CN111605736A - Earth-moon L2 point transfer orbit optimal error correction point selection method - Google Patents

Earth-moon L2 point transfer orbit optimal error correction point selection method Download PDF

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CN111605736A
CN111605736A CN202010386041.4A CN202010386041A CN111605736A CN 111605736 A CN111605736 A CN 111605736A CN 202010386041 A CN202010386041 A CN 202010386041A CN 111605736 A CN111605736 A CN 111605736A
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吴伟仁
唐玉华
乔栋
李翔宇
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Abstract

The invention discloses a method for selecting an optimal error correction point of a march L2 point transfer orbit, belonging to the technical field of aerospace. The implementation method of the invention comprises the following steps: establishing a moon rotation coordinate system, and calculating a moon L2 point nominal transfer orbit state transfer matrix; calculating the change situation of the error along with the time according to the state transition matrix; according to the state transition matrix, establishing a functional relation between the correction maneuver and the correction time and the track error; optimizing the correction time of the detector, and determining an error correction point and a correction speed increment with optimal correction speed increment and terminal speed increment by utilizing the functional relation; and applying speed increment at the optimal correction point by the detector to finish the orbit correction of the march L2 point transfer orbit and finish the march L2 point orbit transfer. The invention can minimize the speed increment required by correction, and has the advantages of high correction efficiency and reduced correction fuel consumption. The invention improves the precision of orbit transfer by considering the influence of the gravity of the moon on the error of the transfer orbit.

Description

Earth-moon L2 point transfer orbit optimal error correction point selection method
Technical Field
The invention relates to a method for selecting an error correction point of a lunar L2 point transfer orbit, in particular to a method for selecting an error correction point and evaluating a speed increment of a lunar L2 point transfer orbit with an error, and belongs to the technical field of aerospace.
Background
In order to realize lunar back detection, relay communication and data transmission are required to be carried out through the relay satellite, and the lunar equilibrium point L2 is an ideal position of the relay satellite due to better dynamic characteristics and geometric positions. The relay satellite is deployed at the earth-moon balance point L2 point periodic orbit, and the transfer orbit design is required, wherein the fuel consumption required by the transfer of the near-flying near the moon by utilizing the three-body system dynamics is less, the transfer time is shorter, and the method is a more common mode in engineering implementation. However, due to the influence of factors such as the execution error of the detector and the error of the dynamic model, the transfer orbit of the detector has deviation from the nominal design orbit in the actual task, and the error correction needs to be executed. Due to the nonlinear characteristics of the dynamics of the three-system, the transfer orbit is sensitive to errors, the errors may diverge exponentially, and the difference of fuel consumption required by applying correction at different positions is large.
Regarding the correction of the transfer orbit error developed, prior art [1] (see japanese, yanville. moon probe transfer orbit midway correction [ J ]. astronavigation report, 2009,25 (1): 89-92) studied the correction method of the transfer orbit midway from the earth to the moon, giving a functional relationship between the correction amount and the terminal constraint, but this method did not consider the orbit from the moon to the earth moon L2 point, and the analysis was performed based on the inertial system, and is not suitable for the orbit correction under three bodies.
In the prior art [2] (see: Li Ming Tao, Zheng Jianhua. translation point task transfer orbit midway correction research [ J ]. space science, 2010,30(6): 540-.
Disclosure of Invention
The invention discloses a method for selecting an optimal error correction point of a march L2 point transfer orbit, which aims to solve the technical problems that: the method for selecting the optimal error correction point in the earth-moon L2 point transfer orbit error correction is provided, the speed increment required by correction can be minimized, and the method has the advantages of high correction efficiency and low correction fuel consumption.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a method for selecting an optimal error correction point of a lunar-lunar L2 point transfer orbit, which comprises the steps of establishing a lunar-lunar rotating coordinate system and calculating a lunar-lunar L2 point nominal transfer orbit state transfer matrix; calculating the change situation of the error along with the time according to the state transition matrix; according to the state transition matrix, establishing a functional relation between the correction maneuver and the correction time and the track error; optimizing the correction time of the detector, and determining an error correction point and a correction speed increment with optimal correction speed increment and terminal speed increment by utilizing the functional relation; and applying speed increment at the optimal correction point by the detector to finish the orbit correction of the march L2 point transfer orbit and finish the march L2 point orbit transfer.
The invention discloses a method for selecting an optimal error correction point of a march L2 point transfer orbit, which comprises the following steps:
the method comprises the following steps: and establishing a moon rotation coordinate system, and calculating a moon L2 point nominal transfer orbit state transfer matrix.
Selecting a mass center of an earth-moon system as an origin to establish a coordinate system, selecting an X axis as a connecting line direction of the earth and the moon, pointing the earth to the moon, selecting a Z axis as an angular speed direction of system rotation, and forming a right-hand coordinate system by the Y axis, the X axis and the Z axis which are vertical to each other;
the kinetic equation of the detector in the system is expressed as
Figure BDA0002483864210000021
Wherein μ ═ m2/(m1+m2) Denotes the mass coefficient of the system, m1Is the mass of the earth, m2In order to be the quality of the moon,
Figure BDA0002483864210000022
is the distance of the detector from the earth,
Figure BDA0002483864210000023
is the distance between the probe and the moon;
the nominal transfer orbit in the earth-moon rotation system is defined as that the kinetic equation (1) is expressed in a matrix form
Figure BDA0002483864210000024
Wherein
Figure BDA0002483864210000025
For representing six-dimensional state variables of nominal track position velocity, linearized near the nominal transition track
Figure BDA0002483864210000026
Wherein
Figure BDA0002483864210000027
Figure BDA0002483864210000028
Figure BDA0002483864210000029
In which U represents the pseudo potential energy of the system, UijRepresenting the second partial derivative in the i, j direction, the solution of the equation being x (t) phi (t, t)0)X(t0) Where Φ (t, t)0) Indicating system from t0State transition matrix to t. Solving by
Figure BDA0002483864210000031
Initial state Φ (0,0) ═ I6×6Is an identity matrix. According to the initial state, the state transition matrix of the nominal orbit at any time t is obtained by solving a matrix differential equation, which is abbreviated as phi (t), and the state transition matrix is also expressed in a form of a block matrix
Figure BDA0002483864210000032
Where M, N, L, K are all 3 × 3 matrices.
And step two, calculating the change situation of the orbit error along with the time according to the state transition matrix.
Defining a track at a time T0Has a position and velocity error of r0,v0The corresponding nominal position velocity state is r0,v0Then, at time T, based on the state transition matrix1The position and velocity error of the real track relative to the nominal track is r1,v1
Figure BDA0002483864210000033
At the same time T1Applying a corrective maneuver Δ v1Then the terminal time T2The terminal error of the real orbit is
Figure BDA0002483864210000034
And step three, establishing a functional relation between the correction maneuver and the correction time and the track error.
Track correction needs to guarantee that the corrected track is at terminal time T2To a position r2I.e. r 20 to obtain M2r1+N1(v1+Δv1)＝0，
Namely, it is
Figure BDA0002483864210000035
According to formula (4) having r1＝M1r0+N1v0，
v1＝L1r0+K1v0. To obtain
Figure BDA0002483864210000036
Simultaneous terminal velocity error v2I.e. the required applied orbital momentum av2
Figure BDA0002483864210000037
The total velocity increment required for error correction is | | Δ v1||+||Δv2L. Equations (6) and (7) establish the corrective maneuvers and the corrective time and orbit errors, i.e., establish the functional relationship of the corrective maneuvers and the corrective time and orbit errors.
And step four, optimizing the error correction time according to the measured track error to minimize the speed increment required by correction so as to obtain an optimal correction point and optimal correction time.
Using the relationship between the orbit error and the correction time and the velocity increment established in the step three, and obtaining the error r by measurement1,v1Optimizing the error correction time T2Let | | | Δ v1||+||Δv2The minimum |, because the optimization variable only has one variable of correction time, the optimal solution can be obtained by adopting traversal search or gradient optimization
Figure BDA0002483864210000038
The corresponding position is the optimal repairA positive point.
And step five, applying a correction maneuver at the optimal correction point by the detector to finish the orbit correction of the Earth-moon L2 point transfer orbit and finish the Earth-moon L2 point orbit transfer.
The detector applies a correction maneuver av at the optimal correction point1Applying the maneuver Δ v again at the terminal2And realizing the nominal track entering. And if errors are measured for multiple times in the transfer process, repeating the step four according to the measured values to obtain a corresponding optimal correction position until the track reaches the terminal position, and completing the track transfer at the point of June L2.
Has the advantages that:
1. according to the method for selecting the optimum error correction point of the lunar L2 point transfer orbit, only the nominal orbit needs to be calculated in the process of selecting the optimum error correction point of the lunar L2 point transfer orbit, multiple times of target shooting correction are not needed, the calculated amount is small, the calculation efficiency is high, and the correction efficiency is further improved.
2. The invention discloses a selection method of optimum error correction points of a Tuesmoon L2 point transfer orbit, which establishes a functional relation between correction maneuver and correction time and orbit errors according to a state transfer matrix, determines error correction points with optimum correction speed increment and terminal speed increment by utilizing the functional relation, and reduces fuel consumption required by correction.
3. The invention discloses a selection method of an optimal error correction point of a Earth-moon L2 point transfer orbit, which is characterized in that correction calculation is carried out under a three-body rotating coordinate system, the influence of lunar gravity on the error of the transfer orbit is considered in the deduction of a kinetic equation and a functional relation between correction maneuvering and correction time and the error of the orbit, and the accuracy of orbit transfer is improved.
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FIG. 1 is a schematic flow chart of a method for selecting an optimum error correction point of a Earth-moon L2 point transfer orbit according to the present invention.
FIG. 2 shows the nominal orbit at Earth's moon L2 in the example of the present invention.
FIG. 3 is a graph of orbital error over time in an example of the invention.
FIG. 4 shows the optimum correction trajectory for the Earth's moon at L2 with the error taken into account in the example of the invention.
Detailed Description
To better illustrate the objects and advantages of the present invention, the present invention is explained in detail below by way of example analysis of the error correction of the Earth's moon L2 point transfer orbit.
Example 1:
as shown in fig. 1, the method for selecting the optimum error correction point of the earth-moon L2 point transfer orbit disclosed in this embodiment is implemented as follows:
the method comprises the following steps: and establishing a moon rotation coordinate system, and calculating a moon L2 point nominal transfer orbit state transfer matrix.
Selecting a mass center of an earth-moon system as an origin to establish a coordinate system, selecting an X axis as a connecting line direction of the earth and the moon, pointing the earth to the moon, selecting a Z axis as an angular velocity direction of system rotation, and forming a right-hand coordinate system by the Y axis, the X axis and the Z axis which are vertical to each other, wherein the coordinate system is shown in figure 1;
the kinetic equation of the detector in the system is expressed as
Figure BDA0002483864210000051
Wherein the mass coefficient mu of the march system is 0.01215.
Since the correction of the orbit segment from the earth to the moon is the same as the conventional correction of the moon-running orbit, the correction of the transfer orbit from the moon to the Earth-moon point L2 is mainly considered, the nominal transfer orbit is an orbit diagram under the Earth-moon rotation system as shown in FIG. 2, and the initial value of the dimensionless position velocity is
x＝0.984459,y＝-0.00353596,z＝0.00158687,
Figure BDA0002483864210000052
Figure BDA0002483864210000053
Equation of dynamics (1) can be expressed in matrix form
Figure BDA0002483864210000054
Wherein
Figure BDA0002483864210000055
To represent the six-dimensional state variable of the nominal track position velocity, linearization near the nominal transition track can be obtained
Figure BDA0002483864210000056
Wherein
Figure BDA0002483864210000057
Figure BDA0002483864210000058
Figure BDA0002483864210000059
The solution of the equation is x (t) ═ Φ (t, t)0)X(t0) Where Φ (t, t)0) Indicating system from t0State transition matrix to t. Can be solved by
Figure BDA00024838642100000510
Initial state Φ (0,0) ═ I6×6Is an identity matrix. According to the initial state, the state transition matrix of the nominal track at any time t can be obtained by solving a matrix differential equation, which is abbreviated as phi (t), and the state transition matrix can also be expressed in a form of a block matrix
Figure BDA0002483864210000061
Where M, N, L, K are all 3 × 3 matrices.
And step two, calculating the change situation of the orbit error along with the time according to the state transition matrix.
Track at time T0Has a position and velocity error of r0,v0The corresponding nominal position velocity state is r0,v0Then, according to the state transition matrix, inTime T1The position and velocity error of the real track relative to the nominal track is r1,v1
Figure BDA0002483864210000062
Time T1Applying a corrective maneuver Δ v1Then the terminal time T2The terminal error of the real orbit is
Figure BDA0002483864210000063
Let T0The initial position error is r for the time when the probe passes through the near-moon point0＝[6.937,6.937,6.937]×10-6Initial velocity error v0＝[0.813,0.813,0.813]×10-3The variation of the available track error with time is shown in fig. 3.
And step three, establishing a functional relation between the correction maneuver and the correction time and the track error.
Track correction needs to guarantee that the corrected track is at terminal time T2To a position r2I.e. r2Is equal to 0, thus obtaining
M2r1+N1(v1+Δv1)＝0，
Namely, it is
Figure BDA0002483864210000064
According to formula (4) having r1＝M1r0+N1v0，v1＝L1r0+K1v0. Can obtain the product
Figure BDA0002483864210000065
Simultaneous terminal velocity error v2I.e. the required applied orbital momentum av2
Figure BDA0002483864210000066
The total velocity increment required for error correction is | | Δ v1||+||Δv2L. Equations (6) and (7) establish the corrected maneuver as a function of the corrected time and orbit errors.
And step four, optimizing the error correction time according to the measured track error to minimize the speed increment required by correction so as to obtain an optimal correction point and optimal correction time.
Optimizing the error correction time T by using the relationship between the track error and the correction time and the speed increment established in the step three2Let | | | Δ v1||+||Δv2The minimum |, because the optimization variable only has one variable of correction time, the optimal solution can be obtained by adopting traversal search or gradient optimization
Figure BDA0002483864210000067
The corresponding position is the optimal correction point. The optimal correction time obtained by traversal optimization is the optimal maneuvering time obtained by measurement
Figure BDA0002483864210000068
The corresponding optimal maneuvering position is r1＝[1.147762,-0.0913892,0.00610041]Desired velocity increment Δ v1＝0.0079，Δv20.0614, the total speed increment Δ v is 0.0693.
Step five, applying a correction maneuver Deltav to the optimal correction point by the detector1Applying the maneuver Δ v again at the terminal2And completing the track correction of the ground moon L2 point transfer track and completing the ground moon L2 point track transfer. The orbit after the orbit correction is shown in fig. 4.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. The method for selecting the optimal error correction point of the earth-moon L2 point transfer orbit is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: establishing a moon rotation coordinate system, and calculating a moon L2 point nominal transfer orbit state transfer matrix;
calculating the change condition of the orbit error along with time according to the state transition matrix;
step three, establishing a functional relation between the correction maneuver and the correction time and the track error;
step four, optimizing error correction time according to the measured track error to minimize the speed increment required by correction so as to obtain an optimal correction point and optimal correction time;
and step five, applying a correction maneuver at the optimal correction point by the detector to finish the orbit correction of the Earth-moon L2 point transfer orbit and finish the Earth-moon L2 point orbit transfer.
2. The method for selecting the optimum error correction point of the earth-moon L2 point transfer orbit as claimed in claim 1, wherein: the first implementation method comprises the following steps of,
selecting a mass center of an earth-moon system as an origin to establish a coordinate system, selecting an X axis as a connecting line direction of the earth and the moon, pointing the earth to the moon, selecting a Z axis as an angular speed direction of system rotation, and forming a right-hand coordinate system by the Y axis, the X axis and the Z axis which are vertical to each other;
the kinetic equation of the detector in the system is expressed as
Figure FDA0002483864200000011
Wherein μ ═ m2/(m1+m2) Denotes the mass coefficient of the system, m1Is the mass of the earth, m2In order to be the quality of the moon,
Figure FDA0002483864200000012
is the distance of the detector from the earth,
Figure FDA0002483864200000013
is the distance between the probe and the moon;
the nominal transfer orbit in the earth-moon rotation system is defined as that the kinetic equation (1) is expressed in a matrix form
Figure FDA0002483864200000014
Wherein
Figure FDA0002483864200000015
For representing six-dimensional state variables of nominal track position velocity, linearized near the nominal transition track
Figure FDA0002483864200000016
Wherein
Figure FDA0002483864200000017
Figure FDA0002483864200000018
Figure FDA0002483864200000021
In which U represents the pseudo potential energy of the system, UijRepresenting the second partial derivative in the i, j direction, the solution of the equation being x (t) phi (t, t)0)X(t0) Where Φ (t, t)0) Indicating system from t0A state transition matrix to t; solving by
Figure FDA0002483864200000022
Initial state Φ (0,0) ═ I6×6Is an identity matrix; according to the initial state, the state transition matrix of the nominal orbit at any time t is solved by solving the matrixThe differential equation is obtained, abbreviated as phi (t), and the state transition matrix is also expressed in the form of a block matrix
Figure FDA0002483864200000023
Where M, N, L, K are all 3 × 3 matrices.
3. The method for selecting the optimum error correction point of the earth-moon L2 point transfer orbit as claimed in claim 2, wherein: the second step is realized by the method that,
defining a track at a time T0Has a position and velocity error of r0,v0The corresponding nominal position velocity state is r0,v0Then, at time T, based on the state transition matrix1The position and velocity error of the real track relative to the nominal track is r1,v1
Figure FDA0002483864200000024
At the same time T1Applying a corrective maneuver Δ v1Then the terminal time T2The terminal error of the real orbit is
Figure FDA0002483864200000025
4. The method for selecting the optimum error correction point of the earth-moon L2 point transfer orbit as claimed in claim 3, wherein: the third step is to realize the method as follows,
track correction needs to guarantee that the corrected track is at terminal time T2To a position r2I.e. r2Is equal to 0, thus obtaining
M2r1+N1(v1+Δv1)＝0
Namely, it is
Figure FDA0002483864200000026
According to formula (4) having r1＝M1r0+N1v0，v1＝L1r0+K1v0(ii) a To obtain
Figure FDA0002483864200000031
Simultaneous terminal velocity error v2I.e. the required applied orbital momentum av2
Figure FDA0002483864200000032
The total velocity increment required for error correction is | | Δ v1||+||Δv2L; equations (6) and (7) establish the corrective maneuvers and the corrective time and orbit errors, i.e., establish the functional relationship of the corrective maneuvers and the corrective time and orbit errors.
5. The method for selecting the optimum error correction point of the earth-moon L2 point transfer orbit as claimed in claim 4, wherein: the implementation method of the fourth step is that,
using the relationship between the orbit error and the correction time and the velocity increment established in the step three, and obtaining the error r by measurement1,v1Optimizing the error correction time T2Let | | | Δ v1||+||Δv2The minimum |, because the optimization variable only has one variable of correction time, the optimal solution is obtained by adopting traversal search or gradient optimization
Figure FDA0002483864200000033
The corresponding position is the optimal correction point.
6. The method for selecting the optimum error correction point of the earth-moon L2 point transfer orbit as claimed in claim 5, wherein: the fifth step is to realize that the method is that,
the detector applies a correction maneuver av at the optimal correction point1Applying the maneuver Δ v again at the terminal2Realizing the nominal track entering;and if errors are measured for multiple times in the transfer process, repeating the step four according to the measured values to obtain a corresponding optimal correction position until the track reaches the terminal position, and completing the track transfer at the point of June L2.
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