CN110826193A - Boundary detection method for spacecraft cluster - Google Patents
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- CN110826193A CN110826193A CN201910980017.0A CN201910980017A CN110826193A CN 110826193 A CN110826193 A CN 110826193A CN 201910980017 A CN201910980017 A CN 201910980017A CN 110826193 A CN110826193 A CN 110826193A
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Abstract
The invention discloses a boundary detection method of a spacecraft cluster, which comprises the following steps: inputting position vectors and inter-satellite communication distance constraints of all N spacecrafts in the cluster; taking a sphere center position vector to be solved as an optimization variable, taking a half of inter-satellite communication distance constraint as radius constraint of a spherical region, taking the number of spacecrafts contained in the spherical region as an optimization target, and establishing an optimization model; iteratively solving the optimization model to obtain a spherical center position vector containing the largest number of spacecrafts in a spherical region; and taking the sphere center position vector obtained by solving as a center, and taking a half of the inter-satellite communication distance constraint as a radius to obtain a spherical area which is taken as a cluster boundary. The cluster boundary detection method provided by the invention can find the optimal cluster center through optimization solution under the condition that the cluster center is not known in advance and further determine the boundary of the cluster; and the calculation model is simple, the calculation efficiency is high, and the problem adaptability is strong.
Description
Technical Field
The invention relates to the technical field of aerospace, in particular to a boundary detection method for a spacecraft cluster.
Background
A spacecraft cluster is a spatially distributed system of wirelessly connected by multiple spacecraft via inter-satellite communication. The spacecraft in the spacecraft cluster have simple functions and limited capability, but can jointly complete some complex space tasks through cooperation and cooperation. For example, hundreds of micro-nano astronomical instruments can virtually form a large astronomical telescope by mounting small-scale cameras, thereby realizing space-based physical observation. To ensure the efficiency of the cooperation, the relative positions of the spacecraft in the cluster cannot be too far apart, so that the actual in-orbit operation of the cluster requires that the spacecraft be kept in a certain spatial range. The size of the space occupied by the cluster is limited by the ability of the spacecraft to communicate between satellites. When the actual distance between the spacecrafts in the cluster exceeds the maximum value of the inter-satellite communication distance, the spacecrafts cannot communicate with each other, and cooperation cannot be completed. To avoid this situation, it is necessary to detect the current boundary of the cluster and the space vehicles located inside and outside the boundary in real time on-track, so as to guide the adjustment of the spatial extent of the cluster. In the past research on a space distribution system (such as formation flight of spacecrafts), it is generally assumed that a certain spacecraft exists in the system as a center, and the rest spacecrafts are constrained and distributed around the spacecraft according to a certain distance. In this case, the boundary of the system can be determined by a sphere centered on the above-mentioned central spacecraft and constrained by the inter-satellite communication distance as a diameter. However, unlike the distributed system described above, since the roles of all the spacecraft in a cluster are generally the same, there is no pre-designated cluster center and therefore no pre-determined cluster boundary.
How to find a reasonable center and determine the boundary of the cluster according to the position distribution of each spacecraft in the current cluster is an important problem of cluster on-orbit application. Since there is no method for detecting the cluster boundary, it brings great difficulty to the spatial task using the cluster.
Disclosure of Invention
Aiming at the problem that the cluster boundary cannot be determined quickly in the prior art, the invention aims to provide a method capable of determining the cluster boundary quickly, so that a necessary theoretical basis is provided for on-orbit application of a spacecraft cluster.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a boundary detection method for a spacecraft cluster comprises the following steps:
s1, acquiring position vectors and inter-satellite communication distance constraints of all N spacecrafts in the cluster;
s2, establishing an optimization model by taking a sphere center position vector to be solved as an optimization variable, taking a half of inter-satellite communication distance constraint as radius constraint of a spherical region and taking the number of spacecrafts contained in the spherical region as an optimization target;
s3, carrying out iterative solution on the optimization model by adopting an optimization method to obtain a sphere center position vector containing the largest number of spacecrafts in a spherical region;
and S4, taking the spherical center position vector obtained by solving as a center, taking a half of the inter-satellite communication distance constraint as a radius to obtain a spherical area, and recording the spherical area as a cluster boundary, thereby determining the spacecraft located in the boundary and the spacecraft located outside the boundary.
The position vector X in S1i＝[xi,yi,zi]TComprising three position coordinate components, where xi,yi,ziBoth in the inertial and in the relative motion coordinate systems; specifically, in which coordinate system the spatial task performed by the cluster or the usage habit of the user is determined.
The sphere center position vector c in S2 is [ c ═ cx,cy,cz]TContaining three position coordinate components.
The optimization model in S2 is specifically:
wherein, | | | |, represents a 2 norm, namely
c is the vector of the position of the sphere center, N is the number of the spacecrafts, dmaxAnd J is an optimization index for inter-satellite communication distance constraint.
The optimization method in the S3 is a genetic algorithm, an ant colony algorithm or a simulated annealing algorithm.
The cluster boundaries determined in S4 are all satisfied with the constraint
X when formed into a set
And if so, the corresponding spacecraft i is positioned in the boundary, otherwise, the spacecraft i is positioned outside the boundary.
Compared with the prior art, the invention has the following advantages:
firstly, taking a sphere center position vector to be solved as an optimization variable, taking a half of inter-satellite communication distance constraint as radius constraint of a spherical region, taking the number of spacecrafts contained in the spherical region as an optimization target, and establishing an optimization model; iterative solution is carried out to obtain a sphere center position vector containing the largest number of spacecrafts in the spherical area; and then, taking the sphere center position vector obtained by solving as a center, taking a half of the inter-satellite communication distance constraint as a radius to obtain a spherical area which is taken as a cluster boundary, and determining the spacecraft positioned in the boundary and the spacecraft positioned outside the boundary. The method has the advantages that the cluster center does not need to be specified in advance when the cluster boundary is determined, and the optimal cluster center is found through the online optimization solution of the actual configuration of the cluster. Due to the comprehensive influence of orbit dynamics and complex space perturbation force in the cluster flying process, the cluster configuration often has more complex shape characteristics. When the actual configuration of the cluster is far away from the design configuration, the fixed cluster center is adopted as the boundary judgment basis, so that most spacecrafts are judged to be separated from the cluster by mistake, and more fuel is wasted to implement cluster boundary control. By adopting the method, the cluster center can be flexibly adjusted, and the cluster boundary can be determined so as to contain as many spacecrafts as possible, thereby reducing the fuel consumed by the overall maintenance of the cluster. The method has remarkable engineering application value for long-term on-orbit maintenance and survival of the cluster. The cluster boundary detection method provided by the invention does not depend on a complex calculation model, and can quickly solve the problem only by simply iterating the candidate cluster center, so that the method is suitable for spacecraft clusters with any number and any topological configuration, and has strong problem adaptability.
Drawings
FIG. 1 is a flow chart of a cluster boundary detection method according to the present invention;
FIG. 2 is a boundary detection result of a planar cluster obtained by the method of the present invention;
fig. 3 shows the boundary detection result of the spatial cluster obtained by the method of the present invention.
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 present invention provides a method for detecting a boundary of a spacecraft cluster, which comprises the following steps:
step 1, inputting position vectors X of all N spacecrafts in a clusteri(i-1, 2, …, N) and an inter-satellite communication distance constraint dmax。
Step 2, taking the ball center position vector c to be solved as an optimization variable and dmaxThe method comprises the following steps that/2, as radius constraint of a spherical region, the number of spacecrafts contained in the spherical region is used as an optimization target, and an optimization model is established;
step 4, taking the spherical center position vector c obtained by solving as a center, and dmaxAnd/2, recording a spherical area obtained by taking the spherical area as the radius as a cluster boundary, and further determining the spacecraft positioned in the boundary and the spacecraft outside the boundary.
As a preferred embodiment, the position vector X in step 1 isi＝[xi,yi,zi]TComprising three position coordinate components, where xi,yi,ziThe method can be represented in an inertial coordinate system or a relative motion coordinate system; specifically, in which coordinate system the spatial task performed by the cluster or the usage habit of the user is determined.
As a preferred embodiment, the sphere center position vector c in step 2 is ═ cx,cy,cz]TContains three position coordinate components, and the corresponding optimization model describes a three-variable optimization problem.
Wherein, the optimization model specifically comprises:
wherein, | | | |, represents a 2 norm, namely
As a preferred embodiment, the optimization method in step 3 may be any one of existing numerical optimization algorithms such as a genetic algorithm, an ant colony algorithm, a simulated annealing algorithm, and the like.
As a preferred embodiment, the cluster boundaries determined in step 4 are all the boundaries satisfying the constraint
X when formed into a set
And if so, the corresponding spacecraft i is positioned in the boundary, otherwise, the spacecraft i is positioned outside the boundary.
Example 1
The following illustrates a plane cluster embodiment to illustrate the specific principles of the present invention. Assuming that a cluster comprises 20 spacecrafts which are all located in the same plane, the specific coordinates are shown in table 1, and the inter-satellite communication distance is constrained to be d max40 km. The method of the present invention is used for cluster boundary detection.
Step 1: input position coordinates of all 20 spacecraft (see Table 1) and communication distance boundary constraint dmax＝40km。
Step 2: using the vector c as [ c ] of the circle center position to be solvedx,cy]TAs optimization variable, with dmaxAnd 2, establishing an optimization model by taking the number of the spacecrafts contained in the circular area as an optimization target as the radius constraint of the circular area, wherein the optimization model comprises the following steps:
and step 3: solving the model by genetic algorithm to obtain cx＝14.59，cy＝55.91。
Step 4, using the circle center position vector c obtained by solving as the center, and using dmaxThe circular area obtained by/2 as the radius is marked as the cluster boundary, as shown in FIG. 2; further determining the space vehicles located in the boundary and the space vehicles located outside the boundary, the results are shown in the table1 last column. It will be appreciated that the remaining spacecraft are all located within the boundary, except for the spacecraft 14, 17, 18.
Table 1 position coordinates and boundary detection results of each spacecraft in a planar cluster
| Spacecraft numbering | x coordinate (km) | y coordinate (km) | Whether or not it is located within the boundary |
| 1 | 34.2 | 54.2 | Is that |
| 2 | 17.3 | 42.8 | Is that |
| 3 | 4.5 | 52.7 | Is that |
| 4 | 13.4 | 50.8 | Is that |
| 5 | 8.8 | 37.1 | Is that |
| 6 | 33.3 | 61.3 | Is that |
| 7 | 30.6 | 56.9 | Is that |
| 8 | 22.5 | 47.2 | Is that |
| 9 | 29.8 | 60.9 | Is that |
| 10 | 13.7 | 51.3 | Is that |
| 11 | 8.6 | 60.2 | Is that |
| 12 | 5.6 | 46.3 | Is that |
| 13 | 10.2 | 46.5 | Is that |
| 14 | 52.8 | 89.8 | Whether or not |
| 15 | 17.5 | 44.4 | Is that |
| 16 | 6.7 | 73.9 | Is that |
| 17 | -7.6 | 59.5 | Whether or not |
| 18 | 54.1 | 70.8 | Whether or not |
| 19 | 21.8 | 51.6 | Is that |
| 20 | -3.6 | 61.6 | Is that |
Example 2
A space cluster embodiment is further illustrated below to illustrate the specific principles of the present invention.
Assuming that a cluster comprises 20 spacecrafts which are randomly distributed in a certain space, the specific coordinates are shown in table 2, and the inter-satellite communication distance is constrained to be dmax40 km. The method of the present invention is used for cluster boundary detection.
Step 1: input position coordinates of all 20 spacecraft (see Table 2) and communication distance boundary constraint dmax＝40km。
Step 2: using the vector c ═ c of the sphere center position to be solvedx,cy,cz]TAs optimization variable, with dmaxAnd 2, establishing an optimization model by taking the number of the spacecrafts contained in the spherical region as an optimization target as the radius constraint of the spherical region, wherein the optimization model comprises the following steps:
and step 3: solving the model by genetic algorithm to obtain cx＝15.03，cy＝49.18，cz＝46.30。
Step 4, taking the spherical center position vector c obtained by solving as a center, and dmaxThe spherical area obtained by/2 as the radius is marked as the cluster boundary, as shown in FIG. 3; the space vehicles located within the boundary and the space vehicles located outside the boundary were further identified and the results are shown in the last column of table 2. It will be appreciated that the remaining spacecraft are all located within the boundary, except for the spacecraft 16, 17, 18, 20.
Table 2 position coordinates and boundary detection results of each spacecraft in the space cluster
Through the two embodiments, the method for detecting the cluster boundary can find the optimal cluster center through optimization solution under the condition that the cluster center is not known in advance, and further determine the boundary of the cluster; and the calculation model is simple, the calculation efficiency is high, and the problem adaptability is strong.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (6)
1. A boundary detection method of a spacecraft cluster is characterized by comprising the following steps:
s1, acquiring position vectors and inter-satellite communication distance constraints of all N spacecrafts in the cluster;
s2, establishing an optimization model by taking a sphere center position vector to be solved as an optimization variable, taking a half of inter-satellite communication distance constraint as radius constraint of a spherical region and taking the number of spacecrafts contained in the spherical region as an optimization target;
s3, carrying out iterative solution on the optimization model by adopting an optimization method to obtain a sphere center position vector containing the largest number of spacecrafts in a spherical region;
and S4, taking the spherical center position vector obtained by solving as a center, taking a half of the inter-satellite communication distance constraint as a radius to obtain a spherical area, and recording the spherical area as a cluster boundary, thereby determining the spacecraft located in the boundary and the spacecraft located outside the boundary.
2. The method of claim 1, wherein the position vector X in S1 isi＝[xi,yi,zi]TComprising three position coordinate components, where xi,yi,ziBoth in the inertial frame and in tablesShown in a relative motion coordinate system; specifically, in which coordinate system the spatial task performed by the cluster or the usage habit of the user is determined.
3. The method of claim 1, wherein the sphere center position vector c ═ c in S2x,cy,cz]TContaining three position coordinate components.
4. The method according to claim 1, wherein the optimization model in S2 specifically is:
wherein, | | | |, represents a 2 norm, namely
c is the vector of the position of the sphere center, N is the number of the spacecrafts, dmaxAnd J is an optimization index for inter-satellite communication distance constraint.
5. The method of claim 1, wherein the optimization method in S3 is a genetic algorithm, an ant colony algorithm or a simulated annealing algorithm.
6. The method of claim 1, wherein the cluster boundaries determined in S4 are all those satisfying the constraint
X when formed into a set
And if so, the corresponding spacecraft i is positioned in the boundary, otherwise, the spacecraft i is positioned outside the boundary.
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| US6072433A (en) * | 1996-07-31 | 2000-06-06 | California Institute Of Technology | Autonomous formation flying sensor |
| CN104076819A (en) * | 2014-07-08 | 2014-10-01 | 清华大学 | Bounded accompanying boundary control method of satellites under circular reference orbit |
| US9248922B1 (en) * | 2011-08-23 | 2016-02-02 | Space Systems/Loral, Llc | Reflector deployment techniques for satellites |
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| US6072433A (en) * | 1996-07-31 | 2000-06-06 | California Institute Of Technology | Autonomous formation flying sensor |
| US9248922B1 (en) * | 2011-08-23 | 2016-02-02 | Space Systems/Loral, Llc | Reflector deployment techniques for satellites |
| CN104076819A (en) * | 2014-07-08 | 2014-10-01 | 清华大学 | Bounded accompanying boundary control method of satellites under circular reference orbit |
| CN106717048A (en) * | 2016-11-10 | 2017-05-24 | 深圳达闼科技控股有限公司 | Method and apparatus for dynamic adjustment of flight position of aircraft |
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