CN114138019B - Method for realizing optimal coverage of spacecraft cluster - Google Patents
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Abstract
The invention discloses a method for realizing optimal coverage of a spacecraft cluster, which is characterized in that a method for uniformly spreading overlapping coverage areas among spacecrafts to effective coverage areas of all spacecrafts is introduced, the influence of the position of any one of the two spacecrafts which are neighbors on the calculation of the effective coverage area of the other spacecraft is quantified, after the extremum solution such as the traditional gradient descent method is further combined on the basis, non-neighbor information which is required by the extremum solution and cannot be acquired by a single spacecraft due to communication limitation can be replaced by neighbor information which can be acquired by communication, so that the method is suitable for configuring a distributed algorithm for all the spacecrafts under the condition of communication constraint and calculating a target moving speed u i which can increase the total effective coverage area of the spacecraft cluster in each adjustment period, and when the target moving speed u i is converged to 0, the total effective coverage area of the spacecraft cluster is effectively increased, and the optimal coverage of the spacecraft cluster is realized.
Description
Technical Field
The invention relates to the technical field of spacecraft clusters, in particular to a method for realizing optimal coverage of a spacecraft cluster.
Background
The small spacecraft has the remarkable advantages of short development period, low investment cost, high flexibility and the like, plays an increasingly important role in the aspects of earth magnetic field detection, deep space detection and space technology verification, and is one of the research hotspots of the international aerospace industry. Because the coverage area and the detection efficiency of a single spacecraft are limited, a plurality of small-sized spacecrafts are generally configured, and a spacecraft cluster is formed through mutual cooperation and communication among the spacecrafts so as to complete the complex task which can be completed by the large-sized spacecrafts.
Currently, spacecraft clusters have been widely used to perform sensing detection tasks such as resource detection, area reconnaissance, deep space exploration, etc. For the spacecraft cluster, the optimal coverage refers to that the coverage of the spacecraft cluster is increased as much as possible on the basis of realizing seamless coverage of a target area, so that resources are saved as much as possible.
Aiming at realizing the optimal coverage problem of multiple agents, a certain research result has been achieved in recent years, and some control algorithms are provided for solving the cooperative optimal coverage problem of the multiple agents. Such as: (1) The method for dividing the target area generally adopts a Voronoi diagram dividing method, firstly divides the target area, calculates the optimal position of each intelligent body by using the Voronoi method, and distributes each intelligent body to the optimal target position by the design of a controller; (2) And on the basis of the method of the objective function, a sensitivity function is established for the objective area, and the controller is designed to enable the multi-agent to pay more attention to the area with higher sensitivity in the objective area, so that the optimal coverage of the objective area is realized.
However, the current research work has a certain limitation, the focus is usually a target area, and it is often assumed that global communication can be performed between each intelligent agent, but for the spacecraft cluster, the communication environment in space is severe, and the communication distance is severely limited, so that the existing multi-intelligent agent optimal coverage algorithm is adopted, even if the optimal target position of each spacecraft can be calculated, because of the limitation on the communication distance between the spacecraft, the optimal target position is not practically available for each spacecraft, so that the existing multi-intelligent agent optimal coverage algorithm cannot be directly applied to the spacecraft cluster control field.
Disclosure of Invention
The invention aims to solve the technical problems and provides a method for realizing optimal coverage of a spacecraft cluster, which is used for realizing optimal coverage of the spacecraft cluster by designing a distributed algorithm without acquiring information of all the spacecraft in the spacecraft cluster under the condition that global communication cannot be realized and increasing the total effective coverage area of the spacecraft cluster as much as possible.
In order to achieve the above purpose, the technical scheme of the invention is as follows: a method for realizing optimal coverage of a spacecraft cluster, which is used for increasing the coverage area of the spacecraft cluster; the spacecraft clusters comprise a plurality of spacecrafts which move at equal height relative to a ground plane, the total effective coverage area of the spacecraft clusters is the sum of the effective coverage areas of the spacecrafts, and the effective coverage area of each spacecraft is defined as the projection area of a sphere orthographic projection onto the ground plane by taking the position of each spacecraft as the sphere center and the coverage radius ri as the radius; each spacecraft has a maximum communication distance L and is suitable for communicating with at least one other spacecraft, and the other spacecraft communicated with each spacecraft is defined as the neighbor of the spacecraft; in the method, each spacecraft performs the following steps at preset adjustment periods: acquiring a self position x i and communicating with each neighbor to acquire each neighbor position x j; wherein j∈N i,Ni is the set of all neighbors of spacecraft i; calculating a target moving speed u i in the adjustment period, wherein the target moving speed u i is a speed vector with a direction; the expression of the target moving speed u i is: The f i is the effective coverage area of the spacecraft i, and the expression is that D i is the number of neighbors of spacecraft i, S m represents the area of the area covered by spacecraft i only when m=1, and S m represents the sum of the areas covered by spacecraft i and m-1 neighbors together when m > 1; g ij is a communication constraint factor, which is positively related to the difference between the distance of spacecraft i from the corresponding neighbor and the maximum communication distance L; the saidA penalty function for the communication constraint factor g ij; and moving according to the target moving speed u i until the target moving speed u i calculated in a certain adjustment period is converged to zero, and stopping the movement of the spacecraft.
Further, the communication constraint factor g ij is directly related to the difference between the euclidean distance of spacecraft i from the corresponding neighbor x i-xj||2 and the maximum communication distance L.
Further, the expression of the communication constraint factor g ij is: g ij＝(xi-xj)2-L2.
Further, the penalty functionThe expression of the interior point penalty function is:
Wherein, gamma k is penalty factor, gamma k >0, and gamma k -0 when k-infinity.
Further, S m in the expression of the effective coverage area f i is calculated by the following method: the said processWherein, Representing the area of set X, set X m represents the set of coordinates of the region covered only by spacecraft when m=1, and set X m represents the set of coordinates within the region commonly covered only by spacecraft i and m-1 neighbors when m > 1.
Compared with the prior art, the method for realizing the optimal coverage of the spacecraft cluster introduces the concept of the effective coverage area f i of the spacecraft, and the calculation method is thatThe physical meaning of the expression is: the coverage of the spacecraft i is divided into at most d i +1 parts, namely, an area covered by the spacecraft and 1 neighbor together, an area covered by the spacecraft and 2 neighbors together, … … and an area covered by the spacecraft and d i neighbors together, and the area of the d i +1 parts is uniformly distributed with respect to the number of the spacecraft, so that the effective coverage area of the spacecraft is obtained after summation. In other words, the method of the invention introduces a method of uniformly spreading the overlapping coverage areas among the spacecrafts to the effective coverage areas of the spacecrafts, and equalizes the influence of the position of any one of the two spacecrafts which are neighbors to the effective coverage area calculation of the other spacecrafts, namely that the two spacecrafts exist
On the basis, after the extremum solution such as the traditional gradient descent method is further combined, non-neighbor information (such as the position of the neighbor j required by calculating f j) which cannot be acquired by a single spacecraft due to the communication limitation in the extremum solution can be replaced by neighbor information (such as the position x j of the neighbor j) which can be acquired through communication with the neighbor, so that a distributed algorithm is configured for each spacecraft under the communication constraint condition, only the position x i of the spacecraft and the position x j of the neighbor which can be acquired through communication are required, the target moving speed u i which increases the total effective coverage area of the spacecraft cluster is calculated by combining the expression of the maximum communication distance L and the target moving speed u i, and when the target moving speed u i is converged to 0, the spacecraft reaches a steady state, the total effective coverage area of the spacecraft cluster is effectively increased, and the optimal coverage of the spacecraft cluster is realized.
Therefore, in the method of the invention, each spacecraft does not need to acquire the position information of all the spacecrafts in the spacecraft cluster, which not only effectively saves the calculation resources, but also overcomes the difficulty that global communication is difficult to realize in the spacecraft cluster, thereby realizing the distributed calculation of each spacecraft and the optimal coverage of the spacecraft cluster under the condition of limited communication. In addition, the communication constraint factors and penalty functions thereof are introduced, so that the state of each spacecraft is quickly approximated to the optimal position under the condition of ensuring the communication distance, and the total effective coverage area of the spacecraft cluster is maximized.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required to be used in the description of the embodiments below are briefly introduced, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a communication topology of a spacecraft cluster of an embodiment of the invention;
FIG. 2 is a schematic representation of the calculation of the effective coverage area f i in the method according to an embodiment of the present invention.
Detailed Description
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. It is to be understood that the described embodiments are preferred embodiments of the invention and should not be taken as excluding other embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without creative efforts, are within the protection scope of the present invention.
In the claims, specification and drawings hereof, unless explicitly defined otherwise, the terms "first," "second," or "third," etc. are used for distinguishing between different objects and not for describing a particular sequential order.
In the claims, specification and drawings of the present invention, the terms "comprising," having, "and variations thereof as used herein, are intended to be" including but not limited to.
The embodiment of the invention provides a method for realizing optimal coverage of a spacecraft cluster, which is used for increasing the total effective coverage area of the spacecraft cluster.
As shown in fig. 1, the spacecraft cluster comprises a plurality of spacecrafts with equal-height activities relative to a ground plane, the total effective coverage area of the spacecraft cluster is the sum of the effective coverage areas of the spacecrafts, and the effective coverage area of each spacecraft is defined as the projection area of a sphere orthographic projected onto the ground plane by taking the position of each spacecraft as the center of sphere and the coverage radius ri as the radius. In the spacecraft cluster of the embodiment, all the spacecrafts are identical, so that all the spacecrafts have the same maximum communication distance L and are suitable for communicating with at least one other spacecraft, and the other spacecraft which is defined to communicate with each spacecraft is the neighbor of the spacecraft.
The method of the embodiment of the invention is a distributed method, taking spacecraft i as an example, each spacecraft in the spacecraft cluster performs the following steps at preset adjustment periods:
Acquiring a self position x i and communicating with each neighbor to acquire each neighbor position x j; where j ε N i,Ni is the set of all neighbors of spacecraft i. In this embodiment, the spacecraft i may perform signal transmission with the base station to obtain its own position x i according to the signal transmission process.
The target moving speed u i in the adjustment period is calculated, and the target moving speed u i is a speed vector having a direction. The expression of the target moving speed u i is: The f i is the effective coverage area of the spacecraft i, and the expression is that D i is the number of neighbors of spacecraft i, S m denotes the area of the area covered by spacecraft i only when m=1, and S m denotes the sum of the areas covered by spacecraft i and m-1 neighbors together when m >1, the specific physical meaning of which will be described below in connection with fig. 2. G ij is a communication constraint factor, which is directly related to the difference between the distance between the spacecraft i and the corresponding neighbor and the maximum communication distance L, so as to represent the size relationship between the distance between the two spacecrafts and the maximum communication distance L, thereby reflecting the communication condition of the two spacecrafts. And saidThe penalty function of the communication constraint factor g ij is used for digitizing and amplifying the situation when the communication constraint factor g ij reflects that the two spacecrafts are difficult to communicate.
And moving according to the target moving speed u i until the target moving speed u i calculated in a certain adjustment period is converged to zero, and stopping the movement of the spacecraft.
Specifically, in the above method of this embodiment, the communication constraint factor g ij is directly related to the difference between the euclidean distance of the spacecraft i and the corresponding neighbor ||x i-xj||2 and the maximum communication distance L. In this embodiment, the expression of the communication constraint factor g ij is: g ij＝(xi-xj)2-L2. It will be appreciated that the communication restriction factor g ij may have other expressions as well. And said penalty functionThe expression of the interior point penalty function is: Wherein, gamma k is penalty factor, gamma k >0, and gamma k -0 when k-infinity. It goes without saying that the penalty function Other forms are also possible. Further, S m in the expression of the effective coverage area f i is calculated by the following method: the said processWherein the method comprises the steps ofRepresenting the area of set X, set X m represents the set of coordinates of the region covered only by spacecraft when m=1, and set X m represents the set of coordinates within the region commonly covered only by spacecraft i and m-1 neighbors when m > 1.
Next, a method for calculating the effective coverage area f i according to an embodiment of the present invention is specifically described with reference to fig. 2, and then the source of the expression of the target moving speed u i is described, so that the reason why the total effective coverage area of the spacecraft cluster can be increased by only following the movement of each spacecraft by the target moving speed u i calculated by the expression of the target moving speed u i by a person skilled in the art is more clear.
As shown in the upper half of fig. 2, it is illustrated with a spacecraft cluster of spacecraft i having 2 neighbors (spacecraft j 1 and spacecraft j 2, respectively). It can be seen that there is an overlap of coverage between the three spacecraft pairs. The area covered by the spacecraft i is the sum of S 1+2+3. Where S 1 is the area of the area covered by spacecraft i alone, corresponding to the case where m=1 in the expression of f i described above; s 2 is the area of the region covered only by spacecraft i and 1 neighbor (including spacecraft j 1 and spacecraft j 2) together, corresponding to the case where m=2 in the expression of f i described above; s 3 is the area of the region covered only by spacecraft i and 2 neighbors together, corresponding to the case where m=3 in the expression of f i described above. According to the foregoing description, in the method of the present invention, overlapping coverage areas between spacecrafts are uniformly spread to each of the spacecrafts to calculate a corresponding effective coverage area, so that the effective coverage area f i of the spacecrafts i is the sum of the areas of the 4 shaded portions shown in the lower half of fig. 2, that is, the effective coverage area f i＝1+2/2+S3/3, which is a specific physical meaning of the expression of f i.
In the prior art, if the moving speed and direction of each spacecraft are to be solved, which makes the total effective coverage area of the spacecraft cluster maximum, the effective coverage area f i of each spacecraft needs to be first solved, the effective coverage areas of all the spacecraft are summed, and then unique solution is performed by using an extremum solution method such as a traditional gradient descent method, so that the solution result finally converges to an optimal value. For example, the total effective coverage area of a spacecraft clusterSolving the total effective coverage area F by adopting a negative gradient descent method to obtain a target moving speed
Under the assumption that global communication can be achieved, each parameter in the above expression is available, and thus, the solution thereof is not difficult to obtain. However, because the communication conditions in the spacecraft cluster environment are severe, it is difficult to obtain the positions of the neighbors j of the spacecraft i only, and further it is difficult to accurately calculate the effective coverage areas f j of the neighbors of the spacecraft i.
In the method of the present invention, S ij＝Sji、xij＝xji is present due to the use of the effective coverage algorithm described above,Wherein S ij and S ji can be both represented as overlapping coverage areas of spacecraft i and spacecraft j, and x ij and x ji can both represent euclidean distance of spacecraft i and corresponding neighbor, ||x i-xj||2, so there isThereby having the following characteristicsFurther, the solution of the target moving speed u i can be expressed as
In other words, the algorithm of the effective coverage area is adopted, and the overlapping coverage areas among the spacecrafts can be uniformly spread to the effective coverage area of each spacecraft, so that the influence of the position of any one of the two spacecrafts which are neighbors to the calculation of the effective coverage area of the other spacecraft is quantified, namely thatOn the basis, non-neighbor information (such as the position x j of the neighbor j required by calculating f j) which cannot be acquired by a single spacecraft due to communication limitation required in the gradient descent method solving process can be replaced by neighbor information (such as the position x j of the neighbor j) which can be acquired through communication with the neighbor, so that a distributed algorithm is configured for each spacecraft under the communication constraint condition, the position x i of the spacecraft and the position x j of the neighbor which can be acquired through communication are only required to be acquired, the target moving speed u i which increases the total effective coverage area of the spacecraft cluster is calculated by combining the maximum communication distance L and the expression of the target moving speed u i, and when the target moving speed u i is converged to 0, the spacecraft reaches a steady state, the total effective coverage area of the spacecraft cluster is effectively increased, and the optimal coverage of the spacecraft cluster is realized.
Furthermore, in consideration of communication constraint, a communication constraint factor g ij and a penalty function thereof can be introduced into the total effective coverage area F of the spacecraft cluster to perform function optimization, so that a total effective coverage area optimization function phi of the spacecraft cluster is obtained, and the method is also used for solving by a negative gradient descent method. Specifically, the total effective coverage area optimization functionThus, the method can be obtained after solving the problems by adopting a negative gradient descent methodNamely, the aforementioned expression of the target moving speed u i.
The method of the embodiment of the invention further introduces a communication constraint factor and a penalty function thereof, and can enable the state of each spacecraft to quickly approach to the optimal position under the condition of ensuring the communication distance, thereby maximizing the total effective coverage area of the spacecraft cluster.
The foregoing description of the embodiments and description is presented to illustrate the scope of the invention, but is not to be construed as limiting the scope of the invention. Modifications, equivalents, and other improvements to the embodiments of the invention or portions of the features disclosed herein, as may occur to persons skilled in the art upon use of the invention or the teachings of the embodiments, are intended to be included within the scope of the invention, as may be desired by persons skilled in the art from a logical analysis, reasoning, or limited testing, in combination with the common general knowledge and/or knowledge of the prior art.
Claims (5)
1. A method for realizing optimal coverage of a spacecraft cluster, which is used for increasing the total effective coverage area of the spacecraft cluster; the method is characterized in that: the spacecraft clusters comprise a plurality of spacecrafts which move at equal height relative to a ground plane, the total effective coverage area of the spacecraft clusters is the sum of the effective coverage areas of the spacecrafts, and the effective coverage area of each spacecraft is defined as the projection area of a sphere orthographic projection onto the ground plane by taking the position of each spacecraft as the sphere center and the coverage radius ri as the radius; each spacecraft has a maximum communication distance L and is suitable for communicating with at least one other spacecraft, and the other spacecraft communicated with each spacecraft is defined as the neighbor of the spacecraft;
in the method, each spacecraft performs the following steps at preset adjustment periods:
Acquiring a self position x i and communicating with each neighbor to acquire each neighbor position x j; wherein j∈N i,Ni is the set of all neighbors of spacecraft i;
Calculating a target moving speed u i in the adjustment period, wherein the target moving speed u i is a speed vector with a direction; the expression of the target moving speed u i is: The f i is the effective coverage area of the spacecraft i, and the expression is that D i is the number of neighbors of spacecraft i, S m represents the area of the area covered by spacecraft i only when m=1, and S m represents the sum of the areas covered by spacecraft i and m-1 neighbors together when m > 1; g ij is a communication constraint factor, which is positively related to the difference between the distance of spacecraft i from the corresponding neighbor and the maximum communication distance L; the saidA penalty function for the communication constraint factor g ij;
And moving according to the target moving speed u i until the target moving speed u i calculated in a certain adjustment period is converged to zero, and stopping the movement of the spacecraft.
2. A method of achieving optimal coverage of a spacecraft cluster as claimed in claim 1, wherein: the communication constraint factor g ij is directly related to the difference of euclidean distance of spacecraft i from the corresponding neighbor x i-xj||2 from the maximum communication distance L.
3. A method of achieving optimal coverage of a spacecraft cluster as claimed in claim 2, wherein: the expression of the communication constraint factor g ij is: g ij＝(xi-xj)2-L2.
4. A method of achieving optimal coverage of a spacecraft cluster as claimed in claim 3, wherein: the penalty functionThe expression of the interior point penalty function is: Wherein, gamma k is penalty factor, gamma k > 0, and gamma k -0 when k-infinity.
5. A method of achieving optimal coverage of a spacecraft cluster as claimed in claim 1, wherein: s m in the expression of the effective coverage area f i is calculated by the following method: the said processWherein, Representing the area of set X, set X m represents the set of coordinates of the region covered only by spacecraft when m=1, and set X m represents the set of coordinates within the region commonly covered only by spacecraft i and m-1 neighbors when m > 1.
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