A spacecraft orbit design method under high-precision four-body dynamics model

Abstract

The application discloses a high-precision spacecraft orbit design method under a four-body dynamics model, and belongs to the field of orbit design. The three-body model is used to predict the spacecraft orbit period, but the predicted spacecraft orbit period is not accurate, the spacecraft position and speed at each time simulated in the spacecraft orbit design process are not accurate, and the simulation effect is poor. According to the resonance period ratio of the moon and the spacecraft, the actual celestial body operation state and the four-body dynamics model, the spacecraft quasi-orbit period is obtained; the four-body dynamics model is used to obtain the spacecraft position and speed at each time in each quasi-orbit period, the position difference and the speed difference between the last time and the starting time of the spacecraft in each quasi-orbit period are detected, and whether the spacecraft orbit in each quasi-orbit period is closed is determined. If not, the speed and position in the corresponding quasi-orbit period are corrected, until the spacecraft position and speed at each time in each quasi-orbit period in the closed state are obtained. The application is used to obtain the spacecraft orbit.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of orbit design. It relates to the design of resonant circulation orbits. BACKGROUND

[0002] With the deepening of human space exploration, the problem of spacecraft orbit design is increasingly concerned. The purpose of spacecraft orbit design is to input the designed spacecraft running position and speed into the spacecraft. After the spacecraft is launched into space, the spacecraft will actually run according to the input position and speed.

[0003] However, the existing spacecraft Earth-Moon three-body model predicts the spacecraft orbit period according to the position and speed of the spacecraft at the first time. However, the existing spacecraft Earth-Moon three-body model mostly uses a circular restricted three-body model or a lunar elliptical orbit model. These traditional models have obvious limitations. Because the circular restricted three-body model oversimplifies the gravitational relationship between celestial bodies, it 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 and other factors.

[0004] Although the lunar elliptical orbit model considers the elliptical shape of the moon's orbit, it does not fully consider the gravitational perturbation of the sun and other celestial bodies in the actual 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 not accurate. When simulating the spacecraft running using the accurate orbit period, the position and speed of the spacecraft at each time are not accurate, resulting in poor simulation effect. SUMMARY

[0005] The purpose of the present application is to solve the problem that the spacecraft orbit period predicted by the existing three-body model is not accurate, resulting in inaccurate position and speed of the spacecraft at each time during the spacecraft orbit design process, and 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] (I) Preparation stage:

[0008] Step 1, construct a four-body dynamics model;

[0009] Step 2, obtain the estimated orbit period of the spacecraft according to the two-body model and the resonance period ratio of the moon and the spacecraft; obtain the position and speed of the spacecraft at the first time according to the estimated orbit period of the spacecraft;

[0010] Step 3, set a preset time period, the preset time period is greater than the estimated orbit period, during the spacecraft movement, the four-body dynamics model predicts the spacecraft position and velocity at the i+1 moment according to the spacecraft position and velocity at the i moment, the initial value of i is 1;

[0011] Step 4, judge whether the running time corresponding to the first moment to the i moment is equal to the preset time period, if not, make i=i+1, execute step 3, if yes, execute step 5;

[0012] Step 5, select the moment corresponding to the spacecraft position closest to the spacecraft position at the first moment from the spacecraft position at the last moment of the first estimated orbit period to the spacecraft position at the i moment as the selected moment, and take the time period from the first moment to the selected moment as the spacecraft quasi-orbit period;

[0013] (II) simulation stage:

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

[0015] Step 7, the four-body dynamics model predicts the speed and position at the j+1 moment of the kth quasi-orbit period according to the speed and position of the spacecraft at the j moment of the kth quasi-orbit period, the initial value of j is 1, and the initial value of k is 1;

[0016] Step 8, judge whether the running time corresponding to the first moment to the j moment of the kth quasi-orbit period is equal to the quasi-orbit period, if not, make j=j+1, execute step 7, if yes, execute step 9;

[0017] Step 9, detect whether two conditions are met at the same time, condition one: the difference between the speed at the last moment of the kth quasi-orbit period and the speed at the first moment of the quasi-orbit period satisfies the preset speed difference; Condition two: the difference between the position at the last moment of the kth quasi-orbit period and the position at the first moment of the quasi-orbit period satisfies the preset position difference,

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

[0019] If not, it is proved that the spacecraft deviates from the orbit in the kth quasi-orbit period, at this time, the value of j is restored to 1, and the spacecraft position and speed at the j moment of the kth quasi-orbit period are corrected by using the shooting method, the corrected position and speed are taken as the speed and position of the spacecraft at the j moment of the kth quasi-orbit period again, and step 7 is executed;

[0020] Step 10, judging whether k is equal to the preset motion circle number, if yes, stopping the simulation, if no, restoring the value of j to 1, taking the position and speed of the spacecraft at the last moment of the kth quasi-orbit period as the position and speed of the spacecraft at the jth moment of the k+1th quasi-orbit period, making k=k+1, and executing step 7.

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

[0022]

[0023] wherein, is the position of the satellite in the J 2000 coordinate system; μ 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 bodies in the ephemeris model except the Earth; is the instantaneous position of the spacecraft and the Sun in the Earth's center of mass inertial coordinate system at a certain UTC moment; is the instantaneous position of the Earth and the Sun in the Earth's center of mass inertial coordinate system at a certain UTC moment; is the instantaneous position of the spacecraft and the Moon in the Earth's center of mass inertial coordinate system at a certain UTC moment; is the instantaneous position of the Earth and the Moon in the Earth's center of mass inertial coordinate system at a certain UTC moment.

[0024] Preferably, the orbit semi-latus rectum is:

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

[0026] wherein, p is the orbit semi-latus rectum, a is the orbit semi-major axis, e is the orbit eccentricity, μ E is the gravitational constant of the Earth, and T is the orbit period.

[0027] Preferably, the position and speed of the spacecraft at the 1st moment are respectively:

[0028]

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

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

[0031]

[0032] wherein 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 earth-centered inertial coordinate system, V is the velocity vector of the moon in the earth-centered 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 following step is further included: converting the last-time velocity in the kth quasi-orbit period and the first-time velocity in the quasi-orbit period to the earth-moon conjunction coordinate system through the earth-moon conjunction coordinate system matrix, wherein the earth-moon conjunction coordinate system matrix is:

[0034]

[0035] wherein 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 as follows:

[0037] Referring to the ephemeris, the positions of the sun and the moon at the ith time are obtained, the instantaneous positions of the spacecraft and the sun in the earth-centered inertial coordinate system, the instantaneous positions of the earth and the sun in the earth-centered inertial coordinate system, the instantaneous positions of the spacecraft and the moon in the earth-centered inertial coordinate system, and the instantaneous positions of the earth and the moon in the earth-centered inertial coordinate system at the ith time are obtained in combination with the position and the velocity of the spacecraft at the ith time, and the position and the velocity of the spacecraft at the i+1th time are predicted through the four-body dynamics model.

[0038] The present application has the following beneficial effects:

[0039] In actual celestial body movement, the gravity of the sun cannot be ignored. In order to more accurately design an orbit in a sun-earth-moon three-body model, the real positions of the sun and the moon are taken as perturbation terms, real-time positions of the sun and the moon are obtained by consulting an ephemeris, and a four-body dynamic model close to the real lunar-earth gravity environment is established, i.e., a four-body model of the sun, the earth, the moon and a spacecraft. The model can more truly reflect the interaction between celestial bodies and provide a more reliable basis for the orbit design of the spacecraft. Therefore, the same orbit period as the actual spacecraft operation period is obtained through the model, and the positions and velocities of the spacecraft at each time during operation are obtained through orbit extrapolation calculation of the model. Therefore, the orbit design of the application enhances the authenticity of the orbit design and is more suitable for actual engineering applications. The designed orbit initial value also has good quasi-periodicity and stability in actual engineering, and long-term tasks such as on-orbit patrol and reconnaissance can be performed.

[0040] In addition, after obtaining the quasi-orbit period of the spacecraft, in order to ensure that the spacecraft runs in a closed state in each orbit period, the orbit in each orbit period is detected every time the spacecraft runs one orbit period, and if the orbit is not closed, the non-closed orbit is corrected until the positions and velocities at each time in each orbit period in a closed state are obtained. When the positions and velocities at each time in each orbit period in a closed state are input into the spacecraft, the spacecraft can run according to the positions and velocities after being launched into space. Therefore, the simulation effect of the application is good, and the authenticity is good. BRIEF DESCRIPTION OF DRAWINGS

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

[0042] Figure 2 It is a three-period orbit trajectory diagram of a 3:1 resonance orbit of the moon and a spacecraft designed under a circular restricted three-body model;

[0043] Figure 3 It is a three-period orbit trajectory diagram of a 3:1 resonance orbit of the moon and a spacecraft designed under a dynamic model;

[0044] Figure 4 It is a three-period orbit trajectory diagram of a 3:1 resonance orbit of the moon and a spacecraft designed under a dynamic model;

[0045] Figure 5 It is a three-period orbit trajectory diagram of a 2:1 resonance orbit of the moon and a spacecraft designed under a circular restricted three-body model;

[0046] Figure 6 It is a three-period orbit trajectory diagram of a 2:1 resonance orbit of the moon and a spacecraft designed under a dynamic model;

[0047] Figure 7 Figure 3 is a three-period orbit trajectory diagram of a lunar spacecraft periodic ratio 2:1 resonance orbit designed under a circular restricted three-body model;

[0048] Figure 8 Figure 3 is a three-period orbit trajectory diagram of a lunar spacecraft periodic ratio 2:1 resonance orbit designed under a circular restricted three-body model;

[0049] Figure 9 Figure 3 is a three-period orbit trajectory diagram of a lunar spacecraft periodic ratio 2:1 resonance orbit designed under a circular restricted three-body model;

[0050] Figure 10 Figure 3 is a three-period orbit trajectory diagram of a lunar spacecraft periodic ratio 2:1 resonance orbit designed under a circular restricted three-body model;

[0051] Figure 11 Figure 3 is a three-period orbit trajectory diagram of a lunar spacecraft periodic ratio 2:1 resonance orbit designed under a circular restricted three-body model; DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0053] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0054] The present application will be further described below with reference to the drawings and specific embodiments, but is not limited by the present application.

[0055] Embodiment:

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

[0057] (I) Pre-preparation stage:

[0058] Step 1, constructing a four-body dynamics model;

[0059] Step 2, obtaining a spacecraft estimated orbit period according to a two-body model and a resonance period ratio of the moon and the spacecraft; obtaining a spacecraft position and speed at the first time according to the spacecraft estimated orbit period;

[0060] Step 3, set a preset time period, the preset time period is greater than the estimated orbit period, during the spacecraft movement, the four-body dynamics model predicts the spacecraft position and velocity at the i+1 moment according to the spacecraft position and velocity at the i moment, the initial value of i is 1;

[0061] Step 4, judge whether the running time corresponding to the first moment to the i moment is equal to the preset time period, if not, make i=i+1, execute step 3, if yes, execute step 5;

[0062] Step 5, select the moment corresponding to the spacecraft position closest to the spacecraft position at the first moment from the spacecraft position at the last moment of the first estimated orbit period to the spacecraft position at the i moment as the selected moment, and take the time period from the first moment to the selected moment as the spacecraft quasi-orbit period;

[0063] (II) simulation stage:

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

[0065] Step 7, the four-body dynamics model predicts the speed and position at the j+1 moment of the kth quasi-orbit period according to the speed and position of the spacecraft at the j moment of the kth quasi-orbit period, the initial value of j is 1, and the initial value of k is 1;

[0066] Step 8, judge whether the running time corresponding to the first moment to the j moment of the kth quasi-orbit period is equal to the quasi-orbit period, if not, make j=j+1, execute step 7, if yes, execute step 9;

[0067] Step 9, detect whether two conditions are met at the same time, condition one: the difference between the speed at the last moment of the kth quasi-orbit period and the speed at the first moment of the quasi-orbit period satisfies the preset speed difference; Condition two: the difference between the position at the last moment of the kth quasi-orbit period and the position at the first moment of the quasi-orbit period satisfies the preset position difference,

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

[0069] If not, it is proved that the spacecraft deviates from the orbit in the kth quasi-orbit period, at this time, the value of j is restored to 1, and the spacecraft position and speed at the j moment of the kth quasi-orbit period are corrected by using the shooting method, the corrected position and speed are taken as the speed and position of the spacecraft at the j moment of the kth quasi-orbit period again, and step 7 is executed;

[0070] Step 10, judge whether k is equal to the preset motion number of turns, if yes, stop simulation, if no, at this time the value of j is restored to 1, the position and velocity of the spacecraft at the last moment of the kth quasi-orbital period are taken as the position and velocity of the spacecraft at the jth moment of the k+1th quasi-orbital period, k=k+1, and step 7 is executed.

[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 stage are equal to the position and velocity of the spacecraft at the first moment in step 2.

[0072] The spacecraft position and velocity at the first moment in this embodiment are obtained by the method of step 2, so this embodiment is a design of a resonant orbit of the spacecraft.

[0073] For step 3, the four-body dynamics model can be solved by orbit extrapolation to predict the position and velocity of the spacecraft at the i+1th moment; the meaning of orbit extrapolation is to solve the four-body dynamics equation by integration to obtain the position and velocity at the next moment.

[0074] For step 5, after obtaining the estimated orbit period of the spacecraft, 0.9-1.1 estimated orbit periods can be set as the standby period, and the spacecraft is transferred from the first moment to the 1.1th estimated orbit period, if the position of 0.986 periods is closest to the initial position, this point is taken as the period terminal point, at this time the quasi-period of the orbit is T1=0.986T. Whether the orbit is closed in the lunar-synodic coordinate system is an important indicator to test the design of the resonant periodic orbit. The difference between the terminal value and the initial value of the orbit will affect the efficiency and quality of subsequent correction. Therefore, the orbit period needs to be corrected.

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

[0076] Due to the complexity of the four-body dynamics model, in the next period, the model changes, and the same initial value cannot guarantee the same good quasi-periodic effect, at the same time, there is a situation of orbit transfer during the operation of the spacecraft, therefore, whether the quasi-periodicity is good or not, during the operation of the spacecraft, it may cause the orbit to be unable to keep closed in each period. Therefore, the orbit of the spacecraft needs to be adjusted to make the adjusted spacecraft orbit closed (not deviated), to ensure that the spacecraft runs in the given orbit, and to facilitate subsequent spacecraft monitoring, maintenance or recycling work. If the spacecraft runs for one quasi-period and finds that the orbit is not closed, the orbit is modified, and this embodiment has two correction methods:

[0077] The first is the orbit transfer method, such as Figure 11Fig. 2B: If the spacecraft has insufficient fuel (energy or velocity increment is not enough to move), the velocity at the initial time of the just completed orbit period is corrected. Using the model, the position and velocity at each time in the orbit period are predicted through multiple iterations. It is determined whether the position and velocity obtained this time meet the requirements. If they do, it is determined that the orbit is closed this time, and thus the position and velocity at each time in the orbit period under this closure are obtained. After correction using the shooting method, the periodicity and stability of the resonant orbit are greatly improved.

[0078] The second is to use the shooting method to correct, such as Figure 11 Fig. 2B: If the spacecraft has insufficient fuel (energy or velocity increment is not enough to move), the velocity at the initial time of the just completed orbit period is corrected. Using the model, the position and velocity at each time in the orbit period are predicted through multiple iterations. It is determined whether the position and velocity obtained this time meet the requirements. If they do, it is determined that the orbit is closed this time, and thus the position and velocity at each time in the orbit period under this closure are obtained. After correction using the shooting method, the periodicity and stability of the resonant orbit are greatly improved.

[0079] The linear shooting method is used to complete the initial value correction in this embodiment, which solves the problem that the correction matrix cannot be calculated in the high-precision ephemeris model.

[0080] The dual termination conditions of the inertial system and the rotating system are designed according to the characteristics of the resonant orbit in this embodiment, which effectively adapts to the numerical solution of the strong nonlinear model and ensures the correctness of the results.

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

[0082]

[0083] In the formula, r is the position of the satellite in the J coordinate system; μearthis the gravitational constant of the Earth; μsunis the gravitational constant of the Sun; μmoonis the gravitational constant of the Moon; ∑F is the gravitational perturbation term of the central celestial body in the ephemeris model other than the Earth; r is the instantaneous position of the spacecraft and the Sun in the Earth's center of mass inertial coordinate system at a certain UTC time; r is the instantaneous position of the Earth and the Sun in the Earth's center of mass inertial coordinate system at a certain UTC time; r is the instantaneous position of the spacecraft and the Moon in the Earth's center of mass inertial coordinate system at a certain UTC time; and r is the instantaneous position of the Earth and the Moon in the Earth's center of mass inertial coordinate system at a certain UTC time. 2000 E S M i

[0084] ​​​​​​​​​Specifically, the current research mostly adopts a circular restricted three-body model to design a resonant circular orbit, and the initial values of the orbit obtained are applied to a real celestial body model to obtain the periodic difference as shown in Figure 2 、 Figure 5 and Figure 8 . High-precision ephemeris models at different times are not consistent. Therefore, the four-body kinematic model established in this embodiment considers the running conditions between the celestial bodies at the same time, and is more realistic. Therefore, the spacecraft period obtained by using the model is more realistic.

[0085] Further defined below, in step 2, the position and velocity of the spacecraft at the first time are obtained, and the specific process is as follows:

[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 orbit period of the spacecraft is obtained in combination with the orbit period of the Moon;

[0087] According to the estimated orbit period of the spacecraft, the orbit semi-major radius is obtained, and the position and velocity of the spacecraft at the first time are obtained according to the orbit semi-major radius.

[0088] Specifically, if the spacecraft needs to reach the vicinity of the Earth-Moon L3, L4, or L5 libration point, a large eccentricity and a 3:1 resonant ratio orbit need to be selected.

[0089] Because the orbit period of the Moon is known, which is about 27.32 days. Therefore, the orbit period of the spacecraft can be directly calculated according to the period ratio. For example, when the resonant period is 3:1, the orbit period of the spacecraft is 27.32 / 3 = 9.1067 days.

[0090] Because the perigee of the resonant circular orbit is near the Earth, the difference between the orbit period under the two-body model and the orbit period under the dynamic model is not large, and the orbit period solved by the two-body model can be used as the initial guess period for the next step.

[0091] Further defined below, the orbit semi-major radius is:

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

[0093] In the formula, p is the orbit semi-major radius, a is the orbit semi-major axis, e is the orbit eccentricity, μ E is the gravitational constant of the Earth, and T is the orbit period.

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

[0095] Further defined below, the position and velocity of the spacecraft at the first time are as follows:

[0096]

[0097] wherein 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] Further defined below, step 9 further comprises: after obtaining the position and velocity of the spacecraft at each time in the kth quasi-orbit period, converting the position and velocity from the lunar orbit coordinate system to the inertial coordinate system, and the position and velocity in the inertial coordinate system are represented as:

[0099]

[0100]

[0101] wherein 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 lunar orbit coordinate system matrix, R Z is the position vector of the spacecraft in the lunar orbit coordinate system, is a unit vector, V S is the velocity vector of the spacecraft in the earth-centered inertial coordinate system, V is the velocity vector of the moon in the earth-centered inertial coordinate system, V Z is the velocity vector of the spacecraft in the lunar orbit 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 prediction is also the spacecraft position and velocity in the inertial coordinate system.

[0103] Further defined below, between step 8 and step 9, further comprises: converting the velocity at the last time in the kth quasi-orbit period and the velocity at the first time in the quasi-orbit period to the lunar orbit coordinate system through the lunar orbit coordinate system matrix, and the lunar orbit coordinate system matrix is:

[0104]

[0105] wherein T M is the lunar orbit 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 targeting method correction uses the spacecraft position and velocity in the geocentric inertial coordinate system. The overall process needs to be dimensionless first, and the geocentric distance is set to 1 for convenient numerical operation, and the time is also dimensionless. The dimensionless orbit data in the inertial coordinate system is transferred to the geocentric inertial coordinate system for subsequent correction operations.

[0107] The position and velocity information in the inertial coordinate system is dimensionless, which is convenient for representation in the rotating coordinate system. The length unit and time unit after dimensionless processing are shown in formula 8.

[0108]

[0109] In the formula, a M is the geocentric distance.

[0110] Further defined below, 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, and combine the positions and velocities of the spacecraft at the i-th moment to obtain the instantaneous positions of the spacecraft and the sun in the geocentric inertial coordinate system, the instantaneous positions of the earth and the sun in the geocentric inertial coordinate system, the instantaneous positions of the spacecraft and the moon in the geocentric inertial coordinate system, and the instantaneous positions of the earth and the moon in the geocentric inertial coordinate system, and predict the positions and velocities of the spacecraft at the i+1-th moment through the four-body dynamics model.

[0112] Specifically, consult the ephemeris to obtain the positions of the sun and the moon at any moment through the interpolation method, and update the perturbation term in the four-body dynamics model.

[0113] Further defined below, the specific process of step 3 is:

[0114] Step 91, add perturbation to the three orthogonal direction velocity vectors of the initial moment velocity of the k-th quasi-orbit period to obtain the perturbed velocity, and use the perturbed velocity and the spacecraft position at the initial moment of the k-th quasi-orbit period to perform multiple iterations until the spacecraft position and velocity at the last moment of the k-th quasi-orbit period are predicted. The difference between the spacecraft position at the last moment of the k-th quasi-orbit period and the spacecraft position at the initial moment of the k-th quasi-orbit period is taken as a linear correction matrix, and the inverse of the linear correction matrix is obtained.

[0115] Step 92, update the initial moment spacecraft velocity: multiply the difference between the spacecraft position at the last moment of the k-th quasi-orbit period and the spacecraft position at the initial moment of the k-th quasi-orbit period by the inverse of the linear correction matrix to obtain the first correction scale, and add the first correction scale to the spacecraft velocity at the initial moment of the k-th quasi-orbit period to obtain the initial moment spacecraft velocity after the m-th correction, and the initial value of m is 1.

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

[0117] Step 94, when it is detected that the difference between the spacecraft position at the final time after the mth correction and the spacecraft position at the initial time after the mth correction does not satisfy the preset position difference, and the difference between the spacecraft velocity at the final time after the mth correction and the spacecraft velocity at the initial time after the mth correction does not satisfy the preset velocity difference, step 95 is performed;

[0118] Step 95, a disturbance is obtained according to the difference between the spacecraft position at the final time after the mth correction and the spacecraft position at the initial time of the kth quasi-orbit period, the linear correction inverse matrix in step 91 is updated using the disturbance, the difference between the spacecraft position at the final time after the mth correction and the spacecraft position at the initial time of the kth quasi-orbit period is multiplied by the inverse matrix of the updated linear correction matrix to obtain the n th correction scale, the n th correction scale is added to the spacecraft velocity at the initial time of the first revolution to obtain the initial time spacecraft velocity after the m+1 th correction, n is 2, m is set to m+1, and step 93 is performed.

[0119] Specifically, the four-body kinematics model has extremely strong nonlinearity, and the traditional iterative algorithm cannot be effectively used. Therefore, the variable step (increasing disturbance) linear targeting correction algorithm is creatively used to solve this problem. Using the linear targeting method can avoid the calculation difficulty problem of the nonlinear system; and using the variable step design can effectively solve the problem that the iterative algorithm cannot converge. By comparing the positions of the final value point and the initial value point, the linear correction matrix is solved, and the inverse matrix of the linear correction matrix can be used to calculate the linear correction value of the position error on the initial value point velocity. This method can effectively correct the strong nonlinear system, but has the shortcomings of slow convergence speed and poor convergence.

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

[0121] ΔV=DF -1 ΔR' formula 6,

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

[0123] Specifically, whether the orbit is closed in the lunar transfer coordinate system is an important index to test the orbit design. The difference between the terminal value and the initial value of the orbit will affect the efficiency and quality of the subsequent correction. Therefore, the orbit period needs to be corrected.

[0124] In order to improve the linear correction method, a variable step correction strategy is adopted. After each velocity correction, a new ΔR' is obtained, which is a vector, and its modulus is also the modulus of the subsequent position error vector. By comparing the modulus of the position error vector of the two corrections with that of the previous correction, the correction step is changed. The correction step corresponds to the perturbation, that is, the linear correction matrix. If the change of the position error modulus is small, the value of the perturbation is increased to speed up the iteration convergence; if the error is close to the termination condition at this time, the value of the perturbation is reduced to prevent the situation of unable to converge. According to the correction ratio, the size of the perturbation is set, and then the correction step is changed. That is, when the step 94 detects that the difference between the spacecraft speed at the last time after the mth correction and the spacecraft speed at the initial time after the mth correction is large, a large step should be used for correction, that is, the perturbation value added in step 91 is increased, and the linear correction matrix DF is updated, so as to speed up the correction of the initial speed.

[0125] The trajectory diagram simulated by using the traditional simulation is shown in Figure 2 、 Figure 5 and Figure 8 As can be seen from Figure 2 、 Figure 5 and Figure 8 , when the spacecraft runs for a period of time, the spacecraft simulated by using the traditional model will deviate from the orbit, and if the spacecraft is adjusted, a great cost will be paid, and by using the embodiment, the spacecraft orbit can be well simulated, as shown in Figure 3 、 Figure 4 、 Figure 6 、 Figure 7 、 Figure 9 and Figure 10 .

[0126] Although the present application is described herein with reference to particular embodiments, it should be understood that these examples are merely illustrative of the principles and applications of the present application. It should therefore be understood that numerous modifications can be made to the illustrative embodiments and that other arrangements can be devised without departing from the spirit and scope of the present application as defined by the appended claims. It should be understood that the features described in connection with one embodiment can be used in conjunction with other embodiments described herein. It should also be understood that features described in connection with separate embodiments can be used in other described embodiments.

Claims

1. A method for designing spacecraft orbits under a high-precision four-body dynamics model, characterized in that: The method includes the following: (1) Preparatory 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 resonance period ratio of the moon and the spacecraft; obtain the spacecraft position and velocity 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 spacecraft motion, the four-body dynamics model predicts the spacecraft position and velocity at time i+1 based on the spacecraft position and velocity at time i, where 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, select the time corresponding to the spacecraft position closest to the spacecraft position at the first moment as the selected time, and use the duration from the first moment to the selected time as the spacecraft quasi-orbital period; (2) Simulation stage: Step 6: Set the spacecraft velocity and position at the first moment of the first quasi-orbital period; Step 7: The four-body dynamics model predicts the velocity and position of the spacecraft at the jth moment in the kth quasi-orbital period based on the velocity and position of the spacecraft at the jth moment in 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 simultaneously: condition 1: the difference between the velocity at the last moment of the k-th quasi-orbital period and the velocity at the first moment of the same period meets the preset velocity difference; condition 2: the difference between the position at the last moment of the k-th quasi-orbital period and the position at the first moment of the same period meets the preset position difference. If yes, prove that the spacecraft has not deviated from its orbit during the kth quasi-orbital period, obtain the position and velocity of the spacecraft at each moment during the kth quasi-orbital period, and execute step 10; If not, it proves that the spacecraft has deviated from its orbit during the kth quasi-orbital period. In this case, 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 using 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: Where, For satellites in J 2000 The position below; μ 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; 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: Based on the spacecraft's reach and the Earth-Moon resonance orbit characteristics specified in the space mission, the resonance period ratio of the Moon and the spacecraft is obtained. Combined with the Moon's orbital period, the estimated orbital period of the spacecraft is obtained. The orbital semi-path is obtained based on the estimated orbital period of the spacecraft, and the position and velocity of the spacecraft at the first moment are obtained based on 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-drift diameter of the track is: p = a(1 - e 2 ) Formula 2 Where p is the semi-diameter of the track, a is the semi-major axis of the track, and e is the eccentricity of the track. 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 moment 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: Where 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 rendezvous 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 k-th quasi-orbital period and the velocity at the first moment in the quasi-orbital period into the Earth-Moon synodic coordinate system using the Earth-Moon synodic coordinate system matrix. The Earth-Moon synodic 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: Consult the ephemeris to obtain the positions of the sun and the moon at moment i. Combined with the spacecraft position and velocity at moment i, obtain the instantaneous positions of the spacecraft and the sun in the inertial coordinate system of the Earth's center of mass, the instantaneous positions of the Earth and the sun in the inertial coordinate system of the Earth's center of mass, the instantaneous positions of the spacecraft and the moon in the inertial coordinate system of the Earth's center of mass, and the instantaneous positions of the Earth and the moon in the inertial coordinate system of the Earth's center of mass at moment i. Then predict the spacecraft position and velocity at moment i+1 through the four-body dynamics model.

9. A high-precision spacecraft trajectory design device under a 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 spacecraft orbit design method under a high-precision four-body dynamics model as described in any one of claims 1 to 7.

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