CN112629539B - Multi-unmanned aerial vehicle path planning method - Google Patents

Multi-unmanned aerial vehicle path planning method Download PDF

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CN112629539B
CN112629539B CN202011476411.XA CN202011476411A CN112629539B CN 112629539 B CN112629539 B CN 112629539B CN 202011476411 A CN202011476411 A CN 202011476411A CN 112629539 B CN112629539 B CN 112629539B
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undirected
flag
undirected complete
complete graph
equal
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CN112629539A (en
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张琰
刘佳玥
焦利彬
索宏泽
岳群彬
聂冬冬
魏艺璇
朱继坡
刘杰
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Xidian University
CETC 54 Research Institute
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CETC 54 Research Institute
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention provides a multi-unmanned aerial vehicle path planning method, which comprises the following steps: constructing a multi-unmanned aerial vehicle path planning scene model; constructing an undirected complete map of the monitoring area; carrying out task allocation on the unmanned aerial vehicle group; and obtaining a path planning result of the unmanned aerial vehicle cluster. The method comprises the steps of establishing an undirected complete graph of a monitoring area, modeling monitoring points traversed by each unmanned aerial vehicle and starting points into the undirected complete graph, continuously optimizing task distribution results by performing point transfer and exchange operation between the undirected complete graphs, obtaining the minimum Hamilton ring of each unmanned aerial vehicle on the basis of the optimized task distribution results, performing point transfer between the minimum Hamilton rings, further optimizing the task distribution results, and simultaneously obtaining a path planning result of an unmanned aerial vehicle cluster, thereby ensuring that the unmanned aerial vehicle with the largest flying distance among the unmanned aerial vehicles has the smallest flying distance and the shortest flying time.

Description

Multi-unmanned aerial vehicle path planning method
Technical Field
The invention belongs to the technical field of unmanned aerial vehicles, and relates to a multi-unmanned aerial vehicle path planning method.
Background
Unmanned Aerial Vehicles (UAVs) are more and more concerned by academia and industry due to their characteristics of high mobility, flexible deployment, low cost, etc., for example, unmanned aerial vehicles can be used for autonomous monitoring in various scenes such as intelligent farms, search and rescue, post-disaster assessment, etc. The single unmanned aerial vehicle has the defects in real-time performance, completeness and reliability when executing tasks, so that a plurality of unmanned aerial vehicles are needed to execute the tasks, when the problems caused by the task execution of the plurality of unmanned aerial vehicles are researched, the cooperation problem is caused by the coupling of the tasks, and the key technical challenge of solving the cooperation problem of the plurality of unmanned aerial vehicles is how to plan an efficient flight path for each unmanned aerial vehicle on the premise of ensuring that all the tasks are completed; the solution steps are generally as follows: firstly, task allocation is carried out on a plurality of unmanned aerial vehicles, then path planning is carried out on the basis of the task allocation, and finally an optimal flight path corresponding to each unmanned aerial vehicle is obtained, and whether the optimal flight path can be planned by the plurality of unmanned aerial vehicles or not is the key point of reasonable task allocation;
for example, patent application publication No. CN109186611A, "unmanned aerial vehicle flight path planning method and apparatus", discloses an unmanned aerial vehicle flight path planning method, which solves the problem of min-max integer planning of task allocation through an improved task allocation algorithm based on the basic idea of branch-and-bound method, and obtains and allocates an optimal flight path corresponding to each unmanned aerial vehicle through the optimized solution, so that the unmanned aerial vehicle fleet guarantees the shortest parallel flight time of multiple unmanned aerial vehicles and realizes optimal path planning on the premise of completing flight tasks and satisfying constraint conditions. However, the method uses the branch-and-bound method to distribute the tasks, and since the efficiency of the branch-and-bound method in solving is basically determined by the value boundary method, when the number of tasks is large, the boundary estimation is difficult to perform, and at this time, the efficiency of the algorithm is low, and a good task distribution result is difficult to solve, so that a path planning result with the shortest flight time cannot be obtained.
Disclosure of Invention
The invention aims to provide a multi-unmanned aerial vehicle path planning method aiming at overcoming the defects of the prior art, and aims to reduce the flight distance of the unmanned aerial vehicle with the largest flight distance in the multi-unmanned aerial vehicles on the basis of ensuring that the multi-unmanned aerial vehicles cooperatively complete flight tasks so as to shorten the flight time.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) constructing a multi-unmanned aerial vehicle path planning scene model:
constructing a monitoring area distributed in a xoy plane of a three-dimensional rectangular coordinate system and an unmanned aerial vehicle group A ═ A in the space of the three-dimensional rectangular coordinate system i I is more than or equal to 1 and less than or equal to M, and the monitoring area comprises a departure point depot of the unmanned aerial vehicle A and N monitoring points V ═ N j J is more than or equal to 1 and less than or equal to N, wherein M represents the number of frames of the unmanned aerial vehicle, M is more than or equal to 2, A i Indicates a flying height of H i The ith unmanned aerial vehicle, n j Indicates a position coordinate of (x) j ,y j ) N is more than or equal to M at the jth monitoring point;
(2) constructing an undirected complete map of the monitored area:
randomly dividing the monitoring points V into M subareas with the number equal to the number of the unmanned aerial vehicle frames, wherein each subarea at least comprises one monitoring point, connecting every two monitoring points in each subarea and each monitoring point in each subarea with the departure point depot of A to form an undirected complete graph set psi { G ═ G i I is more than or equal to 1 and less than or equal to M, wherein G i Is represented by A i A corresponding undirected complete graph;
(3) and (3) carrying out task allocation on the unmanned aerial vehicle group A:
(3a) calculate each undirected complete graph G i Total length of all sides W (G) i ) (ii) a Calculating each monitoring point n j To each undirected complete graph G i Total length Δ W (G) of the edge formed by each monitoring point and departure point i ,n j ) (ii) a Calculate each undirected complete graph G i Size D (G) of i )；
(3b) Setting the inspection parameters of all undirected complete graph pairs combined by every two undirected complete graphs in the undirected complete graph set psi as unchecked, and setting the transition parameters and the exchange parameters of each undirected complete graph pair as flag _ t and flag _ s respectively, when unchecked is 1, indicating that the undirected complete graph pairs which are not inspected exist in psi, when unchecked is 0, indicating that the undirected complete graph pairs which are not inspected do not exist in psi, when flag _ t is 1, indicating that the two undirected complete graphs in the undirected complete graph pairs can be subjected to point transition, and when flag _ t is 0, indicating that the two undirected complete graphs in the undirected complete graph pairs cannot be subjected to point transition; when the flag _ s is equal to 1, the two undirected full graphs in the undirected full graph pair can carry out point exchange, and when the flag _ s is equal to 0, the two undirected full graphs in the undirected full graph pair can not carry out point exchange, and the unchecked is equal to 1, the flag _ t is equal to 1, and the flag _ s is equal to 1;
(3c) optimizing the undirected complete graph set ψ:
(3c1) judging whether unchecked is 1, if yes, executing the step (3c2), otherwise, enabling the program to be executed
Figure BDA0002835632110000031
Obtaining an undirected complete graph set after psi optimization
Figure BDA0002835632110000032
(3c2) Judging whether an undirected complete graph pair of flag _ t-1 exists in the undirected complete graph set psi, if so, randomly selecting an undirected complete graph pair of flag _ t-1 (G) a ,G b ) And performing the step (3c3), otherwise, performing the step (3c 4);
(3c3) when D (G) a )＞D(G b ) When it is, judge G a Whether there is a transition to G b And satisfies max { D (G) a ),D(G b ) Decrease, if so, max { D (G) a ),D(G b ) The point at which the most reduction is made is taken as the optimum transfer point n v * And n is v * From G a Transfer to G b Middle and simultaneous pairs G a And G b W, Δ W and D and G a And G b After all the parameters of the undirected complete graph pair are updated, step (3c1) is executed, otherwise, the step (G) is executed a ,G b ) The corresponding transition parameter flag _ t is equal to 0, and step (3c1) is performed;
(3c4) judging whether the undirected complete graph set psi has undirected complete graph pair of flag _ s-1,if yes, randomly selecting a undirected complete graph pair (G) of flag _ s ═ 1 ε ,G η ) And executing the step (3c5), otherwise, making unchecked equal to 0, and executing the step (3c 1);
(3c5) judgment of G ε And G η Whether there is one undirected complete graph of each swap to the other side, and max { D (G) { D) } ε ),D(G η ) Decrease, if so, max { D (G) ε ),D(G η ) The two points at most reduced are taken as the optimal switching points
Figure BDA0002835632110000033
And will be
Figure BDA0002835632110000034
In undirected complete graph G ε And G η Exchange between them while for G ε And G η W, Δ W and D and G ε And G η After updating the parameters of all undirected complete graph pairs of the composition, step (3c1) is performed, otherwise, order (G) ε ,G η ) The corresponding interchange parameter flag _ s is equal to 0, and step (3c1) is performed;
(3d) for undirected complete set psi π The improvement is as follows:
(3e) let us set the optimized undirected complete atlas psi π Medium maximum undirected full graph size
Figure BDA0002835632110000035
The parameter that can be reduced or not is posable _1, and when posable _1 is equal to 1, this indicates that
Figure BDA0002835632110000036
Can be reduced, when the posable _1 is 0, it means
Figure BDA0002835632110000041
Cannot be reduced, and let the locatable _1 be 1;
(3f) judging whether the possible _1 is 1, if yes, making the order
Figure BDA0002835632110000042
And executing the step (3g), otherwise, order
Figure BDA0002835632110000043
Get a pair psi π Improved undirected complete graph set
Figure BDA0002835632110000044
(3g) For undirected complete set psi * And (3) adjusting:
(3g1) suppose that
Figure BDA0002835632110000045
In which there is a monitoring point n satisfying the following condition j Then n is j For the outlier, get psi * Corresponding anomaly set
Figure BDA0002835632110000046
Figure BDA0002835632110000047
Figure BDA0002835632110000048
Wherein
Figure BDA0002835632110000049
Comprises a
Figure BDA00028356321100000410
Alpha is an abnormal point judgment threshold, and k is more than or equal to 1 * ≤M，k * ≠i * ，
Figure BDA00028356321100000425
To represent
Figure BDA00028356321100000411
Point of inclusionThe number of the cells;
(3g2) will be provided with
Figure BDA00028356321100000412
Each abnormal point n in (1) j From the current undirected complete graph
Figure BDA00028356321100000413
Transfer to n j Distance psi * In (1)
Figure BDA00028356321100000414
Minimal undirected complete graph
Figure BDA00028356321100000415
In the middle, 1 is less than or equal to s * M ≦ and for undirected complete picture
Figure BDA00028356321100000416
And
Figure BDA00028356321100000417
w, Δ W and D and
Figure BDA00028356321100000418
and
Figure BDA00028356321100000419
updating the parameters of all the formed undirected complete graph pairs to obtain an adjusted undirected complete graph set
Figure BDA00028356321100000420
(3h) Making unchecked equal to 1, and performing the method pair of step (3c)
Figure BDA00028356321100000421
Optimizing to obtain optimized undirected complete atlas
Figure BDA00028356321100000422
(3i) Judgment of
Figure BDA00028356321100000423
If true, let psi π ←ψ · And executing the step (3f), otherwise, making the posable _1 equal to 0, and executing the step (3 f);
(4) obtaining a path planning result of the unmanned aerial vehicle group A:
(4a) for psi × Each undirected complete graph in (1)
Figure BDA00028356321100000424
Planning the 1-TSP path to obtain psi × Corresponding minimum Hamiltonian ring set
Figure BDA0002835632110000051
And unmanned aerial vehicle group A flight distance set
Figure BDA0002835632110000052
Figure BDA0002835632110000053
To represent
Figure BDA0002835632110000054
The corresponding minimum hamiltonian ring,
Figure BDA0002835632110000055
to represent
Figure BDA0002835632110000056
The length of (d);
(4b) setting a parameter of a minimum Hamiltonian ring pair consisting of every two minimum Hamiltonian rings in the minimum Hamiltonian ring set h as a flag, when the flag is 1, indicating that the two minimum Hamiltonian rings in the minimum Hamiltonian ring pair can carry out point transfer, when the flag is 0, indicating that the two minimum Hamiltonian rings in the minimum Hamiltonian ring pair can not carry out point transfer, and setting the parameter flag of all the minimum Hamiltonian ring pairs as 1; set the maximum flight distance in h
Figure BDA0002835632110000057
The parameter that can be reduced or not is posable _2, and when posable _2 is equal to 1, this indicates that
Figure BDA0002835632110000058
Can be reduced, when the posable _2 is 0, it indicates
Figure BDA0002835632110000059
Cannot be reduced, and let the posable _2 be 1;
(4c) judging whether the possible _2 is 1, if yes, executing the step (4d), otherwise, making the program
Figure BDA00028356321100000510
And outputs the minimum Hamilton ring set of the unmanned aerial vehicle group A
Figure BDA00028356321100000511
(4d) Judging whether a minimum Hamiltonian ring pair with the flag being 1 exists in h, if so, randomly selecting the minimum Hamiltonian ring pair with the flag being 1 (h) l ,h n ) And executing step (4e), otherwise, making the posable _2 equal to 0, and executing step (4 c);
(4e) when T (h) l )＞T(h n ) When it is, judge h l Whether there is a transition to h n And satisfies max { T (h) l ),T(h n ) Decrease, if so, max { T (h) l ),T(h n ) The point at which the most reduction is achieved is taken as the ring optimum transition point n v · And n is v · From h l Is transferred to h n In, at the same time for h l 、h n 、T(h l ) And T (h) n ) And all with h l 、h n After updating the parameter flag of the formed minimum Hamiltonian ring pair, executing the step (4c), otherwise, ordering (h) l ,h n ) The corresponding parameter flag is 0 and step (4c) is performed.
Compared with the prior art, the invention has the following advantages:
the invention constructs the undirected complete graph of the monitoring area, models the monitoring points traversed by each unmanned aerial vehicle together with the starting point into the undirected complete graph, continuously optimizes the task distribution result by carrying out point transfer and exchange operation between the undirected complete graphs, simultaneously carries out point transfer between minimum Hamilton rings, further optimizes the task distribution result, and has no transfer and exchange to the points between the complete graphs and no influence of the number of tasks on the transfer of the points between the minimum Hamilton rings, thereby reducing the flight distance of the unmanned aerial vehicle with the largest flight distance in the multi-unmanned aerial vehicle.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention.
Fig. 2 is a diagram of a multi-drone path planning scenario employed by the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments.
Referring to fig. 1, the present invention includes the steps of:
step 1) constructing a multi-unmanned aerial vehicle path planning scene model:
constructing a monitoring area distributed in a xoy plane of a three-dimensional rectangular coordinate system and an unmanned aerial vehicle group A ═ A in the space of the three-dimensional rectangular coordinate system i The structure of the multi-unmanned aerial vehicle path planning scene model with the structure of i 1 less than or equal to i less than or equal to M is shown in fig. 2, and the monitoring area comprises a departure point depot of an unmanned aerial vehicle A and N monitoring points V ═ N j J is more than or equal to 1 and less than or equal to N }, wherein M represents the number of frames of the unmanned aerial vehicle, M is more than or equal to 2, A i Indicates a flying height of H i The ith unmanned aerial vehicle, n j Indicates a position coordinate of (x) j ,y j ) N ≧ M, where M is 3 and N is 20 in this embodiment.
Step 2) constructing an undirected complete map of the monitoring area:
randomly dividing the monitoring points V into M subareas with the number equal to that of the unmanned aerial vehicle, wherein each subarea at least comprises one monitoring point, and feeding every two monitoring points in each subarea and each monitoring point in each subarea and the departure point depot of ALine joining to form undirected complete graph set ψ { G } i I is more than or equal to 1 and less than or equal to M, wherein G i Is shown as A i Corresponding undirected complete graphs, each undirected complete graph G i The points in (1) include a monitoring point n j And the starting point depot of A.
Step 3), task allocation is carried out on the unmanned aerial vehicle group A:
(3a) calculate each undirected complete graph G i Total length of all sides W (G) i ) Calculating each monitoring point n j To each undirected complete graph G i Total length Δ W (G) of the edge formed by each monitoring point and departure point i ,n j ) Calculating each undirected complete graph G i Size D (G) of i ) The calculation formulas are respectively as follows:
Figure BDA0002835632110000071
Figure BDA0002835632110000072
Figure BDA0002835632110000073
wherein d (e) represents the length of the edge e,
Figure BDA0002835632110000074
representing point n j To point n j' The length of the formed edge; d (G) i ) The calculation formula (c) can be specifically interpreted as: determine G i The sum of the lengths of all the edges, dividing the sum by G i Total number of edges in
Figure BDA0002835632110000075
To give G i Average length of each side in the graph, multiplying the obtained average length by G i Number of points m i Thus obtaining D (G) i )；
The aim of the invention is to make allThe maximum flight distance and the flight time of the unmanned aerial vehicles are the minimum, namely the minimum Hamiltonian ring length of all the unmanned aerial vehicles is the maximum, and the minimum Hamiltonian ring of the ith unmanned aerial vehicle is set as h i The corresponding minimum Hamiltonian ring length is T (h) i ) Then the goal of the invention can be modeled as:
Figure BDA0002835632110000076
wherein the solution of T (h) i ) The problem to be solved in the present invention is the NP-hard problem, which is the problem of TSP travelers, and the optimal solution cannot be found in polynomial time, which is defined in the present invention as D (G) i ) And T (h) i ) There is a relationship between: t (h) i )＝f(D(G i ) + v, where f is a monotonically increasing function and v is 0-mean noise, and it has been demonstrated that D (G) can be used when v is 0 i ) Substitution of T (h) i ) To solve the problem in the present invention to obtain an optimal solution, a solution close to the optimal solution can be obtained even if v ≠ 0, and thus D (G) is used in the present invention i ) Substitution of T (h) i ) To perform task allocation; because of the need to update G multiple times when there is no point transfer and swap between the complete graphs i D (G) of i ) For convenience of D (G) i ) We define W (G) i )、ΔW(G i ,n j )；
(3b) Setting the inspection parameters of all undirected complete graph pairs combined by every two undirected complete graphs in the undirected complete graph set psi as unchecked, and setting the transition parameters and the exchange parameters of each undirected complete graph pair as flag _ t and flag _ s respectively, when unchecked is 1, indicating that the undirected complete graph pairs which are not inspected exist in psi, when unchecked is 0, indicating that the undirected complete graph pairs which are not inspected do not exist in psi, when flag _ t is 1, indicating that the two undirected complete graphs in the undirected complete graph pairs can be subjected to point transition, and when flag _ t is 0, indicating that the two undirected complete graphs in the undirected complete graph pairs cannot be subjected to point transition; when the flag _ s is equal to 1, the two undirected full graphs in the undirected full graph pair can carry out point exchange, and when the flag _ s is equal to 0, the two undirected full graphs in the undirected full graph pair can not carry out point exchange, and the unchecked is equal to 1, the flag _ t is equal to 1, and the flag _ s is equal to 1;
setting point n α Is composed of
Figure BDA0002835632110000081
One monitoring point of n, n α From
Figure BDA0002835632110000082
Is deleted and added to
Figure BDA0002835632110000083
Such an operation is called a transfer of points; setting point n p Is composed of
Figure BDA0002835632110000084
One monitoring point of (1), point n q Is composed of
Figure BDA0002835632110000085
One monitoring point of n, n p From
Figure BDA0002835632110000086
Is transferred to
Figure BDA0002835632110000087
In, n q From
Figure BDA0002835632110000088
Is transferred to
Figure BDA0002835632110000089
Such an operation is called exchange of points;
(3c) optimizing the undirected complete graph set ψ:
(3c1) judging whether the unchecked is 1, if so, executing the step (3c2), otherwise, enabling the program to be executed
Figure BDA00028356321100000810
Obtaining optimized disorientationWhole picture set
Figure BDA00028356321100000811
(3c2) Judging whether a undirected complete graph pair of flag _ t ═ 1 exists in the undirected complete graph set psi, if so, randomly selecting a undirected complete graph pair of flag _ t ═ 1 (G) a ,G b ) And performing the step (3c3), otherwise, performing the step (3c 4);
(3c3) when D (G) a )＞D(G b ) When it is, judge G a Whether there is a transition to G b And satisfies max { D (G) a ),D(G b ) Decrease, if so, max { D (G) a ),D(G b ) The point at which the most reduction is made is taken as the optimum transfer point n v * And n is v * From G a Transfer to G b Middle and simultaneous pairs G a And G b W, Δ W and D and G a And G b After updating the parameters of all undirected complete graph pairs of the composition, step (3c1) is performed, otherwise, order (G) a ,G b ) The corresponding transition parameter flag _ t is equal to 0, and step (3c1) is performed; wherein
The update formula of W and delta W, D is as follows:
W(G a ')＝W(G a )-ΔW(G a ,n v * )
W(G b ')＝W(G b )+ΔW(G b ,n v * )
Figure BDA0002835632110000091
Figure BDA0002835632110000092
n j ∈V
Figure BDA0002835632110000093
Figure BDA0002835632110000094
wherein n is v * Is G a One monitoring point of;
all of and G a 、G b The updating method of the parameters of the formed undirected complete graph pair comprises the following steps: let G a And G b The method comprises the following steps of 1, exchanging a parameter flag _ s with a transition parameter flag _ t in all other undirected graph pairs formed by undirected graph;
the departure point depot cannot be the optimal transition point;
(3c4) judging whether an undirected complete graph pair of flag _ s-1 exists in the undirected complete graph set psi, if so, randomly selecting an undirected complete graph pair of flag _ s-1 (G) ε ,G η ) And executing the step (3c5), otherwise, making unchecked equal to 0, and executing the step (3c 1);
(3c5) judgment G ε And G η Whether there is one undirected complete graph of each swap to the other side, and max { D (G) { D) } ε ),D(G η ) Decrease, if so, max { D (G) ε ),D(G η ) The two points at most reduced are taken as the optimal switching points
Figure BDA0002835632110000095
And will be
Figure BDA0002835632110000096
In undirected complete graph G ε And G η Exchange between them while for G ε And G η W, Δ W and D and G ε And G η After updating the parameters of all undirected complete graph pairs of the composition, step (3c1) is performed, otherwise, order (G) ε ,G η ) The corresponding interchange parameter flag _ s is equal to 0, and step (3c1) is performed; wherein
The update formula of W and delta W, D is as follows:
Figure BDA0002835632110000097
Figure BDA0002835632110000098
Figure BDA0002835632110000101
Figure BDA0002835632110000102
n j ∈V
Figure BDA0002835632110000103
Figure BDA0002835632110000104
wherein
Figure BDA0002835632110000105
Is G ε The monitoring point(s) in (c) is,
Figure BDA0002835632110000106
is G η A monitoring point in;
all of and G ε 、G η The updating method of the parameters of the formed undirected complete graph pair comprises the following steps: undirected complete graph G ε And G η The flag _ t and the flag _ s in undirected complete graph pairs formed with all other undirected complete graphs are respectively 1 and 1;
the departure point depot cannot be the optimal exchange point;
(3d) for undirected complete set psi π The improvement is as follows:
(3e) let us set the optimized undirected complete atlas psi π Medium maximum undirected full graph size
Figure BDA0002835632110000107
The parameter that can be reduced or not is posable _1, and when posable _1 is equal to 1, this indicates that
Figure BDA0002835632110000108
Can be reduced, when the posable _1 is 0, it means
Figure BDA0002835632110000109
Cannot be decreased, and posable _1 is made 1;
(3f) judging whether the possible _1 is 1, if yes, making the order
Figure BDA00028356321100001010
And executing the step (3g), otherwise, order
Figure BDA00028356321100001011
Obtain a pair psi π Improved undirected complete graph set
Figure BDA00028356321100001012
Figure BDA00028356321100001013
The current task assignment is saved for and against psi * Comparing the results obtained after adjustment and optimization, and judging whether the task allocation result is improved;
(3g) for undirected complete set psi * And (3) adjusting:
(3g1) suppose that
Figure BDA00028356321100001014
In which there is a monitoring point n satisfying the following condition j Then n is j For the outlier, get psi * Corresponding anomaly set
Figure BDA00028356321100001015
Figure BDA0002835632110000111
Figure BDA0002835632110000112
Wherein
Figure BDA0002835632110000113
Comprises a
Figure BDA0002835632110000114
Alpha is an abnormal point judgment threshold, and k is more than or equal to 1 * ≤M，k * ≠i * ，
Figure BDA0002835632110000115
To represent
Figure BDA0002835632110000116
The number of points involved;
alpha is used for controlling the number of detected abnormal points, the number of the abnormal points is reduced along with the increase of the alpha, the effect is best when the alpha is 1.5, and the starting point depot cannot be taken as the abnormal point;
according to
Figure BDA0002835632110000117
Can obtain the product
Figure BDA0002835632110000118
And is
Figure BDA0002835632110000119
As can be seen from this equation, the monitor point n j To
Figure BDA00028356321100001110
Sum of lengths of edges formed by each monitoring point and departure point
Figure BDA00028356321100001111
And
Figure BDA00028356321100001112
is proportional, i.e.
Figure BDA00028356321100001113
To pair
Figure BDA00028356321100001114
Is proportional, so we can look for some points
Figure BDA00028356321100001115
Is provided with
Figure BDA00028356321100001116
I.e. undirected complete map of the current site
Figure BDA00028356321100001117
Is/are as follows
Figure BDA00028356321100001118
Contribution ratio, pair
Figure BDA00028356321100001119
Is
Figure BDA00028356321100001120
To make a small contribution to
Figure BDA00028356321100001121
N can be reduced as much as possible j From the current undirected complete graph
Figure BDA00028356321100001122
Transfer to n j Distance psi * In (1)
Figure BDA00028356321100001123
Minimal undirected complete graph
Figure BDA00028356321100001124
In 1. ltoreq. s * M, the dot transfer condition here being different from the condition for dot transfer in step (3c), step (3c) being a pair of incomplete maps (G) a ,G b ) When a point is shifted, the shift condition is such that max { D (G) } a ),D(G b ) The adjustment section is designed to perform the transition of the abnormal point, because the condition is not satisfied when the two points where the size D of the absolute graph is not almost equal;
(3g2) will be provided with
Figure BDA00028356321100001125
Each abnormal point n in (1) j From the current undirected complete graph
Figure BDA00028356321100001126
Transfer to n j Distance psi * In (1)
Figure BDA00028356321100001127
Minimal undirected complete graph
Figure BDA00028356321100001128
In 1. ltoreq. s * M ≦ and for undirected complete picture
Figure BDA00028356321100001129
And
Figure BDA0002835632110000121
w, Δ W and D and
Figure BDA0002835632110000122
and
Figure BDA0002835632110000123
updating the parameters of all the formed undirected complete graph pairs to obtain an adjusted undirected complete graph set
Figure BDA0002835632110000124
Proceed to thisStep(s) to obtain task allocation results after abnormal point transfer
Figure BDA0002835632110000125
The transition condition due to the outlier is not such that max { D (G) } a ),D(G b ) The task allocation result obtained after the adjustment is not necessarily improved relative to the task allocation result obtained before the adjustment;
(3h) making unchecked equal to 1, and performing the method pair of step (3c)
Figure BDA0002835632110000126
Optimizing to obtain optimized undirected complete atlas
Figure BDA0002835632110000127
As mentioned above, the task allocation result cannot be guaranteed to be improved through the transition of the abnormal point, but the method in the step (3c) can certainly optimize the task allocation result, so that the method in the step (3c) is executed after the adjustment step, and the adjusted task allocation result is subjected to
Figure BDA0002835632110000128
Optimizing;
(3i) judgment of
Figure BDA0002835632110000129
If true, let psi π And (c) either ae step of ← ψ · and execution of step (3f), or else, let posable _1 ═ 0 and execute step (3 f);
if it is not
Figure BDA00028356321100001210
If it is true, indicating that the task assignment result is improved, the result psi is retained · Otherwise, it indicates no further improvement and the foregoing psi remains π 。
Step 4), obtaining a path planning result of the unmanned aerial vehicle group A:
(4a) for psi × Each undirected complete graph in (1)
Figure BDA00028356321100001211
Carrying out TSP path planning to obtain psi × Corresponding minimum Hamiltonian ring set
Figure BDA00028356321100001212
And unmanned aerial vehicle group A flight distance set
Figure BDA00028356321100001213
Figure BDA00028356321100001214
To represent
Figure BDA00028356321100001215
The corresponding minimum hamiltonian ring,
Figure BDA00028356321100001216
to represent
Figure BDA00028356321100001217
Length of (d);
the ring passing through all the vertices in the graph only once is called a Hamiltonian ring, and the minimum Hamiltonian ring is the Hamiltonian ring with the minimum solving length. Because the minimum Hamiltonian ring of the undirected complete graph needs to be calculated for many times, a TSP open source solver LKH is proposed, the minimum Hamiltonian ring of the undirected complete graph can be solved in a short time, and the simulation speed is improved;
(4b) setting a parameter of a minimum Hamiltonian ring pair consisting of every two minimum Hamiltonian rings in the minimum Hamiltonian ring set h as a flag, when the flag is 1, indicating that the two minimum Hamiltonian rings in the minimum Hamiltonian ring pair can carry out point transfer, when the flag is 0, indicating that the two minimum Hamiltonian rings in the minimum Hamiltonian ring pair can not carry out point transfer, and setting the parameter flag of all the minimum Hamiltonian ring pairs as 1; set the maximum flight distance in h
Figure BDA0002835632110000131
The parameter that can be reduced is posable _2, and when posable _2 is equal to 1Is shown by
Figure BDA0002835632110000132
Can be reduced, when the posable _2 is 0, it indicates
Figure BDA0002835632110000133
Cannot be reduced, and let the posable _2 be 1;
(4c) judging whether the possible _2 is 1, if yes, executing the step (4d), otherwise, making the program
Figure BDA0002835632110000134
And outputs the minimum Hamilton ring set of the unmanned aerial vehicle group A
Figure BDA0002835632110000135
(4d) Judging whether a minimum Hamiltonian ring pair with the flag being 1 exists in h, if so, randomly selecting the minimum Hamiltonian ring pair with the flag being 1 (h) l ,h n ) And executing step (4e), otherwise, making the posable _2 equal to 0, and executing step (4 c);
(4e) when T (h) l )＞T(h n ) When it is, judge h l Whether there is a transition to h n And satisfies max { T (h) l ),T(h n ) Decrease, if so, max { T (h) l ),T(h n ) The point at which the most reduction is achieved is taken as the ring optimum transition point n v · And n is v · From h l Is transferred to h n In, at the same time for h l 、h n 、T(h l ) And T (h) n ) And all with h l 、h n After updating the parameter flag of the formed minimum Hamiltonian ring pair, executing the step (4c), otherwise, ordering (h) l ,h n ) The corresponding parameter flag is equal to 0, and step (4c) is performed, in which
h l 、h n 、T(h l ) And T (h) n ) The updating method comprises the following steps: to h again l 、h n The TSP path planning is carried out on the points in the middle to obtain a new minimum Hamiltonian ring h l' 、h n' Corresponding to a new minimum Hamiltonian ringFlight distance T (h) l' )、T(h n' ) By using h l' Replacement of h l ，h n' Replacement of h n ，T(h l' ) Replacement of T (h) l )、T(h n' ) Replacement of T (h) n ) Completing the updating;
all of l 、h n The updating method of the parameter flag of the minimum Hamiltonian ring pair comprises the following steps: let the smallest Hamilton ring h l And h n The flag of the Hamiltonian ring pair formed with all other minimum Hamiltonian rings is 1;
the departure point depot cannot be taken as the optimal transition point of the ring;
as mentioned above, when performing task allocation, the user-defined undirected complete graph size D is used to replace the minimum hamilton ring length of the undirected complete graph for solution, and since v ≠ 0 in general, the task allocation result obtained by the method in step 3) is close to the optimal task allocation result, rather than the optimal solution, and thus step 4) is designed: and (3) transferring points between the minimum Hamiltonian rings, further improving the task allocation result, and only few points are transferred between the minimum Hamiltonian rings in the step 4) because the task allocation result obtained in the step 3) is close to the optimal value.

Claims (5)

1. A multi-unmanned aerial vehicle path planning method is characterized by comprising the following steps:
(1) constructing a multi-unmanned aerial vehicle path planning scene model:
constructing a monitoring area distributed in a xoy plane of a three-dimensional rectangular coordinate system and an unmanned aerial vehicle group A ═ A in the space of the three-dimensional rectangular coordinate system i I is more than or equal to 1 and less than or equal to M, and the monitoring area comprises a departure point depot of the unmanned aerial vehicle group A and N monitoring points V ═ N j J is more than or equal to 1 and less than or equal to N, wherein M represents the number of frames of the unmanned aerial vehicle, M is more than or equal to 2, A i Indicates a flying height of H i The ith unmanned aerial vehicle, n j Indicates a position coordinate of (x) j ,y j ) N is more than or equal to M at the jth monitoring point;
(2) constructing an undirected complete map of the monitored area:
randomly dividing the monitoring points V into M subareas with the number equal to the number of the unmanned aerial vehicle frames, wherein each subarea at least comprises one monitoring point, connecting every two monitoring points in each subarea and each monitoring point in each subarea with the departure point depot of A to form an undirected complete graph set psi { G ═ G i I is more than or equal to 1 and less than or equal to M, wherein G i Is represented by A i A corresponding undirected complete graph;
(3) and (3) carrying out task allocation on the unmanned aerial vehicle group A:
(3a) calculate each undirected complete graph G i Total length of all sides W (G) i ) (ii) a Calculating each monitoring point n j To each undirected complete graph G i Total length Δ W (G) of the edge formed by each monitoring point and departure point i ,n j ) (ii) a Calculate each undirected complete graph G i Size D (G) of i )；
(3b) Setting the inspection parameters of all undirected complete graph pairs combined by every two undirected complete graphs in the undirected complete graph set psi as unchecked, and setting the transition parameters and the exchange parameters of each undirected complete graph pair as flag _ t and flag _ s respectively, when unchecked is 1, indicating that the undirected complete graph pairs which are not inspected exist in psi, when unchecked is 0, indicating that the undirected complete graph pairs which are not inspected do not exist in psi, when flag _ t is 1, indicating that the two undirected complete graphs in the undirected complete graph pairs can be subjected to point transition, and when flag _ t is 0, indicating that the two undirected complete graphs in the undirected complete graph pairs cannot be subjected to point transition; when the flag _ s is equal to 1, the two undirected full graphs in the undirected full graph pair can carry out point exchange, and when the flag _ s is equal to 0, the two undirected full graphs in the undirected full graph pair can not carry out point exchange, and the unchecked is equal to 1, the flag _ t is equal to 1, and the flag _ s is equal to 1;
(3c) optimizing the undirected complete graph set ψ:
(3c1) judging whether the unchecked is 1, if so, executing the step (3c2), otherwise, enabling the program to be executed
Figure FDA0003703646320000021
Obtaining the optimized undirected complete graph set
Figure FDA0003703646320000022
(3c2) Judging whether a undirected complete graph pair of flag _ t ═ 1 exists in the undirected complete graph set psi, if so, randomly selecting a undirected complete graph pair of flag _ t ═ 1 (G) a ,G b ) And performing the step (3c3), otherwise, performing the step (3c 4);
(3c3) when D (G) a )＞D(G b ) When it is, judge G a Whether there is a transition to G b And satisfies max { D (G) a ),D(G b ) Decrease, if so, max { D (G) a ),D(G b ) The point at which the most reduction is made is taken as the optimum transfer point n v * And n is v * From G a Transfer to G b Middle and simultaneous pairs G a And G b W, Δ W and D and G a And G b After updating the parameters of all undirected complete graph pairs of the composition, step (3c1) is performed, otherwise, order (G) a ,G b ) The corresponding transition parameter flag _ t is equal to 0, and step (3c1) is performed;
(3c4) judging whether a undirected complete graph pair of flag _ s ═ 1 exists in the undirected complete graph set psi, if so, randomly selecting a undirected complete graph pair of flag _ s ═ 1 (G) ε ,G η ) And executing step (3c5), otherwise, making unchecked equal to 0, and executing step (3c 1);
(3c5) judgment G ε And G η Whether there is one undirected complete graph of each swap to the other side, and max { D (G) { D) } ε ),D(G η ) Decrease, if so, max { D (G) ε ),D(G η ) The two points at most reduced are taken as the optimal switching points
Figure FDA0003703646320000023
And will be
Figure FDA0003703646320000024
In undirected complete graph G ε And G η Exchange between them while for G ε And G η W, Δ W andd and G ε And G η After updating the parameters of all undirected complete graph pairs of the composition, step (3c1) is performed, otherwise, order (G) ε ,G η ) The corresponding interchange parameter flag _ s is equal to 0, and step (3c1) is performed;
(3d) for undirected complete set psi π The improvement is as follows:
(3e) let us set the optimized undirected complete atlas psi π Medium maximum undirected full graph size
Figure FDA0003703646320000031
The parameter that can be reduced or not is posable _1, and when posable _1 is equal to 1, this indicates that
Figure FDA0003703646320000032
Can be reduced, when the posable _1 is 0, it indicates
Figure FDA0003703646320000033
Cannot be reduced, and let the locatable _1 be 1;
(3f) judging whether the possible _1 is 1, if yes, making the order
Figure FDA0003703646320000034
And executing the step (3g), otherwise, order
Figure FDA0003703646320000035
Obtain a pair psi π Improved undirected complete graph set
Figure FDA0003703646320000036
(3g) For undirected complete set psi * And (3) adjusting:
(3g1) suppose that
Figure FDA0003703646320000037
In which there is a monitoring point n satisfying the following condition j Then n is j As an abnormal point, obtainψ * Corresponding anomaly set
Figure FDA0003703646320000038
Figure FDA0003703646320000039
Figure FDA00037036463200000310
Wherein
Figure FDA00037036463200000311
Comprises a
Figure FDA00037036463200000312
Alpha is an abnormal point judgment threshold, and k is more than or equal to 1 * ≤M，k * ≠i * ，m i* To represent
Figure FDA00037036463200000313
The number of points involved;
(3g2) will be provided with
Figure FDA00037036463200000314
Each abnormal point n in (1) j From the current undirected complete graph
Figure FDA00037036463200000315
Transfer to n j Distance psi * In (1)
Figure FDA00037036463200000316
Minimal undirected complete graph
Figure FDA00037036463200000317
In 1. ltoreq. s * M ≦ and for undirected complete picture
Figure FDA00037036463200000318
And
Figure FDA00037036463200000319
w, Δ W and D and
Figure FDA00037036463200000320
and
Figure FDA00037036463200000321
updating the parameters of all the formed undirected complete graph pairs to obtain an adjusted undirected complete graph set
Figure FDA00037036463200000322
(3h) Making unchecked equal to 1, and performing the method pair of step (3c)
Figure FDA00037036463200000323
Optimizing to obtain optimized undirected complete atlas
Figure FDA00037036463200000324
(3i) Judgment of
Figure FDA00037036463200000325
If true, let psi π ←ψ · And executing the step (3f), otherwise, making the posable _1 equal to 0, and executing the step (3 f);
(4) obtaining a path planning result of the unmanned aerial vehicle group A:
(4a) for psi × Each undirected complete graph in (1)
Figure FDA0003703646320000041
Carrying out TSP path planning to obtain psi × Corresponding minimum Hamiltonian ring set
Figure FDA0003703646320000042
And unmanned aerial vehicle group A flight distance set
Figure FDA0003703646320000043
Figure FDA0003703646320000044
To represent
Figure FDA0003703646320000045
The corresponding minimum hamiltonian ring,
Figure FDA0003703646320000046
to represent
Figure FDA0003703646320000047
Length of (d);
(4b) setting a parameter of a minimum Hamiltonian ring pair consisting of every two minimum Hamiltonian rings in the minimum Hamiltonian ring set h as a flag, when the flag is 1, indicating that the two minimum Hamiltonian rings in the minimum Hamiltonian ring pair can carry out point transfer, when the flag is 0, indicating that the two minimum Hamiltonian rings in the minimum Hamiltonian ring pair can not carry out point transfer, and setting the parameter flag of all the minimum Hamiltonian ring pairs as 1; set the maximum flight distance in h
Figure FDA0003703646320000048
The parameter that can be reduced or not is posable _2, and when posable _2 is equal to 1, this indicates that
Figure FDA0003703646320000049
Can be reduced, when posable _2 is 0, it means
Figure FDA00037036463200000410
Cannot be reduced, and let the posable _2 be 1;
(4c) judging whether the possible _2 is 1, if yes, executing the step (4d), otherwise, making the program
Figure FDA00037036463200000411
And outputs the minimum Hamilton ring set of the unmanned aerial vehicle group A
Figure FDA00037036463200000412
(4d) Judging whether a minimum Hamiltonian ring pair with the flag being 1 exists in h, if so, randomly selecting the minimum Hamiltonian ring pair with the flag being 1 (h) l ,h n ) And executing step (4e), otherwise, making the passive _2 equal to 0, and executing step (4 c);
(4e) when T (h) l )＞T(h n ) When it is, judge h l Whether there is a transition to h n And satisfies max { T (h) l ),T(h n ) Decrease, if so, max { T (h) l ),T(h n ) The point at which the most reduction is achieved is taken as the ring optimum transition point n v · And n is v · From h l Is transferred to h n In, at the same time for h l 、h n 、T(h l ) And T (h) n ) And all are connected with h l 、h n After updating the parameter flag of the formed minimum Hamiltonian ring pair, executing the step (4c), otherwise, ordering (h) l ,h n ) The corresponding parameter flag is 0 and step (4c) is performed.
2. A method for planning the path of multiple drones according to claim 1, wherein each undirected full graph G in step (3a) i The sum W (G) of the lengths of all sides i ) Each monitoring point n j To each undirected complete graph G i The sum Δ W (G) of the lengths of the edges formed by each monitoring point and the departure point i ,n j ) Each undirected complete graph G i Size D (G) of i ) The calculation formulas are respectively
Figure FDA0003703646320000051
Figure FDA0003703646320000052
Figure FDA0003703646320000053
Wherein d (e) represents the length of the edge e,
Figure FDA0003703646320000054
representing point n j To point n j' The length of the edge formed.
3. A method for planning the path of multiple drones according to claim 2, wherein the pair G in step (3c3) a And G b W, Δ W and D and all of and G a 、G b Updating parameters of the composed undirected complete graph pair, wherein
The update formula of W and delta W, D is as follows:
W(G a' )＝W(G a )-ΔW(G a ,n v * )
W(G b' )＝W(G b )+ΔW(G b ,n v * )
Figure FDA0003703646320000055
Figure FDA0003703646320000056
n j ∈V
Figure FDA0003703646320000057
Figure FDA0003703646320000058
wherein n is v * Is G a One monitoring point;
all with G a 、G b The updating method of the parameters of the formed undirected complete graph pair comprises the following steps: let G a And G b And exchanging the parameter flag _ s with 1 with the transition parameter flag _ t in all the other undirected graph pairs formed by undirected graphs.
4. A method according to claim 3, wherein said pair G in step (3c5) ε And G η W, Δ W and D and all of and G ε 、G η Updating parameters of the composed undirected complete graph pair, wherein
The update formula of W and delta W, D is as follows:
Figure FDA0003703646320000061
Figure FDA0003703646320000062
Figure FDA0003703646320000063
Figure FDA0003703646320000064
n j ∈V
Figure FDA0003703646320000065
Figure FDA0003703646320000066
wherein
Figure FDA0003703646320000067
Is G ε The monitoring point(s) in (c) is,
Figure FDA0003703646320000068
is G η A monitoring point in;
all of and G ε 、G η The updating method of the parameters of the formed undirected complete graph pair comprises the following steps: undirected complete graph G ε And G η And the flag _ t and the flag _ s in the undirected complete graph pairs formed with all other undirected complete graphs are respectively 1 and 1.
5. A method for planning the path of multiple drones according to claim 4, wherein the pair h in the step (4e) l 、h n 、T(h l ) And T (h) n ) And all with h l 、h n Updating the parameter flag of the formed minimum Hamiltonian ring pair, wherein
h l 、h n 、T(h l ) And T (h) n ) The updating method comprises the following steps: to h again l 、h n The TSP path planning is carried out on the points in the middle to obtain a new minimum Hamiltonian ring h l' 、h n' Distance of flight T (h) corresponding to the new minimum Hamiltonian ring l' )、T(h n' ) By using h l' Replacement of h l ，h n' Replacement of h n ，T(h l' ) Replacement of T (h) l )、T(h n' ) Replacement of T (h) n ) Completing the updating;
all of l 、h n The updating method of the parameter flag of the minimum Hamiltonian ring pair comprises the following steps: let the smallest Hamilton ring h l And h n The flag of the hamiltonian ring pair formed with all other smallest hamiltonian rings is 1.
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