CN110673651A - Robust formation method for unmanned aerial vehicle cluster under limited communication condition - Google Patents

Robust formation method for unmanned aerial vehicle cluster under limited communication condition Download PDF

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CN110673651A
CN110673651A CN201911230477.8A CN201911230477A CN110673651A CN 110673651 A CN110673651 A CN 110673651A CN 201911230477 A CN201911230477 A CN 201911230477A CN 110673651 A CN110673651 A CN 110673651A
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unmanned aerial
aerial vehicle
communication
communication connection
formation
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CN110673651B (en
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曹先彬
杜文博
徐亮
朱熙
李宇萌
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Beijing University of Aeronautics and Astronautics
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    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
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Abstract

The invention discloses a robust formation method of an unmanned aerial vehicle cluster under a communication limited condition, which comprises the steps of giving a dynamic formula of each unmanned aerial vehicle changing along with time under the condition of considering communication time delay, deducing the relation between formation robustness and a communication connection network topological structure according to the dynamic formula, generating a scale-free communication connection network with different power indexes under the condition that the total communication connection number of the unmanned aerial vehicle cluster is fixed, and obtaining the topological structure with the strongest robustness by analyzing the relation between the formation robustness and the communication connection network degree distribution. Under the conditions of not increasing the cost of establishing communication connection and having communication time delay, the robust formation control of the unmanned aerial vehicle group is realized, the algorithm complexity is low, the calculation precision is high, and the robust formation of the unmanned aerial vehicle group under the condition of limited communication can be effectively realized.

Description

Robust formation method for unmanned aerial vehicle cluster under limited communication condition
Technical Field
The invention relates to the technical field of unmanned aerial vehicles, in particular to a robust formation method of an unmanned aerial vehicle cluster under a limited communication condition.
Background
The unmanned aerial vehicle has the advantages of flexibility, strong controllability and the like, and is more and more widely applied to the aspects of express transportation, disaster detection, pesticide spraying, film and television shooting, military reconnaissance and the like.
When multiple unmanned aerial vehicles cooperatively complete tasks, a formation flight control algorithm is one of key technologies, and can effectively improve the flight efficiency, flight safety and the like of the unmanned aerial vehicle cluster in a task environment, and directly influence the success rate of the unmanned aerial vehicle cluster in completing the tasks.
In the actual flight process of the unmanned aerial vehicle, due to the complexity and changeability of the external environment, the situation that communication is limited may exist. Due to the fact that the information transmission speed between the unmanned aerial vehicles is limited, the receiver obtains signal delay, and factors such as calculation time required by the unmanned aerial vehicles to obtain control input and time for executing an algorithm after control instructions are input are added, communication delay almost exists in the whole system. Communication delay can influence the formation efficiency of the unmanned aerial vehicle cluster, and the formation risk is increased.
Therefore, under the condition of limited communication, particularly under the condition that communication delay exists, the robust formation method of the unmanned aerial vehicle cluster is particularly important, and the robust formation method of the unmanned aerial vehicle cluster is not only related to the success of the task executed by the unmanned aerial vehicle cluster, but also related to the safety of the unmanned aerial vehicle cluster.
Disclosure of Invention
In view of this, the present invention provides a robust formation method for an unmanned aerial vehicle fleet under a limited communication condition, so as to solve an adverse effect of communication delay on formation of the unmanned aerial vehicle fleet.
Therefore, the invention provides a robust formation method of an unmanned aerial vehicle cluster under the condition of limited communication, which comprises the following steps:
s1: establishing an unmanned aerial vehicle cluster formation control model, and giving a dynamic formula of each unmanned aerial vehicle in the unmanned aerial vehicle cluster changing along with time under the condition of considering communication time delay;
s2: deducing the relationship between the formation robustness of the unmanned aerial vehicle cluster and the topological structure of the communication connection network on the basis of the dynamic formula;
s3: under the condition that the total communication connection number of the unmanned aerial vehicle cluster is fixed, scale-free communication connection networks with different power indexes are generated;
s4: calculating the formation robustness of the unmanned aerial vehicle cluster under the topological structure of each scale-free communication connection network to obtain the topological structure with the strongest robustness;
s5: and carrying out formation flying on the unmanned aerial vehicle cluster under the obtained topological structure with the strongest robustness, and realizing formation flying of the unmanned aerial vehicle cluster under the condition of limited communication.
In a possible implementation manner, in the robust formation method for an unmanned aerial vehicle fleet provided by the present invention, step S1 is to establish an unmanned aerial vehicle fleet formation control model, and give a dynamic formula of each unmanned aerial vehicle in the unmanned aerial vehicle fleet changing with time in consideration of existence of communication delay, where the method specifically includes:
the total number of unmanned aerial vehicles in the unmanned aerial vehicle group is
Figure 884321DEST_PATH_IMAGE001
For any unmanned plane in the unmanned plane group
Figure 93585DEST_PATH_IMAGE002
Unmanned planeIn the presence of a signal passing through a communication channel
Figure 37588DEST_PATH_IMAGE004
Reach unmanned aerial vehicle
Figure 568539DEST_PATH_IMAGE005
Pre-existing communication delay
Figure 468361DEST_PATH_IMAGE006
The formation control dynamic formula of the unmanned aerial vehicle group with communication delay is as follows:
Figure DEST_PATH_IMAGE007
wherein,indicating unmanned aerial vehicle
Figure 680348DEST_PATH_IMAGE003
In that
Figure 306502DEST_PATH_IMAGE009
The position of the moment is a three-dimensional vector;
Figure 21517DEST_PATH_IMAGE010
indicating unmanned aerial vehicle
Figure 673209DEST_PATH_IMAGE005
In that
Figure 829384DEST_PATH_IMAGE011
The location of the time of day;
Figure 954335DEST_PATH_IMAGE012
indicating unmanned aerial vehicle
Figure 563170DEST_PATH_IMAGE003
In that
Figure 549712DEST_PATH_IMAGE011
The location of the time of day;representation and unmanned aerial vehicle
Figure 325087DEST_PATH_IMAGE003
Other drones with communication connections;
Figure 421219DEST_PATH_IMAGE005
is composed of
Figure 942943DEST_PATH_IMAGE013
The elements of (1);
Figure 73710DEST_PATH_IMAGE014
indicating unmanned aerial vehicle
Figure 9305DEST_PATH_IMAGE003
With unmanned aerial vehicle
Figure 592733DEST_PATH_IMAGE005
The connection relationship and the connection strength between the two.
In a possible implementation manner, in the robust formation method for a drone swarm provided by the present invention, step S2 is to derive a relationship between the formation robustness of the drone swarm and the topology of the communication connection network based on the dynamic formula, and specifically includes:
and performing Laplace transform on the dynamic formula to obtain:
Figure 655498DEST_PATH_IMAGE015
wherein,a Laplace transform of the representation; the represented laplace transform represents the position of the drone at the time; indicating the position of the drone at the initial moment; representing a transfer function associated with the communication channel; obtaining:
Figure 768554DEST_PATH_IMAGE022
wherein,
Figure DEST_PATH_IMAGE023
means all of
Figure 653334DEST_PATH_IMAGE024
The laplace transform of (a) is performed,to representThe position of each unmanned aerial vehicle at any moment;
Figure 397933DEST_PATH_IMAGE025
representing an identity matrix;
Figure 469925DEST_PATH_IMAGE026
representing the position of each unmanned aerial vehicle at the initial moment;
Figure 958675DEST_PATH_IMAGE027
representing network adjacency matricesA laplacian matrix of;
order to
Figure 812548DEST_PATH_IMAGE029
And, assuming that all communication delays are equal,
Figure 524283DEST_PATH_IMAGE030
then, then
Figure 765908DEST_PATH_IMAGE031
Obtaining:
Figure 368928DEST_PATH_IMAGE032
wherein,
Figure 746820DEST_PATH_IMAGE033
，
Figure 181122DEST_PATH_IMAGE034
representing network adjacency matrices
Figure 644465DEST_PATH_IMAGE035
A laplacian matrix of;
define, order
Figure 51175DEST_PATH_IMAGE036
Is a matrix
Figure 549153DEST_PATH_IMAGE034
All the characteristic values of (1) are arranged in ascending order
Figure 868270DEST_PATH_IMAGE037
Characteristic value
Figure 84487DEST_PATH_IMAGE038
The corresponding feature vector is used as a basis for determining the feature vector,
Figure 29310DEST_PATH_IMAGE039
，
Figure 381794DEST_PATH_IMAGE038
all the characteristic values are arranged according to ascending order; connectivity graph
Figure 871812DEST_PATH_IMAGE040
The eigenvalues of the laplacian matrix of (a) satisfy:
Figure 309747DEST_PATH_IMAGE041
let us orderAnd then:
Figure 265250DEST_PATH_IMAGE043
respectively order
Figure 191749DEST_PATH_IMAGE044
And
Figure 116980DEST_PATH_IMAGE045
obtaining:
Figure 540800DEST_PATH_IMAGE047
multiplying the two sides to obtain:
Figure 825151DEST_PATH_IMAGE048
simplifying to obtain:
Figure 34416DEST_PATH_IMAGE049
then:
Figure 62414DEST_PATH_IMAGE050
require that
Figure 57046DEST_PATH_IMAGE051
，
Figure 574615DEST_PATH_IMAGE052
Then, then
Figure 474438DEST_PATH_IMAGE053
Then, then
Figure 853598DEST_PATH_IMAGE054
For all
Figure 889687DEST_PATH_IMAGE038
If true, then:
Figure 578158DEST_PATH_IMAGE055
wherein,
Figure 512747DEST_PATH_IMAGE056
is a matrix
Figure 882548DEST_PATH_IMAGE034
The maximum eigenvalue of (d); communication delay of unmanned aerial vehicle group
Figure 101040DEST_PATH_IMAGE006
Is less than or equal to
Figure 708214DEST_PATH_IMAGE057
To achieve robust formation of the drone swarm.
In a possible implementation manner, in the above robust formation method for a drone swarm provided by the present invention, step S3, in a case that the total number of communication connections of the drone swarm is fixed, generates scaleless communication connection networks with different power exponents, and specifically includes:
respectively giving weight to any node of a communication connection network formed by unmanned aerial vehicles, and respectively selecting the node and the node according to probability and probabilityAdding a connecting edge between the nodes according to any two values respectively until all communication connecting edges are added, wherein the degrees of the nodes in the generated communication connection network satisfy the following relation:
Figure 97552DEST_PATH_IMAGE067
wherein,
Figure 902697DEST_PATH_IMAGE068
unmanned plane capable of representing any one
Figure 31803DEST_PATH_IMAGE069
For any one nodeDegree of (d);
the generated communication connection network has a degree distribution in the form of power-law:
Figure 148980DEST_PATH_IMAGE070
wherein:
Figure 707001DEST_PATH_IMAGE071
by controlling parameters
Figure 111568DEST_PATH_IMAGE072
To obtain the power indexes with different powersTo the network.
The robust formation method of the unmanned aerial vehicle group, provided by the invention, establishes the control model of the formation of the unmanned aerial vehicle group, gives a dynamic formula of each unmanned aerial vehicle changing along with time under the condition of considering communication time delay, deduces the relation between the robustness of the formation of the unmanned aerial vehicle group and the topological structure of the communication connection network according to the dynamic formula, generates the scale-free communication connection networks with different power indexes under the condition of fixed total communication connection number of the unmanned aerial vehicle group, the total connection edge number of the communication connection networks with different topological structures is the same, namely the total cost consumed by establishing the communication connection between the unmanned aerial vehicles is the same, the difference is that the different communication connection networks have different degree distributions, and then obtains the topological structure with the strongest performance under the condition of existence of the communication time delay by analyzing the relation between the robustness of the formation of the unmanned aerial vehicle group and the degree distribution of the communication connection networks, on the basis, robust formation control with communication time delay can be better realized, after the topological structure of the unmanned aerial vehicle cluster communication connection network is determined, each unmanned aerial vehicle can obtain flight data of neighbor unmanned aerial vehicles with communication connection with the unmanned aerial vehicle, the flight data comprises position and speed information and the like of the neighbor unmanned aerial vehicles, and after the information is obtained, the motion of the current unmanned aerial vehicle is controlled through a control algorithm, so that the effect of robust formation flight is realized. The robust formation control of the unmanned aerial vehicle cluster can be realized on the basis of not increasing the cost of establishing communication connection and under the condition of communication time delay, the algorithm complexity is low, the calculation precision is high, and the robust formation of the unmanned aerial vehicle cluster under the condition of limited communication can be effectively realized; moreover, formation flying of the unmanned aerial vehicle group can be realized under the air complex condition, and a robust formation method is provided aiming at the influence of the actual communication time delay on formation control, so that a new solution is provided for the robustness problem of formation of the unmanned aerial vehicle group; in addition, in the process of realizing robust formation of the unmanned aerial vehicle cluster, a theoretical algorithm and actual operation are implemented separately, a robust unmanned aerial vehicle cluster communication connection network is obtained firstly, and then the network topology structure is applied to an actual unmanned aerial vehicle cluster, so that the safety and the high efficiency of the unmanned aerial vehicle cluster in the implementation process are guaranteed, and unnecessary loss is avoided. The invention can ensure the safety of the unmanned aerial vehicle group flying and the high efficiency of the task completion for the research of the unmanned aerial vehicle group formation flying, so that the unmanned aerial vehicle group can realize the self function under the more complex condition, which has important significance for the more effective use of the unmanned aerial vehicle group.
Drawings
FIG. 1 is a flow chart of a robust formation method for a fleet of unmanned aerial vehicles under limited communication conditions, provided by the present invention;
FIG. 2 shows a communication connection network
Figure 50892DEST_PATH_IMAGE056
Exponent with power
Figure 643678DEST_PATH_IMAGE073
And (5) a change relation graph.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only illustrative and are not intended to limit the present invention.
The robust formation method of the unmanned aerial vehicle cluster under the condition of limited communication, as shown in fig. 1, comprises the following steps:
s1: establishing an unmanned aerial vehicle cluster formation control model, and giving a dynamic formula of each unmanned aerial vehicle in the unmanned aerial vehicle cluster changing along with time under the condition of considering communication time delay;
s2: on the basis of a dynamic formula, deducing the relationship between the formation robustness of the unmanned aerial vehicle group and the topological structure of the communication connection network;
s3: under the condition that the total communication connection number of the unmanned aerial vehicle cluster is fixed, scale-free communication connection networks with different power indexes are generated;
s4: calculating the formation robustness of the unmanned aerial vehicle cluster under the topological structure of each scale-free communication connection network to obtain the topological structure with the strongest robustness;
s5: and carrying out formation flying on the unmanned aerial vehicle cluster under the obtained topological structure with the strongest robustness, and realizing formation flying of the unmanned aerial vehicle cluster under the condition of limited communication.
In specific implementation, in the robust formation method for the unmanned aerial vehicle fleet provided by the present invention, step S1 is to establish an unmanned aerial vehicle fleet formation control model, and to give a dynamic formula of each unmanned aerial vehicle in the unmanned aerial vehicle fleet changing with time in consideration of existence of communication delay, where the method specifically includes:
the total number of unmanned aerial vehicles in the unmanned aerial vehicle group isIf two unmanned aerial vehicles can communicate with each other, one edge exists between the two unmanned aerial vehicles in the communication connection network, and the total number of edges of the communication connection between the unmanned aerial vehicles is
Figure 915576DEST_PATH_IMAGE074
For any unmanned plane in the unmanned plane group
Figure 738039DEST_PATH_IMAGE002
The continuous-time kinetic model is established as follows:
Figure 818121DEST_PATH_IMAGE075
（1）
wherein,
Figure 17022DEST_PATH_IMAGE008
indicating unmanned aerial vehicle
Figure 748217DEST_PATH_IMAGE003
In that
Figure 741581DEST_PATH_IMAGE009
The position of the moment is a three-dimensional vector;
Figure 306030DEST_PATH_IMAGE076
is shown in
Figure 308621DEST_PATH_IMAGE009
Constantly to unmanned aerial vehicle
Figure 894323DEST_PATH_IMAGE003
The applied control is used for finishing the flight at the next moment under the action of the controller; the final aim is that all unmanned aerial vehicles finally fly to the same position under the action of the controller, and the control requirement of formation is met; without considering the communication delay, the basic controller design is as follows:
Figure DEST_PATH_IMAGE077
（2）
wherein,indicating unmanned aerial vehicleAll neighbors in the communication connection network, i.e. with the drone
Figure 716283DEST_PATH_IMAGE003
Other drones with communication connections;
Figure 94175DEST_PATH_IMAGE005
is composed of
Figure 507969DEST_PATH_IMAGE013
The elements of (1); to be explainedThat is, without regard to directed edges, that is, if the drone
Figure 33629DEST_PATH_IMAGE003
Can obtain the unmanned plane
Figure 378022DEST_PATH_IMAGE005
On the contrary, unmanned aerial vehicleCan also obtain unmanned aerial vehicle
Figure 195117DEST_PATH_IMAGE003
The information of (1).Indicating unmanned aerial vehicle
Figure 90578DEST_PATH_IMAGE003
And unmanned aerial vehicle
Figure 253181DEST_PATH_IMAGE005
The connection relation and the connection strength between the unmanned aerial vehicle and the ground vehicle, if the unmanned aerial vehicle
Figure 195729DEST_PATH_IMAGE003
And unmanned aerial vehicle
Figure 695981DEST_PATH_IMAGE005
Without connection, then
Figure 382177DEST_PATH_IMAGE078
If unmanned plane
Figure 402217DEST_PATH_IMAGE003
And unmanned aerial vehicle
Figure 515666DEST_PATH_IMAGE005
With the connection, the consideration is simplified,
Figure 503214DEST_PATH_IMAGE079
. The above two formulas (1) And (2) a basic dynamic formula for the formation control of the unmanned aerial vehicle cluster is given under the condition that the communication network topology is determined;
unmanned plane
Figure 727522DEST_PATH_IMAGE003
In the presence of a signal passing through a communication channel
Figure 867647DEST_PATH_IMAGE004
Reach unmanned aerial vehicle
Figure 886419DEST_PATH_IMAGE005
Pre-existing communication delay
Figure 361263DEST_PATH_IMAGE006
The formation control dynamic formula of the unmanned aerial vehicle group with communication delay is as follows:
Figure 389261DEST_PATH_IMAGE080
（3）
wherein,indicating unmanned aerial vehicle
Figure 839146DEST_PATH_IMAGE005
In that
Figure 535706DEST_PATH_IMAGE011
The location of the time of day;indicating unmanned aerial vehicle
Figure 213605DEST_PATH_IMAGE003
In that
Figure 839758DEST_PATH_IMAGE011
The location of the time of day.
In a specific implementation, in the robust formation method for the unmanned aerial vehicle fleet provided by the present invention, step S2 is to derive a relationship between the formation robustness of the unmanned aerial vehicle fleet and the topology of the communication connection network based on a dynamic formula, and specifically includes:
and performing Laplace transform on the dynamic formula to obtain:
Figure DEST_PATH_IMAGE081
（4）
wherein,
Figure 23615DEST_PATH_IMAGE016
to represent
Figure 940886DEST_PATH_IMAGE008
(ii) a laplace transform of;
Figure 97061DEST_PATH_IMAGE017
to represent
Figure 222012DEST_PATH_IMAGE018
The laplace transform of (a) is performed,
Figure 830848DEST_PATH_IMAGE018
indicating unmanned aerial vehicle
Figure 551810DEST_PATH_IMAGE005
In that
Figure 562492DEST_PATH_IMAGE009
The location of the time of day;
Figure 592764DEST_PATH_IMAGE019
unmanned aerial vehicle for indicating initial moment
Figure 501946DEST_PATH_IMAGE003
The position of (a);presentation and communication channelThe transfer function of the correlation is such that,
Figure 90032DEST_PATH_IMAGE021
(ii) a Obtaining:
Figure 673460DEST_PATH_IMAGE082
（5）
wherein,
Figure 251071DEST_PATH_IMAGE023
means all of
Figure 970766DEST_PATH_IMAGE024
The laplace transform of (a) is performed,
Figure 827994DEST_PATH_IMAGE024
to represent
Figure 226615DEST_PATH_IMAGE009
The position of each unmanned aerial vehicle at any moment;representing an identity matrix;
Figure 667272DEST_PATH_IMAGE026
representing the position of each unmanned aerial vehicle at the initial moment;
Figure 475828DEST_PATH_IMAGE027
a laplacian matrix representing a network adjacency matrix;
order toFor simplicity, all communication delays are assumed to be equal,
Figure 438416DEST_PATH_IMAGE030
then, then
Figure DEST_PATH_IMAGE083
And therefore, the first and second electrodes are,
Figure 929440DEST_PATH_IMAGE084
is an invariant, and
Figure 945717DEST_PATH_IMAGE031
obtaining:
（6）
wherein,
Figure 917401DEST_PATH_IMAGE033
，
Figure 544822DEST_PATH_IMAGE034
representing network adjacency matrices
Figure 367285DEST_PATH_IMAGE086
A laplacian matrix of;
definition of
Figure 962214DEST_PATH_IMAGE087
Let us order
Figure 161114DEST_PATH_IMAGE036
Is a matrix
Figure 377463DEST_PATH_IMAGE034
All the characteristic values of (1) are arranged in ascending orderCharacteristic valueThe corresponding feature vector is used as a basis for determining the feature vector,，
Figure 260920DEST_PATH_IMAGE038
all the characteristic values are arranged according to ascending order; for one connectionDrawing (A)
Figure 690764DEST_PATH_IMAGE040
The characteristic values of the laplacian matrix are in the following relation:is required to make
Figure 269830DEST_PATH_IMAGE042
That is, the following relationship holds:
（7）
respectively order
Figure 324166DEST_PATH_IMAGE044
And substituting into equation (7) to obtain:
Figure 849825DEST_PATH_IMAGE089
（8）
Figure 928640DEST_PATH_IMAGE090
（9）
multiplying both sides of equation (8) and equation (9) yields:
Figure 239666DEST_PATH_IMAGE091
（10）
simplifying to obtain:
Figure 11313DEST_PATH_IMAGE092
（11）
further obtaining:
Figure 24269DEST_PATH_IMAGE093
（12）
therefore, it is required that,
Figure 72307DEST_PATH_IMAGE052
this is required and therefore needs to be satisfied for all, so:
Figure 221343DEST_PATH_IMAGE094
（13）
wherein,
Figure 334792DEST_PATH_IMAGE056
is a matrix
Figure 322340DEST_PATH_IMAGE034
The maximum eigenvalue of (d); this illustrates the communication delay when the unmanned aerial vehicle cluster is in use
Figure 546648DEST_PATH_IMAGE006
Is less than or equal to
Figure 418265DEST_PATH_IMAGE057
Robust formation can be achieved, and,
Figure 702615DEST_PATH_IMAGE057
the larger the robustness is. The next step is therefore how to connect the network by reducing the communication link
Figure 177459DEST_PATH_IMAGE056
To improve communication formation robustness under communication limited conditions.
In a specific implementation, in the foregoing robust formation method for a drone swarm provided by the present invention, step S3, in a case that the total number of communication connections of the drone swarm is fixed, generates scaleless communication connection networks with different power exponents, which specifically includes:
to pairAny node of communication connection network formed by unmanned aerial vehicles
Figure 200090DEST_PATH_IMAGE059
Giving weight
Figure 389763DEST_PATH_IMAGE060
By probabilityAnd probability
Figure 918013DEST_PATH_IMAGE062
Selecting nodes separately
Figure 32731DEST_PATH_IMAGE063
And node
Figure 393305DEST_PATH_IMAGE064
，Are respectively as
Figure 212542DEST_PATH_IMAGE066
At the node of any two values
Figure 916187DEST_PATH_IMAGE063
And node
Figure 713242DEST_PATH_IMAGE064
Adding a connecting edge, if the connecting edge exists, reselecting the node until all communication connecting edges (namely M communication connecting edges) are added, wherein the degree of the node in the generated communication connection network satisfies the following relation:
wherein,
Figure 557887DEST_PATH_IMAGE068
unmanned plane capable of representing any one
Figure 378688DEST_PATH_IMAGE069
For any one node
Figure 346644DEST_PATH_IMAGE059
Degree of (d);
the generated communication connection network has a degree distribution in the form of power-law:
Figure 505093DEST_PATH_IMAGE070
wherein:
Figure 216697DEST_PATH_IMAGE071
thus, by controlling the parametersDifferent power indexes can be obtained
Figure 33791DEST_PATH_IMAGE073
The total number of connected edges can be kept unchanged, that is, the total cost consumed for establishing different communication connection networks is the same. It is then found in these communication connection networks
Figure 679536DEST_PATH_IMAGE056
Less valued communication links the network to enhance the robustness of fleet formation of the drone under communication-constrained conditions.
In specific implementation, in the robust formation method for the unmanned aerial vehicle cluster provided by the invention, step S4 is performed to calculate the formation robustness of the unmanned aerial vehicle cluster under the topological structure of each scale-free communication connection network, so as to obtain the topological structure with the strongest robustness. May be expressed by a power exponentMeasure the variation of different scale-free communication connection networks, in particular of a scale-free communication connection network
Figure 727575DEST_PATH_IMAGE073
The larger the value is, the smaller the node degree difference in the communication connection network is, namely the more homogeneous the communication connection network is; of a scale-free communication connection network
Figure 37334DEST_PATH_IMAGE073
The smaller the value, the greater the node degree variability in the communication connection network, i.e. the more heterogeneous the communication connection network. As a result of the step S3, robustness of fleet formation of unmanned aerial vehicles under communication-restricted conditions can be obtained by utilizing the communication connection network
Figure 170375DEST_PATH_IMAGE056
And (4) showing. In step S3, the different power exponents are generated by a formulation method
Figure 36831DEST_PATH_IMAGE073
The total number of edges of the communication connection networks is the same, that is, the total cost consumed for establishing the communication connection networks is the same,power exponent for networks connected with these communications
Figure 357271DEST_PATH_IMAGE073
The graph of the variation relationship is shown in fig. 2. As can be seen from FIG. 2, the power exponent of the UAV cluster communication connection network
Figure 712029DEST_PATH_IMAGE073
The larger the communication connection network, the smaller the communication connection network, in extreme cases, the difference
Figure 569126DEST_PATH_IMAGE056
Even about ten times of difference exists between the unmanned aerial vehicle fleet formation and the unmanned aerial vehicle fleet formation, which shows that under different communication network connections and in the presence of communication delay, the robustness of different unmanned aerial vehicle fleet formations has great difference, so that a proper communication connection network needs to be selected to accelerate the unmanned aerial vehicle fleet formation to flyAnd (6) rows.
In specific implementation, in the robust formation method for the unmanned aerial vehicle fleet provided by the invention, step S5 is performed to perform formation flying of the unmanned aerial vehicle fleet under the obtained topological structure with the strongest robustness, so as to realize formation flying of the unmanned aerial vehicle fleet under the condition of limited communication. Under the condition of no change of total connection edge number of communication connection network of unmanned aerial vehicle group, power exponent is generated as much as possible
Figure 73532DEST_PATH_IMAGE073
Larger scale-free communication connection network topologies, i.e. communication connection network topologies that are more homogenous, to reduce the size of the communication connection network
Figure 725093DEST_PATH_IMAGE056
Therefore, robust formation flying of the unmanned aerial vehicle cluster under the condition of limited communication can be better realized. The robust formation of the unmanned aerial vehicle cluster is realized under the limited communication condition, the unmanned aerial vehicle can more efficiently achieve the formation effect and keep the formation in the flying process, the energy consumption is reduced, the flying efficiency is improved, convenience is provided for the subsequent operation of the unmanned aerial vehicle, and the method has positive significance.
According to the robust formation method for the unmanned aerial vehicle cluster, each unmanned aerial vehicle in the unmanned aerial vehicle cluster can acquire flight state information of a neighbor unmanned aerial vehicle with communication connection, and due to the existence of communication time delay, data acquired by the unmanned aerial vehicle is actually flight position and speed information of the neighbor unmanned aerial vehicle before a short time. After the information is acquired, the current unmanned aerial vehicle flies to the central position of the neighbor unmanned aerial vehicle under the action of the controller, so that the formation control effect is realized. The communication connection between the unmanned aerial vehicles can be represented by using a network topology structure, and in the case of communication time delay, the formation robustness of the unmanned aerial vehicle cluster is deduced to be related to certain parameters of the communication connection network. Under the condition that the total number of communication connections is not changed, scale-free communication networks with different power indexes are generated, then the relation between robustness of unmanned aerial vehicle cluster formation and the power indexes of the communication connection networks is explored under the condition that communication time delay exists, the communication connection networks with strong robustness are reserved, the formation effect is achieved, and finally the purpose is to enable all unmanned aerial vehicles to fly according to the unified position and speed direction.
The robust formation method of the unmanned aerial vehicle group, provided by the invention, establishes the control model of the formation of the unmanned aerial vehicle group, gives a dynamic formula of each unmanned aerial vehicle changing along with time under the condition of considering communication time delay, deduces the relation between the robustness of the formation of the unmanned aerial vehicle group and the topological structure of the communication connection network according to the dynamic formula, generates the scale-free communication connection networks with different power indexes under the condition of fixed total communication connection number of the unmanned aerial vehicle group, the total connection edge number of the communication connection networks with different topological structures is the same, namely the total cost consumed by establishing the communication connection between the unmanned aerial vehicles is the same, the difference is that the different communication connection networks have different degree distributions, and then obtains the topological structure with the strongest performance under the condition of existence of the communication time delay by analyzing the relation between the robustness of the formation of the unmanned aerial vehicle group and the degree distribution of the communication connection networks, on the basis, robust formation control with communication time delay can be better realized, after the topological structure of the unmanned aerial vehicle cluster communication connection network is determined, each unmanned aerial vehicle can obtain flight data of neighbor unmanned aerial vehicles with communication connection with the unmanned aerial vehicle, the flight data comprises position and speed information and the like of the neighbor unmanned aerial vehicles, and after the information is obtained, the motion of the current unmanned aerial vehicle is controlled through a control algorithm, so that the effect of robust formation flight is realized. The robust formation control of the unmanned aerial vehicle cluster can be realized on the basis of not increasing the cost of establishing communication connection and under the condition of communication time delay, the algorithm complexity is low, the calculation precision is high, and the robust formation of the unmanned aerial vehicle cluster under the condition of limited communication can be effectively realized; moreover, formation flying of the unmanned aerial vehicle group can be realized under the air complex condition, and a robust formation method is provided aiming at the influence of the actual communication time delay on formation control, so that a new solution is provided for the robustness problem of formation of the unmanned aerial vehicle group; in addition, in the process of realizing robust formation of the unmanned aerial vehicle cluster, a theoretical algorithm and actual operation are implemented separately, a robust unmanned aerial vehicle cluster communication connection network is obtained firstly, and then the network topology structure is applied to an actual unmanned aerial vehicle cluster, so that the safety and the high efficiency of the unmanned aerial vehicle cluster in the implementation process are guaranteed, and unnecessary loss is avoided. The invention can ensure the safety of the unmanned aerial vehicle group flying and the high efficiency of the task completion for the research of the unmanned aerial vehicle group formation flying, so that the unmanned aerial vehicle group can realize the self function under the more complex condition, which has important significance for the more effective use of the unmanned aerial vehicle group.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (4)

1. A robust formation method for a unmanned aerial vehicle cluster under a communication limited condition is characterized by comprising the following steps:
s1: establishing an unmanned aerial vehicle cluster formation control model, and giving a dynamic formula of each unmanned aerial vehicle in the unmanned aerial vehicle cluster changing along with time under the condition of considering communication time delay;
s2: deducing the relationship between the formation robustness of the unmanned aerial vehicle cluster and the topological structure of the communication connection network on the basis of the dynamic formula;
s3: under the condition that the total communication connection number of the unmanned aerial vehicle cluster is fixed, scale-free communication connection networks with different power indexes are generated;
s4: calculating the formation robustness of the unmanned aerial vehicle cluster under the topological structure of each scale-free communication connection network to obtain the topological structure with the strongest robustness;
s5: and carrying out formation flying on the unmanned aerial vehicle cluster under the obtained topological structure with the strongest robustness, and realizing formation flying of the unmanned aerial vehicle cluster under the condition of limited communication.
2. The robust formation method of the drone swarm according to claim 1, wherein step S1 is to establish a drone swarm control model, and to give a dynamic formula of each drone in the drone swarm over time in consideration of the existence of communication delay, and specifically includes:
the total number of unmanned aerial vehicles in the unmanned aerial vehicle group is
Figure 331476DEST_PATH_IMAGE001
For any unmanned plane in the unmanned plane group
Figure 789002DEST_PATH_IMAGE002
Unmanned plane
Figure 337795DEST_PATH_IMAGE003
In the presence of a signal passing through a communication channel
Figure 235956DEST_PATH_IMAGE004
Reach unmanned aerial vehiclePre-existing communication delay
Figure 764206DEST_PATH_IMAGE006
The formation control dynamic formula of the unmanned aerial vehicle group with communication delay is as follows:
Figure 167506DEST_PATH_IMAGE007
wherein,
Figure 239498DEST_PATH_IMAGE008
indicating unmanned aerial vehicleIn that
Figure 793156DEST_PATH_IMAGE009
The position of the moment is a three-dimensional vector;
Figure 316542DEST_PATH_IMAGE010
indicating unmanned aerial vehicle
Figure 559435DEST_PATH_IMAGE005
In that
Figure 535482DEST_PATH_IMAGE011
The location of the time of day;
Figure 138501DEST_PATH_IMAGE012
indicating unmanned aerial vehicle
Figure 595021DEST_PATH_IMAGE003
In that
Figure 930188DEST_PATH_IMAGE011
The location of the time of day;
Figure 659109DEST_PATH_IMAGE013
representation and unmanned aerial vehicle
Figure 800241DEST_PATH_IMAGE003
Other drones with communication connections;
Figure 108338DEST_PATH_IMAGE005
is composed of
Figure 614406DEST_PATH_IMAGE013
The elements of (1);
Figure 892940DEST_PATH_IMAGE014
indicating unmanned aerial vehicle
Figure 775445DEST_PATH_IMAGE003
With unmanned aerial vehicle
Figure 940979DEST_PATH_IMAGE005
The connection relationship and the connection strength between the two.
3. The robust formation method for the unmanned aerial vehicle fleet according to claim 2, wherein the step S2 derives the relationship between the formation robustness of the unmanned aerial vehicle fleet and the topology of the communication connection network based on the dynamic formula, and specifically comprises:
and performing Laplace transform on the dynamic formula to obtain:
Figure 883527DEST_PATH_IMAGE015
wherein,
Figure 383778DEST_PATH_IMAGE016
to represent
Figure 804395DEST_PATH_IMAGE008
(ii) a laplace transform of;
Figure 90014DEST_PATH_IMAGE017
to represent
Figure 937885DEST_PATH_IMAGE018
The laplace transform of (a) is performed,
Figure 925432DEST_PATH_IMAGE018
indicating unmanned aerial vehicle
Figure 149740DEST_PATH_IMAGE005
In that
Figure 289866DEST_PATH_IMAGE009
The location of the time of day;unmanned aerial vehicle for indicating initial moment
Figure 49060DEST_PATH_IMAGE003
The position of (a);
Figure 811480DEST_PATH_IMAGE020
presentation and communication channelThe transfer function of the correlation is such that,(ii) a Obtaining:
wherein,
Figure 786685DEST_PATH_IMAGE023
means all of
Figure 635823DEST_PATH_IMAGE024
The laplace transform of (a) is performed,
Figure 324293DEST_PATH_IMAGE024
to represent
Figure 711412DEST_PATH_IMAGE009
The position of each unmanned aerial vehicle at any moment;
Figure 628684DEST_PATH_IMAGE025
representing an identity matrix;
Figure 784859DEST_PATH_IMAGE026
representing the position of each unmanned aerial vehicle at the initial moment;
Figure 644230DEST_PATH_IMAGE027
representing network adjacency matrices
Figure 253066DEST_PATH_IMAGE028
A laplacian matrix of;
order to
Figure 239608DEST_PATH_IMAGE029
And, assuming that all communication delays are equal,
Figure 250289DEST_PATH_IMAGE030
then, then
Figure 280562DEST_PATH_IMAGE031
Obtaining:
Figure 376694DEST_PATH_IMAGE032
wherein,，
Figure 763606DEST_PATH_IMAGE034
representing network adjacency matrices
Figure 964780DEST_PATH_IMAGE035
A laplacian matrix of;
definition of
Figure 548208DEST_PATH_IMAGE036
Let us orderIs a matrixAll the characteristic values of (1) are arranged in ascending orderCharacteristic value
Figure 852095DEST_PATH_IMAGE039
The corresponding feature vector is used as a basis for determining the feature vector,
Figure 905502DEST_PATH_IMAGE040
，
Figure 807599DEST_PATH_IMAGE039
all the characteristic values are arranged according to ascending order; connectivity graph
Figure 288259DEST_PATH_IMAGE041
The eigenvalues of the laplacian matrix of (a) satisfy:
Figure 393749DEST_PATH_IMAGE042
let us order
Figure 313164DEST_PATH_IMAGE043
And then:
Figure 7450DEST_PATH_IMAGE044
respectively make and
Figure 492569DEST_PATH_IMAGE045
obtaining:
Figure 600202DEST_PATH_IMAGE046
Figure 995411DEST_PATH_IMAGE047
multiplying the two sides to obtain:
Figure 357253DEST_PATH_IMAGE048
simplifying to obtain:
Figure 507612DEST_PATH_IMAGE049
then:
Figure 774645DEST_PATH_IMAGE050
require that，
Figure 189894DEST_PATH_IMAGE052
Then, then
Figure 511154DEST_PATH_IMAGE053
Then, thenFor all
Figure 815545DEST_PATH_IMAGE039
If true, then:
wherein,
Figure 565512DEST_PATH_IMAGE056
is a matrix
Figure 617257DEST_PATH_IMAGE034
The maximum eigenvalue of (d); communication delay of unmanned aerial vehicle group
Figure 157960DEST_PATH_IMAGE006
Is less than or equal toTo achieve robust formation of the drone swarm.
4. The robust fleet management method according to claim 3, wherein step S3, generating scaleless communication connection networks with different power exponents under the condition that the total number of communication connections of the fleet is fixed, specifically comprises:
to pair
Figure 198914DEST_PATH_IMAGE058
Any node of communication connection network formed by unmanned aerial vehicles
Figure 475306DEST_PATH_IMAGE059
Giving weight
Figure 882016DEST_PATH_IMAGE060
By probability
Figure 193043DEST_PATH_IMAGE061
And probability respectively selecting nodes
Figure 977645DEST_PATH_IMAGE063
And node，
Figure 25684DEST_PATH_IMAGE065
Respectively, are any two values of m, at the node
Figure 702653DEST_PATH_IMAGE063
And nodeUntil all communication connection edges are added, the degree of the nodes in the generated communication connection network satisfies the following relation:
wherein,
Figure 906211DEST_PATH_IMAGE067
unmanned plane capable of representing any one
Figure 19660DEST_PATH_IMAGE068
For any one node
Figure 7208DEST_PATH_IMAGE069
Degree of (d);
the generated communication connection network has a degree distribution in the form of power-law:
Figure 247828DEST_PATH_IMAGE070
wherein:
Figure 574904DEST_PATH_IMAGE071
by controlling parameters
Figure 718309DEST_PATH_IMAGE072
To obtain the power indexes with different powers
Figure 865257DEST_PATH_IMAGE073
To the network.
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