CN110807248A - Grouping judgment method for spacecraft cluster - Google Patents
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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
Technical Field
The invention relates to the technical field of aerospace, in particular to a method for judging grouping conditions of a spacecraft cluster.
Background
Spacecraft clustering is a distributed satellite system concept emerging in the aerospace field in recent years. Typical spacecraft cluster flight plans are the U.S. F6 plan, Israel's SAMSON plan, and the like. Although the concept of spacecraft clustering has been in progress for nearly a decade, the definition of clusters is still ambiguous. In the description of existing spacecraft clusters, a cluster is generally defined as a cluster of "close-range flying" spacecraft. However, in engineering practice, it is often the case that the spacecraft, although in close proximity, do not actually belong to the same cluster. In contrast, even if some spacecraft are far from each other, they can keep information communicating through "hops" of inter-spacecraft communications, and thus remain essentially the same cluster. This means that it is not strict to use distance to define whether multiple space vehicles belong to the same cluster. For this purpose, the literature proposes defining spacecraft clusters as "multi-spacecraft distributed systems interconnected by an inter-satellite wireless communication network". However, such a definition is problematic because inter-satellite communications are not an essential condition for clustering. It has been documented that cluster flight can also be achieved using relative navigation instead of some or all of the inter-satellite communications. The current research situation is deeply analyzed, and the main reason for causing fuzzy and inaccurate cluster definition is that a judgment method for clustering multiple spacecrafts is not provided. So-called clustering, i.e. a plurality of spacecraft form one and the same cluster. Due to the lack of such a clustering condition judgment method, there are difficulties in on-orbit application of spacecraft clustering.
In order to overcome the problems, an effective method for judging the clustering of the multiple spacecrafts is needed to be established, and the quantitative judgment on whether the multiple spacecrafts are clustered or not is realized through the mathematical quantitative calculation of the information interaction topology of the multiple spacecrafts, so that a foundation is laid for the on-orbit application of the clustered flight of the spacecrafts.
Disclosure of Invention
The method provides a necessary theoretical basis for on-orbit application of the spacecraft cluster, and solves the problem that whether a plurality of spacecrafts belong to the same cluster cannot be determined quantitatively in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for judging the clustering of spacecraft clusters comprises the following steps:
s1, acquiring an inter-satellite communication relation, and establishing a communication topology subgraph among multiple spacecrafts;
s2, acquiring a relative navigation relation, and establishing a relative navigation topological subgraph among the multiple spacecrafts;
s3, combining the communication topological subgraph and the relative navigation topological subgraph to construct an information topological graph among the multiple spacecrafts;
and S4, constructing an adjacency 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 communication topology subgraph in S1 is a node set V formed by nodes representing spacecraft sequence numbers and an edge set E with an inter-satellite communication relationship1Jointly formed doublet G1(V,E1);
Wherein, the node set V ═ { V ═ of the communication topology subgraphi1, …, N, where N is the number of spacecraft, viRepresenting nodes which are natural numbers from 1 to N; edge set E of communication topology subgraph1={eij|(vi∈V;vjE is V; i ≠ j) }, where edge eijRepresenting a node viWhether or not to point to vjPerforming one-way communication, if yes, then the edge eij1, otherwise eij=0。
The relative navigation topological subgraph in S2 is a node set V formed by nodes representing spacecraft sequence numbers and an edge set E with relative navigation relation2Jointly formed doublet G2(V,E2);
Wherein, the node set of the relative navigation topological subgraph is the same as the node set of the communication topological subgraph, and the edge set E of the relative navigation topological subgraph2={eij|(vi∈V;vjE is V; i ≠ j) }, where edge eijRepresenting a node vjWhether it is for node viPerforming relative navigation measurement, if yes, determining edge eij1, otherwise eij=0。
The information topology graph G (V, E) in S3 is a union of the communication topology subgraph and the relative navigation topology subgraph, i.e. G ═ G1∪G2。
The node set of the information topological graph is equivalent to the node set of the communication topological subgraph and is also equivalent to the node set of the relative navigation topological subgraph.
Edge set E of communication topology graph1With respect to the set of edges E of the navigation map2The formed union constitutes the edge set of the information topology, i.e. E ═ E1∪E2。
The adjacency matrix a of the information topological graph in S4 is an N-th order square matrix corresponding to the information topological graph G (V, E) one to one; the element a of the ith row and the jth column on the off-diagonal lineij=eij(i ≠ j), element a on the diagonalii=0(vi∈V)。
Whether the multiple spacecrafts belong to the same cluster is determined by whether the information topological graph G contains a directed spanning tree or not:
when G comprises the directed spanning tree, N spacecrafts belong to the same cluster; and when G does not contain the directed spanning tree, the N spacecrafts do not belong to the same cluster.
Whether the information topological graph G contains the directed spanning tree is judged through the adjacency matrix A, and the specific judgment steps are as follows:
s401, calculating the power of 1-N-1 order of the matrix A: A. a. the2、A3、……、AN-1;
S403, checking and matrix A∑All elements of (a):
if a row (denoted as jth row, j 1. ltoreq. N) exists, all elements except the diagonal are greater than zero, i.e.The information topological graph G comprises a directed spanning tree; if there is always some off-diagonal element as zero for any row, the information topology G does not contain a directed spanning tree.
Compared with the prior art, the invention has the following advantages:
according to the method, firstly, an information topological graph among the multiple spacecrafts is constructed by combining a communication topological subgraph and a relative navigation topological subgraph, then an adjacent matrix corresponding to the information topological graph is constructed, and the existence of a directed spanning tree is further calculated through the adjacent matrix, so that whether the multiple spacecrafts are clustered or not is judged. The method provides a quantitative calculation step, so that the difficulty that the existing literature cannot quantitatively judge whether multiple spacecrafts belong to the same cluster is overcome. In addition, the method fully utilizes the equivalence of the adjacent matrix and the topological relation in the specific calculation process, so that the difficult problem of judging whether the topology has the spanning tree is converted into the simple problem of finding whether the power sum matrix has the off-diagonal zero element. Therefore, the method can rapidly and quantitatively determine whether a plurality of spacecrafts with complex information interaction relationship belong to the same cluster, and further lays a theoretical foundation for clearly defining the cluster and designing a cluster cooperative control method. 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.
Drawings
Fig. 1 is a schematic flow chart of a method for determining a cluster of spacecraft clusters according to the present invention;
FIG. 2 is an inter-satellite communication and relative navigation relationship of three spacecraft in a particular embodiment;
FIG. 3 is an inter-satellite communication topology diagram of three spacecraft in a particular embodiment;
FIG. 4 is a relative navigation topology sub-graph of three spacecraft in a particular embodiment;
FIG. 5 is an information topology diagram of three space vehicles in a particular embodiment.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
Unless defined otherwise, 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 terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the 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, the method for determining a cluster of a spacecraft cluster of the present invention includes the following steps:
step 1, inputting an inter-satellite communication relation, and establishing a communication topology subgraph among multiple spacecrafts;
step 2, inputting a relative navigation relation, and establishing a relative navigation topological subgraph among the multiple spacecrafts;
and 4, constructing an adjacency matrix corresponding to the information topological graph, and judging whether the multiple spacecrafts are grouped or not through existence of the directed spanning tree.
In a preferred embodiment, the communication topology subgraph in step 1 is a node set V composed of nodes representing spacecraft sequence numbers and an edge set E having an inter-satellite communication relationship1Jointly formed doublet G1(V,E1)。
Wherein, the node set V ═ { V ═ of the communication topology subgraphi1, …, N, where N is the number of spacecraft, viRepresenting nodesAnd is a natural number from 1 to N. Edge set E of communication topology subgraph1={eij|(vi∈V;vjE is V; i ≠ j) }, where edge eijRepresenting a node viWhether or not to point to vjPerforming one-way communication, if yes, then the edge eij1, otherwise eij=0。
As a preferred embodiment, the relative navigation topological subgraph in step 2 is a node set V formed by nodes representing spacecraft sequence numbers and an edge set E having a relative navigation relationship2Jointly formed doublet G2(V,E2)。
Wherein the set of nodes of the relative navigation topology subgraph is the same as the set of nodes of the communication topology subgraph.
Edge set E of relative navigation topological subgraph2={eij|(vi∈V;vjE is V; i ≠ j) }, where edge eijRepresenting a node vjWhether it is for node viPerforming relative navigation measurement, if yes, determining edge eij1, otherwise eij=0。
As a preferred embodiment, the information topology graph G (V, E) in step 3 is a union of the communication topology subgraph and the relative navigation topology subgraph, that is, G ═ G1∪G2。
Preferably, the set of nodes of the information topology graph is equivalent to the set of nodes of the communication topology subgraph and is also equivalent to the set of nodes of the relative navigation topology subgraph. Edge set E of communication graph1With respect to the set of edges E of the navigation map2The formed union constitutes the edge set of the information topology, i.e. E ═ E1∪E2。
As a preferred embodiment, the adjacency matrix a of the information topology in step 4 is an N-th-order square matrix corresponding to the information topology G (V, E) one to one; the element a of the ith row and the jth column on the off-diagonal lineij=eij(i ≠ j), element a on the diagonalii=0(vi∈V)。
Preferably, whether the N spacecrafts belong to the same cluster is determined by whether the information topological graph G includes a directed spanning tree; when G comprises the directed spanning tree, N spacecrafts belong to the same cluster; and when G does not contain the directed spanning tree, the N spacecrafts do not belong to the same cluster.
Preferably, whether the information topology graph G includes a directed spanning tree is determined by an adjacency matrix a; the determination steps are as follows:
s1, calculating the power of 1-N-1 order of the matrix A: A. a. the2、A3、……、AN-1;
S2, summing all the powers of the N-1 order to obtain a power sum matrix
S3, check sum matrix A∑All of the elements of (a); if a row (denoted as jth row, j 1. ltoreq. N) exists, all elements except the diagonal are greater than zero, i.e.The information topological graph G comprises a directed spanning tree; if there is always some off-diagonal element as zero for any row, the information topology G does not contain a directed spanning tree.
Example 1
As shown in fig. 2, the inter-satellite communication relationship of 3 spacecrafts is: two-way communication between the spacecraft 1 and 3 is possible, but the spacecraft 2 does not have any communication with other spacecraft; the relative navigation relationships of the 3 spacecrafts are as follows: the spacecraft 1 and 3 can respectively perform relative navigational measurements on the spacecraft 2. The method of the invention is used for judging whether the three spacecrafts form the same cluster.
Step 1, according to the inter-satellite communication relationship, a communication topology subgraph G can be established1(V,E1) As shown in fig. 3. Where, V ═ {1,2,3}, E1={e13,e31}。
Step 2, according to the relative navigation relationship, a relative navigation topological subgraph can be established as shown in fig. 4. Where, V ═ {1,2,3}, E2={e21,e23}
Step 4, according to the specific form of the information topological graph in fig. 5, the adjacency matrix is obtained as follows:
further, whether the information topological graph G contains a directed spanning tree is judged according to the following method:
s1, calculating the 1-2 order power of the matrix A:
S3, checking the matrix A∑All elements a except diagonal of∑,ij(i ∈ V; j ∈ V; i ≠ j); since the elements of the 2 nd row except the diagonal elements are all larger than zero, the information topology G contains a directed spanning tree.
Since the information topological graph G contains a directed spanning tree, the three spacecrafts form a cluster on the basis of a given inter-satellite communication and relative navigation interaction relationship.
To further illustrate the beneficial effects of the method of the present invention, in step 4, clustering decisions are made for two other hypothetical cases.
The first scenario is that the three space vehicles described above have only inter-satellite communication (as shown by the solid arrows in figure 2),
the second hypothetical situation is that the three space vehicles described above have only relative navigation (as indicated by the dashed arrows in fig. 2).
The results obtained by the determination method of the present invention are shown in table 1. As can be seen from the results in the table, no clustering was possible in either of the hypothetical cases. From this result, the following conclusions can be drawn: whether the clusters are clustered or not is more accurate by adopting the information topological graph; and when the cluster can not be formed by simple inter-satellite communication or simple relative navigation, the two information transmission modes can be combined, thereby completing the cluster forming. Therefore, the grouping judgment method is closer to the practical application of engineering and has good use benefit.
TABLE 1 clustering results in two hypothetical cases calculated using the method of the present invention
Through the embodiment, the judgment method established by the invention can be obtained, and the essential equivalence of inter-satellite communication and relative navigation in the problem of cluster formation of multiple spacecrafts is considered, so that the method is more suitable for the practical application of spacecraft clusters.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be construed as the protection scope of the present invention.
Claims (9)
1. A method for judging the clustering of a spacecraft cluster is characterized by comprising the following steps:
s1, acquiring an inter-satellite communication relation, and establishing a communication topology subgraph among multiple spacecrafts;
s2, acquiring a relative navigation relation, and establishing a relative navigation topological subgraph among the multiple spacecrafts;
s3, combining the communication topological subgraph and the relative navigation topological subgraph to construct an information topological graph among the multiple spacecrafts;
and S4, constructing an adjacency matrix corresponding to the information topological graph, and judging whether the multiple spacecrafts are clustered or not through existence of the directed spanning tree.
2. The method according to claim 1, wherein the communication topology sub-graph in S1 is a node set V composed of nodes representing serial numbers of spacecraft and an edge set E having inter-satellite communication relationship1Jointly formed doublet G1(V,E1);
Wherein, the node set V ═ { V ═ of the communication topology subgraphi1, …, N, where N is the number of spacecraft, viRepresenting nodes which are natural numbers from 1 to N; edge set E of communication topology subgraph1={eij|(vi∈V;vjE is V; i ≠ j) }, where edge eijRepresenting a node viWhether or not to point to vjPerforming one-way communication, if yes, then the edge eij1, otherwise eij=0。
3. The method according to claim 1, wherein the relative navigation topological subgraph in S2 is a node set V composed of nodes representing spacecraft sequence numbers and an edge set E having a relative navigation relationship2Jointly formed doublet G2(V,E2);
Wherein, the node set of the relative navigation topological subgraph is the same as the node set of the communication topological subgraph, and the edge set E of the relative navigation topological subgraph2={eij|(vi∈V;vjE is V; i ≠ j) }, where edge eijRepresenting a node vjWhether it is for node viPerforming relative navigation measurement, if yes, determining edge eij1, otherwise eij=0。
4. The method according to claim 1, wherein the information topology graph G (V, E) in S3 is a combination of a communication topology subgraph and a relative navigation topology subgraph, i.e. G ═ G1∪G2。
5. The method according to claim 4, wherein the set of nodes of the information topology graph is equivalent to the set of nodes of the communication topology subgraph and is also equivalent to the set of nodes of the relative navigation topology subgraph.
6. The method according to claim 4, wherein the edge set E of the communication topology map is1With respect to the set of edges E of the navigation map2The formed union constitutes the edge set of the information topology, i.e. E ═ E1∪E2。
7. The method according to claim 1, wherein the adjacency matrix a of the information topology map in S4 is an N-th-order square matrix corresponding to the information topology map G (V, E) one by one; the element a of the ith row and the jth column on the off-diagonal lineij=eij(i ≠ j), element a on the diagonalii=0(vi∈V)。
8. The method according to claim 1, wherein whether the multiple space vehicles belong to the same cluster is determined by whether an information topology graph G includes a directed spanning tree:
when G comprises the directed spanning tree, N spacecrafts belong to the same cluster; and when G does not contain the directed spanning tree, the N spacecrafts do not belong to the same cluster.
9. The method according to claim 8, wherein whether the information topology G contains a directed spanning tree is determined by an adjacency matrix A, and the specific determination steps are as follows:
s401, calculating the power of 1-N-1 order of the matrix A: A. a. the2、A3、……、AN-1;
S403, checking and matrix A∑All elements of (a):
if a row (denoted as jth row, j 1. ltoreq. N) exists, all elements except the diagonal are greater than zero, i.e.The information topological graph G comprises a directed spanning tree; if there is always some off-diagonal element as zero for any row, the information topology G does not contain a directed spanning tree.
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