Transfer orbit design method, device and medium from gto to earth-sun coplanar libration point

Abstract

Embodiments of the present application disclose a transfer orbit design method from GTO to the Sun-Earth collinear libration point, a device and a medium; the method comprises: calculating and obtaining an invariant manifold connected with the Halo orbit around the libration point according to the spacecraft dynamics equation and the potential function in the Sun-Earth barycenter coordinate system; taking the geosynchronous transfer orbit as the earth parking orbit to construct the constraint variable, taking the Halo orbit as the target orbit to construct the control variable, and correcting the control variable by using the least square differential correction method; based on the set constraint condition and performance index, the optimal HOI point corresponding to the optimal performance transfer orbit is selected from the transfer orbit meeting the constraint condition; according to the optimal HOI point, the relationship between the control variable and the parking orbit constraint variable is analyzed, and the differential correction initial value expression for determining the control variable initial value of the multi-constraint orbit design is constructed; the transfer orbit meeting multiple constraints is obtained by using the multi-stage differential correction method according to the differential correction initial value expression.

Description

Technical Field

[0001] This invention relates to the field of spacecraft orbit design technology, and in particular to a method, apparatus and medium for designing a transfer orbit from a geostationary transfer orbit (GTO) to a Sun-Earth collinear translation point. Background Technology

[0002] Among the libration points of the Sun-Earth system, L1 and L2 have received much attention in deep space exploration due to their unique spatial locations. Periodic libration orbits, represented by the Halo orbit, are very suitable for planetary exploration and relay communication missions, and are ideal working locations for future probes.

[0003] In the restricted three-body model, there exists a series of periodic and quasi-periodic orbits and a series of invariant manifolds around the collinear translation points. Therefore, there is a series of energy-efficient transfer orbits between the same three-body system and different three-body systems.

[0004] Generally speaking, the transfer trajectory from the ground-circling parking orbit to the Halo orbit is not unique. The required maneuvering speed and transfer time for the transfer trajectory corresponding to different Halo Orbit Insertion (HOI) are different. It is necessary to analyze the characteristics of different transfer trajectories in order to select the appropriate transfer method according to the mission requirements. Summary of the Invention

[0005] In view of this, embodiments of the present invention aim to provide a method, apparatus, and medium for designing a transfer trajectory from GTO to the Sun-Earth collinear translational point; which can reduce the maneuvering speed requirements of the transfer trajectory and improve the accuracy of the transfer trajectory design.

[0006] The technical solution of this invention is implemented as follows:

[0007] In a first aspect, embodiments of the present invention provide a method for designing a transfer orbit from a GTO to a Sun-Earth collinear translational point, the method comprising:

[0008] Based on the spacecraft dynamics equations and potential functions in the Sun-Geological Center synoptic coordinate system, the invariant manifold connected to the Halo orbit around the translation point is calculated;

[0009] The constrained variables were constructed using the geosynchronous transfer orbit as the Earth parking orbit, and the control variables were constructed using the Halo orbit as the target orbit. The control variables were then corrected using the least squares differential correction method.

[0010] Based on the set constraints and performance indicators, the optimal HOI point corresponding to the transfer trajectory with the best performance is selected from the transfer trajectories that meet the constraints.

[0011] Based on the optimal HOI point, the relationship between the control variables and the parking track constraint variables is analyzed, and a differential correction initial value expression for determining the initial values ​​of the control variables for multi-constraint track design is constructed.

[0012] Based on the differential correction initial value expression, a transfer trajectory satisfying multiple constraints is obtained using the multi-level differential correction method.

[0013] Secondly, embodiments of the present invention provide a transfer trajectory design device from GTO to a Sun-Earth collinear translational point. The device includes: a calculation section, a correction section, a selection section, a construction section, and a multi-level differential correction section.

[0014] The calculation section is configured to calculate the invariant manifold connected to the Halo orbit around the translation point based on the spacecraft dynamics equations and potential functions in the Sun-Geocene synoptic coordinate system.

[0015] The correction part is configured to construct constraint variables with the geosynchronous transfer orbit as the Earth parking orbit, construct control variables with the Halo orbit as the target orbit, and correct the control variables using the least squares differential correction method.

[0016] The selection section is configured to select the optimal HOI point corresponding to the transfer trajectory with the best performance from the transfer trajectories that meet the set constraints and performance indicators.

[0017] The construction part is configured to analyze the relationship between control variables and parking track constraint variables based on the optimal HOI point, and construct a construction differential correction initial value expression for determining the initial values ​​of control variables for multi-constraint track design;

[0018] The multi-level differential correction section is configured to obtain a transfer trajectory that satisfies multiple constraints using the multi-level differential correction method based on the differential correction initial value expression.

[0019] Thirdly, embodiments of the present invention provide a computing device, the computing device comprising: a communication interface, a memory, and a processor; the various components are coupled together via a bus system; wherein...

[0020] The communication interface is used for receiving and sending signals during the process of sending and receiving information with other external network elements;

[0021] The memory is used to store computer programs that can run on the processor;

[0022] The processor is configured to, when running the computer program, execute the steps of the transfer orbit design method from GTO to the Sun-Earth collinear translational point described in the first aspect.

[0023] Fourthly, embodiments of the present invention provide a computer storage medium storing a transfer orbit design program from GTO to the Sun-Earth collinear translation point. When the transfer orbit design program from GTO to the Sun-Earth collinear translation point is executed by at least one processor, it implements the steps of the transfer orbit design method from GTO to the Sun-Earth collinear translation point described in the first aspect.

[0024] This invention provides a method, apparatus, and medium for designing transfer tracks from a GTO to a Sun-Earth collinear translational point. By quantitatively providing the performance indicators of transfer tracks corresponding to different HOI points, the method allows for the selection of HOI points and transfer tracks that meet mission requirements, demonstrating significant engineering application value. Furthermore, by constructing constraint definitions using the GTO as the parking track, the method further reduces the maneuvering speed requirements of the transfer track, thereby improving the accuracy of the transfer track design. Attached Figure Description

[0025] Figure 1 This is a schematic flowchart of a transfer trajectory design method from GTO to a Sun-Earth collinear translational point provided by an embodiment of the present invention;

[0026] Figure 2 A schematic diagram of the transfer trajectory and design control variables provided in an embodiment of the present invention;

[0027] Figure 3 A schematic diagram illustrating the implementation process of the three-level differential correction strategy provided in an embodiment of the present invention;

[0028] Figure 4 This is a schematic diagram illustrating the change in total speed increment provided in an embodiment of the present invention;

[0029] Figure 5 This is a schematic diagram illustrating the change in transfer time provided in an embodiment of the present invention;

[0030] Figure 6 This is a schematic diagram illustrating the changes in performance indicators provided in an embodiment of the present invention;

[0031] Figure 7 This is a schematic diagram of the transfer orbit from GTO to Sun-Earth L1 provided in an embodiment of the present invention;

[0032] Figure 8 This is a schematic diagram of a transfer orbit design device from GTO to the Sun-Earth collinear translation point provided in an embodiment of the present invention;

[0033] Figure 9 This is a schematic diagram of the specific hardware structure of a computing device provided in an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0035] For transfer orbits from an Earth-orbiting parking orbit to a Halo orbit (the translation point of the Sun-Earth system), typically only the case where the parking orbit is a near-Earth circular orbit is considered. However, the Geostationary Transfer Orbit (GTO), a common transfer orbit, significantly reduces the velocity increment requirement compared to a near-Earth circular parking orbit at an altitude of 200 km, thus saving considerable fuel and transfer time. However, the GTO's elliptical orbit introduces new requirements for transfer orbit design due to perigee azimuth constraints. Furthermore, conventional schemes often fail to consider the impact of the HOI (Homo-Orbital Indication) on transfer orbit characteristics when defining the relationship between constraints and control variables. Therefore, this invention aims to provide a transfer orbit design scheme from a GTO to a collinear Sun-Earth translation point. By quantitatively providing performance indicators for transfer orbits corresponding to different HOI points, it allows for the selection of HOI points and transfer orbits that meet mission requirements, offering significant engineering application value. Moreover, it provides a constraint definition method for using the GTO as a parking orbit, further reducing the maneuvering velocity requirements of the transfer orbit and improving the accuracy of the transfer orbit design.

[0036] Based on this, see Figure 1 This illustrates a method for designing a transfer orbit from the GTO to a Sun-Earth collinear translational point, provided by an embodiment of the present invention. The method may include:

[0037] S101: Based on the spacecraft dynamics equations and potential functions in the Sun-Geological Center synoptic coordinate system, the invariant manifold connected to the Halo orbit around the translation point is calculated;

[0038] S102: Use the geosynchronous transfer orbit (GTO) as the Earth parking orbit to construct constraint variables, use the Halo orbit as the target orbit to construct control variables, and use the least squares differential correction method to correct the control variables;

[0039] S103: Based on the set constraints and performance indicators, select the optimal HOI point corresponding to the transfer trajectory with the best performance from the transfer trajectories that meet the constraints.

[0040] S104: Based on the optimal HOI point, analyze the relationship between the control variables and the parking track constraint variables, and construct a differential correction initial value expression for determining the initial values ​​of the control variables for multi-constraint track design;

[0041] S105: Based on the differential correction initial value expression, a transfer trajectory satisfying multiple constraints is obtained using the multi-level differential correction method.

[0042] pass Figure 1 The technical solution shown provides quantitative performance indicators for transfer tracks corresponding to different HOI points, thereby enabling the selection of HOI points and transfer tracks that meet mission requirements, which has significant engineering application value. Furthermore, by constructing a constraint definition with GTO as the parking track, the maneuvering speed requirement of the transfer track is further reduced, improving the accuracy of the transfer track design.

[0043] for Figure 1 In some possible implementations of the technical solution shown, the calculation of the invariant manifold connected to the Halo orbit around the translation point based on the spacecraft dynamics equations and potential functions in the Sun-Geocene synoptic coordinate system includes:

[0044] The Sun-Earth synchrotron coordinate system is defined, wherein the center of mass of the Sun-Earth three-body system is the origin of the coordinate system, the x-axis points from the Sun to the Earth, the z-axis is in the same direction as the angular velocity of the Sun-Earth system, and the y-axis forms a right-handed system with the x-axis and z-axis.

[0045] Based on the aforementioned Sun-Geocene coordinate system, the spacecraft's dynamic equations are expressed as follows:

[0046]

[0047] in, The spacecraft's position, velocity, and acceleration state variables are represented in the Sun-Geocene synoptic coordinate system; μ represents the system's mass coefficient, which is 3.0083 × 10⁻⁶ in the Sun-Earth system. -6 ; The distance between the spacecraft and the sun. The distance between the spacecraft and the Earth;

[0048] Define potential function The state variables of the spacecraft in the coinciding coordinate system of the center of mass are The potential function with respect to the position state quantity r = [x, y, z] T The partial derivatives are respectively the right-hand side of the equation representing the dynamics equation of the spacecraft;

[0049] The single-valued matrix M = Φ(t0+T,t0) of the periodic orbit is determined based on the state transition matrix Φ(t,t0); where T is one orbital period. 03 and I3 are the 3×3 zero matrix and identity matrix, respectively. Let Φ(t0,t0) = I6 be the second-order partial derivative of the potential function with respect to the position state vector.

[0050] By selecting the stable eigenvalues ​​and stable eigenvectors of the corresponding system from the eigenvalues ​​and eigenvectors of the single-valued matrix M, the stable eigenvector corresponding to any given time t on the translational point orbit is obtained. in, These are the stable eigenvectors corresponding to a single-valued matrix;

[0051] Setpoint X on Halo orbit h By applying a small perturbation ξ along its corresponding stable and unstable eigenvalues, the set point X is obtained based on the stable eigenvector. h The initial values ​​of the connected integrals are Where, ω s For stable feature vectors;

[0052] Substituting the initial integral value into the dynamic equation and integrating backwards along time, we obtain the stable and invariant manifold connected to the Halo orbit of the translational point.

[0053] Regarding the above implementation, it should be noted that the single-valued matrix represents the state change of a periodic orbit after one period following a certain perturbation in its initial state. For the single-valued matrix, real eigenvalues ​​less than 1 correspond to the stable eigenvalues ​​of the system, and their corresponding eigenvectors point asymptotically towards the stable manifold. Choosing a perturbation factor ξ that is too large or too small will cause the invariant manifold calculation to fail. Based on practical experience, in the Sun-Earth three-body system, a value of approximately 200 km for ξ is suitable. When calculating the stable invariant manifold, integration should be performed along the negative time direction. ± correspond to the two branches of the manifold towards the massive and small-mass objects, respectively.

[0054] In some implementations of the aforementioned technical solutions, the step of constructing constraint variables using a geostationary transfer orbit (GTO) as the Earth parking orbit, constructing control variables using a Halo orbit as the target orbit, and then correcting the control variables using the least squares differential correction method includes:

[0055] Let the state vector at the transfer trajectories insertion point (TTI) in the geocentric inertial frame be X. If =[r If ;v If The state at point TTI in the Sun-Geological Center synoptic coordinate system is X. f =[r ef ;v ef The Earth's radius is R. E The Earth's orbital elements satisfy the following formula:

[0056]

[0057] Where, ref =[x f -1+μ,y f ,z f ] T , r f =[x f ,y f ,z f ] T , The state quantity r of the TTI point in the geological center rendezvous coordinate system on that day. efxy It is r f In the Sun-Geological Center Coordinate System Planar components;

[0058] Considering four constraints—track angle, orbital altitude, orbital inclination, and right ascension of the ascending node—the three-axis velocity increments and transfer time at the Halo Orbit Insertion (HOI) are used as free variables C = [ΔV]. HOI ,t f ] T =[ΔV x ,ΔV y ,ΔV z ,t f ] T Construct the objective function Wherein, the constraint variable D = [γ hia] T The subscript d indicates the expected value of the constraint;

[0059] With the initial free variable C set j The objective function is then subjected to a first-order Taylor expansion to obtain the Jacobian matrix.

[0060] By correcting the control variable C using the least squares differential correction method, we obtain the following equation:

[0061]

[0062] Where k is the downhill factor, initially set to 1. When the iteration diverges due to an excessively long step size, k is appropriately reduced to achieve convergence.

[0063] For the above implementation, this embodiment of the invention preferably uses reverse time integration to solve for the transfer trajectory, that is, HOI is the initial point of integration and TTI is the final point of integration. The spacecraft transfer process is as follows: Figure 2 As shown, the spacecraft initially operates in a near-Earth circular orbit, and performs a near-Earth escape maneuver ΔV at an appropriate location. TTI Then, it glides along an invariant manifold onto the Halo orbit, and applies an orbital insertion maneuver ΔV at the HOI point. HOIIt eventually entered the target mission orbit. Figure 2 In the middle, at point HOI, ΔV xy It is ΔV HOI In the Sun-Geological Center Coordinate System Planar components, ΔV z It is ΔV HOI In the Sun-Geological Center Coordinate System The components of the axis. β is ΔV HOI and The angle between the position vector and the velocity vector. At the TTI point, the track angle γ is the angle between the position vector's normal direction and the velocity vector; α is the angle between the position vector's normal direction and the velocity vector's velocity direction. Planar component r fxy and The included angle of the axis. In this embodiment of the invention, the Earth parking orbit is selected as a geosynchronous transfer orbit. If the stable manifold can be tangent to the parking orbit at perigee, then when performing orbital maneuvers at this point, only the magnitude of the velocity needs to be changed, not the direction, which can save a lot of fuel. Compared with a near-Earth circular orbit, it can save even more fuel. In order to save fuel consumption and design a more accurate transfer orbit, the following constraints are considered: perigee altitude h, flight path angle γ relative to Earth, parking orbit inclination i, and perigee azimuth angle α in the geocentric synodic system.

[0064] For the aforementioned technical solutions, in some examples, based on set constraints and performance indicators, the optimal HOI point corresponding to the transfer trajectory with the best performance is selected from the transfer trajectories that meet the constraints, including:

[0065] The Halo orbital of a period is divided into multiple sub-parts according to the integration time, and each sub-part corresponds to a HOI point;

[0066] Using the invariant manifold corresponding to each HOI point as the initial value, and considering only the two constraints of perigee orbital altitude and flight path angle, the transfer orbit that meets the constraints is obtained by applying the modified calculation formula for the control variable C.

[0067] The performance index is defined as J = λ1ΔV + λ2t f And calculate the performance index of each transfer orbit, where λ1 and λ2 are weighting coefficients, and ΔV is the total velocity increment required for the transfer;

[0068] The HOI point corresponding to the minimum value of the performance index is determined as the optimal HOI point.

[0069] For the above implementation, after determining the optimal Halo orbit entry point, in some examples, the step of analyzing the relationship between control variables and parking track constraint variables based on the optimal HOI point, and constructing a differential correction initial value expression for determining the initial values ​​of control variables for multi-constraint track design, includes:

[0070] Using the optimal HOI point, the z-axis velocity increment is performed at equal intervals within a set velocity increment range to obtain multiple z-axis velocity increment values ​​ΔV. z ;

[0071] For each z-axis velocity increment ΔV z By changing the coordinate system of the Sun-Geological Center rendezvous The velocity component increment ΔV in the plane xy Candidate transfer orbits that satisfy the perigee orbital altitude constraint are obtained through the modified calculation formula of the control variable C.

[0072] Based on the triaxial velocity increments, α angle, β angle, orbital inclination i, and right ascension Ω of the ascending node at the HOI points corresponding to all candidate transfer orbits, the quantitative relationships between the triaxial velocity increments and the α angle, β angle, orbital inclination i, and right ascension Ω of the ascending node are analyzed. Data fitting is then performed to obtain an initial value expression for the control variables, including constraint variables, where β is ΔV. HOI exist Plane components and The included angle of the axis.

[0073] For the example above, preferably, the range of the z-axis velocity increment at point HOI is limited to [-20m / s, 20m / s], and 21 sets of z-axis velocity increment values ​​ΔV are obtained at intervals of 2m / s. z For each ΔV z By changing ΔV xy After correction, a series of transfer orbits satisfying the height constraints can be obtained. Based on the aforementioned Earth parking orbit elements, a large amount of data on the three-axis velocity increments and the α angle, β angle, orbital inclination i, and right ascension Ω of the ascending node can be obtained. Based on this data, the quantitative relationship between the three-axis velocity increments and the α angle, β angle, orbital inclination i, and right ascension Ω of the ascending node is obtained by curve fitting. Data fitting is then performed to obtain the initial value expression of the control quantity containing the constraint variables.

[0074] Based on the above example, preferably, obtaining the transfer trajectory satisfying multiple constraints using a multi-level differential correction method according to the differential correction initial value expression includes:

[0075] Determine the departure date, the perigee altitude h0 of the GTO, the orbital inclination i0, the azimuth α0 of the eccentricity vector in the geocentric coordinate system, and the right ascension Ω0 of the ascending node. Substitute i0, α0, and Ω0 into the differential correction initial value expression to obtain the initial values ​​of the control quantities.

[0076] A transfer orbit that satisfies the constraints of perigee altitude, orbit inclination, and perigee azimuth is obtained through a three-level differential correction strategy.

[0077] For the above preferred examples, combined with Figure 3 Specifically, the transfer orbit obtained through the three-level differential correction strategy, which satisfies the constraints of perigee altitude, orbital inclination, and perigee azimuth, includes:

[0078] The first-level correction only considers the perigee orbital altitude constraint. The initial value obtained from the initial value expression is integrated under a circularly constrained three-body model. If the resulting altitude error Δh1 is less than the given error tolerance tol... h Then proceed to the second level of correction;

[0079] The second-level correction incorporates orbital inclination constraints: using the state variable that last met the orbital altitude constraint in the first-level correction, integration is performed under a circular restricted three-body model. When the altitude error Δh2 and orbital inclination error Δi1 of the orbital terminus are less than the tolerance tol... h ,tol i At that time, it enters the third level of correction;

[0080] The third-level correction adds the constraint of angle α. The state variables from the second level, which simultaneously satisfy the constraints of track height and track inclination, are used as the initial values ​​for this level of integration. Integration is performed under the circular restricted three-body model. If the obtained track height error Δh3, track inclination error Δi2, and angle α error Δα are all less than the tolerance tol... h ,tol i ,tol a The iteration ends at that time.

[0081] Otherwise, continue to adjust the control variables until a precise transfer orbit is obtained that simultaneously satisfies the constraints of perigee orbital altitude, orbital inclination, and perigee azimuth.

[0082] In detail, for the above specific scheme, if the tolerance is exceeded during each level of correction, the control variables will be adjusted in the corresponding level of correction to meet the tolerance requirements of the corresponding level of correction.

[0083] To illustrate the effects of the aforementioned technical solutions, their implementation methods, and examples, this invention presents a simulation experiment. The simulation conditions are as follows: a Halo orbit with a normal amplitude of 300,000 km is selected as the target orbit; the state of the GTO orbit and various constraints are shown in Table 1, to verify the transfer orbit design scheme from the GTO to the Sun-Earth collinear translational point described in the aforementioned technical solution.

[0084] Table 1

[0085] constraint numerical values Perimeter altitude / km 500 apogee altitude / km 36000 Track inclination angle / (°) 30 Right ascension of the ascending node / (°) -55 Track angle / (°) 0 Azimuth of perigee / (°) 15 Position error tolerance / (°) 0.1 Angular error tolerance / (°) 0.01

[0086] After obtaining the optimal HOI point through S103, the total velocity increment ΔV is obtained. totalThe variation patterns of the transfer time are as follows: Figure 4 and Figure 5 As shown. Taking weighting factors λ1 = 0.4 and λ2 = 0.6, the variation law of the performance index is obtained as follows. Figure 6 As shown, point HOI 200 has the best performance index, at 372.9688. This point is chosen as the entry point for the Halo orbit. After passing through S104, the magnitude of the z-axis velocity increment ΔV at point HOI is limited. z For each ΔV ∈ [-20m / s, 20m / s], 21 sets of z-axis velocity increments are obtained at 2m / s intervals. z By changing ΔV xy After adjusting for the magnitude of the parameters, a series of transfer orbits satisfying the altitude constraints were obtained, yielding a large amount of data, including the triaxial velocity increments, α angle, β angle, orbital inclination i, and right ascension Ω of the ascending node. Based on this data, the curve fitting tool 1stOpt was used to analyze the quantitative relationship between the triaxial velocity increments at the HOI point and parameters such as orbital inclination, right ascension of the ascending node, flight time, and α angle. Data fitting was performed to obtain the initial value expression including parameters such as constraint variables, as follows.

[0087] t f =0.8858α + 96.15

[0088]

[0089]

[0090]

[0091] Based on the constrained target values, initial values ​​for the triaxial velocity increments at the HOI point can be obtained. Then, through S105, a transfer orbit satisfying a GTO perigee altitude of 500 km, an orbital inclination of 30°, and a perigee azimuth of 15° can be obtained. Figure 7 As shown, the transfer time was 109.1384 days, and the required velocity increment for the transfer was 767.0876 m / s.

[0092] The simulation experiments described above demonstrate that the technical solution proposed in this invention provides quantitative performance indicators for transfer tracks corresponding to different HOI points, thereby enabling the selection of HOI points and transfer tracks that meet mission requirements, which has significant engineering application value. Furthermore, by constructing a constraint definition using GTO as the parking track, the maneuvering speed requirement of the transfer track is further reduced, improving the accuracy of the transfer track design.

[0093] Based on the same inventive concept as the aforementioned technical solution, see [link to inventive concept]. Figure 8This invention illustrates a transfer trajectory design device 80 from GTO to a Sun-Earth collinear translational point provided by an embodiment of the present invention. The device 80 includes: a calculation section 801, a correction section 802, a selection section 803, a construction section 804, and a multi-level differential correction section 805.

[0094] The calculation section 801 is configured to calculate the invariant manifold connected to the Halo orbit around the translation point based on the spacecraft dynamics equations and potential functions in the Sun-Geocene coordinate system.

[0095] The correction part 802 is configured to construct constraint variables with the geosynchronous transfer orbit as the Earth parking orbit, construct control variables with the Halo orbit as the target orbit, and correct the control variables using the least squares differential correction method.

[0096] The selection section 803 is configured to select the optimal HOI point corresponding to the transfer track with the best performance from the transfer tracks that meet the set constraints and performance indicators.

[0097] The construction part 804 is configured to analyze the relationship between control variables and parking track constraint variables based on the optimal HOI point, and construct a construction differential correction initial value expression for determining the initial values ​​of control variables for multi-constraint track design;

[0098] The multi-level differential correction section 805 is configured to obtain a transfer trajectory that satisfies multiple constraints using the multi-level differential correction method based on the differential correction initial value expression.

[0099] It should be noted that for the specific implementation of the functions configured in each "part" of the above-mentioned device, please refer to the aforementioned... Figure 1 The implementation methods and examples of the corresponding steps in the transfer orbit design method from GTO to the Sun-Earth collinear translation point shown are not repeated here.

[0100] Understandably, in this embodiment, "part" can be a part of a circuit, a part of a processor, a part of a program or software, etc., or it can be a unit, a module, or a non-modular one.

[0101] Furthermore, in this embodiment, the components can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional module.

[0102] If the integrated unit is implemented as a software functional module and not sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this embodiment, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the method described in this embodiment. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0103] Therefore, this embodiment provides a computer storage medium storing a transfer orbit design program from GTO to the Sun-Earth collinear translation point. When the transfer orbit design program from GTO to the Sun-Earth collinear translation point is executed by at least one processor, it implements the steps of the transfer orbit design method from GTO to the Sun-Earth collinear translation point described in the above technical solution.

[0104] Based on the aforementioned transfer trajectory design device 80 from GTO to the Sun-Earth collinear translation point and the computer storage medium, see [link to device]. Figure 9 This illustration shows the specific hardware structure of a computing device 90 provided by an embodiment of the present invention, capable of implementing the aforementioned transfer orbit design device 80 from GTO to the Sun-Earth collinear translational point. The computing device 90 can be a wireless device, mobile or cellular phone (including so-called smartphones), personal digital assistant (PDA), video game console (including video display, mobile video game device, mobile video conferencing unit), laptop computer, desktop computer, set-top box, tablet computing device, e-book reader, fixed or mobile media player, etc. The computing device 90 includes: a communication interface 901, a memory 902, and a processor 903; the various components are coupled together through a bus system 904. It is understood that the bus system 904 is used to realize the connection and communication between these components. In addition to a data bus, the bus system 904 also includes a power bus, a control bus, and a status signal bus. However, for clarity, in... Figure 9 The general designated all buses as Bus System 904.

[0105] The communication interface 901 is used for receiving and sending signals during the process of sending and receiving information with other external network elements;

[0106] The memory 902 is used to store computer programs that can run on the processor 903;

[0107] The processor 903 is used to execute the steps of the transfer orbit design method from GTO to the Sun-Earth collinear translation point described in the above technical solution when running the computer program.

[0108] It is understood that the memory 902 in the embodiments of the present invention can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory 902 of the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0109] The processor 903 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of the processor 903 or by instructions in software form. The processor 903 can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory 902, and the processor 903 reads the information in memory 902 and, in conjunction with its hardware, completes the steps of the above method.

[0110] It is understood that the embodiments described herein can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described herein, or combinations thereof.

[0111] For software implementation, the techniques described herein can be achieved through modules (e.g., procedures, functions, etc.) that perform the functions described herein. The software code can be stored in memory and executed by a processor. The memory can be implemented within the processor or externally.

[0112] It is understood that the exemplary technical solutions of the transfer orbit design apparatus 80 and computing device 90 from GTO to the Sun-Earth collinear translation point described above belong to the same concept as the technical solutions of the transfer orbit design method from GTO to the Sun-Earth collinear translation point described above. Therefore, all details not described in detail above regarding the technical solutions of the transfer orbit design apparatus 80 and computing device 90 from GTO to the Sun-Earth collinear translation point can be found in the description of the technical solutions of the transfer orbit design method from GTO to the Sun-Earth collinear translation point described above. This embodiment of the invention will not elaborate further on this.

[0113] It should be noted that the technical solutions described in the embodiments of the present invention can be combined arbitrarily without conflict.

[0114] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A transfer orbit design method from GTO to Earth-Sun co-linear libration point, characterized in that, The method includes: Based on the spacecraft dynamics equations and potential functions in the Sun-Geological Center synoptic coordinate system, the invariant manifold connected to the Halo orbit around the translation point is calculated; The constrained variables were constructed using the geosynchronous transfer orbit as the Earth parking orbit, and the control variables were constructed using the Halo orbit as the target orbit. The control variables were then corrected using the least squares differential correction method. Based on the set constraints and performance indicators, the optimal HOI point corresponding to the transfer trajectory with the best performance is selected from the transfer trajectories that meet the constraints. Based on the optimal HOI point, the relationship between the control variables and the parking track constraint variables is analyzed, and a differential correction initial value expression for determining the initial values ​​of the control variables for multi-constraint track design is constructed. Based on the differential correction initial value expression, a multi-level differential correction method is used to obtain a transfer trajectory that satisfies multiple constraints; The process of constructing constraint variables using the geosynchronous transfer orbit as the Earth parking orbit and control variables using the Halo orbit as the target orbit, and then correcting the control variables using the least squares differential correction method, includes: Let the state vector of parking orbit at TTI of escape point in geocentric inertial system be , the state of TTI point in geocentric inertial system be , and the radius of the earth be , then the parking orbit root number of the earth satisfies the following formula: wherein , ; , is the state of the TTI point in the geocentric heliocentric coordinate system, is In the geocentric heliocentric coordinate system plane; Considering the four constraints of the flight path angle, the orbital height, the orbital inclination, and the right ascension of the ascending node, taking the three-axis velocity increment at the Halo orbit injection point HOI and the transfer time as the free variables Constructing the objective function ; wherein the constraint variable , the subscript represents the expected value of the constraint; with a set initial free variable and first order Taylor expansion of the objective function, Jacobian matrix is obtained ; The control variables are corrected using a least squares differential correction method to obtain the following equation: Where k is the downhill factor, and its initial value is set to 1.

2. The method of claim 1, wherein, Based on the set constraints and performance indicators, the optimal HOI point corresponding to the transfer trajectory with the best performance is selected from the transfer trajectories that meet the constraints, including: The Halo orbital of one period is divided into multiple sub-parts according to the integration time, and each sub-part corresponds to a HOI point; With the initial value of the invariant manifold corresponding to each HOI point, only considering the constraints of the perigee altitude and flight path angle, the transfer orbit satisfying the constraints is obtained by the modified calculation formula of the control variable . The performance index is defined as and the performance index of each transfer orbit is calculated, wherein, and is a weight coefficient, is the total velocity increment size required for the transfer; The HOI point corresponding to the minimum value of the performance index is determined as the optimal HOI point.

3. The method of claim 2, wherein, The step involves analyzing the relationship between control variables and parking track constraint variables based on the optimal HOI point, and constructing a differential correction initial value expression for determining the initial values ​​of control variables in multi-constraint track design, including: At the optimal HOI point, a plurality of z-direction velocity increments are obtained by equally spacing the z-direction velocity increments within a set velocity increment range ; For each z-axis velocity increment By changing the coordinate system of the Sun-Geological Center rendezvous Planar velocity component increment After the aforementioned control variables The modified calculation formula yields candidate transfer orbits that satisfy the perigee orbital altitude constraint; Based on the triaxial velocity increments of the HOI points corresponding to all candidate transfer orbits, horn, Angle, track inclination angle Right ascension of ascending node Analysis of triaxial velocity increments and horn, Angle, track inclination angle Right ascension of ascending node The quantitative relationship between them is used to fit the data, resulting in an initial value expression for the control quantity that includes the constraint variables, where... yes exist Plane components and The included angle of the axis.

4. The method of claim 3, wherein, The process of obtaining a transfer trajectory satisfying multiple constraints using a multi-level differential correction method based on the differential correction initial value expression includes: determining a departure date, a perigee height of the GTO , an orbit inclination , an azimuth of the eccentricity vector in the geocentric heliocentric coordinate system , a longitude of the ascending node , substituting , , into the differential correction initial value expression to obtain an initial value of the control variable; A transfer orbit that satisfies the constraints of perigee altitude, orbit inclination, and perigee azimuth is obtained through a three-level differential correction strategy.

5. The method of claim 4, wherein, The transfer orbit obtained through the three-level differential correction strategy, which satisfies the constraints of perigee altitude, orbital inclination, and perigee azimuth, includes: The first order correction only considers the constraint of the perigee height. The initial value obtained from the initial value expression is integrated in the circular restricted three-body model. If the height error obtained is less than the given error tolerance , the second order correction is entered. ​ Second stage correction with inclination constraint: the state variable at the end of the first stage correction, which satisfies the altitude constraint, is integrated in the circular restricted three-body model, and when the end of the orbit has an altitude error and an inclination error less than the tolerance , , the third stage correction is entered. Third order correction added again The constraint of the angle, taking the state variable which satisfies the orbit height and orbit inclination constraint at last simultaneously as the integral initial value of this level, integrating under the circular restricted three-body model, if the orbit height error , orbit inclination error and angle error are all less than the tolerance , , , the iteration ends; Otherwise, continue to adjust the control variables until a precise transfer orbit is obtained that simultaneously satisfies the constraints of perigee orbital altitude, orbital inclination, and perigee azimuth.

6. A transfer orbit design device from GTO to Earth-Sun co-linear libration points, characterized by, The device includes: a calculation section, a correction section, a selection section, a construction section, and a multi-level differential correction section, wherein, The calculation section is configured to calculate the invariant manifold connected to the Halo orbit around the translation point based on the spacecraft dynamics equations and potential functions in the Sun-Geocene synoptic coordinate system. The correction part is configured to construct constraint variables with the geosynchronous transfer orbit as the Earth parking orbit, construct control variables with the Halo orbit as the target orbit, and correct the control variables using the least squares differential correction method. The selection section is configured to select the optimal HOI point corresponding to the transfer trajectory with the best performance from the transfer trajectories that meet the set constraints and performance indicators. The construction part is configured to analyze the relationship between the control variable and the parking orbit constraint variable according to the optimal HOI point, and construct a construction differential correction initial value expression for determining the control variable initial value of the multi-constraint orbit design. The multi-stage differential correction part is configured to obtain the transfer orbit satisfying multiple constraints by using a multi-stage differential correction method according to the differential correction initial value expression. The correction part is configured to: Let the state vector of parking orbit at TTI of escape point be , the state of TTI point in the geocentric synodic coordinate system be , and the radius of the earth be , then the parking orbit root number of the earth satisfies the following formula: wherein , ; , is the state of the TTI point in the geocentric heliocentric coordinate system, is the component of the position of the TTI point in the geocentric heliocentric coordinate system plane; Considering the four constraints of the flight path angle, the orbital height, the orbital inclination, and the right ascension of the ascending node, taking the three-axis velocity increment at the Halo orbit injection point HOI and the transfer time as the free variables Constructing the objective function ; wherein the constraint variable , the subscript represents the expected value of the constraint; with a set initial free variable and first order Taylor expansion of the objective function, Jacobian matrix is obtained ; The control variables are corrected using a least squares differential correction method to obtain the following equation: Wherein k is a downhill factor, and the initial value is set to 1.

7. A computing device, comprising: The computing device comprises a communication interface, a memory and a processor; each component is coupled together through a bus system; wherein, The communication interface is used for receiving and sending signals in the process of transceiving information with other external network elements; The memory is used for storing a computer program capable of running on the processor; The processor is used for executing the steps of the transfer orbit design method from GTO to the sun-earth collinear libration point according to any one of claims 1 to 5 when the computer program is running.

8. A computer storage medium, characterized in that The computer storage medium stores a transfer orbit design program from GTO to the sun-earth collinear libration point, and the transfer orbit design program from GTO to the sun-earth collinear libration point implements the steps of the transfer orbit design method from GTO to the sun-earth collinear libration point according to any one of claims 1 to 5 when executed by at least one processor.

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