A method and system for maintaining the position of NRHO track stations

Abstract

This invention discloses a method and system for maintaining the position of an NRHO orbit station, belonging to the field of spacecraft technology. The method includes obtaining single-valued matrix eigenvalues ​​based on the nominal NRHO orbit, screening the eigenvalues ​​to form a candidate target set; obtaining parameter data based on the candidate target set; establishing a target optimization model based on the parameter data; and using the target optimization model to determine the NRHO orbit, thus completing the NRHO orbit station maintenance. This invention uses whether the eigenvalues ​​of the NRHO orbit single-valued matrix possess periodic orbital characteristics as a criterion for screening selectable candidate targets, avoiding the problem of excessively large velocity increments required for maintenance or even maintenance failure due to the instability of the target itself.

Description

Technical Field

[0001] This invention relates to the field of spacecraft technology, specifically to a method and system for maintaining the position of an NRHO orbital station. Background Technology

[0002] Near Rectilinear Halo Orbits (NRHOs) are a type of periodic translational point orbit that evolves from Halo orbits near the L1 or L2 points in the Earth-Moon restricted three-body problem. Located near the Moon, these orbits offer unobstructed communication with Earth and ensure that spacecraft orbiting them remain over the lunar south pole for extended periods. Therefore, NRHO orbits have significant engineering value for lunar polar exploration missions. Whitley et al. evaluated translational point orbits near the L1 and L2 points in terms of communication and thermal control, summarizing the following advantages of NRHO orbits: For lunar communication, NRHO orbits offer the best communication coverage, especially since their perigee is very close to the lunar south pole, allowing for relay-free direct communication with the south pole region 86% of the time; for Earth communication, NRHO orbits are completely unobstructed by the Moon, ensuring uninterrupted communication; and for thermal control, the NRHO orbit's thermal environment is relatively favorable, reducing the thermal stress on spacecraft. In summary, the NRHO orbit is more suitable for deploying spacecraft to support exploration missions in the lunar south polar region compared to other translational point orbits.

[0003] Although the NRHO orbit itself has high stability, the actual orbit of the spacecraft will still deviate from the nominal NRHO orbit during long-term operation. At the same time, considering the existence of errors such as navigation errors and actuator errors, the orbit deviation will occur in a short period of time, thus affecting the mission. Therefore, it is necessary to maintain the orbit position of the spacecraft.

[0004] Methods for maintaining orbital position at translational points can be categorized into pulsed thrust maintenance and continuous thrust maintenance. Continuous thrust maintenance primarily relies on the control system, but in practice, the control system operates continuously, preventing the navigation system from providing high-precision navigation data in real time, posing challenges in practical applications. Common methods for pulsed thrust maintenance include X-axis velocity control, the Floquet method, and the target method. The X-axis velocity control method, based on the characteristic that the X-axis velocity is zero when a periodic orbit crosses the XZ plane under three-body conditions, restricts the spacecraft's X-axis velocity each time it crosses the XZ plane. However, this characteristic is not present in real-world dynamic environments. The Floquet method combines the concept of invariant manifolds and Floquet theory, using pulses to eliminate unstable states in unstable directions to maintain orbital position. The unstable states in these directions are calculated using Floquet modes. However, Floquet theory is only applicable to linear time-varying systems, while the dynamic environment of translational points is highly nonlinear, making the theoretical framework challenging and difficult to implement in engineering.

[0005] X-axis velocity control and the Floquet method in continuous thrust maintenance and pulsed thrust maintenance both present engineering challenges. In contrast, the target method proposed by Marchand and Marchand is simple in structure, easy to implement in engineering, and has been applied in several translational point control missions. The target method is a method for maintaining a spacecraft near its nominal orbit. First, a target point is selected on the orbit. Then, a corrective velocity pulse is applied at the target point to correct the positioning error at the previous target point, thereby maintaining the spacecraft near its nominal orbit. However, traditional target methods do not address target selection strategies. Due to the unique dynamic characteristics of the NRHO orbit, its orbit maintenance results largely depend on the target point selection. An inappropriate target point selection can lead to excessively large velocity increments required for maintenance or even disastrous consequences such as position maintenance failure.

[0006] In summary, due to the unique dynamic characteristics of the NRHO orbit, traditional translational point orbit station maintenance methods are not suitable for the NRHO orbit. Therefore, it is essential to develop a station maintenance method suitable for the NRHO orbit that can meet various engineering constraints and achieve long-term low-energy effects. Summary of the Invention

[0007] Existing technologies for maintaining orbits largely depend on the selection of target points. Inappropriate target point selection can lead to excessively large velocity increments required for maintenance, or even station maintenance failure. This invention provides an NRHO orbit station maintenance method that uses the periodic orbital characteristics of the NRHO orbit single-value matrix eigenvalues ​​as a criterion to screen candidate target points. This avoids the problem of excessively large velocity increments required for maintenance, or even maintenance failure, caused by the instability of the target points themselves.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for maintaining the position of an NRHO orbital station includes:

[0010] Based on the nominal NRHO orbital, single-value matrix eigenvalues ​​are obtained, and the single-value matrix eigenvalues ​​are selected to form a candidate target set;

[0011] Based on the candidate target set, obtain parameter data;

[0012] Develop a target optimization model based on parametric data;

[0013] The target optimization model was used to determine the orbit of NRHO and maintain the NRHO orbit station position.

[0014] As a further improvement of the present invention, the step of obtaining the eigenvalues ​​of the single-value matrix based on the nominal NRHO orbit requires discretizing the nominal NRHO orbit into several points and calculating [R0V0] for each point. T The single-valued matrix Φ(T,0);

[0015] In the formula, R0 represents the position information of the point; V0 represents the velocity information of the point; and T represents the NRHO orbital period.

[0016] As a further improvement of the present invention, it is necessary to discretize the nominal NRHO orbit into several points, each point including position information and velocity information.

[0017] As a further improvement of the present invention, [R0V0] is calculated for each point. T The eigenvalues ​​of the single-valued matrix Φ(T,0) are used to select points from the eigenvalues ​​that conform to the characteristics of a periodic orbit to enter the candidate target point set. As a further improvement of the present invention, the parameter data includes optimization variables, fitness functions, and optimization constraints.

[0018] As a further improvement to the present invention, the optimization variables are established, including:

[0019] Assuming two maintenance cycles are performed within each orbital period, two target points are arbitrarily selected from the candidate target point set. Considering that the first maintenance after orbit insertion needs to correct the orbit insertion error, the target points for the first maintenance need to be considered separately. Therefore, the target point sequence consists of three target points and the time corresponding to each maintenance cycle.

[0020]

[0021] In the formula, X_list is the state sequence representing the target point, including position and velocity information; T_list is the time sequence representing the target point, indicating the time point when the sustaining pulse is applied; X1 is responsible for correcting the orbit insertion error; X2 is responsible for correcting the navigation mechanism error during long-term operation; and X3 is responsible for correcting the actuator error during long-term operation.

[0022] As a further improvement of the present invention, the fitness function is established, including:

[0023] Near the first entry point, due to entry error... The spacecraft will deviate from its insertion point X0, at which point the first pulse sustaining operation is required. The goal was to enable the spacecraft to reach the first target point X1 at the scheduled time T1, but navigation errors prevented it from doing so. and actuator error The presence of the spacecraft will allow it to reach a location near the first target point. Computer dynamic pulse again This enabled the spacecraft to reach the second target point X2, but also due to navigation errors... and actuator error The presence of the spacecraft will allow it to reach a location near the second target point. This process continues, applying sustaining pulses to allow the spacecraft to correct errors at the previous target point, until the entire sequence of target points has been traversed, yielding the sum of all sustaining velocity increments ΔV. total This is called fitness.

[0024] As a further improvement to the present invention, the optimization constraints are established, including:

[0025] Δv min ≤Δv≤Δv max

[0026] ΔT>ΔT min

[0027] ΔPos≤ΔPos max

[0028] In the formula, ΔV is the magnitude of the velocity increment required to maintain the pulse for each time; ΔV min ΔV represents the minimum velocity increment required to maintain the pulse for each pulse. max ΔT is the maximum value of the pulse velocity increment required for each sustaining period; ΔT is the time interval between two sustaining periods; ΔT min ΔPos is the minimum time interval between two sustaining pulses; ΔPos is the distance between the actual position reached by the spacecraft under the sustaining pulse and the target point; ΔPos min This represents the maximum distance between the actual position reached by the spacecraft under the sustaining pulse and the target point.

[0029] As a further improvement of the present invention, the target optimization model includes:

[0030] min(||Δv total ||)=min f([X_list, T_list])

[0031]

[0032] In the formula, X_list is the state sequence of the target points; T_list is the time sequence of the target points; ΔV total ΔV is the sum of all velocity increments required for maintenance; ΔV is the magnitude of the velocity increment required for each maintenance pulse; ΔV min ΔV represents the minimum velocity increment required to maintain the pulse for each pulse. max ΔT is the maximum value of the pulse velocity increment required for each sustaining period; ΔT is the time interval between two sustaining periods; ΔT min ΔPos is the minimum time interval between two sustaining pulses; ΔPos is the distance between the actual position reached by the spacecraft under the sustaining pulse and the target point; ΔPos min This represents the maximum distance between the actual position reached by the spacecraft under the sustaining pulse and the target point.

[0033] An NRHO track station maintenance system includes:

[0034] Target selection module: used to obtain single-value matrix eigenvalues ​​based on the nominal NRHO orbitals, and select single-value matrix eigenvalues ​​to form a candidate target set;

[0035] Parameter acquisition module: used to acquire parameter data based on the candidate target set;

[0036] Model building module: used to build target optimization models based on parameter data;

[0037] Station maintenance module: Used to determine the NRHO orbit using the target optimization model and complete the station maintenance of the NRHO orbit.

[0038] Compared with the prior art, the present invention has the following beneficial effects.

[0039] This invention improves the target selection strategy of the traditional target-based method. From a dynamic perspective, it uses the eigenvalues ​​of the nominal NRHO orbit single-value matrix to screen candidate targets, avoiding excessive velocity increments or even maintenance failure due to the instability of the target itself. Then, it optimizes the target sequence, avoiding uncontrollable targets while reducing the velocity increment required for maintenance. This achieves long-term low-energy maintenance of the NRHO orbit while meeting engineering constraints. Compared to the traditional target-based method, this invention not only significantly reduces the velocity increment required for maintenance but also improves the accuracy of maintenance. This invention not only improves the stability and reliability of orbit maintenance but also helps extend the lifespan of spacecraft. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating a method for maintaining the position of an NRHO track station according to the present invention.

[0041] Figure 2 The eigenvalue distribution of the NRHO track station maintenance method of the present invention conforms to the periodic track characteristics;

[0042] Figure 3 The eigenvalue distribution of the NRHO track station maintenance method of the present invention does not conform to the periodic track characteristics;

[0043] Figure 4 This is a flowchart of the target method for maintaining the NRHO orbital station position according to the present invention.

[0044] Figure 5 The distribution of the candidate target set of the NRHO orbit station maintenance method of the present invention on the NRHO orbit;

[0045] Figure 6 This is the optimal target point distribution for an NRHO track station maintenance method according to the present invention;

[0046] Figure 7 The station maintenance effect of the NRHO track station maintenance method of the present invention;

[0047] Figure 8 This refers to the speed increment required to maintain the NRHO track station position maintenance method of the present invention.

[0048] Figure 9 This invention relates to the maintenance accuracy of an NRHO track station maintenance method.

[0049] Figure 10 The image shows the Monte Carlo target shooting results of an NRHO orbital station maintenance method according to the present invention. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0051] The following detailed description is exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. The terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0052] Existing technologies for maintaining orbital positions largely depend on the selection of target points. Inappropriate target point selection can lead to excessively large velocity increments required for maintenance, or even station maintenance failure. This invention provides an NRHO (National Railway Orbital Maintenance) station maintenance method, such as... Figure 1 As shown, the method includes:

[0053] Based on the nominal NRHO orbital, single-value matrix eigenvalues ​​are obtained, and the single-value matrix eigenvalues ​​are selected to form a candidate target set;

[0054] Based on the candidate target set, obtain parameter data;

[0055] Develop a target optimization model based on parametric data;

[0056] The target optimization model was used to determine the orbit of NRHO and maintain the NRHO orbit station position.

[0057] The present invention will be further explained below with reference to the accompanying drawings:

[0058] This method improves the target selection strategy based on the traditional target method, and achieves long-term low-energy station maintenance of the NRHO orbit using the improved target method. The input is the nominal NRHO orbit. A candidate target set is screened by calculating the eigenvalues ​​of the orbit's single-value matrix. Further, an optimization algorithm is used to determine the optimal target sequence from the candidate target set obtained in the previous step, using the maintenance of the required velocity pulses as the optimization index. Substituting the optimal target sequence into the target method for station maintenance enables long-term low-energy maintenance of the NRHO orbit. The overall scheme can be divided into two parts, and the specific process is as follows:

[0059] S1: Screening the candidate target set:

[0060] S1.1: Discretize the nominal NRHO orbit into multiple points, each point including position and velocity information.

[0061] S1.2: Calculate [R0V0] for each point. TThe single-valued matrix Φ(T,0) is obtained by integrating formula (1) with formulas (2) and (3).

[0062]

[0063]

[0064]

[0065] In the formula, A(T) is the Jacobian matrix, and U xx U yy U zz U xy U xz and U yz These are the derivatives of the potential energy function in different directions, where U xx It is the second derivative of the spacecraft's potential energy in the x-direction, U yy It is the second derivative of the spacecraft's potential energy in the y-direction, U zz It is the spacecraft potential energy U zz The second derivative in the z-direction, U xy It is the second-order partial derivative of the spacecraft's potential energy in the x and y directions, U xz It is the second-order partial derivative of the spacecraft's potential energy in the x and z directions, u yz R1 is the second-order partial derivative of the spacecraft's potential energy in the y and z directions, R2 is the distance between the spacecraft and the Earth, R1 is the distance between the spacecraft and the Moon, μ is the mass parameter of the Earth-Moon system, [r x r y r z [R0V0] represents the spacecraft's position after one period T. T The result is obtained by integration under the three-body dynamics model.

[0066] S1.3: Calculate the eigenvalues ​​of each single-valued matrix Φ(T,0), and select points whose eigenvalues ​​conform to the periodic orbit characteristics to enter the candidate target point set. The distribution of eigenvalues ​​conforming to the periodic orbit characteristics in phase space is as follows: Figure 2 As shown, the distribution of eigenvalues ​​that do not conform to the characteristics of periodic orbits in phase space is as follows: Figure 3 As shown.

[0067] S2: Obtain the optimal target sequence through genetic algorithm optimization.

[0068] S2.1: Establish optimization variables. The optimization variables are determined as the target sequence required for station maintenance. Assuming that maintenance is carried out twice in each orbital cycle, two target points need to be selected from the candidate target point set. At the same time, considering that the first maintenance after orbit insertion needs to correct the orbit insertion error, the target point for the first maintenance needs to be considered separately. Therefore, the target sequence consists of three target points and the time corresponding to each maintenance, as shown in formula (4).

[0069]

[0070] In the formula, X_list is the state sequence of the target points, which includes position and velocity information; T_list is the time sequence of the target points, which represents the time points when the sustaining pulse is applied; X1 is the first target point; X2 is the second target point; and X3 is the third target point. Among them, the first target point X1 is responsible for correcting the orbital insertion error, while the second target point X2 and the third target point X3 are responsible for correcting navigation and actuator errors during long-term operation.

[0071] S2.2: Establish the fitness function.

[0072] Fitness was determined as the velocity increment required for long-term station maintenance on the NRHO orbit. The velocity increment was calculated using the target method. Figure 3 This is the procedure for the target-point method. Near the first orbital insertion point, due to orbital insertion error... The spacecraft will deviate from its insertion point X0, at which point the first pulse sustaining operation is required. The goal was to enable the spacecraft to reach the first target point X1 at the scheduled time T1, but navigation errors prevented this. and actuator error The spacecraft will reach a position near the first target point X1 due to its presence. Computer dynamic pulse again This enabled the spacecraft to reach the second target point X2, but also due to navigation errors... and actuator error The presence of this location means the spacecraft will reach a position near the second target point X2. This process continues, applying sustaining pulses to allow the spacecraft to correct errors at the previous target point, until all target point sequences have been traversed. The calculation of sustaining pulses is performed using a differential correction algorithm, where the sum of all required velocity increments ΔV is used for sustaining. total This is called fitness.

[0073] S2.3: Establish optimization constraints. The constraints for track maintenance consist of actuator constraints, navigation constraints, and maintenance accuracy constraints. Among them, the actuator constraints must satisfy that the maintenance pulse cannot be lower than the minimum maneuver pulse that the power system can provide, nor can it be greater than the maximum maneuver pulse that the power system can provide, as shown in formula (5); the navigation constraints must satisfy that the track maintenance interval is greater than the sampling time of the navigation system, as shown in formula (6); the maintenance accuracy constraints must satisfy that the station position deviation between the actual track and the nominal track cannot exceed the maximum value, as shown in formula (7).

[0074] Δv min ≤Δv≤Δv max (5)

[0075] ΔT>ΔT min (6)

[0076] ΔPos≤ΔPos max (7)

[0077] In the formula, ΔV is the magnitude of the velocity increment required for each pulse to maintain its position, which is calculated by the differential correction algorithm; ΔV min ΔV represents the minimum velocity increment required to maintain the pulse for each pulse. max ΔT is the maximum value of the pulse velocity increment required for each sustaining period; ΔT is the time interval between two sustaining periods; ΔT min ΔPos represents the minimum time interval between two sustaining pulses; ΔPos represents the distance between the actual position reached by the spacecraft under sustaining pulses and the target point, characterizing the position error, which is calculated by a differential correction algorithm; ΔPos min This represents the maximum distance between the actual position reached by the spacecraft under the sustaining pulse and the target point.

[0078] S2.4: Establish and optimize the target optimization model. The optimization model for maintaining a long-term low-energy station in the NRHO orbit can be expressed by formulas (8) and (9):

[0079] min(||Δv total ||)=min f([X_liat, T_lisr]) (8)

[0080]

[0081] The constraints are embodied in the form of a penalty function, and the fitness is set to infinity when the constraints are not satisfied. Substituting the target sequence into the target method yields the corresponding velocity increment, and then the optimization algorithm optimizes the velocity increment to obtain the optimal target sequence. The optimal target sequence can be used for long-term low-energy station maintenance in the NRHO orbit.

[0082] The present invention will be further explained and described below with reference to specific embodiments:

[0083] The data of this invention were tested using an NRHO orbital with a resonance ratio of 9:2. The initial values ​​of the NRHO orbital are [1.0134,0,-0.1754,0,-0.0837,0]. The simulation error settings are as follows:

[0084] Table 1 Error Simulation

[0085]

[0086] The simulation parameters, such as constraints, are set as follows:

[0087] Table 2 Simulation Parameter Settings

[0088]

[0089] The population size and number of iterations for the genetic algorithm were set to 20. The distribution of the candidate target set obtained through process 1 on the NRHO orbit is as follows. Figure 5 As shown, the candidate target area is concentrated in all regions except for the near-lunar point. Points near the near-lunar point, whether used as the target point of the previous maneuver or the maintenance point of the current maneuver, may cause a sharp increase in the maintained velocity increment and state error. Therefore, the target will be selected from the candidate target set, and the optimal target sequence for velocity increment will be solved by a genetic algorithm.

[0090] The optimal target point distribution for velocity increments obtained through process 2 is as follows: Figure 6 As shown in the diagram, the target points used to correct the orbital insertion error are located somewhere after the apollo point, while the target points responsible for routine maintenance are located after the apollo point and after the perigee point. After passing the target point for correcting the orbital insertion error, the spacecraft continues to run to the first routine maintenance target point after the apollo point, and then after about 2.99 days, it arrives at the second routine maintenance target point located after the perigee point. After running for about 3.09 days, it returns to the first target point. The interval between the two maintenance operations is roughly equal, and the two target points are also close to the center of symmetry in the orbit.

[0091] Maintenance effect Figure 7 As shown, the actual orbit of the spacecraft almost coincides with the nominal orbit, and this invention can maintain the spacecraft in the NRHO orbit.

[0092] The required speed increment and the maintenance error are as follows: Figure 8 and Figure 9As shown, a total of 121 maintenance maneuvers were performed throughout the year, including one correction for the orbital insertion error and 120 routine corrections. The average velocity increment required for each maintenance was approximately 0.029 m / s, with the largest velocity increment not exceeding 0.09 m / s and the smallest just exceeding 0.01 m / s. The maximum position error did not exceed 5 km, and the error distribution in the three directions was relatively even, with the largest not exceeding 5 km. Considering that the simulated position error reached the order of 2 km, keeping the spacecraft within 5 km of the nominal orbit is already a good result, and relative to the amplitude of the NRHO orbit, this order of magnitude of position error will not significantly affect the characteristics of the NRHO orbit.

[0093] Since simulation errors are random, a single simulation has an element of chance. Therefore, Monte Carlo simulations are performed to better statistically analyze velocity increment consumption. The results of 100 Monte Carlo simulations are as follows: Figure 10 As shown in the figure. The results show that the velocity increment required for the long-term low-energy station maintenance of the NRHO orbit using the present invention is very low, with an average velocity increment of 3.5 m / s per year. The largest velocity increment in 100 simulations does not exceed 3.8 m / s, while the smallest velocity increment is about 3.1 m / s.

[0094] Therefore, this invention can be applied to station maintenance on NRHO tracks, requiring an annual velocity increment of approximately 3.5 m / s, achieving long-term low-energy maintenance while ensuring high maintenance accuracy.

[0095] In summary, this invention improves the target selection strategy of the traditional target method. From the perspective of dynamic principles, it uses the periodic orbital characteristics of the eigenvalues ​​of the NRHO orbital single-value matrix as a criterion to screen candidate targets, avoiding excessive velocity increments required for maintenance or even maintenance failure due to the instability of the target itself. By optimizing the target sequence using a genetic algorithm, uncontrollable targets are avoided while reducing the velocity increment required for maintenance. This achieves long-term low-energy maintenance of the NRHO orbit while satisfying engineering constraints. Compared with the traditional target method, it not only significantly reduces the velocity increment required for maintenance but also improves the accuracy of maintenance. Therefore, this invention uses the periodic orbital characteristics of the NRHO orbital single-value matrix as the criterion for screening the candidate target set, avoiding poor maintenance results caused by the instability of the target's dynamic characteristics. Simultaneously, by optimizing the target sequence, long-term low-energy maintenance of the NRHO orbit can be achieved while satisfying engineering constraints and reducing the velocity increment required for maintenance.

[0096] The second objective of this invention is to provide an NRHO track station maintenance system, comprising:

[0097] Target selection module: used to obtain single-value matrix eigenvalues ​​based on the nominal NRHO orbitals, and select single-value matrix eigenvalues ​​to form a candidate target set;

[0098] Parameter acquisition module: used to acquire parameter data based on the candidate target set;

[0099] Model building module: used to build target optimization models based on parameter data;

[0100] Station maintenance module: Used to determine the NRHO orbit using the target optimization model and complete the station maintenance of the NRHO orbit.

[0101] A third objective of this invention is to provide an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the NRHO orbital station maintenance method.

[0102] The method for maintaining the NRHO track station position includes the following steps:

[0103] Based on the nominal NRHO orbital, single-value matrix eigenvalues ​​are obtained, and the single-value matrix eigenvalues ​​are selected to form a candidate target set;

[0104] Based on the candidate target set, obtain parameter data;

[0105] Develop a target optimization model based on parametric data;

[0106] The target optimization model was used to determine the orbit of NRHO and maintain the NRHO orbit station position.

[0107] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the NRHO orbital station maintenance method.

[0108] The method for maintaining the NRHO track station position includes the following steps:

[0109] Based on the nominal NRHO orbital, single-value matrix eigenvalues ​​are obtained, and the single-value matrix eigenvalues ​​are selected to form a candidate target set;

[0110] Based on the candidate target set, obtain parameter data;

[0111] Develop a target optimization model based on parametric data;

[0112] The target optimization model was used to determine the orbit of NRHO and maintain the NRHO orbit station position.

[0113] A fifth objective of this invention is to provide a computer program product comprising computer instructions that, when executed by a processor, implement the above-described... Figure 1The various processes of the method embodiments shown can achieve the same technical effect, and will not be described again here to avoid repetition.

[0114] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0115] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0116] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0117] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for maintaining the position of an NRHO track station, characterized in that, include: Based on the nominal NRHO orbital, single-value matrix eigenvalues ​​are obtained, and the single-value matrix eigenvalues ​​are selected to form a candidate target set; Based on the candidate target set, obtain parameter data; Develop a target optimization model based on parametric data; The target optimization model was used to determine the NRHO orbit and maintain the NRHO orbit station position. To obtain the eigenvalues ​​of the single-value matrix based on the nominal NRHO orbit, the nominal NRHO orbit needs to be discretized into several points, and the eigenvalues ​​of each point need to be calculated. single-valued matrix ; In the formula, This is the location information for that point; This provides the speed information for that point. For the NRHO orbital period; The nominal NRHO orbit needs to be discretized into several points, each point including position information and velocity information; Calculate each point single-valued matrix The eigenvalues ​​of the single-value matrix are used to select points that conform to the characteristics of a periodic orbit and enter them into the candidate target set.

2. The NRHO track station maintenance method according to claim 1, characterized in that, The parameter data includes optimization variables, fitness functions, and optimization constraints.

3. The NRHO track station maintenance method according to claim 2, characterized in that, The optimization variables are established, including: Assuming two maintenance cycles are performed within each orbital period, two target points are arbitrarily selected from the candidate target point set. Considering that the first maintenance after orbit insertion needs to correct the orbit insertion error, the target points for the first maintenance need to be considered separately. Therefore, the target point sequence consists of three target points and the time corresponding to each maintenance cycle. In the formula, To characterize the state sequence of the target point, including position and velocity information; The time series characterizing the target indicates the time point at which the sustaining pulse is applied; To be responsible for correcting orbital insertion errors, To be responsible for correcting errors in navigation mechanisms that have been in operation for a long time; To be responsible for correcting the errors of the actuators during long-term operation.

4. The NRHO track station maintenance method according to claim 2, characterized in that, Establishing the fitness function includes: Near the first entry point, due to entry error... The spacecraft will deviate from its orbital insertion point. At this point, the first pulse maintenance is required. To enable the spacecraft to arrive at the scheduled time Able to reach the first target However, due to navigation errors and actuator error The presence of the spacecraft will allow it to reach a location near the first target point. Computer pulse again Enables the spacecraft to reach the second target. However, also due to navigation errors and actuator error The presence of the spacecraft will allow it to reach a location near the second target point. This process continues, applying sustaining pulses to allow the spacecraft to correct errors at the previous target point, until all target point sequences have been traversed, obtaining the sum of all velocity increments required for sustaining the operation. This is called fitness.

5. A method for maintaining the position of an NRHO track station according to claim 2, characterized in that, The optimization constraints are established as follows: In the formula, The magnitude of the pulse velocity increment required to maintain the pulse for each pulse; This is the minimum value of the velocity increment required to maintain the pulse for each time. This represents the maximum value of the velocity increment required to maintain the pulse for each duration. The time interval between two maintenance sessions; It is the minimum time interval between two maintenance periods; This is the distance between the actual position reached by the spacecraft under the sustaining pulse and the target point; This represents the maximum distance between the actual position reached by the spacecraft under the sustaining pulse and the target point.

6. The NRHO track station maintenance method according to claim 1, characterized in that, The target optimization model includes: In the formula, The state sequence of the target point; The time series of the target; This is the sum of all speed increments required to maintain the speed. The magnitude of the pulse velocity increment required to maintain the pulse for each pulse; This is the minimum value of the velocity increment required to maintain the pulse for each time. This represents the maximum value of the velocity increment required to maintain the pulse for each duration. The time interval between two maintenance sessions; It is the minimum time interval between two maintenance periods; This is the distance between the actual position reached by the spacecraft under the sustaining pulse and the target point; This represents the maximum distance between the actual position reached by the spacecraft under the sustaining pulse and the target point.

7. An NRHO track station position maintenance system, characterized in that, The NRHO track station maintenance system is used to implement the NRHO track station maintenance method according to any one of claims 1-6, including: Target selection module: used to obtain single-value matrix eigenvalues ​​based on the nominal NRHO orbitals, and select single-value matrix eigenvalues ​​to form a candidate target set; Parameter acquisition module: used to acquire parameter data based on the candidate target set; Model building module: used to build target optimization models based on parameter data; Station maintenance module: Used to determine the NRHO orbit using the target optimization model and complete the station maintenance of the NRHO orbit.

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