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
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formation
uav
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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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Beihang University
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Abstract

本发明公开了一种通信受限条件下的无人机群鲁棒编队方法，在考虑通信时延的情况下给出每个无人机随时间变化的动力学公式，根据动力学公式推导编队鲁棒性与通信连接网络拓扑结构之间关系，在无人机群总通信连接数目固定的情况下生成具有不同幂指数的无标度通信连接网络，通过分析编队鲁棒性与通信连接网络度分布之间的关系，得到鲁棒性最强的拓扑结构，这样，在拓扑结构确定后，每个无人机可以获得邻居无人机的飞行数据，通过控制算法对当前无人机的运动进行控制，实现鲁棒编队飞行。在不增加建立通信连接代价且存在通信时延的情况下，实现无人机群的鲁棒编队控制，算法复杂度低，计算精度高，能够有效实现在通信受限条件下的无人机群鲁棒编队。

Figure 201911230477

The invention discloses a robust formation method of unmanned aerial vehicles under the condition of limited communication. The dynamic formula of each unmanned aerial vehicle changing with time is given under the condition of considering the communication time delay, and the formation robustness is deduced according to the dynamic formula. The relationship between the robustness and the topology of the communication connection network is to generate a scale-free communication connection network with different power exponents when the total number of communication connections in the UAV swarm is fixed. By analyzing the relationship between the formation robustness and the degree distribution of the communication connection network. In this way, after the topology structure is determined, each UAV can obtain the flight data of neighboring UAVs, and control the movement of the current UAV through the control algorithm. Robust formation flight is achieved. The robust formation control of UAV swarms is realized without increasing the cost of establishing a communication connection and there is a communication delay, with low algorithm complexity and high computational accuracy, which can effectively realize the robustness of UAV swarms under the condition of limited communication. formation.

Figure 201911230477

Description

一种通信受限条件下的无人机群鲁棒编队方法A robust formation method for UAV swarms under the condition of limited communication

技术领域technical field

本发明涉及无人机技术领域，尤其涉及一种通信受限条件下的无人机群鲁棒编队方法。The invention relates to the technical field of unmanned aerial vehicles, in particular to a method for robust formation of unmanned aerial vehicles under the condition of limited communication.

背景技术Background technique

无人机凭借机动灵活、可控性强等优点，在快递运输、灾情检测、农药喷洒、影视拍摄、军事侦察等方面得到越来越广泛的应用。UAVs are more and more widely used in express transportation, disaster detection, pesticide spraying, film and television shooting, military reconnaissance, etc.

在多架无人机协同完成任务时，编队飞行控制算法是关键技术之一，它能有效提高无人机群在任务环境中的飞行效率、飞行安全等，直接影响无人机群完成任务的成功率。When multiple UAVs cooperate to complete the task, the formation flight control algorithm is one of the key technologies. It can effectively improve the flight efficiency and flight safety of the UAV group in the mission environment, and directly affect the success rate of the UAV group to complete the task. .

无人机在实际飞行过程中，由于外界环境的复杂多变，可能会存在通信受限的情况。由于无人机间的信息传递速度有限、接收器获取信号延迟，再加上无人机获得控制输入所需要的计算时间以及输入控制指令后执行算法的时间等因素，通信时延几乎存在于整个系统中。通信时延会影响无人机群的编队效率，增加编队风险。During the actual flight of the UAV, due to the complex and changeable external environment, there may be limited communication. Due to the limited speed of information transfer between UAVs, the delay of the receiver to obtain the signal, the calculation time required for the UAV to obtain the control input and the time to execute the algorithm after inputting the control command, the communication delay exists in almost the entire in the system. The communication delay will affect the formation efficiency of the UAV swarm and increase the formation risk.

因此，在通信受限条件下，尤其是具体体现在通信时延存在的情况下，无人机群鲁棒编队方法显得尤为重要，它不光关系到无人机群执行任务的成功与否，更关系到无人机群本身的安全。Therefore, under the condition of limited communication, especially in the presence of communication delay, the robust formation method of UAV swarms is particularly important. It is not only related to the success of UAV swarms to perform tasks, but also to The safety of the drone swarm itself.

发明内容SUMMARY OF THE INVENTION

有鉴于此，本发明提供了一种通信受限条件下的无人机群鲁棒编队方法，用以解决通信时延对无人机群编队的不良影响。In view of this, the present invention provides a robust formation method of UAV swarms under the condition of limited communication, so as to solve the adverse effect of communication delay on the formation of UAV swarms.

因此，本发明提供了一种通信受限条件下的无人机群鲁棒编队方法，包括如下步骤：Therefore, the present invention provides a method for robust formation of UAV swarms under the condition of limited communication, including the following steps:

S1：建立无人机群编队控制模型，在考虑通信时延的情况下，给出无人机群中每个无人机随时间变化的动力学公式；S1: Establish the formation control model of the UAV swarm, and give the dynamic formula of each UAV in the UAV swarm over time while considering the communication delay;

S2：在所述动力学公式的基础上，推导出无人机群的编队鲁棒性与通信连接网络的拓扑结构之间的关系；S2: On the basis of the dynamic formula, deduce the relationship between the formation robustness of the UAV swarm and the topology of the communication connection network;

S3：在无人机群总通信连接数目固定的情况下，生成具有不同幂指数的无标度通信连接网络；S3: When the total number of communication connections in the UAV swarm is fixed, generate a scale-free communication connection network with different power exponents;

S4：计算各所述无标度通信连接网络的拓扑结构下无人机群的编队鲁棒性，得到鲁棒性最强的拓扑结构；S4: Calculate the formation robustness of the UAV swarm under the topology structure of each of the scale-free communication connection networks, and obtain the topology structure with the strongest robustness;

S5：在得到的鲁棒性最强的拓扑结构下进行无人机群编队飞行，实现在通信受限条件下无人机群的编队飞行。S5: Under the obtained topology with the strongest robustness, the formation flight of the UAV group is carried out, and the formation flight of the UAV group is realized under the condition of limited communication.

在一种可能的实现方式中，在本发明提供的上述无人机群鲁棒编队方法中，步骤S1，建立无人机群编队控制模型，在考虑通信时延存在的情况下，给出无人机群中每个无人机随时间变化的动力学公式，具体包括：In a possible implementation manner, in the above-mentioned robust formation method for UAV swarms provided by the present invention, in step S1, a formation control model for UAV swarms is established, and the UAV swarm is given in consideration of the existence of communication delay. The dynamic formula of each UAV in time-varying, specifically including:

无人机群中无人机的总数量为

Figure 884321DEST_PATH_IMAGE001
，对于无人机群中任意一架无人机
Figure 93585DEST_PATH_IMAGE002
，无人机的信号在通过通信信道
Figure 37588DEST_PATH_IMAGE004
到达无人机
Figure 568539DEST_PATH_IMAGE005
之前存在通信时延
Figure 468361DEST_PATH_IMAGE006
，存在通信时延的无人机群编队控制动力学公式如下：The total number of drones in the drone swarm is
Figure 884321DEST_PATH_IMAGE001
, for any drone in the drone swarm
Figure 93585DEST_PATH_IMAGE002
, UAV signal over the communication channel
Figure 37588DEST_PATH_IMAGE004
reach the drone
Figure 568539DEST_PATH_IMAGE005
There was communication delay before
Figure 468361DEST_PATH_IMAGE006
, the dynamic formula of UAV group formation control with communication delay is as follows:

Figure DEST_PATH_IMAGE007
Figure DEST_PATH_IMAGE007

其中，表示无人机

Figure 680348DEST_PATH_IMAGE003
在
Figure 306502DEST_PATH_IMAGE009
时刻的位置，是一个三维向量；
Figure 21517DEST_PATH_IMAGE010
表示无人机
Figure 673209DEST_PATH_IMAGE005
在
Figure 829384DEST_PATH_IMAGE011
时刻的位置；
Figure 954335DEST_PATH_IMAGE012
表示无人机
Figure 563170DEST_PATH_IMAGE003
在
Figure 549712DEST_PATH_IMAGE011
时刻的位置；表示与无人机
Figure 325087DEST_PATH_IMAGE003
有通信连接的其它无人机；
Figure 421219DEST_PATH_IMAGE005
为
Figure 942943DEST_PATH_IMAGE013
中的元素；
Figure 73710DEST_PATH_IMAGE014
表示无人机
Figure 9305DEST_PATH_IMAGE003
与无人机
Figure 592733DEST_PATH_IMAGE005
之间的连接关系和连接强度。in, Represents a drone
Figure 680348DEST_PATH_IMAGE003
exist
Figure 306502DEST_PATH_IMAGE009
The position of the moment is a three-dimensional vector;
Figure 21517DEST_PATH_IMAGE010
Represents a drone
Figure 673209DEST_PATH_IMAGE005
exist
Figure 829384DEST_PATH_IMAGE011
position at the moment;
Figure 954335DEST_PATH_IMAGE012
Represents a drone
Figure 563170DEST_PATH_IMAGE003
exist
Figure 549712DEST_PATH_IMAGE011
position at the moment; Representation with drone
Figure 325087DEST_PATH_IMAGE003
other drones with a communication connection;
Figure 421219DEST_PATH_IMAGE005
for
Figure 942943DEST_PATH_IMAGE013
elements in;
Figure 73710DEST_PATH_IMAGE014
Represents a drone
Figure 9305DEST_PATH_IMAGE003
with drone
Figure 592733DEST_PATH_IMAGE005
connection and connection strength.

在一种可能的实现方式中，在本发明提供的上述无人机群鲁棒编队方法中，步骤S2，在所述动力学公式的基础上，推导出无人机群的编队鲁棒性与通信连接网络的拓扑结构之间的关系，具体包括：In a possible implementation manner, in the above-mentioned method for robust formation of UAV swarms provided by the present invention, in step S2, on the basis of the dynamic formula, the formation robustness and communication connection of the UAV swarm are deduced The relationship between the topological structures of the network, including:

对动力学公式做拉普拉斯变换，得到：Laplace transform of the kinetic formula, we get:

Figure 655498DEST_PATH_IMAGE015
Figure 655498DEST_PATH_IMAGE015

其中，表示的拉普拉斯变换；表示的拉普拉斯变换，表示无 人机在时刻的位置；表示初始时刻无人机的位置；表示与通信信道相 关的转移函数，；得到： in, The Laplace transform of the representation; the Laplace transform of the representation, representing the position of the UAV at the moment; representing the position of the UAV at the initial moment; representing the transfer function associated with the communication channel,; get:

Figure 768554DEST_PATH_IMAGE022
Figure 768554DEST_PATH_IMAGE022

其中，

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表示所有
Figure 653334DEST_PATH_IMAGE024
的拉普拉斯变换，表示时刻各无人机的位置；
Figure 397933DEST_PATH_IMAGE025
表示单位矩阵；
Figure 469925DEST_PATH_IMAGE026
表示初始时刻各无人机的位置；
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表示网络邻接矩阵的拉普拉斯矩阵；in,
Figure DEST_PATH_IMAGE023
means all
Figure 653334DEST_PATH_IMAGE024
The Laplace transform of , express The position of each drone at time;
Figure 397933DEST_PATH_IMAGE025
represents the identity matrix;
Figure 469925DEST_PATH_IMAGE026
Indicates the position of each UAV at the initial moment;
Figure 958675DEST_PATH_IMAGE027
Represents the network adjacency matrix The Laplace matrix of ;

令

Figure 812548DEST_PATH_IMAGE029
，假设所有的通信时延都相等，
Figure 524283DEST_PATH_IMAGE030
，则
Figure 765908DEST_PATH_IMAGE031
，得到：make
Figure 812548DEST_PATH_IMAGE029
, assuming all communication delays are equal,
Figure 524283DEST_PATH_IMAGE030
,but
Figure 765908DEST_PATH_IMAGE031
,get:

Figure 368928DEST_PATH_IMAGE032
Figure 368928DEST_PATH_IMAGE032

其中，

Figure 746820DEST_PATH_IMAGE033
，
Figure 181122DEST_PATH_IMAGE034
表示网络邻接矩阵
Figure 644465DEST_PATH_IMAGE035
的拉普拉斯矩阵；in,
Figure 746820DEST_PATH_IMAGE033
,
Figure 181122DEST_PATH_IMAGE034
Represents the network adjacency matrix
Figure 644465DEST_PATH_IMAGE035
The Laplace matrix of ;

定义，令

Figure 51175DEST_PATH_IMAGE036
是矩阵
Figure 549153DEST_PATH_IMAGE034
的所有特征值按升序排列后第
Figure 868270DEST_PATH_IMAGE037
个特征值
Figure 84487DEST_PATH_IMAGE038
对应的特征向量，
Figure 29310DEST_PATH_IMAGE039
，
Figure 381794DEST_PATH_IMAGE038
是所有特征值按升序进行排列；连通图
Figure 871812DEST_PATH_IMAGE040
的拉普拉斯矩阵的特征值满足：
Figure 309747DEST_PATH_IMAGE041
，令，则：define, let
Figure 51175DEST_PATH_IMAGE036
is the matrix
Figure 549153DEST_PATH_IMAGE034
All eigenvalues of are sorted in ascending order after the first
Figure 868270DEST_PATH_IMAGE037
eigenvalues
Figure 84487DEST_PATH_IMAGE038
The corresponding eigenvectors,
Figure 29310DEST_PATH_IMAGE039
,
Figure 381794DEST_PATH_IMAGE038
is that all eigenvalues are arranged in ascending order; a connected graph
Figure 871812DEST_PATH_IMAGE040
The eigenvalues of the Laplace matrix satisfy:
Figure 309747DEST_PATH_IMAGE041
,make ,but:

Figure 265250DEST_PATH_IMAGE043
Figure 265250DEST_PATH_IMAGE043

分别令

Figure 191749DEST_PATH_IMAGE044
和
Figure 116980DEST_PATH_IMAGE045
，得到：Separate orders
Figure 191749DEST_PATH_IMAGE044
and
Figure 116980DEST_PATH_IMAGE045
,get:

Figure 540800DEST_PATH_IMAGE047
Figure 540800DEST_PATH_IMAGE047

两边相乘得到：Multiply both sides to get:

Figure 825151DEST_PATH_IMAGE048
Figure 825151DEST_PATH_IMAGE048

化简得到：Simplify to get:

Figure 34416DEST_PATH_IMAGE049
Figure 34416DEST_PATH_IMAGE049

则：but:

Figure 62414DEST_PATH_IMAGE050
Figure 62414DEST_PATH_IMAGE050

要求

Figure 57046DEST_PATH_IMAGE051
，
Figure 574615DEST_PATH_IMAGE052
，则
Figure 474438DEST_PATH_IMAGE053
，则
Figure 853598DEST_PATH_IMAGE054
对所有
Figure 889687DEST_PATH_IMAGE038
成立，则：Require
Figure 57046DEST_PATH_IMAGE051
,
Figure 574615DEST_PATH_IMAGE052
,but
Figure 474438DEST_PATH_IMAGE053
,but
Figure 853598DEST_PATH_IMAGE054
to all
Figure 889687DEST_PATH_IMAGE038
established, then:

Figure 578158DEST_PATH_IMAGE055
Figure 578158DEST_PATH_IMAGE055

其中，

Figure 512747DEST_PATH_IMAGE056
为矩阵
Figure 882548DEST_PATH_IMAGE034
的最大特征值；令无人机群的通信时延
Figure 101040DEST_PATH_IMAGE006
小于或等于
Figure 708214DEST_PATH_IMAGE057
，以实现无人机群的鲁棒编队。in,
Figure 512747DEST_PATH_IMAGE056
is a matrix
Figure 882548DEST_PATH_IMAGE034
The maximum eigenvalue of ; make the communication delay of the UAV swarm
Figure 101040DEST_PATH_IMAGE006
less than or equal to
Figure 708214DEST_PATH_IMAGE057
, to achieve robust formation of UAV swarms.

在一种可能的实现方式中，在本发明提供的上述无人机群鲁棒编队方法中，步骤S3，在无人机群总通信连接数目固定的情况下，生成具有不同幂指数的无标度通信连接网络，具体包括：In a possible implementation manner, in the above-mentioned method for robust formation of a swarm of unmanned aerial vehicles provided by the present invention, in step S3, when the total number of communication connections of the swarm of unmanned aerial vehicles is fixed, generate scale-free communication with different power exponents Connect to the Internet, including:

对个无人机组成的通信连接网络的任意一个节点分别赋予权重，以概率和概率分别选择节点和节 点，分别为的任意两个取值，在节点和节点之间加入一条连边，直到加完所有通 信连边为止，则生成的通信连接网络中节点的度满足如下关系： Assign weights to any node of the communication connection network composed of drones, and select nodes and nodes with probability and probability respectively. , are any two values of , respectively, add an edge between the node and the node until all the communication edges are added, then the degree of the nodes in the generated communication connection network satisfies the following relationship:

Figure 97552DEST_PATH_IMAGE067
Figure 97552DEST_PATH_IMAGE067

其中，

Figure 902697DEST_PATH_IMAGE068
表示任意一架无人机
Figure 31803DEST_PATH_IMAGE069
的通信连接数目，为任意一个节点的度；in,
Figure 902697DEST_PATH_IMAGE068
Represents any drone
Figure 31803DEST_PATH_IMAGE069
The number of communication connections for any node degree;

生成的通信连接网络具有幂率形式的度分布：The resulting network of communication connections has a degree distribution in the form of a power law:

Figure 148980DEST_PATH_IMAGE070
Figure 148980DEST_PATH_IMAGE070

其中：in:

Figure 707001DEST_PATH_IMAGE071
Figure 707001DEST_PATH_IMAGE071

通过控制参数

Figure 111568DEST_PATH_IMAGE072
，得到具有不同幂指数的无标度通信连接网络。Via control parameters
Figure 111568DEST_PATH_IMAGE072
, to obtain exponents with different powers The scale-free communication connection network.

本发明提供的上述无人机群鲁棒编队方法，建立无人机群编队控制模型，在考虑通信时延的情况下，给出每个无人机随时间变化的动力学公式，根据动力学公式推导无人机群编队鲁棒性与通信连接网络拓扑结构之间的关系，在无人机群总通信连接数目固定的情况下，生成具有不同幂指数的无标度通信连接网络，这些不同拓扑结构的通信连接网络总连边数是一样的，即建立无人机之间通信连接所消耗的总代价是一样的，区别是不同的通信连接网络具有不同的度分布，然后在通信时延存在的情况下，通过分析无人机群的编队鲁棒性与通信连接网络度分布之间的关系，得到鲁棒性最强的拓扑结构，在此基础上可以更好实现具有通信时延的鲁棒编队控制，在无人机群通信连接网络拓扑结构确定后，每个无人机可以获得与其具有通信连接的邻居无人机的飞行数据，包括邻居无人机的位置和速度信息等，在获得这些信息后，通过控制算法对当前无人机的运动进行控制，实现鲁棒编队飞行的效果。本发明能够在不增加建立通信连接代价的基础上，且在通信时延存在的情况下，实现无人机群的鲁棒编队控制，算法复杂度低，计算精度高，能够有效实现在通信受限条件下的无人机群鲁棒编队；并且，能够在空中复杂条件下实现无人机群的编队飞行，并针对实际存在的通信时延对编队控制的影响，提出一种鲁棒编队方法，这为无人机群编队鲁棒性的问题提出了一个新的解决方案；此外，在实现无人机群鲁棒编队的过程中，将理论算法与实际操作分开施行，先得到鲁棒的无人机群通信连接网络，再将这种网络拓扑结构运用到实际的无人机集群中，保障了无人机群在实现过程中的安全和高效，避免造成不必要的损失。本发明对于无人机群编队飞行的研究，可以保障无人机群飞行的安全和完成任务的高效，使得无人机群可以在更复杂的情况下实现自身功能，这对于无人机群更有效的使用具有重要意义。The above-mentioned robust formation method of the UAV swarm provided by the present invention establishes a formation control model of the UAV swarm, and under the condition of considering the communication delay, gives the dynamic formula of each UAV with time, and deduces it according to the dynamic formula The relationship between the robustness of the UAV swarm formation and the topology of the communication connection network. Under the condition that the total number of communication connections in the UAV swarm is fixed, a scale-free communication connection network with different power exponents is generated. The communication of these different topologies The total number of connections in the connection network is the same, that is, the total cost of establishing a communication connection between UAVs is the same. The difference is that different communication connection networks have different degree distributions, and then in the presence of communication delays , by analyzing the relationship between the formation robustness of the UAV swarm and the degree distribution of the communication connection network, the topological structure with the strongest robustness is obtained. On this basis, the robust formation control with communication delay can be better realized. After the topology of the communication connection network of the drone swarm is determined, each drone can obtain the flight data of the neighboring drones with which it has communication connections, including the position and speed information of the neighboring drones. The movement of the current UAV is controlled by the control algorithm to achieve the effect of robust formation flight. The invention can realize the robust formation control of the unmanned aerial vehicle group without increasing the cost of establishing a communication connection and in the presence of communication delay, with low algorithm complexity and high calculation accuracy, and can effectively realize the communication limitation Robust formation of UAV swarms under the conditions of the swarm; and can realize the formation flight of UAV swarms under complex air conditions, and according to the influence of the actual communication delay on formation control, a robust formation method is proposed, which is A new solution is proposed to the problem of the robustness of UAV swarm formation; in addition, in the process of realizing the robust formation of UAV swarms, the theoretical algorithm and practical operation are implemented separately, and a robust UAV swarm communication connection is obtained first. Network, and then apply this network topology to the actual UAV swarm, which ensures the safety and efficiency of the UAV swarm in the implementation process and avoids unnecessary losses. The research on the formation flight of the UAV group in the present invention can ensure the safety of the UAV group flight and the efficiency of completing the task, so that the UAV group can realize its own function in a more complicated situation, which has the advantages of more effective use of the UAV group. important meaning.

附图说明Description of drawings

图1为本发明提供的通信受限条件下的无人机群鲁棒编队方法的流程图；1 is a flowchart of a method for robust formation of a swarm of unmanned aerial vehicles under the condition of limited communication provided by the present invention;

图2为通信连接网络的

Figure 50892DEST_PATH_IMAGE056
随幂指数
Figure 643678DEST_PATH_IMAGE073
变化关系图。Figure 2 shows the communication connection network
Figure 50892DEST_PATH_IMAGE056
exponent
Figure 643678DEST_PATH_IMAGE073
Change graph.

具体实施方式Detailed ways

下面将结合本发明实施方式中的附图，对本发明实施方式中的技术方案进行清楚、完整的描述，显然，所描述的实施方式仅仅是作为例示，并非用于限制本发明。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are merely illustrative and not intended to limit the present invention.

本发明提供的一种通信受限条件下的无人机群鲁棒编队方法，如图1所示，包括如下步骤：A method for robust formation of UAV swarms under the condition of limited communication provided by the present invention, as shown in FIG. 1 , includes the following steps:

S1：建立无人机群编队控制模型，在考虑通信时延的情况下，给出无人机群中每个无人机随时间变化的动力学公式；S1: Establish the formation control model of the UAV swarm, and give the dynamic formula of each UAV in the UAV swarm over time while considering the communication delay;

S2：在动力学公式的基础上，推导出无人机群的编队鲁棒性与通信连接网络的拓扑结构之间的关系；S2: On the basis of the dynamic formula, deduce the relationship between the formation robustness of the UAV swarm and the topology of the communication connection network;

S3：在无人机群总通信连接数目固定的情况下，生成具有不同幂指数的无标度通信连接网络；S3: When the total number of communication connections in the UAV swarm is fixed, generate a scale-free communication connection network with different power exponents;

S4：计算各无标度通信连接网络的拓扑结构下无人机群的编队鲁棒性，得到鲁棒性最强的拓扑结构；S4: Calculate the formation robustness of the UAV swarm under the topology of each scale-free communication connection network, and obtain the most robust topology;

S5：在得到的鲁棒性最强的拓扑结构下进行无人机群编队飞行，实现在通信受限条件下无人机群的编队飞行。S5: Under the obtained topology with the strongest robustness, the formation flight of the UAV group is carried out, and the formation flight of the UAV group is realized under the condition of limited communication.

在具体实施时，在本发明提供的上述无人机群鲁棒编队方法中，步骤S1，建立无人机群编队控制模型，在考虑通信时延存在的情况下，给出无人机群中每个无人机随时间变化的动力学公式，具体包括：In specific implementation, in the above-mentioned robust formation method for UAV swarms provided by the present invention, in step S1, a formation control model for UAV swarms is established, and in the case of considering the existence of communication delay, each unmanned aerial vehicle swarm is given for each unmanned aerial vehicle swarm. The dynamic formula of man-machine changes with time, including:

无人机群中无人机的总数量为，若两架无人机之间可以互相通信，则通信连接网络中这两架无人机之间存在一条边，无人机之间通信连接的总边数为

Figure 915576DEST_PATH_IMAGE074
，对于无人机群中任意一架无人机
Figure 738039DEST_PATH_IMAGE002
，建立连续时间的动力学模型如下：The total number of drones in the drone swarm is , if the two UAVs can communicate with each other, there is an edge between the two UAVs in the communication connection network, and the total number of edges in the communication connection between the UAVs is
Figure 915576DEST_PATH_IMAGE074
, for any drone in the drone swarm
Figure 738039DEST_PATH_IMAGE002
, and the continuous-time kinetic model is established as follows:

Figure 818121DEST_PATH_IMAGE075
（1）
Figure 818121DEST_PATH_IMAGE075
(1)

其中，

Figure 17022DEST_PATH_IMAGE008
表示无人机
Figure 748217DEST_PATH_IMAGE003
在
Figure 741581DEST_PATH_IMAGE009
时刻的位置，是一个三维向量；
Figure 306030DEST_PATH_IMAGE076
表示在
Figure 308621DEST_PATH_IMAGE009
时刻对无人机
Figure 894323DEST_PATH_IMAGE003
施加的控制，使其在控制器的作用下完成下一时刻的飞行；最终目标是在控制器的作用下，所有无人机最终飞行到同一个位置，实现编队的控制要求；在不考虑通信时延的情况下，基础的控制器设计如下：in,
Figure 17022DEST_PATH_IMAGE008
Represents a drone
Figure 748217DEST_PATH_IMAGE003
exist
Figure 741581DEST_PATH_IMAGE009
The position of the moment is a three-dimensional vector;
Figure 306030DEST_PATH_IMAGE076
expressed in
Figure 308621DEST_PATH_IMAGE009
time to drone
Figure 894323DEST_PATH_IMAGE003
The applied control makes it complete the next moment of flight under the action of the controller; the ultimate goal is that under the action of the controller, all UAVs will eventually fly to the same position to achieve the control requirements of the formation; regardless of communication In the case of delay, the basic controller design is as follows:

Figure DEST_PATH_IMAGE077
（2）
Figure DEST_PATH_IMAGE077
(2)

其中，表示无人机在通信连接网络中的所有邻居，也就是与无人机

Figure 716283DEST_PATH_IMAGE003
有通信连接的其它无人机；
Figure 94175DEST_PATH_IMAGE005
为
Figure 507969DEST_PATH_IMAGE013
中的元素；需要说明的是，不考虑有向连边，也就是说，如果无人机
Figure 33629DEST_PATH_IMAGE003
可以获得无人机
Figure 378022DEST_PATH_IMAGE005
的信息，反之，无人机也可以获得无人机
Figure 195117DEST_PATH_IMAGE003
的信息。表示无人机
Figure 90578DEST_PATH_IMAGE003
和无人机
Figure 253181DEST_PATH_IMAGE005
之间的连接关系和连接强度，如果无人机
Figure 195729DEST_PATH_IMAGE003
和无人机
Figure 695981DEST_PATH_IMAGE005
无连接，则
Figure 382177DEST_PATH_IMAGE078
，如果无人机
Figure 402217DEST_PATH_IMAGE003
和无人机
Figure 515666DEST_PATH_IMAGE005
有连接，简化考虑，
Figure 503214DEST_PATH_IMAGE079
。以上两个公式（1）和（2）给出了在通信网络拓扑结构确定的情况下，无人机群编队控制的基础动力学公式；in, Represents a drone All neighbors in the communication network, that is, with the drone
Figure 716283DEST_PATH_IMAGE003
other drones with a communication connection;
Figure 94175DEST_PATH_IMAGE005
for
Figure 507969DEST_PATH_IMAGE013
elements in ; it should be noted that directed edges are not considered, that is, if the drone
Figure 33629DEST_PATH_IMAGE003
drones available
Figure 378022DEST_PATH_IMAGE005
information, and conversely, drones Drones are also available
Figure 195117DEST_PATH_IMAGE003
Information. Represents a drone
Figure 90578DEST_PATH_IMAGE003
and drones
Figure 253181DEST_PATH_IMAGE005
The connection relationship and connection strength between the drones
Figure 195729DEST_PATH_IMAGE003
and drones
Figure 695981DEST_PATH_IMAGE005
no connection, then
Figure 382177DEST_PATH_IMAGE078
, if the drone
Figure 402217DEST_PATH_IMAGE003
and drones
Figure 515666DEST_PATH_IMAGE005
There are connections, simplifying considerations,
Figure 503214DEST_PATH_IMAGE079
. The above two formulas (1) and (2) give the basic dynamic formula for the formation control of UAV swarms when the communication network topology is determined;

无人机

Figure 727522DEST_PATH_IMAGE003
的信号在通过通信信道
Figure 867647DEST_PATH_IMAGE004
到达无人机
Figure 886419DEST_PATH_IMAGE005
之前存在通信时延
Figure 361263DEST_PATH_IMAGE006
，存在通信时延的无人机群编队控制动力学公式如下：drone
Figure 727522DEST_PATH_IMAGE003
signal over the communication channel
Figure 867647DEST_PATH_IMAGE004
reach the drone
Figure 886419DEST_PATH_IMAGE005
There was communication delay before
Figure 361263DEST_PATH_IMAGE006
, the dynamic formula of UAV group formation control with communication delay is as follows:

Figure 389261DEST_PATH_IMAGE080
（3）
Figure 389261DEST_PATH_IMAGE080
(3)

其中，表示无人机

Figure 839146DEST_PATH_IMAGE005
在
Figure 535706DEST_PATH_IMAGE011
时刻的位置；表示无人机
Figure 213605DEST_PATH_IMAGE003
在
Figure 839758DEST_PATH_IMAGE011
时刻的位置。in, Represents a drone
Figure 839146DEST_PATH_IMAGE005
exist
Figure 535706DEST_PATH_IMAGE011
position at the moment; Represents a drone
Figure 213605DEST_PATH_IMAGE003
exist
Figure 839758DEST_PATH_IMAGE011
position at the moment.

在具体实施时，在本发明提供的上述无人机群鲁棒编队方法中，步骤S2，在动力学公式的基础上，推导出无人机群的编队鲁棒性与通信连接网络的拓扑结构之间的关系，具体包括：In specific implementation, in the above-mentioned method for robust formation of UAV swarms provided by the present invention, step S2, on the basis of the dynamic formula, deduces the relationship between the formation robustness of UAV swarms and the topology of the communication connection network relationship, including:

对动力学公式做拉普拉斯变换，得到：Laplace transform of the kinetic formula, we get:

Figure DEST_PATH_IMAGE081
（4）
Figure DEST_PATH_IMAGE081
(4)

其中，

Figure 23615DEST_PATH_IMAGE016
表示
Figure 940886DEST_PATH_IMAGE008
的拉普拉斯变换；
Figure 97061DEST_PATH_IMAGE017
表示
Figure 222012DEST_PATH_IMAGE018
的拉普拉斯变换，
Figure 830848DEST_PATH_IMAGE018
表示无人机
Figure 551810DEST_PATH_IMAGE005
在
Figure 562492DEST_PATH_IMAGE009
时刻的位置；
Figure 592764DEST_PATH_IMAGE019
表示初始时刻无人机
Figure 501946DEST_PATH_IMAGE003
的位置；表示与通信信道相关的转移函数，
Figure 90032DEST_PATH_IMAGE021
；得到：in,
Figure 23615DEST_PATH_IMAGE016
express
Figure 940886DEST_PATH_IMAGE008
Laplace transform of ;
Figure 97061DEST_PATH_IMAGE017
express
Figure 222012DEST_PATH_IMAGE018
The Laplace transform of ,
Figure 830848DEST_PATH_IMAGE018
Represents a drone
Figure 551810DEST_PATH_IMAGE005
exist
Figure 562492DEST_PATH_IMAGE009
position at the moment;
Figure 592764DEST_PATH_IMAGE019
Indicates the initial moment of the drone
Figure 501946DEST_PATH_IMAGE003
s position; Representation and Communication Channel The associated transfer function,
Figure 90032DEST_PATH_IMAGE021
;get:

Figure 673460DEST_PATH_IMAGE082
（5）
Figure 673460DEST_PATH_IMAGE082
(5)

其中，

Figure 251071DEST_PATH_IMAGE023
表示所有
Figure 970766DEST_PATH_IMAGE024
的拉普拉斯变换，
Figure 827994DEST_PATH_IMAGE024
表示
Figure 226615DEST_PATH_IMAGE009
时刻各无人机的位置；表示单位矩阵；
Figure 667272DEST_PATH_IMAGE026
表示初始时刻各无人机的位置；
Figure 475828DEST_PATH_IMAGE027
表示网络邻接矩阵的拉普拉斯矩阵；in,
Figure 251071DEST_PATH_IMAGE023
means all
Figure 970766DEST_PATH_IMAGE024
The Laplace transform of ,
Figure 827994DEST_PATH_IMAGE024
express
Figure 226615DEST_PATH_IMAGE009
The position of each drone at time; represents the identity matrix;
Figure 667272DEST_PATH_IMAGE026
Indicates the position of each UAV at the initial moment;
Figure 475828DEST_PATH_IMAGE027
Laplacian matrix representing the network adjacency matrix;

令，为了简化考虑，假设所有的通信时延都相等，

Figure 438416DEST_PATH_IMAGE030
，则
Figure DEST_PATH_IMAGE083
，因此，
Figure 929440DEST_PATH_IMAGE084
是一个不变量，且
Figure 945717DEST_PATH_IMAGE031
，得到：make , for simplicity, assuming that all communication delays are equal,
Figure 438416DEST_PATH_IMAGE030
,but
Figure DEST_PATH_IMAGE083
,therefore,
Figure 929440DEST_PATH_IMAGE084
is an invariant, and
Figure 945717DEST_PATH_IMAGE031
,get:

（6） (6)

其中，

Figure 917401DEST_PATH_IMAGE033
，
Figure 544822DEST_PATH_IMAGE034
表示网络邻接矩阵
Figure 367285DEST_PATH_IMAGE086
的拉普拉斯矩阵；in,
Figure 917401DEST_PATH_IMAGE033
,
Figure 544822DEST_PATH_IMAGE034
Represents the network adjacency matrix
Figure 367285DEST_PATH_IMAGE086
The Laplace matrix of ;

定义

Figure 962214DEST_PATH_IMAGE087
，令
Figure 161114DEST_PATH_IMAGE036
是矩阵
Figure 377463DEST_PATH_IMAGE034
的所有特征值按升序排列后第个特征值对应的特征向量，，
Figure 260920DEST_PATH_IMAGE038
是所有特征值按升序进行排列；对于一个连通图
Figure 690764DEST_PATH_IMAGE040
而言，其拉普拉斯矩阵的特征值有如下关系：，需要使
Figure 269830DEST_PATH_IMAGE042
，也就是说以下关系成立：definition
Figure 962214DEST_PATH_IMAGE087
,make
Figure 161114DEST_PATH_IMAGE036
is the matrix
Figure 377463DEST_PATH_IMAGE034
All eigenvalues of are sorted in ascending order after the first eigenvalues The corresponding eigenvectors, ,
Figure 260920DEST_PATH_IMAGE038
is that all eigenvalues are arranged in ascending order; for a connected graph
Figure 690764DEST_PATH_IMAGE040
In terms of , the eigenvalues of its Laplace matrix have the following relationship: , need to make
Figure 269830DEST_PATH_IMAGE042
, that is, the following relationship holds:

（7） (7)

分别令

Figure 324166DEST_PATH_IMAGE044
和代入公式（7），得到：Separate orders
Figure 324166DEST_PATH_IMAGE044
and into formula (7), we get:

Figure 849825DEST_PATH_IMAGE089
（8）
Figure 849825DEST_PATH_IMAGE089
(8)

Figure 928640DEST_PATH_IMAGE090
（9）
Figure 928640DEST_PATH_IMAGE090
(9)

将公式（8）和公式（9）的两边相乘，得到：Multiplying both sides of Equation (8) and Equation (9) gives:

Figure 239666DEST_PATH_IMAGE091
（10）
Figure 239666DEST_PATH_IMAGE091
(10)

化简得到：Simplify to get:

Figure 11313DEST_PATH_IMAGE092
（11）
Figure 11313DEST_PATH_IMAGE092
(11)

进一步得到：Further get:

Figure 24269DEST_PATH_IMAGE093
（12）
Figure 24269DEST_PATH_IMAGE093
(12)

因此，要求，

Figure 72307DEST_PATH_IMAGE052
，这就要求，因此需要满足对所有成立，因此： Therefore, it is required,
Figure 72307DEST_PATH_IMAGE052
, which requires and therefore needs to be satisfied for all true, therefore:

Figure 221343DEST_PATH_IMAGE094
（13）
Figure 221343DEST_PATH_IMAGE094
(13)

其中，

Figure 334792DEST_PATH_IMAGE056
为矩阵
Figure 322340DEST_PATH_IMAGE034
的最大特征值；这说明当无人机群的通信时延
Figure 546648DEST_PATH_IMAGE006
小于或等于
Figure 418265DEST_PATH_IMAGE057
时，可以实现鲁棒编队，并且，
Figure 702615DEST_PATH_IMAGE057
越大，鲁棒性越强。因此，下一步的工作是如何通过减小通信连接网络的
Figure 177459DEST_PATH_IMAGE056
来提高通信受限条件下的通信编队鲁棒性。in,
Figure 334792DEST_PATH_IMAGE056
is a matrix
Figure 322340DEST_PATH_IMAGE034
The largest eigenvalue of
Figure 546648DEST_PATH_IMAGE006
less than or equal to
Figure 418265DEST_PATH_IMAGE057
, robust formation can be achieved, and,
Figure 702615DEST_PATH_IMAGE057
The larger the value, the stronger the robustness. Therefore, the next step is how to connect the network by reducing the communication
Figure 177459DEST_PATH_IMAGE056
To improve the robustness of the communication formation under the condition of limited communication.

在具体实施时，在本发明提供的上述无人机群鲁棒编队方法中，步骤S3，在无人机群总通信连接数目固定的情况下，生成具有不同幂指数的无标度通信连接网络，具体包括：In specific implementation, in the above-mentioned robust formation method for UAV swarms provided by the present invention, step S3 is to generate scale-free communication connection networks with different power exponents under the condition that the total number of communication connections of the UAV swarm is fixed. include:

对个无人机组成的通信连接网络的任意一个节点

Figure 200090DEST_PATH_IMAGE059
赋予权重
Figure 389763DEST_PATH_IMAGE060
，以概率和概率
Figure 918013DEST_PATH_IMAGE062
分别选择节点
Figure 32731DEST_PATH_IMAGE063
和节点
Figure 393305DEST_PATH_IMAGE064
，分别为
Figure 212542DEST_PATH_IMAGE066
的任意两个取值，在节点
Figure 916187DEST_PATH_IMAGE063
和节点
Figure 713242DEST_PATH_IMAGE064
之间加入一条连边，如果已经有连边则重新选择节点，直到加完所有通信连边（即M条通信连边）为止，则生成的通信连接网络中节点的度满足如下关系：right Any node of the communication connection network composed of drones
Figure 200090DEST_PATH_IMAGE059
give weight
Figure 389763DEST_PATH_IMAGE060
, with probability and probability
Figure 918013DEST_PATH_IMAGE062
Select nodes individually
Figure 32731DEST_PATH_IMAGE063
and node
Figure 393305DEST_PATH_IMAGE064
, respectively
Figure 212542DEST_PATH_IMAGE066
Any two values of , at the node
Figure 916187DEST_PATH_IMAGE063
and node
Figure 713242DEST_PATH_IMAGE064
Add a connecting edge between them. If there is already a connecting edge, re-select the node until all communication connecting edges (that is, M communication connecting edges) are added. The degree of the nodes in the generated communication connection network satisfies the following relationship:

其中，

Figure 557887DEST_PATH_IMAGE068
表示任意一架无人机
Figure 378688DEST_PATH_IMAGE069
的通信连接数目，为任意一个节点
Figure 346644DEST_PATH_IMAGE059
的度；in,
Figure 557887DEST_PATH_IMAGE068
Represents any drone
Figure 378688DEST_PATH_IMAGE069
The number of communication connections for any node
Figure 346644DEST_PATH_IMAGE059
degree;

生成的通信连接网络具有幂率形式的度分布：The resulting network of communication connections has a degree distribution in the form of a power law:

Figure 505093DEST_PATH_IMAGE070
Figure 505093DEST_PATH_IMAGE070

其中：in:

Figure 216697DEST_PATH_IMAGE071
Figure 216697DEST_PATH_IMAGE071

因此，通过控制参数，可以得到不同幂指数

Figure 33791DEST_PATH_IMAGE073
的无标度通信连接网络，并且，可以保持总连边数不变，也就是建立不同通信连接网络所消耗的总代价是一样的。接下来就是在这些通信连接网络中发现
Figure 679536DEST_PATH_IMAGE056
值较小的通信连接网络，以增强在通信受限条件下的无人机群编队鲁棒性。Therefore, by controlling the parameters , you can get different power exponents
Figure 33791DEST_PATH_IMAGE073
The scale-free communication connection network, and the total number of connected edges can be kept unchanged, that is, the total cost of establishing different communication connection networks is the same. The next step is to find in these communication connection networks
Figure 679536DEST_PATH_IMAGE056
A communication connection network with a small value is used to enhance the robustness of the UAV swarm formation under communication-constrained conditions.

在具体实施时，在本发明提供的上述无人机群鲁棒编队方法中，步骤S4，计算各无标度通信连接网络的拓扑结构下无人机群的编队鲁棒性，得到鲁棒性最强的拓扑结构。可以通过幂指数的大小来衡量不同无标度通信连接网络的变化，具体地，一个无标度通信连接网络的

Figure 727575DEST_PATH_IMAGE073
值越大，通信连接网络中的节点度差异性越小，即通信连接网络越同质；一个无标度通信连接网络的
Figure 37334DEST_PATH_IMAGE073
值越小，通信连接网络中的节点度差异性越大，即通信连接网络越异质。由步骤S3得到的结果，通信受限条件下的无人机群编队鲁棒性可以利用通信连接网络的
Figure 170375DEST_PATH_IMAGE056
表示。在步骤S3中，通过一种配制方法生成具有不同幂指数
Figure 36831DEST_PATH_IMAGE073
的无标度通信连接网络，这些通信连接网络的总连边数是一样的，也就是说，建立这些通信连接网络所消耗的总代价是一样的，随这些通信连接网络的幂指数
Figure 357271DEST_PATH_IMAGE073
变化关系图如图2所示。由图2可以看出，无人机群通信连接网络的幂指数
Figure 712029DEST_PATH_IMAGE073
越大，通信连接网络的越小，在极端情况下，不同的
Figure 569126DEST_PATH_IMAGE056
之间甚至有将近十倍的差距，这说明在不同的通信网络连接下，在通信时延存在的情况下，不同的无人机群编队鲁棒性具有巨大的差异，因此，我们需要选择合适的通信连接网络来加速无人机群编队飞行。During specific implementation, in the above-mentioned method for robust formation of UAV swarms provided by the present invention, in step S4, the formation robustness of the UAV swarm under the topology structure of each scale-free communication connection network is calculated, and the strongest robustness is obtained. topology. power exponent to measure the variation of different scale-free communication connection networks, specifically, the size 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, that is, the more homogeneous the communication connection network is; the value of a scale-free communication connection network is
Figure 37334DEST_PATH_IMAGE073
The smaller the value, the greater the degree of node difference in the communication connection network, that is, the more heterogeneous the communication connection network. From the result obtained in step S3, the robustness of the UAV swarm formation under the condition of limited communication can use the communication connection network.
Figure 170375DEST_PATH_IMAGE056
express. In step S3, a compounding method is used to generate exponents with different powers
Figure 36831DEST_PATH_IMAGE073
The scale-free communication connection network, the total number of edges of these communication connection networks is the same, that is to say, the total cost of establishing these communication connection networks is the same, The power exponent of the network connected with these communications
Figure 357271DEST_PATH_IMAGE073
The change relationship diagram is shown in Figure 2. As can be seen from Figure 2, the power exponent of the UAV swarm communication connection network
Figure 712029DEST_PATH_IMAGE073
The larger, the smaller the communication connection network, and in extreme cases, different
Figure 569126DEST_PATH_IMAGE056
There is even a nearly ten-fold gap between them, which shows that under different communication network connections and in the presence of communication delays, the robustness of different UAV swarm formations has huge differences. Therefore, we need to choose a suitable Communication links the network to speed up swarms of drones flying in formation.

在具体实施时，在本发明提供的上述无人机群鲁棒编队方法中，步骤S5，在得到的鲁棒性最强的拓扑结构下进行无人机群编队飞行，实现在通信受限条件下无人机群的编队飞行。在无人机群通信连接网络总连边数不变的情况下，尽量生成幂指数

Figure 73532DEST_PATH_IMAGE073
较大的无标度通信连接网络拓扑结构，也就是说，通信连接网络拓扑结构更加同质，以减小通信连接网络的
Figure 725093DEST_PATH_IMAGE056
，从而可以更好地实现在通信受限条件下无人机群的鲁棒编队飞行。在通信受限条件下实现无人机群的鲁棒编队，可以使无人机在飞行过程中更高效地达到编队效果并保持队形，减小能源消耗，提高飞行效率，并为无人机的后续操作提供便利，具有积极的意义。In specific implementation, in the above-mentioned robust formation method for UAV swarms provided by the present invention, in step S5, the UAV swarm formation flight is carried out under the obtained topology with the strongest robustness, so as to achieve no communication under the condition of limited communication. Formation flight of a swarm of people. Under the condition that the total number of connections in the UAV swarm communication network remains unchanged, try to generate a power exponent
Figure 73532DEST_PATH_IMAGE073
Larger scale-free communication connection network topology, that is, communication connection network topology is more homogeneous to reduce the communication connection network topology.
Figure 725093DEST_PATH_IMAGE056
, which can better realize the robust formation flight of UAV swarms under the condition of limited communication. Realizing the robust formation of the UAV swarm under the condition of limited communication can make the UAV achieve the formation effect more efficiently and maintain the formation during the flight process, reduce energy consumption, improve the flight efficiency, and provide for the UAV's flight. Subsequent operations provide convenience and have a positive meaning.

本发明提供的上述无人机群鲁棒编队方法，无人机群中的每个无人机可以获取具有通信连接的邻居无人机的飞行状态信息，由于通信时延的存在，无人机获得的数据实际上是邻居无人机在一小段时间之前的飞行位置和速度信息。在获取这些信息后，当前无人机在控制器的作用下向邻居无人机的中心位置飞行，从而实现编队控制的效果。无人机之间的通信连接可以利用网络拓扑结构来表示，在通信时延存在的情况下，推导出无人机群的编队鲁棒性与通信连接网络的某些参数有关。在总的通信连接数目不变的情况下，生成具有不同幂指数的无标度通信网络，然后探究在通信时延存在的情况下，无人机群编队鲁棒性与通信连接网络幂指数之间的关系，以保留鲁棒性强的通信连接网络，实现编队的效果，最终目的是使所有无人机按照统一的位置和速度方向飞行。According to the above-mentioned robust formation method for UAV swarms provided by the present invention, each UAV in the UAV swarm can obtain the flight status information of neighboring UAVs with communication connections. The data is actually information about the flying position and speed of the neighbor drones a short period of time ago. After obtaining this information, the current UAV flies to the center of the neighboring UAV under the action of the controller, so as to realize the effect of formation control. The communication connection between UAVs can be represented by the network topology. In the presence of communication delay, it is deduced that the formation robustness of the UAV swarm is related to some parameters of the communication connection network. Under the condition that the total number of communication connections remains unchanged, scale-free communication networks with different power exponents are generated, and then the relationship between the robustness of the UAV swarm formation and the power exponent of the communication connection network in the presence of communication delay is explored. In order to retain a robust communication connection network and achieve the effect of formation, the ultimate goal is to make all UAVs fly in a unified position and speed direction.

本发明提供的上述无人机群鲁棒编队方法，建立无人机群编队控制模型，在考虑通信时延的情况下，给出每个无人机随时间变化的动力学公式，根据动力学公式推导无人机群编队鲁棒性与通信连接网络拓扑结构之间的关系，在无人机群总通信连接数目固定的情况下，生成具有不同幂指数的无标度通信连接网络，这些不同拓扑结构的通信连接网络总连边数是一样的，即建立无人机之间通信连接所消耗的总代价是一样的，区别是不同的通信连接网络具有不同的度分布，然后在通信时延存在的情况下，通过分析无人机群的编队鲁棒性与通信连接网络度分布之间的关系，得到鲁棒性最强的拓扑结构，在此基础上可以更好实现具有通信时延的鲁棒编队控制，在无人机群通信连接网络拓扑结构确定后，每个无人机可以获得与其具有通信连接的邻居无人机的飞行数据，包括邻居无人机的位置和速度信息等，在获得这些信息后，通过控制算法对当前无人机的运动进行控制，实现鲁棒编队飞行的效果。本发明能够在不增加建立通信连接代价的基础上，且在通信时延存在的情况下，实现无人机群的鲁棒编队控制，算法复杂度低，计算精度高，能够有效实现在通信受限条件下的无人机群鲁棒编队；并且，能够在空中复杂条件下实现无人机群的编队飞行，并针对实际存在的通信时延对编队控制的影响，提出一种鲁棒编队方法，这为无人机群编队鲁棒性的问题提出了一个新的解决方案；此外，在实现无人机群鲁棒编队的过程中，将理论算法与实际操作分开施行，先得到鲁棒的无人机群通信连接网络，再将这种网络拓扑结构运用到实际的无人机集群中，保障了无人机群在实现过程中的安全和高效，避免造成不必要的损失。本发明对于无人机群编队飞行的研究，可以保障无人机群飞行的安全和完成任务的高效，使得无人机群可以在更复杂的情况下实现自身功能，这对于无人机群更有效的使用具有重要意义。The above-mentioned robust formation method of the UAV swarm provided by the present invention establishes a formation control model of the UAV swarm, and under the condition of considering the communication delay, gives the dynamic formula of each UAV with time, and deduces it according to the dynamic formula The relationship between the robustness of the UAV swarm formation and the topology of the communication connection network. Under the condition that the total number of communication connections in the UAV swarm is fixed, a scale-free communication connection network with different power exponents is generated. The communication of these different topologies The total number of connections in the connection network is the same, that is, the total cost of establishing a communication connection between UAVs is the same. The difference is that different communication connection networks have different degree distributions, and then in the presence of communication delays , by analyzing the relationship between the formation robustness of the UAV swarm and the degree distribution of the communication connection network, the topological structure with the strongest robustness is obtained. On this basis, the robust formation control with communication delay can be better realized. After the topology of the communication connection network of the drone swarm is determined, each drone can obtain the flight data of the neighboring drones with which it has communication connections, including the position and speed information of the neighboring drones. The movement of the current UAV is controlled by the control algorithm to achieve the effect of robust formation flight. The invention can realize the robust formation control of the unmanned aerial vehicle group without increasing the cost of establishing a communication connection and in the presence of communication delay, with low algorithm complexity and high calculation accuracy, and can effectively realize the communication limitation Robust formation of UAV swarms under the conditions of the swarm; and can realize the formation flight of UAV swarms under complex air conditions, and according to the influence of the actual communication delay on formation control, a robust formation method is proposed, which is A new solution is proposed to the problem of the robustness of UAV swarm formation; in addition, in the process of realizing the robust formation of UAV swarms, the theoretical algorithm and practical operation are implemented separately, and a robust UAV swarm communication connection is obtained first. Network, and then apply this network topology to the actual UAV swarm, which ensures the safety and efficiency of the UAV swarm in the implementation process and avoids unnecessary losses. The research on the formation flight of the UAV group in the present invention can ensure the safety of the UAV group flight and the efficiency of completing the task, so that the UAV group can realize its own function in a more complicated situation, which has the advantages of more effective use of the UAV group. important meaning.

显然，本领域的技术人员可以对本发明进行各种改动和变型而不脱离本发明的精神和范围。这样，倘若本发明的这些修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit and scope of the invention. Thus, provided that these 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 these 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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