (2) is comprising such as Lower step:
(2-1) calculates the cost that orographic factor threatens opposite side:
P i - F j = Ke - kr j
Wherein,Fixed threat source j is represented to i-th cost on side;K is the threat level of threat source j;K is artificial agreement system Number;rijIt is threat source j to i-th distance on side;
(2-2) calculates the cost for having investigation ability but the threat opposite side without attacking ability:
P i - R j = L i ( 1 d 1 / 8 , i , j 4 + 1 d 3 / 8 , i , j 4 + 1 d 5 / 8 i , j 4 + 1 d 7 / 8 i , j 4 ) Q j
Wherein,It is radar j to i-th cost on side;LiIt is the length of side i;d1/8,i,jIt is to radar j at i-th the 1/8 of side Distance;QjIt is the transmission power of radar j, QjComputing formula is as follows:
P = P t GA e &delta; ( 4 &pi; ) 2 R 4
Wherein, P is the transmission power of radar;PtIt is transmitter power;G is wireless gain;AeIt is the effective area of emitter, δ It is the area of section of radar;R is the length apart from radar;
(2-3) calculates the cost that existing investigation ability has the threat opposite side of attacking ability again:
P i - G j = B ( 1 - &alpha; ) p i j
Wherein,Threat for guided missile j to the i-th paths;B is the attacking ability of guided missile;(1- α) is Hitting Accuracy of Missile;pijFor The probability that unmanned plane is detected on i-th side;
(2-4) calculates the length cost on side:
Pi-L=λ Li
Wherein, Pi-LIt is the cost of length opposite side i;λ is a coefficient;LiIt is i-th length on side.
The cost computing formula on (2-5) total side:
P i = a &Sigma; j = 1 m Ke - kr i j + b &Sigma; j = 1 n &lsqb; L i ( 1 d 1 / 8 , i , j 4 + 1 d 3 / 8 , i , j 4 + 1 d 5 / 8 , i , j 4 + 1 d 7 / 8 , i , j 4 ) Q j &rsqb; + c &Sigma; j = 1 r &lsqb; B ( 1 - &alpha; ) p i j &rsqb; + d&lambda;L i
Wherein a, b, c, d are constant, meet a+b+c+d=1;M is fixed obstacle number, and n is radar number, and r is guided missile Number.
4. a kind of multiple no-manned plane based on ant group algorithm cooperates with paths planning method, it is characterised in that described in the step (3) Ant group algorithm is:
(3-1) ant is by start node, according to transition probability formula
One transfering node of selection, and start node is added into taboo list, wherein
ηij(t):Heuristic information when representing t on < i, j > paths;
It is the inverse of cost;
τij(t):Represent the pheromones on t < i, j > paths;
α, β represent τ respectivelyij(t)、ηijThe weight coefficient of (t);
The abutment points of the i positions that expression was not accessed;
ηir(t):Represent t<i,j>Heuristic information on path;
τir(t):Represent t<i,j>Pheromone concentration on path;
(3-2) ant selects transfering node according to transition probability, and selected transfering node is added into taboo list;Judge transfer Whether node reaches home, if not reaching home, constantly (3-2) is repeated, until reaching home;Gone to if reaching home (3-3);
Whether (3-3) iterations reaches fixed value, (3-4) fresh information element is gone to if fixed value is not reaching to, if iteration Number of times reaches fixed value and then goes to (3-5) fresh information element;
(3-4) updates the path of this circulation according to Pheromone update formula, and iterations+1 goes to (3-6)
(3-5) updates the path in circulating several times recently according to Pheromone update formula, and iterations+1 goes to (3-6);
(3-6), if iterations is more than maximum algebraically, search is completed, and obtains shortest path, is otherwise gone to (3-1);Wherein, information Plain more new formula is as follows:
&tau; i j ( t + h ) = ( 1 - &rho; ) * &tau; i j ( t ) + &Sigma; k = 1 m &Delta;&tau; i j k ( t )
ρ:Represent pheromones volatility coefficient;
Q:Represent the constant of pheromone concentration;
Lk:Ant k paths traversed total lengths in this circulation.
5. a kind of multiple no-manned plane based on ant group algorithm cooperates with paths planning method, it is characterised in that the step (4) is comprising such as Lower step:
(4-1) is unsatisfactory for the angle of certain predetermined angle to initial path turning and carries out the path length area after being smoothed Between;
(4-2) takes the maximum of each unmanned plane respective paths length of interval lower limit, is designated as A, takes each unmanned plane respective paths length The minimum value of the interval upper limit, is designated as B;
(4-3) judges the value of A-B;
(4-4) completes collaboration if A-B≤0;
(4-5) is if A-B > 0, it is impossible to complete collaboration.
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