CN110807248A - Grouping judgment method for spacecraft cluster - Google Patents

Abstract

The invention discloses a method for judging the clustering of spacecraft clusters, which comprises the following steps: 1, inputting an inter-satellite communication relation, and establishing a communication topology subgraph among multiple spacecrafts; 2, inputting relative navigation relations and establishing relative navigation topological subgraphs among the multiple spacecrafts; 3, combining the communication topological subgraph and the relative navigation topological subgraph to construct an information topological graph among the multiple spacecrafts; and 4, constructing an adjacent matrix corresponding to the information topological graph, and judging whether the multiple spacecrafts are clustered or not through existence of the directed spanning tree. The judgment method established by the invention considers the essential equivalence of inter-satellite communication and relative navigation in the problem of cluster formation of multiple spacecrafts, thereby being more suitable for the practical application of spacecraft clusters.

Description

A method for swarm determination of spacecraft swarms

technical field

The invention relates to the technical field of aerospace, in particular to a method for judging group conditions of spacecraft clusters.

Background technique

Spacecraft cluster is a new concept of distributed satellite system in the aerospace field in recent years. Typical spacecraft cluster flight plans include the F6 plan of the United States and the SAMSON plan of Israel. Although the concept of a spacecraft swarm has been around for nearly a decade, the definition of a swarm remains vague. In the description system of existing spacecraft clusters, clusters are usually defined as a group of spacecraft that "fly at close range". In engineering practice, however, there are often spacecraft that, despite their close proximity, do not actually belong to the same cluster. Conversely, even though some spacecraft are far apart from each other, they are able to maintain information communication through the "multi-hop" of inter-spacecraft communication and thus remain essentially the same cluster. This shows that it is not rigorous to use distance to define whether multiple spacecraft belong to the same cluster. For this reason, some literature proposes to define a spacecraft cluster as "a multi-spacecraft distributed system formed by the interconnection of inter-satellite wireless communication networks". But such a definition is still problematic, because inter-satellite communication is not a necessary and sufficient condition to form a cluster. Existing literature points out that the use of relative navigation to replace part or all of the inter-satellite communication can also achieve swarm flight. In-depth analysis of the current research status shows that the main reason for the vague and inaccurate definition of clusters is that there is no method for judging clusters of multiple spacecraft. The so-called swarm, that is, multiple spacecraft form the same cluster. Due to the lack of such a swarm condition judgment method, there are many difficulties in the on-orbit application of spacecraft swarms.

In order to overcome the above problems, it is necessary to establish an effective multi-spacecraft group determination method, through the mathematical quantitative calculation of the multi-spacecraft information interaction topology to realize the quantitative determination of whether the multi-spacecraft is in a group or not, so as to provide a basis for the spacecraft cluster. Lay the groundwork for on-orbit applications of flight.

SUMMARY OF THE INVENTION

Aiming at the problem that the multi-spacecraft cluster determination cannot be effectively completed in the prior art, the purpose of the present invention is to provide a cluster determination method for a spacecraft cluster. Theoretical basis, so as to solve the difficulty of quantitatively determining whether multiple spacecraft belong to the same cluster in the existing technology.

In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

A swarm determination method for a spacecraft swarm, comprising the following steps:

S1, obtain the inter-satellite communication relationship, and establish a communication topology subgraph between multiple spacecraft;

S2, obtain a relative navigation relationship, and establish a relative navigation topology subgraph among multiple spacecraft;

S3, combine the communication topology sub-map and the relative navigation topology sub-map to construct an information topology map between multiple spacecraft;

S4, construct the adjacency matrix corresponding to the information topology graph, and determine whether the multi-spacecraft is in a group through the existence of the directed spanning tree.

The communication topology subgraph in the S1 is a binary group G ₁ (V, E ₁ ) that is jointly formed by a node set V composed of nodes representing spacecraft serial numbers and an edge set E ₁ with an inter-satellite communication relationship;

Among them, the node set V={v _i |i=1,...,N} of the communication topology subgraph, where N is the number of spacecraft, and v _i represents the node, which is a natural number from 1 to N; the edge of the communication topology subgraph Set E ₁ ={e _ij |(vi ∈V; v _j ∈ V; i≠ _j )}, where edge e _ij indicates whether node v _i points to v _j for unidirectional communication, and if so, edge e _ij =1 , otherwise e _ij =0.

The relative navigation topology subgraph in S2 is a binary group G ₂ (V, E ₂ ) formed by the joint formation of a node set V composed of nodes representing the spacecraft serial numbers and an edge set E ₂ with a relative navigation relationship;

Among them, the node set of the relative navigation topology subgraph is the same as the node set of the communication topology subgraph, and the edge set of the relative navigation topology subgraph E ₂ ={e _ij |(vi ∈V; v _j ∈V; i≠ _j ) }, where edge e _ij represents whether node v _j has performed relative navigation measurement to node v _i , if so, edge e _ij =1, otherwise e _ij =0.

The information topology graph G(V, E) in S3 is the combination of the communication topology subgraph and the relative navigation topology subgraph, that is, G=G ₁ ∪ G ₂ .

The node set of the information topology graph is equivalent to the node set of the communication topology subgraph, and it is also equivalent to the node set of the relative navigation topology subgraph.

The union formed by the edge set E ₁ of the communication topology graph and the edge set E ₂ of the relative navigation graph constitutes the edge set of the information topology graph, that is, E=E ₁ ∪ E ₂ .

The adjacency matrix A of the information topology map in S4 is an N-order square matrix corresponding to the information topology map G(V, E) one-to-one; the elements a _ij in the i-th row and the j-th column on the off-diagonal =e _ij (i≠j), the elements on the diagonal a _ii =0(vi _∈V ).

Whether the multiple spacecraft belong to the same cluster is determined by whether the information topology graph G contains a directed spanning tree:

When G contains a directed spanning tree, N spacecraft belong to the same cluster; when G does not contain a directed spanning tree, N spacecraft do not belong to the same cluster.

Whether the information topology graph G contains a directed spanning tree is determined by the adjacency matrix A, and the specific determination steps are as follows:

S401, calculate the 1-N-1 order power of the matrix A: A, A ² , A ³ , ..., A ^N-1 ;

S402, sum all N-1 order powers to obtain a power sum matrix

S403, check all elements of the _sum matrix A∑:

则信息拓扑图G包含有向生成树；若对于任意一行，总是存在某个非对角线元素为零，则信息拓扑图G不包含有向生成树。If there is a row (denoted as the jth row, 1≤j≤N), all elements except the diagonal are greater than zero, that is

Then the information topology graph G contains a directed spanning tree; if for any row, there is always a non-diagonal element that is zero, then the information topology graph G does not contain a directed spanning tree.

Compared with the prior art, the present invention has the following advantages:

The invention firstly constructs the information topology map among multiple spacecraft by combining the communication topology submap and the relative navigation topology submap, then constructs the adjacency matrix corresponding to the information topology map, and further calculates the existence of the directed spanning tree through the adjacency matrix and calculates the existence of the directed spanning tree according to the data. This determines whether multiple spacecraft are swarmed. This method gives the steps of quantitative calculation, so it overcomes the difficulty that the existing literature cannot quantitatively judge whether multiple spacecraft belong to the same cluster. In addition, this method makes full use of the equivalence between the adjacency matrix and the topological relationship in the specific calculation process, so the difficult problem of judging whether there is a spanning tree in the topology is transformed into the problem of finding whether there are off-diagonal zero elements in the power sum matrix. Simple question. Therefore, this method can quickly and quantitatively determine whether multiple spacecraft with complex information interaction relationships belong to the same cluster, thereby laying a theoretical foundation for clearly defining clusters and designing cluster collaborative control methods. The determination method established by the present invention also considers the essential equivalence of inter-satellite communication and relative navigation in the problem of multi-spacecraft cluster formation, so it is more suitable for the practical application of spacecraft clusters.

Description of drawings

1 is a schematic flowchart of a method for determining a group of a spacecraft cluster according to the present invention;

Fig. 2 is the inter-satellite communication and relative navigation relationship of three spacecraft in the specific embodiment;

Fig. 3 is the inter-satellite communication topology subgraph of three spacecraft in the specific embodiment;

Fig. 4 is the relative navigation topology subgraph of three spacecraft in the specific embodiment;

FIG. 5 is an information topology diagram of three spacecraft in a specific embodiment.

Detailed ways

In order to make those skilled in the art better understand the technical solutions of the present invention, 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 The embodiments are only some of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terms used herein in the description of the present invention are for the purpose of describing specific embodiments only, and are not intended to limit the present invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

As shown in FIG. 1 , a method for judging groups of spacecraft clusters of the present invention includes the following steps:

Step 1, enter the inter-satellite communication relationship, and establish a communication topology subgraph between multiple spacecraft;

Step 2, input the relative navigation relationship, and establish the relative navigation topology subgraph between multiple spacecraft;

Step 3, combine the communication topology sub-map and the relative navigation topology sub-map to construct an information topology map between multiple spacecraft;

Step 4, construct an adjacency matrix corresponding to the information topology graph, and determine whether multiple spacecraft are grouped by the existence of a directed spanning tree.

As a preferred embodiment, the communication topology subgraph in the step _{1 is a binary group G 1 (} V ,E1 ₎ .

Among them, the node set V={v _i |i=1,...,N} of the communication topology subgraph, where N is the number of spacecraft, and v _i represents nodes, which are natural numbers from 1 to N. The edge set E ₁ ={e _ij |(vi ∈V; v _j ∈ V; i≠ _j )} of the communication topology subgraph, where the edge e _ij indicates whether the node v _i points to v _j for one-way communication, and if so Then edge e _ij =1, otherwise e _ij =0.

As a preferred embodiment, the relative navigation topology subgraph in step _{2 is a binary group G 2 (} V , _E2 ).

The node set of the relative navigation topology subgraph is the same as the node set of the communication topology subgraph.

The edge set E ₂ ={e _ij |(vi ∈V; v _j ∈ V; i≠ _j )} of the relative navigation topology subgraph, where the edge e _ij represents whether the node v _j has performed relative navigation measurements to the node v _i , if the edge e _ij =1, otherwise e _ij =0.

As a preferred embodiment, the information topology graph G(V, E) in the step 3 is a combination of the communication topology subgraph and the relative navigation topology subgraph, that is, G=G ₁ ∪ G ₂ .

Preferably, the node set of the information topology graph is equivalent to the node set of the communication topology subgraph, and is also equivalent to the node set of the relative navigation topology subgraph. The union formed by the edge set E ₁ of the communication graph and the edge set E ₂ of the relative navigation graph constitutes the edge set of the information topology graph, that is, E=E ₁ ∪ E ₂ .

As a preferred embodiment, the adjacency matrix A of the information topology map in the step 4 is an N-order square matrix corresponding to the information topology map G(V, E) one-to-one; The element in the jth column a _ij =e _ij (i≠j), the element on the diagonal a _ii =0 (vi _∈V ).

Preferably, whether the N spacecraft belong to the same cluster is determined by whether the information topology graph G includes a directed spanning tree; when G includes a directed spanning tree, N spacecraft belong to the same cluster; when G does not include a directed spanning tree In a directed spanning tree, N spacecraft do not belong to the same cluster.

Preferably, whether the information topology graph G contains a directed spanning tree is determined by the adjacency matrix A; the steps of its determination are as follows:

S1, calculate the 1-N-1 order power of the matrix A: A, A ² , A ³ , ..., A ^N-1 ;

S2, sum all N-1 order powers to get the power sum matrix

则信息拓扑图G包含有向生成树；若对于任意一行，总是存在某个非对角线元素为零，则信息拓扑图G不包含有向生成树。S3, check all elements of the sum matrix A _∑ ; if there is a row (denoted as the jth row, 1≤j≤N), all elements except the diagonal are greater than zero, that is

Then the information topology graph G contains a directed spanning tree; if for any row, there is always a non-diagonal element that is zero, then the information topology graph G does not contain a directed spanning tree.

Example 1

As shown in Figure 2, the inter-satellite communication relationship of the three spacecraft is: two-way communication is possible between spacecraft 1 and 3, but spacecraft 2 does not communicate with other spacecraft; the relative navigation relationship of the three spacecraft For: spacecraft 1 and 3 can respectively perform relative navigation measurements on spacecraft 2. The method of the present invention is used below to determine whether the three spacecraft form the same cluster.

Step 1, according to the inter-satellite communication relationship, a communication topology subgraph G ₁ (V, E ₁ ) can be established as shown in FIG. 3 . Wherein, V={1,2,3}, E1 ₌ { _e13 , _e31 }.

Step 2, according to the relative navigation relationship, a relative navigation topology subgraph can be established as shown in FIG. 4 . where, V={1,2,3}, E ₂ ={e ₂₁ ,e ₂₃ }

In step 3, the communication topology subgraph and the relative navigation topology subgraph are combined to obtain the information topology graph as shown in FIG. 5 . Wherein, V={1, 2, 3}, E=E ₁ ∪ E ₂ ={e ₁₃ , e ₃₁ , e ₂₁ , e ₂₃ }.

Step 4, according to the specific form of the information topology diagram in Figure 5, the adjacency matrix is obtained as:

Further, determine whether the information topology graph G contains a directed spanning tree according to the following method:

S1, calculate the 1st to 2nd order power of matrix A:

S2, sum all 2nd order powers to get the sum matrix

S3, check all elements a _∑,ij (i∈V; j∈V; i≠j) of the matrix A _∑ except the diagonal elements; since all elements in the second row except the diagonal elements are greater than zero, so The information topology graph G contains a directed spanning tree.

Since the information topology graph G contains a directed spanning tree, the above three spacecraft form clusters based on the given inter-satellite communication and relative navigation interactions.

In order to further illustrate the beneficial effect of the method of the present invention, in step 4, group judgment is performed on the other two hypothetical situations.

The first assumption is that the above three spacecraft only have inter-satellite communication (as shown by the solid arrows in Figure 2),

The second hypothetical situation is that the above three spacecraft only have relative navigation (as shown by the dashed arrows in Figure 2).

Using the judgment method of the present invention, the obtained results are shown in Table 1. From the results in the table, it can be seen that the two hypothetical situations cannot be grouped. From this result, the following conclusions can be drawn: it is more accurate to use the information topology map to describe whether clusters are clustered; and when pure inter-satellite communication or pure relative navigation cannot be clustered, the two types of information transmission methods can be combined to complete cluster formation. group. It can be seen that the group determination method of the present invention is closer to the practical application of engineering, and has good use benefits.

Table 1. Clustering results under two hypothetical situations calculated by the method of the present invention

Through the above embodiments, the determination method established by the present invention can be obtained, and the essential equivalence of inter-satellite communication and relative navigation in the multi-spacecraft cluster formation problem can be considered, so it is more suitable for the practical application of spacecraft clusters.

The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be It is regarded as the protection scope of the present invention.

Claims (9)

1. a group determination method of spacecraft cluster, is characterized in that, comprises the steps as follows: S1, obtain the inter-satellite communication relationship, and establish a communication topology subgraph between multiple spacecraft; S2, obtain a relative navigation relationship, and establish a relative navigation topology subgraph among multiple spacecraft; S3, combine the communication topology sub-map and the relative navigation topology sub-map to construct an information topology map between multiple spacecraft; S4, construct the adjacency matrix corresponding to the information topology graph, and determine whether the multi-spacecraft is in a group through the existence of the directed spanning tree. 2. The method for group determination of a spacecraft cluster according to claim 1, wherein the communication topology subgraph in the S1 is a node set V composed of nodes representing the spacecraft serial numbers and a set of nodes with inter-satellite numbers. A binary group G ₁ (V, E ₁ ) formed by the joint set of edges E ₁ of the communication relationship; Among them, the node set V={v _i |i=1,...,N} of the communication topology subgraph, where N is the number of spacecraft, and v _i represents the node, which is a natural number from 1 to N; the edge of the communication topology subgraph Set E ₁ ={e _ij |(vi ∈V; v _j ∈ V; i≠ _j )}, where edge e _ij indicates whether node v _i points to v _j for unidirectional communication, and if so, edge e _ij =1 , otherwise e _ij =0. 3. The method for group determination of a spacecraft cluster according to claim 1, wherein the relative navigation topology subgraph in S2 is a node set V composed of nodes representing spacecraft serial numbers and a relative navigation topology sub-graph. A binary group G ₂ (V, E ₂ ) formed by the joint set of edges E ₂ of the navigation relation; Among them, the node set of the relative navigation topology subgraph is the same as the node set of the communication topology subgraph, and the edge set of the relative navigation topology subgraph E ₂ ={e _ij |(vi ∈V; v _j ∈V; i≠ _j ) }, where edge e _ij represents whether node v _j has performed relative navigation measurement to node v _i , if so, edge e _ij =1, otherwise e _ij =0. 4. The method for grouping determination of a spacecraft cluster according to claim 1, wherein the information topology graph G(V, E) in the S3 is the communication topology subgraph and the relative navigation topology subgraph. Union, ie G=G ₁ ∪ G ₂ . 5. the method for grouping determination of a kind of spacecraft cluster according to claim 4 is characterized in that, the node set of the information topology graph is equivalent to the node set of the communication topology subgraph, and is also equivalent to the relative navigation topology subgraph set of nodes. 6. The method for grouping determination of a spacecraft cluster according to claim 4, wherein the combination formed by the edge set E ₁ of the communication topology graph and the edge set E ₂ of the relative navigation graph constitutes the information topology graph. The set of edges, that is, E=E ₁ ∪ E ₂ . 7. The method for grouping determination of a spacecraft cluster according to claim 1, wherein the adjacency matrix A of the information topology graph in the S4 is one-to-one with the information topology graph G(V, E). The corresponding N-order square matrix; its off-diagonal element a _ij = e _ij (i≠j) in the i-th row and j-th column, and the diagonal element a _ii =0 (vi _∈V ). 8. The method for group determination of a spacecraft cluster according to claim 1, wherein whether the multiple spacecraft belong to the same cluster is determined by whether the information topology graph G contains a directed spanning tree: When G contains a directed spanning tree, N spacecraft belong to the same cluster; when G does not contain a directed spanning tree, N spacecraft do not belong to the same cluster. 9. The method for group determination of a spacecraft cluster according to claim 8, wherein whether the information topology graph G contains a directed spanning tree is determined by an adjacency matrix A, and the concrete determination steps are as follows : S401, calculate the 1-N-1 order power of the matrix A: A, A ² , A ³ , ..., A ^N-1 ; S402, sum all N-1 order powers to obtain a power sum matrix

S403, check all elements of the _sum matrix A∑: If there is a row (denoted as the jth row, 1≤j≤N), all elements except the diagonal are greater than zero, that is

Then the information topology graph G contains a directed spanning tree; if for any row, there is always a non-diagonal element that is zero, then the information topology graph G does not contain a directed spanning tree.

Images