Space gravitational wave detection regular triangle formation optimal reconstruction configuration determination method

Abstract

The invention discloses a space gravitational wave detection regular triangle formation optimal reconstruction configuration determination method, and belongs to the technical field of spaceflight. The method comprises the steps of obtaining the position of a current space gravitational wave detection triangle formation; according to the reconstruction task type, reconstructing the position of the current space gravitational wave detection triangle formation to an equilateral triangle configuration, and obtaining a reconstruction target; aiming at a task requirement of space gravitational wave detection of a regular triangle formation configuration reconstruction scene, according to a reconstruction target and a configuration reconstruction behavior in a reconstruction process, constructing a regular triangle formation optimal reconstruction configuration in the reconstruction scene; and the current space gravitational wave detects the position of the triangle formation, and position movement is carried out according to the optimal reconstruction shape of the regular triangle formation in the reconstruction scene. According to the method, the optimal configuration determination method for different formation reconstruction fields is provided, the problem that the target position of the spacecraft cannot be determined in the formation reconstruction process is solved, and it is guaranteed that the formation can be rapidly and stably restored to the regular triangle configuration.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and particularly relates to a method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection. Background Technique

[0002] The space gravitational wave detection mission, as one of the frontier technologies for human exploration of the mysteries of the universe, is self-evidently complex and challenging. The core of this mission lies in a space equilateral triangle formation composed of three spacecraft. This unique configuration is designed based on the Michelson interference principle, aiming to capture and characterize the extremely weak gravitational wave signal carrying information from the depths of the universe by precisely measuring the arm length changes between adjacent spacecraft. Gravitational waves, as the ripples of spacetime predicted by Einstein's general theory of relativity, their direct detection not only verifies the correctness of the general theory of relativity but also opens a new window for observing the universe, enabling us to peek into the secrets behind extreme astrophysical events such as black hole collisions and neutron star mergers.

[0003] However, to achieve precise measurement of gravitational waves, the stability of the formation configuration is a crucial link. Ideally, these three spacecraft should always maintain a perfect equilateral triangle configuration to ensure the accuracy and reliability of measurement data. However, in actual missions, due to the complex and ever-changing space environment, such as the influence of uncertain factors like solar wind, micro-meteorite impacts, the system errors of the spacecraft itself, and control precision limitations, the formation configuration will inevitably deviate from the equilateral triangle during the long mission cycle. Such deviation not only reduces the measurement accuracy but may even lead to mission failure. Therefore, formation reconfiguration control has become a key technology to ensure the smooth progress of the space gravitational wave detection mission.

[0004] Although formation reconfiguration control is not a new thing in the aerospace field, many scholars and engineers have conducted in-depth research on it and achieved fruitful results. However, when applying these technologies to the specific background of the space gravitational wave detection formation, many challenges and limitations are faced. First of all, most of the formation reconfiguration control technologies in existing research focus on near-Earth orbits and small-scale spacecraft formations. The near-Earth orbit environment is relatively simple, the distance between spacecraft is relatively close, and communication and control are relatively convenient. Therefore, these technologies have been widely applied and verified in such formations. However, the space gravitational wave detection formation is very different. It is usually deployed in the deep space environment far from the Earth, the distance between spacecraft may reach millions or even tens of millions of kilometers, with large communication delays, high control difficulty, and the need to maintain a highly stable configuration for a long time, which poses higher requirements for formation reconfiguration control technologies.

[0005] Secondly, in the existing research on formation reconfiguration control, the focus has often been placed on transfer orbit optimization and spacecraft trajectory tracking problems. Transfer orbit optimization aims to find an optimal or sub-optimal orbit that enables the spacecraft to complete configuration adjustment with minimum energy consumption and time; while trajectory tracking is to ensure that the spacecraft can fly accurately along a predetermined orbit. These two aspects are undoubtedly important components of formation reconfiguration control, but they ignore a crucial problem in the formation reconfiguration process - the determination of the target positions of spacecraft. In the process of formation reconfiguration, how to accurately and quickly determine the target positions of each spacecraft to ensure that the formation can quickly and stably return to the equilateral triangle configuration is a rarely involved but extremely crucial link in the existing research. Summary of the Invention

[0006] Aiming at the problem in the existing technology of how to accurately and quickly determine the target positions of each spacecraft to ensure that the formation can quickly and stably return to the equilateral triangle configuration. The present invention provides a method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection, and proposes an optimal configuration determination method for different formation reconfiguration scenarios, solving the problem that the target positions of spacecraft cannot be determined during the formation reconfiguration process, and ensuring that the formation can quickly and stably return to the equilateral triangle configuration.

[0007] To achieve the above object, the present invention provides the following technical solutions.

[0008] In the first aspect, the present invention provides a method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection, including:

[0009] Obtain the position of the current equilateral triangle formation for space gravitational wave detection;

[0010] According to the type of reconfiguration task, reconfigure the position of the current equilateral triangle formation for space gravitational wave detection to an equilateral triangle configuration to obtain a reconfiguration target;

[0011] For the task requirements of the formation reconfiguration scenario of the equilateral triangle formation for space gravitational wave detection, according to the reconfiguration target, obtain the formation reconfiguration behavior during the reconfiguration process, and construct the optimal reconfiguration configuration of the equilateral triangle formation in the reconfiguration scenario;

[0012] Move the position of the current equilateral triangle formation for space gravitational wave detection according to the optimal reconfiguration configuration of the equilateral triangle formation in the reconfiguration scenario.

[0013] As a further improvement of the present invention, the obtaining the position of the current equilateral triangle formation for space gravitational wave detection includes:

[0014] Obtain the position of the current equilateral triangle formation for space gravitational wave detection according to the operating states of 3 spacecraft in the current space gravitational wave detection formation.

[0015] As a further improvement of the present invention, according to the reconstruction behavior, reconstructing the position of the current space gravitational wave detection triangular formation into an equilateral triangle configuration to obtain a reconstruction target includes:

[0016] Obtaining the reconstruction behavior according to the mission requirements;

[0017] Judging whether the current space gravitational wave detection triangular formation is an equilateral triangle configuration under the mission conditions. If not, reconstructing the position of the current space gravitational wave detection triangular formation into an equilateral triangle configuration to obtain a reconstruction target.

[0018] As a further improvement of the present invention, judging whether the current space gravitational wave detection triangular formation is an equilateral triangle configuration under the mission conditions includes:

[0019] If it does not satisfy the equilateral triangle configuration under the mission conditions, obtaining the configuration reconstruction behavior during the process of reconstructing the position of the current space gravitational wave detection triangular formation into an equilateral triangle configuration.

[0020] As a further improvement of the present invention, judging whether the current space gravitational wave detection triangular formation is an equilateral triangle configuration under the mission conditions includes:

[0021] If it satisfies the equilateral triangle configuration under the mission conditions, judging whether the current space gravitational wave detection triangular formation meets the optimization requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection;

[0022] If it meets the optimization requirements, the position of the current space gravitational wave detection triangular formation does not need to be reconstructed into an equilateral triangle configuration;

[0023] If it does not meet the optimization requirements, obtaining the configuration reconstruction behavior during the process of reconstructing the position of the current space gravitational wave detection triangular formation into an equilateral triangle configuration.

[0024] As a further improvement of the present invention, the configuration reconstruction behavior during the reconstruction process includes configuration restoration, scale adjustment, or detection target switching.

[0025] As a further improvement of the present invention, for the mission requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection, obtaining the configuration reconstruction behavior during the reconstruction process according to the reconstruction target and constructing the optimal reconstruction configuration of the equilateral triangle formation under the reconstruction scenario includes:

[0026] For the mission requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection, selecting the phase angle of the first spacecraft in the current space gravitational wave detection triangular formation as the optimization variable and constructing the optimal reconstruction configuration of the equilateral triangle formation under the configuration restoration reconstruction scenario includes:

[0027]

[0028] In the formula, i is the number of the three spacecrafts in the equilateral triangle formation; l is the formation arm length; α is the phase angle of the leading spacecraft in the formation; J is the energy consumption of the entire formation reconstruction task; n is the orbital angular velocity of the reference orbit; t0 is the initial moment of the formation reconstruction task; t f is the end moment of the formation reconstruction task. When t0, t f is the task time of the entire formation reconstruction task; ΔV i 1 is the first pulse of the i-th spacecraft; ΔV i 2 is the second pulse of the i-th spacecraft; is the initial state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; is the terminal state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit;

[0029] Solving the above formula based on the genetic algorithm, the optimal reconstruction configuration of the equilateral triangle formation in the configuration recovery reconstruction scenario is obtained.

[0030] As a further improvement of the present invention, aiming at the optimization requirements of the equilateral triangle formation configuration reconstruction scenario for space gravitational wave detection, according to the reconstruction target, the configuration reconstruction behavior during the reconstruction process is obtained, and the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario is constructed, including:

[0031] Aiming at the optimization requirements of the equilateral triangle formation configuration reconstruction scenario for space gravitational wave detection, a new fly-around circular orbit is obtained according to the expected arm length, and the optimal reconstruction configuration of the equilateral triangle formation in the scale adjustment reconstruction scenario is constructed, including:

[0032]

[0033] Among them, i is the number of the three spacecrafts in the equilateral triangle formation; α is the phase angle of the leading spacecraft in the formation; J is the energy consumption of the entire formation reconstruction task; n is the orbital angular velocity of the reference orbit; t0 is the initial moment of the formation reconstruction task; t f is the end moment of the formation reconstruction task. When t0, t f is the task time of the entire formation reconstruction task; ΔV i 1 is the first pulse of the i-th spacecraft; ΔV i 2 is the second pulse of the i-th spacecraft; l * is the final expected formation arm length; is the initial state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; is the terminal state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit;

[0034] Solving the above equation based on the genetic algorithm to obtain the optimal reconstruction configuration of the equilateral triangle formation in the scale-adjusted reconstruction scenario.

[0035] As a further improvement of the present invention, aiming at the optimization requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection, according to the reconstruction target, obtaining the formation reconstruction behavior during the reconstruction process, and constructing the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario, including:

[0036] Aiming at the optimization requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection, calculating the reconstruction configuration parameters under the reference orbit of the new detection target, transforming the reconstruction configuration parameters under the reference orbit of the new detection target to the reference orbit of the original detection target, and constructing the optimal reconstruction configuration of the equilateral triangle formation in the detection target switching reconstruction scenario, including:

[0037]

[0038] In the formula, is the target configuration state in the LVLH coordinate system of the new reference orbit; represents the initial state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; represents the terminal state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; n * is the orbital angular velocity of the new reference orbit; the nonlinear function g(·) represents the state transformation relationship from the LVLH coordinate system of the new reference orbit to the LVLH coordinate system of the original reference orbit; i is the number of the three spacecraft in the equilateral triangle formation; l is the formation arm length; α is the phase angle of the leading spacecraft in the formation; J is the energy consumption of the entire formation reconstruction task; n is the orbital angular velocity of the reference orbit; t0 is the initial moment of the formation reconstruction task; t f is the end moment of the formation reconstruction task, when t0, t f is the task time of the entire formation reconstruction task; ΔV i 1 is the first pulse of the i-th spacecraft; ΔV i 2 is the second pulse of the i-th spacecraft;

[0039] Solving the above equation based on the genetic algorithm to obtain the optimal reconstruction configuration of the equilateral triangle formation in the detection target switching reconstruction scenario.

[0040] As a further improvement of the present invention, the position of the current space gravitational wave detection triangle formation is moved according to the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario, including:

[0041] The position of the current triangular formation for space gravitational wave detection. According to the optimal reconstruction shape of the equilateral triangle formation in the reconstruction scenario, the formation will move its position towards the optimal reconstruction shape of the equilateral triangle formation based on the current position.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The present invention can effectively solve the problem that the target position of a spacecraft cannot be accurately and quickly determined in the prior art. Especially in the space gravitational wave detection mission, through the restoration of the equilateral triangle formation, the precise reconstruction of the spacecraft position is achieved. The method of the present invention first obtains the position of the current triangular formation for space gravitational wave detection and reconstructs it into an equilateral triangle configuration, ensuring that the formation can quickly and stably return to the target configuration in any complex environment. By analyzing the configuration reconstruction behavior during the formation reconstruction process and combining the optimization requirements of the reconstruction scenario, the optimal configuration can be calculated in real-time during the movement of the spacecraft, enabling the target position of each spacecraft to be accurately determined and the optimal spatial layout to be achieved, thus avoiding the errors and risks brought by position uncertainty during the formation process.

[0044] Furthermore, in the mission requirements of space gravitational wave detection, the present invention can significantly improve the stability and reliability of the formation, ensuring the smooth completion of the mission. In addition, based on the determination of the optimal reconstruction configuration, the spacecraft can reduce unnecessary adjustments during the formation adjustment, reducing fuel consumption, thereby extending the service life of the spacecraft and reducing the overall cost of the mission. By reducing the fuel consumption of the spacecraft, the present invention not only optimizes the resource utilization rate of the space mission but also improves the efficiency of mission execution, ensuring the high efficiency and accuracy of the detection process. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings described herein are for illustrative purposes only and are not intended to limit the scope of the disclosure of the present invention in any way. In the drawings:

[0046] Figure 1 is a schematic flow chart of a method for determining the optimal reconstruction configuration of an equilateral triangle formation for space gravitational wave detection according to the present invention;

[0047] Figure 2 is a schematic specific flow chart of a method for determining the optimal reconstruction configuration of an equilateral triangle formation for space gravitational wave detection according to the present invention;

[0048] Figure 3 is a schematic diagram of formation reconstruction for configuration restoration according to the present invention;

[0049] Figure 4 is a schematic diagram of formation reconstruction for scale adjustment according to the present invention;

[0050] Figure 5Schematic diagram of formation reconfiguration for detecting target switching according to the present invention;

[0051] Figure 6 Schematic diagram of the physical meaning of the first phase angle of the formation configuration according to the present invention;

[0052] Figure 7 Simulation diagram of the optimal reconfiguration configuration example of formation reconfiguration for configuration recovery according to the present invention;

[0053] Figure 8 Simulation diagram of the optimal reconfiguration configuration example of formation reconfiguration for scale adjustment according to the present invention;

[0054] Figure 9 Simulation diagram of the optimal reconfiguration configuration example of formation reconfiguration for detecting target switching according to the present invention. Detailed implementation manners

[0055] In order to enable those skilled in the art of the present technology to better understand the technical solutions in the present invention, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. The described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments, and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0057] In view of the lack of in-depth research on the formation reconfiguration control technology for the space gravitational wave detection formation in the prior art, and the problem of determining the target position of the spacecraft during the formation reconfiguration process has not been systematically discussed. The present invention provides a method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection, as Figure 1 shown, the method includes:

[0058] S100: Obtain the position of the current space gravitational wave detection triangle formation;

[0059] S200: According to the type of reconfiguration task, reconfigure the position of the current space gravitational wave detection triangle formation to an equilateral triangle configuration to obtain a reconfiguration target;

[0060] S300: According to the task requirements of the regular triangle formation reconfiguration scenario for space gravitational wave detection, obtain the formation reconfiguration behavior during the reconfiguration process based on the reconfiguration target, and construct the optimal reconfiguration formation of the regular triangle formation in the reconfiguration scenario.

[0061] S400: Move the position of the current triangle formation for space gravitational wave detection according to the optimal reconfiguration formation of the regular triangle formation in the reconfiguration scenario.

[0062] The present invention proposes three types of formation reconfiguration scenarios for space gravitational wave detection tasks and a method for determining the optimal formation with fuel consumption as an index, solving the problem of unable to determine the target position of spacecraft during the formation reconfiguration process.

[0063] The following further explains the present invention in conjunction with specific embodiments.

[0064] In view of the background of space gravitational wave detection tasks, three types of formation reconfiguration task scenarios are proposed; at the same time, corresponding methods for determining the optimal reconfiguration formation are designed for the three types of formation reconfiguration scenarios. With fuel consumption as the performance index and the phase angle of the leading spacecraft as the optimization variable, a double-pulse control is used as the control model to establish an optimization problem for determining the optimal formation; a genetic algorithm is used to solve the established optimization problem. As Figure 2 shown, the method includes:

[0065] S1: Divide the formation reconfiguration behavior of the regular triangle formation for space gravitational wave detection into three categories: formation recovery, scale adjustment, and detection target switching, and then construct a series of methods for determining the optimal reconfiguration formation.

[0066] Specifically, according to the operating states of the three spacecraft in the current formation for space gravitational wave detection, obtain the position of the current triangle formation for space gravitational wave detection. Determine whether the current triangle formation for space gravitational wave detection is a regular triangle formation, and the specific determination is as follows:

[0067] According to the task requirements, obtain the reconfiguration behavior.

[0068] Determine whether the current triangle formation for space gravitational wave detection is a regular triangle formation that meets the task conditions. If not, reconfigure the position of the current triangle formation for space gravitational wave detection to a regular triangle formation and obtain the reconfiguration process.

[0069] If it does not meet the regular triangle formation condition of the task, obtain the formation reconfiguration behavior during the process of reconfiguring the position of the current triangle formation for space gravitational wave detection to a regular triangle formation.

[0070] If it meets the regular triangle formation condition of the task, determine whether the current triangle formation for space gravitational wave detection meets the optimization requirements of the regular triangle formation reconfiguration scenario for space gravitational wave detection;

[0071] If the optimization requirements are met, the position of the current triangular formation for space gravitational wave detection does not need to be reconstructed into an equilateral triangle configuration;

[0072] If the optimization requirements are not met, obtain the configuration reconstruction behavior during the process of reconstructing the position of the current triangular formation for space gravitational wave detection into an equilateral triangle configuration.

[0073] As Figure 3 shown, formation reconstruction for configuration recovery means that during long-term on-orbit operation, the space gravitational wave detection formation is affected by various measurement errors and external disturbances, resulting in the formation configuration deviating from the standard equilateral triangle configuration. To ensure the normal progress of subsequent gravitational wave detection tasks, it is necessary to reconstruct the current formation configuration into the standard equilateral triangle configuration.

[0074] Formation reconstruction for configuration recovery is a key technology for realizing long-term operation of space gravitational wave detection. In addition to ensuring the long-term stable operation of the detection formation, formation reconstruction can also serve different accuracy requirements for gravitational wave detection. As Figure 4 shown, according to the principle of space gravitational wave detection, by adjusting the arm lengths of the equilateral triangle formation, the detection requirements for gravitational waves in different frequency bands can be achieved.

[0075] For the equilateral triangle formation designed based on the CW equation, the angle between its formation plane and the reference orbit plane can only be 60°, which also results in a very limited detection range. Therefore, if a gravitational wave detection task in a specific direction is to be achieved, it is necessary to adjust the azimuth of the reference orbit where the formation center is located. As Figure 5 shown, it changes from the original detection direction to another direction, and thus a formation reconstruction scenario for switching detection targets is proposed.

[0076] S2: For the three types of formation reconstruction task scenarios, construct the optimal reconstruction configuration optimization problem for configuration recovery based on the double-pulse control mode.

[0077] S21: For the formation configuration reconstruction scenario for configuration recovery, construct the optimal reconstruction configuration optimization problem for configuration recovery based on the double-pulse control mode;

[0078] Specifically, for the formation configuration reconstruction scenario for configuration recovery, the reconstructed configuration refers to a certain equilateral triangle configuration on the "space circle" where the original equilateral triangle configuration is located. By selecting the phase angle of the first spacecraft as the optimization variable, as Figure 6 shown, all reconstructed configurations are discretized, the fuel consumption is calculated based on the double-pulse control mode and used as a performance index, and the optimal reconstruction configuration optimization problem for configuration recovery is constructed.

[0079] The optimal reconstruction configuration optimization problem for configuration recovery is specifically expressed as follows:

[0080]

[0081]

[0082] In the formula, i represents the numbers of the three spacecrafts in the equilateral triangle formation; l represents the formation arm length; α represents the phase angle of Spacecraft No. 1 in the formation (also known as the phase angle of the leading spacecraft). Due to the geometric constraints of the equilateral triangle, an equilateral triangle on the fly-around orbit can be determined only by the phase angle of the leading spacecraft, as shown in Figure 6 ; the index J represents the energy consumption of the entire formation reconfiguration mission; represents the initial state quantity of Spacecraft No. i in the LVLH coordinate system of the original reference orbit; represents the terminal state quantity of Spacecraft No. i in the LVLH coordinate system of the original reference orbit, which can be calculated by the optimization variable α; n represents the orbital angular velocity of the reference orbit; t₀ represents the initial moment of the formation reconfiguration mission, usually taken as 0; t f represents the end moment of the formation reconfiguration mission. When t₀, t f also represents the mission time of the entire formation reconfiguration mission; ΔV i 1 and ΔV i 2 respectively represent the first pulse and the second pulse of Spacecraft No. i; Φ(t f , t₀) and Φ v (t f , t₀) respectively represent the state transition matrix of the CW equation and its sub-matrix, and the specific expressions are as follows:

[0083]

[0084]

[0085] S22: For the formation configuration reconfiguration scenario for scale adjustment, an optimal reconfiguration configuration optimization problem for configuration recovery is constructed based on the double-pulse control mode;

[0086] Specifically, for the formation configuration reconfiguration scenario for scale adjustment, the reconfiguration configuration refers to a certain equilateral triangle configuration on the "space circle" where the new-scale equilateral triangle configuration is located. First, calculate the "space circle" where the new configuration is located, discretize the reconfiguration configuration on the new "space circle", and then, also based on the double-pulse control mode, calculate the fuel consumption and use it as a performance index to construct an optimal reconfiguration configuration optimization problem for scale adjustment;

[0087] For the optimal reconfiguration configuration optimization problem for scale adjustment, a new fly-around circular orbit can be defined according to the expected arm length, and based on the optimization model of S21 on the new fly-around circular orbit, the following optimization problem can be constructed:

[0088]

[0089] In the formula, l * represents the formation arm length that is finally desired to be formed.

[0090] S23: For the formation configuration reconstruction scenario for switching to a detection target, an optimal reconstruction configuration optimization problem for configuration recovery is constructed based on the double-pulse control mode;

[0091] Specifically, for the formation configuration reconstruction scenario for switching to a detection target, the reconstructed configuration refers to a certain equilateral triangle configuration on the "space circle" where the equilateral triangle configuration is located under the new reference orbit. First, the parameters of the reconstructed configuration under the new reference orbit need to be calculated. Secondly, it is transformed to the original reference orbit. Subsequently, the fuel consumption is also calculated based on the double-pulse control mode and used as a performance index to construct an optimal reconstruction configuration optimization problem for switching to a detection target;

[0092] The optimal reconstruction configuration optimization problem for switching to a detection target is specifically expressed as follows:

[0093]

[0094] In the formula, represents the target configuration state in the LVLH coordinate system of the new reference orbit; and represent the target configuration state and the initial state in the LVLH coordinate system of the original reference orbit; n * represents the orbital angular velocity of the new reference orbit; the nonlinear function g() represents the state transformation relationship from the LVLH coordinate system of the new reference orbit to the LVLH coordinate system of the original reference orbit.

[0095] S3: Solve the three optimization problems constructed in S2 based on the genetic algorithm. The input of the algorithm is the initial relative state of the spacecraft in the formation, and the output is the initial phase angle of the formation configuration. Finally, the optimal reconstruction configuration of the formation under three types of configuration reconstruction scenarios is calculated according to the initial phase angle.

[0096] The initial relative state of the spacecraft in the current space gravitational wave detection triangular formation input by the genetic algorithm refers to The initial phase angle of the current space gravitational wave detection triangular formation configuration output by the algorithm refers to α, and the optimal reconstruction configuration of the formation under three types of configuration reconstruction scenarios calculated according to the initial phase angle refers to calculating The specific calculation formula is:

[0097]

[0098] According to the optimal reconstruction shape of the equilateral triangle formation under the reconstruction scenario, the phase angle of the first spacecraft in the current space gravitational wave detection triangle formation is adjusted, and the current space gravitational wave detection triangle formation is driven by the first spacecraft to move towards the optimal reconstruction shape of the equilateral triangle formation under the reconstruction scenario.

[0099] In summary, this paper proposes a method for determining the optimal reconstruction configuration of an equilateral triangle formation for space gravitational wave detection. Three types of formation reconstruction mission scenarios are proposed. Based on a dual-pulse control mode, the optimal reconstruction configuration optimization problem for each scenario is established. Ultimately, the optimal reconstruction configuration is obtained using a genetic algorithm. Compared to existing research on formation reconstruction for space gravitational wave detection, this method clarifies three mission scenarios for formation reconstruction, addressing the lack of clear mission context in existing research. It also proposes methods for determining the optimal formation reconstruction configuration for these three mission scenarios, addressing the lack of optimality in reconstruction terminal targets in existing research.

[0100] The present invention will be further explained below with reference to specific embodiments.

[0101] Example

[0102] S1: Determination of the optimal reconfiguration of the formation for configuration recovery

[0103] The optimal reconstruction configuration determination method in the configuration recovery scenario is verified. The relative initial states of the three spacecraft in the formation at the given initial moment are shown in Table 1. As shown. By solving the problem through genetic algorithm, the optimized phase angle of the first spacecraft is 82.45°, and then the target states of the three spacecraft are calculated as shown in Table 1. As shown. The final optimized reconstruction configuration is as follows Figure 7 shown.

[0104] Table 1 Optimization results of the optimal reconstruction configuration of the formation for configuration recovery

[0105]

[0106]

[0107] S2: Determination of the optimal reconfiguration configuration for formations oriented to scale adjustment

[0108] The optimal reconstruction configuration determination method in the configuration recovery scenario is verified. The relative initial states of the three spacecraft in the formation at the given initial moment are shown in Table 2. As shown. By solving the problem through genetic algorithm, the optimized phase angle of the first spacecraft is 185.52°, and then the target states of the three spacecraft are calculated as shown in Table 2. As shown. The final optimized reconstruction configuration is as follows Figure 8 shown.

[0109] Table 2 Optimal Reconfiguration Configuration Optimization Results for Scale Adjustment Oriented Formation

[0110]

[0111] S3: Determination of the Optimal Reconfiguration Configuration for Probe Target Switching Oriented Formation

[0112] Verify the method for determining the optimal reconfiguration configuration in the configuration recovery scenario. Given the relative initial states of three spacecraft in the formation at the initial moment as shown in Table 3 shown. Solve through the genetic algorithm. The phase angle of the leading spacecraft is optimized to 359.84°, and then the target states of the three spacecraft are calculated respectively as shown in Table 3 shown. The finally optimized reconfiguration configuration is as shown in Figure 9 shown.

[0113] Table 3 Optimal Reconfiguration Configuration Optimization Results for Probe Target Switching Oriented Formation

[0114]

[0115] Upon reading the above description, many embodiments and many applications other than the provided examples will be obvious to those skilled in the art. Therefore, the scope of this teaching should not be determined with reference to the above description, but should be determined with reference to the full scope of the foregoing claims and the equivalents of these claims. For the sake of comprehensiveness, all articles and references including patent applications and published announcements are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the foregoing claims is not intended to abandon such subject matter, nor should the applicant be considered not to have considered such subject matter as part of the disclosed inventive subject matter.

[0116] The above content is a further detailed description of the present invention. It cannot be determined that the specific implementation of the present invention is limited to this. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as falling within the protection scope determined by the claims submitted for the present invention.

Claims

1. A method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection, characterized in that, Including: Obtain the position of the current triangular formation for space gravitational wave detection; According to the type of reconstruction task, reconstruct the position of the current triangular formation for space gravitational wave detection into an equilateral triangle configuration to obtain a reconstruction target; For the task requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection, according to the reconstruction target, obtain the formation reconstruction behavior during the reconstruction process, and construct the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario; The position of the current triangular formation for space gravitational wave detection is moved according to the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario.

2. The method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection according to claim 1, characterized in that The obtaining of the position of the current equilateral triangle formation for space gravitational wave detection includes: Obtain the position of the current equilateral triangle formation for space gravitational wave detection according to the operating states of 3 spacecraft in the current space gravitational wave detection formation.

3. The optimal reconfiguration configuration determination method for an equilateral triangle formation in space gravitational wave detection according to claim 1, characterized in that The reconstructing of the position of the current triangular formation for space gravitational wave detection into an equilateral triangle configuration according to the reconstruction behavior to obtain a reconstruction target includes: Obtain the reconstruction behavior according to the task requirements; Judge whether the current triangular formation for space gravitational wave detection is an equilateral triangle configuration that meets the task conditions. If not, reconstruct the position of the current triangular formation for space gravitational wave detection into an equilateral triangle configuration to obtain a reconstruction target.

4. The method for determining the optimal reconstruction configuration of an equilateral triangle formation for space gravitational wave detection according to claim 3, characterized in that The judging whether the current triangular formation for space gravitational wave detection is an equilateral triangle configuration that meets the task conditions includes: If it is not an equilateral triangle configuration that meets the task conditions, obtain the formation reconstruction behavior during the process of reconstructing the position of the current triangular formation for space gravitational wave detection into an equilateral triangle configuration.

5. The method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection according to claim 3, characterized in that The judging whether the current triangular formation for space gravitational wave detection is an equilateral triangle configuration that meets the task conditions includes: If it is an equilateral triangle configuration that meets the task conditions, judge whether the current triangular formation for space gravitational wave detection meets the optimization requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection; If it meets the optimization requirements, the position of the current triangular formation for space gravitational wave detection does not need to be reconstructed into an equilateral triangle configuration; If it does not meet the optimization requirements, obtain the formation reconstruction behavior during the process of reconstructing the position of the current triangular formation for space gravitational wave detection into an equilateral triangle configuration.

6. The method for determining the optimal reconstruction configuration of an equilateral triangle formation for space gravitational wave detection according to claim 1, wherein The formation reconstruction behavior during the reconstruction process includes formation restoration, scale adjustment or detection target switching.

7. The optimal reconstruction configuration determination method for an equilateral triangle formation in space gravitational wave detection according to claim 6, characterized in that The obtaining of the formation reconstruction behavior during the reconstruction process according to the reconstruction target for the task requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection and constructing the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario includes; For the task requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection, select the phase angle of the first spacecraft in the current triangular formation for space gravitational wave detection as the optimization variable, and construct the optimal reconstruction configuration of the equilateral triangle formation in the formation restoration reconstruction scenario, including: In the formula, i is the number of the three spacecrafts in the equilateral triangle formation; l is the formation arm length; α is the phase angle of the leading spacecraft in the formation; J is the energy consumption of the entire formation reconstruction mission; n is the orbital angular velocity of the reference orbit; t0 is the initial time of the formation reconstruction mission; t f is the end time of the formation reconstruction mission. When t0, t f is the mission time of the entire formation reconstruction mission; ΔV i 1 is the first pulse of the i-th spacecraft; ΔV i 2 is the second pulse of the i-th spacecraft; is the initial state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; is the terminal state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; Solve the above formula based on the genetic algorithm to obtain the optimal reconstruction configuration of the equilateral triangle formation in the formation restoration reconstruction scenario.

8. The method for determining the optimal reconfiguration configuration of an equilateral triangle formation for space gravitational wave detection according to claim 6, wherein For the optimization requirements of the equilateral triangle formation reconstruction scenario for space gravitational wave detection, according to the reconstruction target, obtain the formation reconstruction behavior during the reconstruction process, and construct the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario, including: According to the optimization requirements for the scenario of reconstructing the equilateral triangle formation configuration in space gravitational wave detection, a new fly-around circular orbit is obtained based on the desired arm length, and the optimal reconstruction configuration of the equilateral triangle formation in the scale-adjusted reconstruction scenario is constructed, including: Among them, i is the number of the three spacecraft in the equilateral triangle formation; α is the phase angle of the leading spacecraft in the formation; J is the energy consumption of the entire formation reconstruction mission; n is the orbital angular velocity of the reference orbit; t0 is the initial time of the formation reconstruction mission; t f is the end time of the formation reconstruction mission. When t0, t f is the mission time of the entire formation reconstruction mission; ΔV i 1 is the first pulse of the i-th spacecraft; ΔV i 2 is the second pulse of the i-th spacecraft; l * is the formation arm length that is finally desired to be formed; is the initial state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; is the terminal state quantity of the i-th spacecraft in the LVLH coordinate system of the original reference orbit; Solving the above formula based on the genetic algorithm to obtain the optimal reconstruction configuration of the equilateral triangle formation in the scale-adjusted reconstruction scenario.

9. The method for determining the optimal reconstruction configuration of an equilateral triangle formation for space gravitational wave detection according to claim 6, wherein According to the optimization requirements for the scenario of reconstructing the equilateral triangle formation configuration in space gravitational wave detection, the configuration reconstruction behavior during the reconstruction process is obtained according to the reconstruction target, and the optimal reconstruction configuration of the equilateral triangle formation in the reconstruction scenario is constructed, including: According to the optimization requirements for the scenario of reconstructing the equilateral triangle formation configuration in space gravitational wave detection, the reconstruction configuration parameters under the reference orbit of the new detection target are calculated, and the reconstruction configuration parameters under the reference orbit of the new detection target are transformed to the reference orbit of the original detection target, and the optimal reconstruction configuration of the equilateral triangle formation in the detection target switching reconstruction scenario is constructed, including: In the formula, is the target configuration state in the new reference orbit LVLH coordinate system; represents the initial state quantity of the i-th spacecraft in the original reference orbit LVLH coordinate system; represents the terminal state quantity of the i-th spacecraft in the original reference orbit LVLH coordinate system; n * is the orbital angular velocity of the new reference orbit; the non-linear function g(·) represents the state transformation relationship from the new reference orbit LVLH coordinate system to the original reference orbit LVLH coordinate system; i is the number of the three spacecraft in the equilateral triangle formation; l is the formation arm length; α is the phase angle of the leading spacecraft in the formation; J is the energy consumption of the entire formation reconfiguration mission; n is the orbital angular velocity of the reference orbit; t0 is the initial time of the formation reconfiguration mission; t f is the end time of the formation reconfiguration mission. When t0, t f is the mission time of the entire formation reconfiguration mission; ΔV i 1 is the first pulse of the i-th spacecraft; ΔV i 2 is the second pulse of the i-th spacecraft; Solving the above formula based on the genetic algorithm to obtain the optimal reconstruction configuration of the equilateral triangle formation in the detection target switching reconstruction scenario.

10. The method for determining the optimal reconstruction configuration of an equilateral triangle formation for space gravitational wave detection according to claim 1, characterized in that The position of the current equilateral triangle formation in space gravitational wave detection is moved according to the optimal reconstruction shape of the equilateral triangle formation in the reconstruction scenario, including: For the position of the current equilateral triangle formation in space gravitational wave detection, according to the optimal reconstruction shape of the equilateral triangle formation in the reconstruction scenario, the formation will move its position towards the optimal reconstruction shape of the equilateral triangle formation according to the current position.

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