Spacecraft orbit design method under high-precision four-body kinetic model

Abstract

The invention discloses a spacecraft orbit design method under a high-precision four-body kinetic model, and belongs to the field of orbit design. The problems that the spacecraft orbit period predicted by adopting a three-body model is not accurate, so that the simulated spacecraft position and speed at each moment in the spacecraft orbit design process are not accurate, and the simulation effect is poor are solved. Obtaining a spacecraft quasi-orbit period according to the resonance period ratio of the moon to the spacecraft, the actual celestial body operation state and the four-body dynamics model; obtaining each position and speed of the spacecraft in each quasi-orbit period by utilizing a four-body dynamics model, judging whether the spacecraft orbit in each quasi-orbit period is closed or not by detecting a position difference value and a speed difference value between the final moment and the starting moment of the spacecraft in each quasi-orbit period, and if not, determining that the spacecraft orbit is closed. And if not, correcting the speed and the position in the corresponding quasi-orbit period until each position and speed of the spacecraft in each quasi-orbit period in a closed state are obtained. The method is used for obtaining the spacecraft orbit.

Description

Technical Field

[0001] The invention belongs to the field of track design and relates to the design of a resonance cycle track. Background Art

[0002] As human beings continue to explore space, the design of spacecraft orbits has received increasing attention. The purpose of spacecraft orbit design is to input the designed spacecraft operating position and speed into the spacecraft. When the spacecraft is launched into space, the spacecraft actually operates according to the input position and speed.

[0003] The existing spacecraft Earth-Moon three-body model predicts the spacecraft orbital period based on the position and velocity of the spacecraft at the first moment; however, the existing spacecraft Earth-Moon three-body model mostly adopts a circular restricted three-body model or a lunar elliptical orbit model. These traditional models have obvious limitations. This is because the circular restricted three-body model oversimplifies the gravitational relationship between celestial bodies, ignores the actual elliptical shape of the moon, simulates the moon as a circle, and ignores the uneven mass distribution of actual celestial bodies and the influence of other celestial bodies.

[0004] Although the lunar elliptical orbit model takes into account the elliptical shape of the lunar orbit, it fails to fully consider the gravitational perturbations of other celestial bodies such as the sun in the real celestial body movement. Therefore, the spacecraft orbit period predicted by the existing spacecraft Earth-Moon three-body model is different from the actual spacecraft orbit period, and the prediction is inaccurate; when the accurate orbit period is used to simulate the spacecraft operation, the simulated spacecraft position and speed at each moment are inaccurate, resulting in poor simulation results. Summary of the invention

[0005] The purpose of the present invention is to solve the problem that the spacecraft orbit period predicted by the three-body model is inaccurate, which leads to inaccurate spacecraft position and speed at each moment simulated in the spacecraft orbit design process, resulting in poor simulation effect. A spacecraft orbit design method under a high-precision four-body dynamics model is proposed.

[0006] A spacecraft orbit design method under a high-precision four-body dynamics model, the method comprising the following contents:

[0007] 1. Pre-preparation stage:

[0008] Step 1: Construct a four-body dynamics model;

[0009] Step 2: Obtain the estimated orbital period of the spacecraft based on the two-body model and the resonant period ratio of the moon and the spacecraft; obtain the position and velocity of the spacecraft at the first moment based on the estimated orbital period of the spacecraft;

[0010] Step 3: Set a preset duration, which is greater than the estimated orbital period. During the motion of the spacecraft, the four-body dynamics model predicts the position and velocity of the spacecraft at the i+1th moment based on the position and velocity of the spacecraft at the i-th moment. The initial value of i is 1.

[0011] Step 4: determine whether the running time corresponding to the time between the first moment and the i-th moment is equal to the preset time. If not, set i=i+1 and execute step 3. If yes, execute step 5.

[0012] Step 5: From the spacecraft position at the last moment of the first estimated orbital period to the spacecraft position at the i-th moment, the time corresponding to the spacecraft position closest to the spacecraft position at the first moment is selected as the selected time, and the duration from the first moment to the selected time is taken as the spacecraft quasi-orbital period;

[0013] (II) Simulation stage:

[0014] Step 6, setting the speed and position of the spacecraft at the first moment of the first quasi-orbital period;

[0015] Step 7, the four-body dynamics model predicts the speed and position of the spacecraft at the j+1th moment of the kth quasi-orbital period based on the speed and position of the spacecraft at the jth moment of the kth quasi-orbital period, where the initial value of j is 1 and the initial value of k is 1;

[0016] Step 8: Determine whether the running time corresponding to the time from the first moment to the jth moment of the kth quasi-orbital period is equal to the quasi-orbital period. If not, set j=j+1 and execute step 7. If yes, execute step 9.

[0017] Step 9: Check whether two conditions are met at the same time: condition 1: the difference between the velocity at the last moment in the k-th quasi-orbital cycle and the velocity at the first moment in the quasi-orbital cycle meets the preset velocity difference; condition 2: the difference between the position at the last moment in the k-th quasi-orbital cycle and the position at the first moment in the quasi-orbital cycle meets the preset position difference.

[0018] If yes, it is proved that the spacecraft has not deviated from the orbit in the kth quasi-orbital period, the position and velocity of the spacecraft at each moment in the kth quasi-orbital period are obtained, and step 10 is executed;

[0019] If not, it proves that the spacecraft has deviated from the orbit in the kth quasi-orbital period. At this time, the value of j is restored to 1, and the position and velocity of the spacecraft at the jth moment of the kth quasi-orbital period are corrected by the shooting method. The corrected position and velocity are used as the velocity and position of the spacecraft at the jth moment of the kth quasi-orbital period, and step 7 is executed;

[0020] Step 10, determine whether k is equal to the preset number of movement circles. If so, stop the simulation. If not, restore the value of j to 1, and use the spacecraft position and velocity at the last moment of the k-th quasi-orbital period as the position and velocity of the spacecraft at the j-th moment of the k+1 quasi-orbital period, so that k=k+1, and execute step 7.

[0021] Preferably, the four-body dynamics model is:

[0022]

[0023] In the formula, For satellites in J 2000 The position below: E is the gravitational constant of the Earth; μ S is the gravitational constant of the sun; μ M is the gravitational constant of the moon; ∑F i is the gravitational perturbation term of the central celestial body other than the Earth in the ephemeris model; is the instantaneous position of the spacecraft and the sun in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; It is the instantaneous position of the Earth and the Sun in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; is the instantaneous position of the spacecraft and the moon in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; It is the instantaneous position of the Earth and the Moon in the inertial coordinate system of the Earth's center of mass at a certain UTC moment.

[0024] Preferably, the track semi-diameter is:

[0025] p=a(1-e 2 ) Formula 2,

[0026] Where p is the orbital semi-diameter, a is the orbital semi-major axis, and e is the orbital eccentricity. μ E is the gravitational constant of the Earth, and T is the orbital period.

[0027] Preferably, the position and velocity of the spacecraft at the first moment are:

[0028]

[0029] Where R0 is the initial value of the spacecraft position, θ is the true anomaly, and V0 is the initial value of the spacecraft velocity.

[0030] Preferably, step 9 further comprises: after obtaining the position and velocity of the spacecraft at each time in the kth quasi-orbital period, converting the position and velocity from the Earth-Moon conjunction coordinate system to the inertial coordinate system, the position and velocity in the inertial coordinate system are respectively expressed as:

[0031]

[0032] In the formula, R S is the position vector of the spacecraft in the inertial coordinate system, R is the position vector of the moon in the inertial coordinate system, T M is the Earth-Moon conjunction coordinate system matrix, R Z is the position vector of the spacecraft in the Earth-Moon conjunction coordinate system, is a unit vector, V S is the velocity vector of the spacecraft in the geocentric inertial coordinate system, V is the velocity vector of the moon in the geocentric inertial coordinate system, V Z is the velocity vector of the spacecraft in the Earth-Moon conjunction coordinate system, T V is the velocity conversion matrix,

[0033] Preferably, between step 8 and step 9, the method further includes: converting the velocity at the last moment in the kth quasi-orbital period and the velocity at the first moment in the quasi-orbital period to the Earth-Moon conjunction coordinate system through the Earth-Moon conjunction coordinate system matrix, and the Earth-Moon conjunction coordinate system matrix is:

[0034]

[0035] Where, T M is the Earth-Moon conjunction coordinate system matrix, R is the position vector of the Moon in the Earth-centered inertial coordinate system, and V is the velocity vector of the Moon in the Earth-centered inertial coordinate system.

[0036] Preferably, the specific process of step 2 is:

[0037] Consult the ephemeris to obtain the positions of the sun and the moon at the i-th moment. Combined with the spacecraft position and velocity at the i-th moment, obtain the instantaneous position of the spacecraft and the sun in the inertial coordinate system of the earth's center of mass, the instantaneous position of the earth and the sun in the inertial coordinate system of the earth's center of mass, the instantaneous position of the spacecraft and the moon in the inertial coordinate system of the earth's center of mass, and the instantaneous position of the earth and the moon in the inertial coordinate system of the earth's center of mass at the i-th moment, and predict the spacecraft position and velocity at the i+1 moment through the four-body dynamics model.

[0038] The beneficial effects of the present invention are:

[0039] In the actual movement of celestial bodies, the gravitational effect of the sun cannot be ignored. In order to more accurately design the orbit in the three-body model of the sun, earth and moon, we use the real positions of the sun and moon as perturbations, and obtain the real-time positions of the sun and moon by consulting the ephemeris, so as to establish a four-body dynamic model that is almost the same as the real earth-moon gravitational environment, that is, the four-body model of the sun, earth, moon and spacecraft. This model can more realistically reflect the interaction between celestial bodies and provide a more reliable basis for the design of spacecraft orbits. Thus, the orbital period that is the same as the actual spacecraft operation period is obtained through the model, and then the position and speed of the spacecraft at each moment of operation are obtained through the extrapolation calculation of the model orbit. Therefore, the design of the orbit of the present invention enhances the authenticity of the orbital design and is more suitable for actual engineering applications. In addition, the designed orbital initial value also has good quasi-periodicity and stability in actual engineering, and can perform long-term tasks such as on-orbit patrol and reconnaissance.

[0040] In addition, after obtaining the quasi-orbital period of the spacecraft, in order to ensure that the spacecraft is closed in each orbital period, the present invention detects whether the orbit under the orbital period is closed every time the spacecraft rotates through each orbital period. If not, the unclosed orbit is corrected until the position and speed at each moment in each orbital period forming a closed state are obtained. When the position and speed at each moment in each orbital period forming a closed state are input into the spacecraft, the spacecraft can be operated according to this position and speed after the spacecraft is launched into space. Therefore, the present invention has good simulation effect and good authenticity. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flowchart of a spacecraft orbit design method under a high-precision four-body dynamics model;

[0042] Figure 2 The trajectory diagrams of three periodic orbits designed for the resonant orbit with a moon-spacecraft period ratio of 3:1 under the circular restricted three-body model;

[0043] Figure 3 The trajectory diagrams of three periodic orbits for the resonant orbit with a moon-spacecraft period ratio of 3:1 designed under the dynamic model;

[0044] Figure 4 The trajectory diagrams of three periods of the resonant orbit with a lunar-spacecraft period ratio of 3:1 after orbit maintenance under the dynamic model;

[0045] Figure 5 The trajectory diagrams of three periodic orbits designed for the resonant orbit with a period ratio of 2 between the moon and the spacecraft under the circular restricted three-body model;

[0046] Figure 6 The trajectory diagrams of three periodic orbits for the resonant orbit with a period ratio of 2:1 between the moon and the spacecraft designed under the dynamic model;

[0047] Figure 7 The trajectory diagrams of three periods of the resonant orbit with a lunar-spacecraft period ratio of 2:1 after orbit maintenance under the dynamic model;

[0048] Figure 8 The trajectory diagrams of three periodic orbits designed for the resonant orbit with a 1:1 period ratio between the moon and the spacecraft under the circular restricted three-body model;

[0049] Fig. 9 The trajectory diagrams of three periodic orbits for the resonant orbit with a 1:1 period ratio between the moon and the spacecraft designed under the dynamic model;

[0050] Fig.10 The trajectory diagrams of three period orbits of the resonant orbit with a 1:1 period ratio between the moon and the spacecraft after orbit maintenance under the dynamic model;

[0051] Fig.11 Two orbital maintenance algorithms for resonant orbits under the dynamic model. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0054] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0055] Example:

[0056] A spacecraft orbit design method under a high-precision four-body dynamics model, the method comprising the following contents:

[0057] 1. Pre-preparation stage:

[0058] Step 1: Construct a four-body dynamics model;

[0059] Step 2: Obtain the estimated orbital period of the spacecraft based on the two-body model and the resonant period ratio of the moon and the spacecraft; obtain the position and velocity of the spacecraft at the first moment based on the estimated orbital period of the spacecraft;

[0060] Step 3: Set a preset duration, which is greater than the estimated orbital period. During the motion of the spacecraft, the four-body dynamics model predicts the position and velocity of the spacecraft at the i+1th moment based on the position and velocity of the spacecraft at the i-th moment. The initial value of i is 1.

[0061] Step 4: determine whether the running time corresponding to the time between the first moment and the i-th moment is equal to the preset time. If not, set i=i+1 and execute step 3. If yes, execute step 5.

[0062] Step 5: From the spacecraft position at the last moment of the first estimated orbital period to the spacecraft position at the i-th moment, the time corresponding to the spacecraft position closest to the spacecraft position at the first moment is selected as the selected time, and the duration from the first moment to the selected time is taken as the spacecraft quasi-orbital period;

[0063] (II) Simulation stage:

[0064] Step 6, setting the speed and position of the spacecraft at the first moment of the first quasi-orbital period;

[0065] Step 7, the four-body dynamics model predicts the speed and position of the spacecraft at the j+1th moment of the kth quasi-orbital period based on the speed and position of the spacecraft at the jth moment of the kth quasi-orbital period, where the initial value of j is 1 and the initial value of k is 1;

[0066] Step 8: Determine whether the running time corresponding to the time from the first moment to the jth moment of the kth quasi-orbital period is equal to the quasi-orbital period. If not, set j=j+1 and execute step 7. If yes, execute step 9.

[0067] Step 9: Check whether two conditions are met at the same time: condition 1: the difference between the velocity at the last moment in the k-th quasi-orbital cycle and the velocity at the first moment in the quasi-orbital cycle meets the preset velocity difference; condition 2: the difference between the position at the last moment in the k-th quasi-orbital cycle and the position at the first moment in the quasi-orbital cycle meets the preset position difference.

[0068] If yes, it is proved that the spacecraft has not deviated from the orbit in the kth quasi-orbital period, the position and velocity of the spacecraft at each moment in the kth quasi-orbital period are obtained, and step 10 is executed;

[0069] If not, it proves that the spacecraft has deviated from the orbit in the kth quasi-orbital period. At this time, the value of j is restored to 1, and the position and velocity of the spacecraft at the jth moment of the kth quasi-orbital period are corrected by the shooting method. The corrected position and velocity are used as the velocity and position of the spacecraft at the jth moment of the kth quasi-orbital period, and step 7 is executed;

[0070] Step 10, determine whether k is equal to the preset number of movement circles. If so, stop the simulation. If not, restore the value of j to 1, and use the spacecraft position and velocity at the last moment of the k-th quasi-orbital period as the position and velocity of the spacecraft at the j-th moment of the k+1 quasi-orbital period, so that k=k+1, and execute step 7.

[0071] Specifically, the velocity and position of the spacecraft at the first moment of the first quasi-orbital period set in step 6 of the simulation phase are equal to the position and velocity of the spacecraft at the first moment in step 2.

[0072] This embodiment uses the method of step 2 to obtain the spacecraft position and velocity at the first moment, so this embodiment is a design for the spacecraft resonant orbit.

[0073] For step 3, this embodiment can use orbital extrapolation to solve the four-body dynamics model, thereby predicting the position and velocity of the spacecraft at time i+1; orbital extrapolation means using integration to solve the four-body dynamics equation to obtain the position and velocity at the next moment.

[0074] For step 5, after obtaining the estimated orbital period of the spacecraft, 0.9-1.1 estimated orbital periods can be set as alternative time periods, and the spacecraft can be transferred from the first moment to the 1.1 estimated orbital period. If the position of the 0.986 period is closest to the initial moment position, this point is taken as the final value of the period. At this time, the orbital quasi-period is T1 = 0.986T. Whether the orbit is closed in the Earth-Moon conjunction coordinate system is an important indicator for testing the quality of the resonant cycle orbit design. The difference between the final value and the initial value of the orbit is too large, which will affect the efficiency and quality of subsequent corrections. Therefore, the orbital period needs to be corrected.

[0075] In step 9, the preset position difference is ΔR<10km, and the preset speed difference is ΔV<0.001km / s.

[0076] Due to the complexity of the four-body dynamics model, the model changes in the next cycle, and the same initial value cannot guarantee the same good quasi-periodic effect. At the same time, there is a situation of changing orbits during the operation of the spacecraft. Therefore, regardless of the quality of the quasi-periodicity, when the spacecraft is in operation, it may cause the orbit to fail to remain closed in each cycle. Therefore, it is necessary to adjust the orbit of the spacecraft so that the adjusted spacecraft orbit is closed (not off track) to ensure that it runs in a predetermined orbit, which is convenient for subsequent spacecraft monitoring, maintenance or recycling. If the spacecraft is found to be not closed after running a quasi-cycle, the orbit is modified and corrected. There are two correction methods in this embodiment:

[0077] The first is the track change method, such as Fig.11Figure A: When the first quasi-cycle is a closed orbit, the second quasi-cycle is run. If the spacecraft deviates from the orbit during the second quasi-cycle, the universal variable method is used to calculate the velocity increment of the spacecraft maneuvering after the second quasi-cycle simulation. If the increment is greater than the preset orbit increment, the position and velocity at the last moment of the second quasi-cycle are moved to the position and velocity at the initial moment of the first quasi-cycle. This method is used when judging whether the current energy or velocity increment of the spacecraft is enough to move to the position and velocity at the initial moment of the first quasi-cycle.

[0078] The second method is to use the shooting method to correct, such as Fig.11 Middle B: If the spacecraft has too little fuel (not enough energy or speed increment to move), correct the speed at the initial moment of the orbital cycle that has just completed, and use the model to predict the position and speed at each moment in the orbital cycle after multiple iterations, and judge whether the position and speed obtained this time meet the requirements. If they meet the requirements, it means that the orbit is closed, so as to obtain the position and speed at each moment in the orbital cycle under this closure. After the correction by the shooting method, the periodicity and stability of the resonant orbit are greatly improved.

[0079] This embodiment designs a linear shooting method to complete the initial value correction, which solves the problem that the correction matrix cannot be derived and calculated in the high-precision ephemeris model.

[0080] This embodiment designs dual termination conditions for the inertial system and the rotating system according to the characteristics of the resonant orbit, effectively adapts to the numerical solution problem of the strong nonlinear model, and ensures the correctness of the results.

[0081] The model is introduced below: The four-body dynamics model is:

[0082]

[0083] In the formula, For satellites in J 2000 The position below: E is the gravitational constant of the Earth; μ S is the gravitational constant of the sun; μ M is the gravitational constant of the moon; ∑F i is the gravitational perturbation term of the central celestial body other than the Earth in the ephemeris model; is the instantaneous position of the spacecraft and the sun in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; It is the instantaneous position of the Earth and the Sun in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; is the instantaneous position of the spacecraft and the moon in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; It is the instantaneous position of the Earth and the Moon in the inertial coordinate system of the Earth's center of mass at a certain UTC moment.

[0084] Specifically, most current studies use a circular restricted three-body model to design resonant cyclic orbits, and the initial values ​​of the orbits obtained are poorly periodic when applied to real celestial models, such as Figure 2 , Figure 5 and Figure 8 As shown. The high-precision ephemeris models at different times are not consistent. Therefore, the four-body kinematic model established in this embodiment takes into account the movement of each celestial body at the same time, which is more realistic. Therefore, the spacecraft period obtained by this model is more realistic.

[0085] The following further defines that in step 2, the spacecraft position and velocity at the first moment are obtained, and the specific process is:

[0086] According to the reachable range of the spacecraft and the characteristics of the Earth-Moon resonant orbit specified in the space mission, the resonant period ratio of the Moon and the spacecraft is obtained, and the estimated orbital period of the spacecraft is obtained in combination with the lunar orbital period;

[0087] The orbital semi-path is obtained according to the estimated orbital period of the spacecraft, and the position and velocity of the spacecraft at the first moment are obtained according to the orbital semi-path.

[0088] Specifically, if the spacecraft needs to reach the vicinity of the Earth-Moon L3, L4, or L5 libration points, it will need to select an orbit with a large eccentricity and a 3:1 resonance ratio.

[0089] Because the orbital period of the moon is known, which is about 27.32 days, the orbital period of the spacecraft can be directly calculated based on the period ratio. For example, when the resonance period is 3:1, the orbital period of the spacecraft is 27.32 / 3 = 9.1067 days.

[0090] Since the perigee of the resonant cycle orbit is near the earth, the orbital period under the two-body model is not much different from that under the dynamic model. The orbital period solved by the two-body model can be used as the initial guess period for the next step of processing.

[0091] The following further defines that the orbital semi-diameter is:

[0092] p=a(1-e 2 ) Formula 2,

[0093] Where p is the orbital semi-diameter, a is the orbital semi-major axis, and e is the orbital eccentricity. μ E is the gravitational constant of the Earth, and T is the orbital period.

[0094] Specifically, the eccentricity of the resonant orbit is generally selected to be a large eccentricity, e is generally 0.75-0.95, and the selection will not affect the orbit characteristics, but will only cause a slight deviation in the trajectory.

[0095] The following further defines that the position and velocity of the spacecraft at the first moment are:

[0096]

[0097] Where R0 is the initial value of the spacecraft position, θ is the true anomaly, and V0 is the initial value of the spacecraft velocity.

[0098] It is further defined below that step 9 also includes: after obtaining the position and velocity of the spacecraft at each time in the k-th quasi-orbital period, converting the position and velocity from the Earth-Moon conjunction coordinate system to the inertial coordinate system, the position and velocity in the inertial coordinate system are respectively expressed as:

[0099]

[0100]

[0101] In the formula, R S is the position vector of the spacecraft in the inertial coordinate system, R is the position vector of the moon in the inertial coordinate system, T M is the Earth-Moon conjunction coordinate system matrix, R Z is the position vector of the spacecraft in the Earth-Moon conjunction coordinate system, is a unit vector, V S is the velocity vector of the spacecraft in the geocentric inertial coordinate system, V is the velocity vector of the moon in the geocentric inertial coordinate system, V Z is the velocity vector of the spacecraft in the Earth-Moon conjunction coordinate system, T V is the velocity conversion matrix,

[0102] Specifically, the four-body dynamics model supports the spacecraft position and velocity in the inertial coordinate system. Therefore, the model prediction uses the spacecraft position and velocity in the inertial coordinate system, and the predicted position and velocity are also in the inertial coordinate system.

[0103] It is further defined below that between step 8 and step 9, the method further includes: converting the velocity at the last moment in the k-th quasi-orbital period and the velocity at the first moment in the quasi-orbital period to the Earth-Moon conjunction coordinate system through the Earth-Moon conjunction coordinate system matrix, and the Earth-Moon conjunction coordinate system matrix is:

[0104]

[0105] Where, T M is the Earth-Moon conjunction coordinate system matrix, R is the position vector of the Moon in the Earth-centered inertial coordinate system, and V is the velocity vector of the Moon in the Earth-centered inertial coordinate system.

[0106] Specifically, the shooting method uses the spacecraft position and velocity in the Earth-Moon rotating coordinate system. The overall process needs to be dimensionless first, and the Earth-Moon distance is set to 1 to facilitate numerical calculations. At the same time, time is also dimensionless. The dimensionless inertial orbital data is transferred to the Earth-Moon rotating coordinate system to facilitate subsequent correction operations.

[0107] The position and velocity information of the inertial coordinate system is processed dimensionlessly to facilitate representation in the rotating coordinate system. The dimensionless length unit and time unit are shown in Formula 8.

[0108]

[0109] In the formula, a M is the distance between the Earth and the Moon.

[0110] The following further defines that the specific process of step 3 is:

[0111] Consult the ephemeris to obtain the positions of the sun and the moon at the i-th moment. Combined with the spacecraft position and velocity at the i-th moment, obtain the instantaneous position of the spacecraft and the sun in the inertial coordinate system of the earth's center of mass, the instantaneous position of the earth and the sun in the inertial coordinate system of the earth's center of mass, the instantaneous position of the spacecraft and the moon in the inertial coordinate system of the earth's center of mass, and the instantaneous position of the earth and the moon in the inertial coordinate system of the earth's center of mass at the i-th moment, and predict the spacecraft position and velocity at the i+1 moment through the four-body dynamics model.

[0112] Specifically, the ephemeris is consulted, and the positions of the sun and the moon at any time are obtained through interpolation methods, and the perturbation terms in the four-body dynamics model are updated.

[0113] The following further defines that the shooting method is used for correction. The specific process is as follows:

[0114] Step 91, adding disturbances to the velocity vectors in three orthogonal directions of the velocity at the initial moment of the k-th quasi-orbital period to obtain the velocity after the disturbance is added, and the four-body dynamics model uses the velocity after the disturbance and the spacecraft position at the initial moment of the k-th quasi-orbital period to perform multiple iterations until the spacecraft position and velocity at the last moment of the k-th quasi-orbital period are predicted, and the difference between the spacecraft position at the last moment of the k-th quasi-orbital period and the spacecraft position at the initial moment of the k-th quasi-orbital period is taken as a linear correction matrix, and the linear correction matrix is ​​inverted to obtain a linear correction inverse matrix;

[0115] Step 92, updating the spacecraft velocity at the initial moment: multiplying the difference between the spacecraft position at the last moment of the k-th quasi-orbital period and the spacecraft position at the initial moment of the k-th quasi-orbital period by the inverse matrix of the linear correction matrix to obtain the first correction scale, adding the spacecraft velocity at the initial moment of the k-th quasi-orbital period to the first correction scale to obtain the spacecraft velocity at the initial moment after the m-th correction, where the initial value of m is 1;

[0116] Step 93, the four-body dynamics model uses the spacecraft velocity at the initial moment after the mth correction and the spacecraft position at the initial moment of the kth quasi-orbital period to perform multiple iterations until the spacecraft position and velocity at the last moment after the mth correction are predicted;

[0117] Step 94: when it is detected that the difference between the spacecraft position at the last moment after the mth correction and the spacecraft position at the initial moment after the mth correction does not meet the preset position difference, and the difference between the spacecraft speed at the last moment after the mth correction and the spacecraft speed at the initial moment after the mth correction does not meet the preset speed difference, execute step 95;

[0118] Step 95. Obtain a disturbance based on the difference between the spacecraft position at the last moment after the m-th correction and the spacecraft position at the initial moment of the k-th quasi-orbital period. Use the disturbance to update the linear correction inverse matrix in step 91. Multiply the difference between the spacecraft position at the last moment after the m-th correction and the spacecraft position at the initial moment of the k-th quasi-orbital period by the inverse matrix of the updated linear correction matrix to obtain the n-th correction scale. Add the n-th correction scale to the spacecraft velocity at the initial moment of the 1st circle to obtain the spacecraft velocity at the initial moment after the m+1-th correction. n is 2, so that m=m+1. Execute step 93.

[0119] Specifically, the four-body kinematic model has extremely strong nonlinearity, and traditional iterative algorithms cannot be effectively used. Therefore, a variable step size (increasing disturbance) linear shooting correction algorithm is creatively used to solve this problem. The use of linear shooting method can circumvent the problem of computational difficulties of nonlinear systems; and the use of variable step size design can effectively solve the problem of iterative algorithm failure to converge. By comparing the position of the final value point with the initial value point, the linear correction matrix is ​​solved, and the inverse matrix of the linear correction matrix is ​​used to calculate the linear correction value of the position error to the initial value point velocity. This method can achieve effective correction of strong nonlinear systems, but it has the disadvantages of slow convergence speed and poor convergence. The purpose of changing the disturbance is to speed up the convergence of the algorithm and prevent the failure to converge.

[0120] It is further defined below that in step 92 and step 95, the correction scale ΔV is expressed as:

[0121] ΔV=DF -1 ΔR' Formula 6,

[0122] Where DF is the linear correction matrix, DF = [ΔR' 2x ,ΔR' 2y ,ΔR' 2z ], ΔR' is the difference between the spacecraft orbit terminal position after the disturbance is added and the spacecraft orbit initial position.

[0123] Specifically, whether the orbit is closed in the Earth-Moon conjunction coordinate system is an important indicator for testing the quality of the spacecraft orbit design. If the difference between the final value and the initial value of the orbit is too large, it will affect the efficiency and quality of subsequent corrections. Therefore, it is necessary to correct the orbit period.

[0124] In order to improve the linear correction method, a variable step correction strategy is adopted. After each speed correction, a new ΔR' will be obtained. ΔR' is a vector, and its modulus is the modulus of the subsequent position error vector. The correction step size is changed by comparing the modulus of the position error vector between the two corrections with the previous one. This correction step size corresponds to the disturbance, that is, the linear correction matrix. If the change in the position error modulus is small, the value of the disturbance is increased to speed up the iterative convergence; if the error is close to the termination condition at this time, the value of the disturbance is reduced to prevent the situation where convergence cannot occur. The disturbance size is set according to the correction ratio, and then the correction step size is changed. That is: when step 94 detects that the difference between the spacecraft speed at the last moment after the mth correction and the spacecraft speed at the initial moment after the mth correction is relatively large, a large step size should be used for correction, that is, the disturbance value added in step 91 is increased, and the linear correction matrix DF is updated to speed up the correction of the initial speed.

[0125] Using traditional simulation, the trajectory diagram obtained by simulation is as follows: Figure 2 , Figure 5 and Figure 8 As shown, from Figure 2 , Figure 5 and Figure 8 It can be seen from the figure that after the spacecraft has been running for a period of time, the spacecraft simulated by the traditional model will deviate from the orbit. If the spacecraft is adjusted, it will cost a lot. However, by using this embodiment, the orbit of the spacecraft can be well simulated. Figure 3 , Figure 4 , Figure 6 , Figure 7 , Fig. 9 and Fig.10 shown.

[0126] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A spacecraft orbit design method under a high-precision four-body dynamics model, characterized in that: The method includes the following:

1. Pre-preparation stage: Step 1: Construct a four-body dynamics model; Step 2: Obtain the estimated orbital period of the spacecraft based on the two-body model and the resonant period ratio of the moon and the spacecraft; obtain the position and velocity of the spacecraft at the first moment based on the estimated orbital period of the spacecraft; Step 3: Set a preset duration, which is greater than the estimated orbital period. During the motion of the spacecraft, the four-body dynamics model predicts the position and velocity of the spacecraft at the i+1th moment based on the position and velocity of the spacecraft at the i-th moment. The initial value of i is 1. Step 4: determine whether the running time corresponding to the time between the first moment and the i-th moment is equal to the preset time. If not, set i=i+1 and execute step 3. If yes, execute step 5. Step 5: From the spacecraft position at the last moment of the first estimated orbital period to the spacecraft position at the i-th moment, the time corresponding to the spacecraft position closest to the spacecraft position at the first moment is selected as the selected time, and the duration from the first moment to the selected time is taken as the spacecraft quasi-orbital period; (II) Simulation stage: Step 6, setting the speed and position of the spacecraft at the first moment of the first quasi-orbital period; Step 7, the four-body dynamics model predicts the speed and position of the spacecraft at the j+1th moment of the kth quasi-orbital period based on the speed and position of the spacecraft at the jth moment of the kth quasi-orbital period, where the initial value of j is 1 and the initial value of k is 1; Step 8: Determine whether the running time corresponding to the time from the first moment to the jth moment of the kth quasi-orbital period is equal to the quasi-orbital period. If not, set j=j+1 and execute step 7. If yes, execute step 9. Step 9: Check whether two conditions are met at the same time: condition 1: the difference between the velocity at the last moment in the k-th quasi-orbital cycle and the velocity at the first moment in the quasi-orbital cycle meets the preset velocity difference; condition 2: the difference between the position at the last moment in the k-th quasi-orbital cycle and the position at the first moment in the quasi-orbital cycle meets the preset position difference. If yes, it is proved that the spacecraft has not deviated from the orbit in the kth quasi-orbital period, the position and velocity of the spacecraft at each moment in the kth quasi-orbital period are obtained, and step 10 is executed; If not, it proves that the spacecraft has deviated from the orbit in the kth quasi-orbital period. At this time, the value of j is restored to 1, and the position and velocity of the spacecraft at the jth moment of the kth quasi-orbital period are corrected by the shooting method. The corrected position and velocity are used as the velocity and position of the spacecraft at the jth moment of the kth quasi-orbital period, and step 7 is executed; Step 10, determine whether k is equal to the preset number of movement circles. If so, stop the simulation. If not, restore the value of j to 1, and use the spacecraft position and velocity at the last moment of the k-th quasi-orbital period as the position and velocity of the spacecraft at the j-th moment of the k+1 quasi-orbital period, so that k=k+1, and execute step 7.

2. The method for designing a spacecraft trajectory under a high-precision four-body dynamics model according to claim 1, characterized in that: The four-body dynamics model is: In the formula, For satellites in J 2000 The position below: E is the gravitational constant of the Earth; μ S is the gravitational constant of the sun; μ M is the gravitational constant of the moon; ∑F i is the gravitational perturbation term of the central celestial body other than the Earth in the ephemeris model; is the instantaneous position of the spacecraft and the sun in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; It is the instantaneous position of the Earth and the Sun in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; is the instantaneous position of the spacecraft and the moon in the inertial coordinate system of the Earth's center of mass at a certain UTC moment; It is the instantaneous position of the Earth and the Moon in the inertial coordinate system of the Earth's center of mass at a certain UTC moment.

3. The method for designing a spacecraft trajectory under a high-precision four-body dynamics model according to claim 1, characterized in that: In step 2, the spacecraft position and velocity at the first moment are obtained. The specific process is: According to the reachable range of the spacecraft and the characteristics of the Earth-Moon resonant orbit specified in the space mission, the resonant period ratio of the Moon and the spacecraft is obtained, and the estimated orbital period of the spacecraft is obtained in combination with the lunar orbital period; The orbital semi-path is obtained according to the estimated orbital period of the spacecraft, and the position and velocity of the spacecraft at the first moment are obtained according to the orbital semi-path.

4. The method for designing a spacecraft trajectory under a high-precision four-body dynamics model according to claim 3, characterized in that: The semi-diameter of the track is: p = a(1 - e 2 ) Formula 2 Where p is the orbital semi-diameter, a is the orbital semi-major axis, and e is the orbital eccentricity. μ E is the gravitational constant of the Earth, and T is the orbital period.

5. The method for designing a spacecraft trajectory under a high-precision four-body dynamics model according to claim 4, characterized in that: The position and velocity of the spacecraft at the first moment are: Where R0 is the initial value of the spacecraft position, θ is the true anomaly, and V0 is the initial value of the spacecraft velocity.

6. The method for designing a spacecraft trajectory under a high-precision four-body dynamics model according to claim 1, characterized in that: Step 9 also includes: after obtaining the position and velocity of the spacecraft at each time in the kth quasi-orbital period, converting the position and velocity from the Earth-Moon conjunction coordinate system to the inertial coordinate system, the position and velocity in the inertial coordinate system are respectively expressed as: In the formula, R S is the position vector of the spacecraft in the inertial coordinate system, R is the position vector of the moon in the inertial coordinate system, T M is the Earth-Moon conjunction coordinate system matrix, R Z is the position vector of the spacecraft in the Earth-Moon conjunction coordinate system, is a unit vector, V S is the velocity vector of the spacecraft in the geocentric inertial coordinate system, V is the velocity vector of the moon in the geocentric inertial coordinate system, V Z is the velocity vector of the spacecraft in the Earth-Moon conjunction coordinate system, T V is the velocity conversion matrix, 7. The method for designing a spacecraft trajectory under a high-precision four-body dynamics model according to claim 2, characterized in that: Between step 8 and step 9, the method further includes: converting the velocity at the last moment in the kth quasi-orbital period and the velocity at the first moment in the quasi-orbital period to the Earth-Moon conjunction coordinate system through the Earth-Moon conjunction coordinate system matrix. The Earth-Moon conjunction coordinate system matrix is: Where, T M is the Earth-Moon conjunction coordinate system matrix, R is the position vector of the Moon in the Earth-centered inertial coordinate system, and V is the velocity vector of the Moon in the Earth-centered inertial coordinate system.

8. The method for designing a spacecraft trajectory under a high-precision four-body dynamics model according to claim 1, characterized in that: The specific process of step 2 is as follows: Consult the ephemeris to obtain the positions of the sun and the moon at the i-th moment. Combined with the spacecraft position and velocity at the i-th moment, obtain the instantaneous position of the spacecraft and the sun in the inertial coordinate system of the earth's center of mass, the instantaneous position of the earth and the sun in the inertial coordinate system of the earth's center of mass, the instantaneous position of the spacecraft and the moon in the inertial coordinate system of the earth's center of mass, and the instantaneous position of the earth and the moon in the inertial coordinate system of the earth's center of mass at the i-th moment, and predict the spacecraft position and velocity at the i+1 moment through the four-body dynamics model.

9. A spacecraft trajectory design device under a high-precision four-body dynamics model, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that: The processor executes a computer program to implement a resonant cyclic orbit design method under a high-precision four-body dynamics model as described in any one of claims 1 to 7.

10. A computer-readable storage device, characterized in that: The storage device stores a computer program, characterized in that when the computer program is executed, it implements a method for designing a spacecraft orbit under a high-precision four-body dynamics model as described in any one of claims 1 to 7.

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