CN115343960B - Spacecraft illumination shadow avoidance control method in earth-moon system - Google Patents

Spacecraft illumination shadow avoidance control method in earth-moon system Download PDF

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CN115343960B
CN115343960B CN202211276284.8A CN202211276284A CN115343960B CN 115343960 B CN115343960 B CN 115343960B CN 202211276284 A CN202211276284 A CN 202211276284A CN 115343960 B CN115343960 B CN 115343960B
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温昶煊
尚雨秾
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Beijing Institute of Technology BIT
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Abstract

The invention discloses a spacecraft illumination shadow avoidance control method in a terrestrial-lunar system, and belongs to the field of aerospace. The implementation method of the invention comprises the following steps: analyzing the earth natural illumination rule and the shadow condition of the spacecraft through the earth-moon system shadow constraint condition under a circular restrictive three-body model; the method comprises the steps of predicting and judging whether a track of the spacecraft on a track enters a shadow region, dividing active maneuver into two stages of avoidance-return when a prediction interval is detected to be located in the shadow region, applying pulses according to the maneuver strategy to carry out shadow avoidance and return to a three-pulse transfer of a nominal track by deducing a maneuver strategy which is obtained by taking minimum fuel consumption cost as an optimization target, realizing active avoidance control on minimum fuel consumption of track illumination shadow, avoiding adverse effects of long-time shadow regions on the spacecraft, ensuring that the spacecraft keeps more relatively stable working states in the whole task period, and prolonging the effective task running time of the spacecraft.

Description

Spacecraft illumination shadow avoidance control method in earth-moon system
Technical Field
The invention relates to a spacecraft illumination evasion control method, and belongs to the field of aerospace.
Background
Earth-moon space orbit design is the main content of human aerospace activities. The large-scale lunar orbit station deployed in the earth lunar space can obviously reduce the lunar development cost and can even be used as a transfer station for other deep space exploration tasks farther away. Considering that the designed orbits of the spacecraft are different, part of the spacecraft can frequently shuttle to shadow parts of natural celestial bodies, such as the shadow areas of the earth and the moon, during the space mission, which brings a series of adverse effects on the activity of the spacecraft. Aiming at the problem that the spacecraft can frequently enter the earth shadow, the active orbit control problem of avoiding the earth shadow of the spacecraft in the earth-moon space orbit is researched, the minimum fuel consumption cost meeting the illumination shadow constraint is analyzed, a 'prediction + execution' closed-loop pulse orbit control strategy is provided, and the problem of avoiding the design shadow of the spacecraft orbit can be effectively solved.
For the characteristics of resonant tracks, the prior art [1] (see Minimizing eclipses vitamin synthetic resistant orders with applications to EQUULEULEUS and MMX [ J ]. Acta Astronicas, CHIKAZAWA T, BARRESI N, CAMPAGNOLA S, OZAKI N, KAWAKATSU Y, 2021, 180: 679-692.) introduces a two-dimensional eclipse map to determine the optimal track insertion conditions to avoid or minimize eclipse intervals, bidimensionalizes the track along eclipse direction, and calculates the track design parameters to minimize or avoid eclipse through geometric relationships. The method can achieve good shadow avoiding effect by changing the geometric shape of the track. However, the method has poor practicability, needs to redesign different initial value orbits, has poor robustness, and cannot meet the requirement of high-precision tasks, so that the method is difficult to have high applicability on space engineering tasks.
Considering the problem of avoiding Solar Eclipse of spacecraft on a remote Retrograde Orbit in a terrestrial-lunar system, an initial Orbit value which better meets the illumination constraint condition is found out through a multi-target genetic algorithm and Monte Carlo simulation in the prior art [2] (Let the less of Light-Minimizing Solar Eclipse on distance Retrograde Orbit [ J ]. AAS, YANG SUN, CHIHANG YANG, HAO ZHANG, 21-716), and the Solar Eclipse remote Retrograde Orbit task without Solar Eclipse in four years can be met. However, the method has high sensitivity to spacecraft disturbance and poor stability. For a spacecraft which does not apply active control to correct disturbance quantity, the method cannot meet the requirements of more practical space missions.
Disclosure of Invention
The invention mainly aims to provide a control method for avoiding illumination shadows of a spacecraft in a terrestrial-lunar system, which is used for analyzing and obtaining the earth natural illumination rule and the shadow condition of the spacecraft through the shadow constraint condition of the terrestrial-lunar system under a circular restrictive three-body model; the method comprises the steps of analyzing shadow conditions according to a spacecraft orbit of a specified orbit initial value, predicting and judging whether a track of the spacecraft on the orbit enters a shadow region, dividing active maneuver into two stages of 'evading-returning' when a prediction interval is detected to be located in the shadow region, applying pulses according to the maneuver strategy to carry out three-pulse transfer of shadow evading and returning to a nominal orbit by using a maneuver strategy with minimum fuel consumption cost as an optimization target, realizing active evading control on minimum fuel consumption of orbit illumination shadow, avoiding adverse effects of long-time shadow regions on the spacecraft, ensuring that the spacecraft keeps more relatively stable working states in the whole task period, and prolonging the effective task running time of the spacecraft.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a spacecraft illumination shadow avoidance control method in a terrestrial-lunar system, which comprises the following steps:
the method comprises the following steps: analyzing the earth natural illumination rule and the shadow condition of the spacecraft through the earth-moon system shadow constraint condition under a circular restrictive three-body model; and analyzing the shadow condition according to the spacecraft orbit of the appointed orbit initial value, judging the ground shadow constraint critical state aiming at the orbit of the spacecraft on the orbit, and preliminarily judging whether the orbit enters a shadow area.
The spacecraft dynamics equation of the earth-moon rotation coordinate system under the circular restrictive three-system is expressed as follows:
Figure 393658DEST_PATH_IMAGE001
（1）
in the formula (I), the compound is shown in the specification,
Figure 28907DEST_PATH_IMAGE002
represents the acceleration vector of the spacecraft in the earth-moon rotation system,
Figure 277486DEST_PATH_IMAGE003
represents the acceleration vector of the spacecraft in the earth-moon rotation system,
Figure 407116DEST_PATH_IMAGE004
representing a position vector of the spacecraft under the earth-moon rotation system;
Figure 690330DEST_PATH_IMAGE005
represents the potential energy of the system,
Figure 230902DEST_PATH_IMAGE006
represents the effective potential energy of the system:
Figure 232356DEST_PATH_IMAGE007
in the earth-moon system,
Figure 900097DEST_PATH_IMAGE008
in order to be a constant of the attractive force,
Figure 303397DEST_PATH_IMAGE009
representing the distances of the particles to the main celestial body 1 and 2, respectively, by the expression:
Figure 31181DEST_PATH_IMAGE010
in order to investigate the illumination shadow relation of the original track, the relation conversion is carried out on the coordinate system of the defined track; firstly, translating the origin of coordinates of the Earth-moon rotation system to the Earth-moon rotation system through coordinate translation, and translating vectors
Figure 254352DEST_PATH_IMAGE011
For the earth-centered earth-moon rotation system and the earth-centered earth-sun rotation system, the transformation matrix between the coordinate systems is:
Figure 712403DEST_PATH_IMAGE012
（2）
wherein
Figure 970209DEST_PATH_IMAGE013
The rotation angle of the earth-moon rotation system to the earth center inertia system is a time variable,
Figure 868895DEST_PATH_IMAGE014
the angle between the original orbit plane of the earth-moon system and the sunlight incident angle is shown; the position coordinates of the original spacecraft are set as
Figure 844941DEST_PATH_IMAGE015
The coordinate system being rotated by time and place
Figure 588906DEST_PATH_IMAGE016
In-plane, spacecraft position coordinates
Figure 950486DEST_PATH_IMAGE017
The following steps are changed:
Figure 20074DEST_PATH_IMAGE018
（3）
the ground-center distance of the spacecraft is
Figure 217837DEST_PATH_IMAGE019
When the center distance of the spacecraft is smaller than the radius of the earth
Figure 765493DEST_PATH_IMAGE020
And is located atxWhen the axis is positive to the half axis, the spacecraft is judged to enter the earth shadow area;
for the original orbit of the spacecraft, a projection matrix is defined
Figure 981579DEST_PATH_IMAGE021
Sum matrix
Figure 487647DEST_PATH_IMAGE022
Respectively as follows:
Figure 907127DEST_PATH_IMAGE023
（4）
defining a spacecraft intThe orbital parameter at a time is
Figure 258474DEST_PATH_IMAGE024
(ii) a The condition that the spacecraft enters the earth shadow is an equation (5), the condition that the spacecraft leaves the earth shadow range is an equation (6), and the flight path is the closest point to the earth centerCThe formula (7) is required to be satisfied; preliminarily judging whether the track enters a shadow area or not through the ground shadow constraint of the original orbit of the spacecraft;
Figure 345379DEST_PATH_IMAGE025
（5）
Figure 6036DEST_PATH_IMAGE026
（6）
Figure 912812DEST_PATH_IMAGE027
（7）。
step two: when the spacecraft trajectory prediction interval is detected to be located in the shadow area in the first step, setting a safety distance by taking the closest point of the corrected orbit to the ground center as a division point, and dividing the shadow avoiding problem into two stages of avoiding-returning according to the division point. And deriving a pulse avoidance analytic solution with the minimum fuel consumption cost in an avoidance stage, and actively applying an avoidance pulse according to the pulse avoidance analytic solution to correct the trajectory of the spacecraft, so that error interference in an actual task is avoided, the spacecraft is ensured to keep more relatively stable working states in the avoidance stage, and the effective task running time of the spacecraft is prolonged.
And continuously detecting whether the next state of the spacecraft enters a shadow area along with the operation of the spacecraft on the original orbit, and setting forward prediction time length for preventing the spacecraft from being unable to complete due to overlong orbital transfer time. When the spacecraft enters the earth shadow within the future preset time, pulse control needs to be applied to the spacecraft in advance.
Before the spacecraft enters the earth shadow
Figure 802271DEST_PATH_IMAGE028
At the moment, the corresponding initial state is
Figure 9261DEST_PATH_IMAGE029
And
Figure 591552DEST_PATH_IMAGE030
to which a velocity pulse is applied
Figure 237822DEST_PATH_IMAGE031
Performing track correction, wherein the corrected track is closest to the geocentric point
Figure 196550DEST_PATH_IMAGE032
Is controlled to be just at the boundary of the earth shadow and corresponds to the time of
Figure 726889DEST_PATH_IMAGE033
At this time, the spacecraft state quantity is
Figure 214502DEST_PATH_IMAGE034
(ii) a Before correctionThe closest point of the track to the geocentric
Figure 345138DEST_PATH_IMAGE035
Corresponding to a time of
Figure 841978DEST_PATH_IMAGE036
At this time, the spacecraft state quantity is
Figure 492402DEST_PATH_IMAGE037
，
When the correction amount is a small amount, the deviation amount is:
Figure 150917DEST_PATH_IMAGE038
（8）
wherein
Figure 768849DEST_PATH_IMAGE039
，
Figure 803801DEST_PATH_IMAGE040
，
Figure 839890DEST_PATH_IMAGE041
Then (8) is written as
Figure 669306DEST_PATH_IMAGE042
And
Figure 774534DEST_PATH_IMAGE043
involving state transition matrices
Figure 613177DEST_PATH_IMAGE044
Wherein the state transition matrix is derived from a state space form of a state differential equation;
Figure 972614DEST_PATH_IMAGE045
（9）
will be provided with
Figure 238510DEST_PATH_IMAGE046
Merging into a 1 × 42 dimensional matrix, converting the final state value obtained by corresponding to the original unit matrix into a 6 × 6 matrix after state equation integration
Figure 556666DEST_PATH_IMAGE047
Then, the corresponding state transition matrix is obtained:
Figure 933421DEST_PATH_IMAGE048
（10）
because the original track and the corrected track both meet the requirements
Figure 678523DEST_PATH_IMAGE049
And (3) under the plane near-location condition, neglecting high-order small quantity to obtain the formula (11):
Figure 115321DEST_PATH_IMAGE050
（11）
substituting equation (9) into equation (11) and calculating the corrected track plane perigee position state quantity:
Figure 945874DEST_PATH_IMAGE051
（12）
wherein the content of the first and second substances,
Figure 375587DEST_PATH_IMAGE052
when the position of the track plane near the place is corrected
Figure 975195DEST_PATH_IMAGE053
And if the position is located at the boundary of the earth shadow, the following requirements are met:
Figure 317315DEST_PATH_IMAGE054
（13）
deducing to obtain the speed pulse applied by the active avoiding shadow area
Figure 369585DEST_PATH_IMAGE055
Analytic solution of (2):
Figure 337409DEST_PATH_IMAGE056
（14）
wherein the content of the first and second substances,
Figure 525945DEST_PATH_IMAGE057
；
according to the pulse avoidance analytic solution shown in the formula (14), the orbit originally located in the shadow region is actively corrected, so that the spacecraft is prevented from entering the shadow region, more relatively stable working states of the spacecraft in an avoidance stage are guaranteed, and the effective task running time of the spacecraft is prolonged.
Step three: after the spacecraft reaches a division point, double-pulse track design with minimum fuel consumption cost is carried out aiming at a return stage, and active control is carried out through the double-pulse track design to ensure that the spacecraft is prevented from entering a shadow area in the process of returning to an original orbit, so that the spacecraft can be ensured to keep more relatively stable working states in the return stage, and the effective task running time of the spacecraft is prolonged.
After the spacecraft reaches the dividing point, the spacecraft needs to be timely pulsed to return to the original orbit. Aiming at a double-pulse track design with minimum fuel consumption cost in a return stage, the double-pulse track design implementation method comprises the following steps:
the design variable designed by the double-pulse track is
Figure 570125DEST_PATH_IMAGE058
，
Figure 109690DEST_PATH_IMAGE058
To correct the track departure time; transfer time to return to track
Figure 146785DEST_PATH_IMAGE059
Then arrive at the time of the original track
Figure 455407DEST_PATH_IMAGE060
(ii) a The initial state of the spacecraft leaving the correction orbit is
Figure 670488DEST_PATH_IMAGE061
The target state from the spacecraft to the original orbit is that the applied pulse velocity is calculated by adopting a differential correction strategy
Figure 431770DEST_PATH_IMAGE062
；
In the geocentric inertial system, the kinetic equation of the sun, earth and moon spacecraft four-body system is deduced and the state quantity is used
Figure 23289DEST_PATH_IMAGE063
Integrating step by step to obtain the final state
Figure 173035DEST_PATH_IMAGE064
And corresponding state transition matrix
Figure 559017DEST_PATH_IMAGE065
At the calculation of the amount of end position deviation
Figure 73175DEST_PATH_IMAGE066
Judging whether the precision requirement is met or not; if the precision requirement is met, terminating the iteration; otherwise, continuing to perform differential correction; obtaining pulse velocity quantity by final state velocity matching calculation
Figure 202805DEST_PATH_IMAGE067
；
Based on the obtained pulse velocity quantity
Figure 220439DEST_PATH_IMAGE068
Pulse velocity volume
Figure 292169DEST_PATH_IMAGE067
Active control ensures that the spacecraft avoids shadow areas and can return to the original orbit, therebyThe spacecraft can be ensured to keep more relatively stable working states in the return stage, and the effective task running time of the spacecraft is prolonged.
Has the advantages that:
1. the invention discloses a method for avoiding control over illumination shadow of a spacecraft in a terrestrial-lunar system, which is characterized in that the natural earth illumination rule and the shadow condition of the spacecraft are obtained by analyzing the constraint condition of the terrestrial-lunar system shadow under a circular restrictive three-body model; and analyzing the shadow condition according to the spacecraft orbit of the appointed orbit initial value to obtain an active control strategy aiming at the shadow region, so that the interference of the shadow region is avoided when the spacecraft runs on the task orbit.
2. The invention discloses a method for avoiding control over illumination shadow of a spacecraft in a terrestrial-lunar system, which can detect whether the spacecraft can enter a terrestrial shadow region for a long time or not in advance by dividing a shadow avoiding problem into two stages of avoiding-returning and respectively applying active control, takes a closest point of a correction orbit to the ground as a dividing point and sets a safety distance, avoids error interference in an actual task, returns to an original orbit to continuously execute the task by braking after correction, prolongs the effective task running time of the spacecraft, and is suitable for the spacecraft with higher requirements on natural illumination.
3. The invention discloses a spacecraft illumination shadow avoidance control method in a terrestrial-lunar system, which is characterized in that one-time pulse maneuver is actively applied to avoidance, two-time pulse maneuvers are actively applied to return, the three-time pulse maneuver can be expressed by analysis, the calculation speed is high, optimization is carried out at the cost of minimum fuel consumption in the operation process, only a small pulse speed is needed in the whole correction process, and the actual task requirements can be better met.
Drawings
FIG. 1 is a flowchart of a spacecraft illumination shadow avoidance control method in a terrestrial-lunar system.
FIG. 2 is a schematic diagram of the method of the present invention for actively evading impulse application to earth shadow.
FIG. 3 is a schematic diagram of the double pulse return to original orbit of the method of the present invention.
FIG. 4 is a schematic diagram of a single corrected trajectory and an original trajectory according to the method of the present invention.
FIG. 5 is a 6 year project mission of the method of the present invention
Figure 28044DEST_PATH_IMAGE069
And (4) a plane projection track graph.
FIG. 6 is a post 6 year engineering mission of the method of the present invention
Figure 961365DEST_PATH_IMAGE069
And (4) a plane projection track graph.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
to verify the feasibility of the method, the initial value of the Earth-moon rotation system is selected as
Figure 826870DEST_PATH_IMAGE071
The remote retrograde orbit carries out actual engineering task simulation, has good resonance characteristics, starts from 1 month and 1 day in 2023, ends at the end of 2029 years, and is a space mission in six years.
As shown in fig. 1, the method for controlling avoiding of illumination shadows of a spacecraft in a terrestrial-lunar system disclosed in this embodiment includes the following specific steps:
the method comprises the following steps: analyzing the earth natural illumination rule and the shadow condition of the spacecraft through the earth-moon system shadow constraint condition under a circular restrictive three-body model; and analyzing the shadow condition according to the spacecraft orbit of the appointed orbit initial value, judging the ground shadow constraint critical state aiming at the orbit of the spacecraft on the orbit, and preliminarily judging whether the orbit enters a shadow area.
The spacecraft dynamics equation of the earth-moon rotation coordinate system under the circular restrictive three-system is expressed as follows:
Figure 299309DEST_PATH_IMAGE001
（1）
in the formula (I), the compound is shown in the specification,
Figure 505162DEST_PATH_IMAGE002
represents the acceleration vector of the spacecraft in the earth-moon rotation system,
Figure 762968DEST_PATH_IMAGE003
represents the acceleration vector of the spacecraft in the earth-moon rotation system,
Figure 927233DEST_PATH_IMAGE004
representing the position vector of the spacecraft under the earth-moon rotation system;
Figure 372121DEST_PATH_IMAGE005
represents the potential energy of the system,
Figure 647244DEST_PATH_IMAGE006
representing the effective potential energy of the system:
Figure 274404DEST_PATH_IMAGE007
in the earth-moon system,
Figure 78412DEST_PATH_IMAGE072
，
Figure 541754DEST_PATH_IMAGE009
representing the distances of the particles to the main celestial body 1 and 2, respectively, by the expression:
Figure 89410DEST_PATH_IMAGE010
in order to investigate the illumination shadow relation of the original track, the relation conversion is carried out on the coordinate system of the defined track; firstly, translating the origin of coordinates of the Earth-moon rotation system to the Earth-moon rotation system through coordinate translation, and translating vectors
Figure 321808DEST_PATH_IMAGE011
For the earth-centered earth-moon rotation system and the earth-centered earth-sun rotation system, the transformation matrix between the coordinate systems is:
Figure 548915DEST_PATH_IMAGE012
（2）
wherein
Figure 499553DEST_PATH_IMAGE013
The rotation angle of the earth-moon rotation system to the earth center inertia system is a time variable,
Figure 850900DEST_PATH_IMAGE073
the sunlight incident angle of the plane of the long-distance retrograde orbit under the geocentric inertial system. The position coordinates of the original spacecraft are set as
Figure 672226DEST_PATH_IMAGE015
The coordinate system being rotated by the time of day
Figure 349195DEST_PATH_IMAGE016
In-plane, spacecraft position coordinates
Figure 505238DEST_PATH_IMAGE017
The following steps are changed:
Figure 660276DEST_PATH_IMAGE018
（3）
the ground-center distance of the spacecraft is
Figure 601687DEST_PATH_IMAGE019
When the center distance of the spacecraft is smaller than the radius of the earth
Figure 918399DEST_PATH_IMAGE074
And is located atxWhen the axis is positive to the half axis, the spacecraft is judged to enter the earth shadow area;
for the original orbit of the spacecraft, a projection matrix is defined
Figure 578051DEST_PATH_IMAGE021
Sum matrix
Figure 536779DEST_PATH_IMAGE022
Respectively as follows:
Figure 581965DEST_PATH_IMAGE023
（4）
defining a spacecraft intThe orbital parameter at a time is
Figure 600736DEST_PATH_IMAGE024
(ii) a The condition that the spacecraft enters the earth shadow is an equation (5), the condition that the spacecraft leaves the earth shadow range is an equation (6), and the flight path is the closest point to the earth centerCThe formula (7) is required to be satisfied; preliminarily judging whether the track enters a shadow area or not through the ground shadow constraint of the original orbit of the spacecraft;
Figure 747684DEST_PATH_IMAGE025
（5）
Figure 978945DEST_PATH_IMAGE026
（6）
Figure 894948DEST_PATH_IMAGE027
（7）
the analysis of the selected remote retrograde orbit results in the earth shadow of the original orbit as shown in fig. 5.
Step two: when the spacecraft trajectory prediction interval is detected to be located in the shadow area in the first step, setting a safety distance by taking a closest point of a corrected orbit to the ground center as a dividing point, and dividing the shadow avoidance problem into two stages of avoidance and return according to the dividing point. And deriving a pulse avoidance analytic solution with the minimum fuel consumption cost in an avoidance stage, and actively applying an avoidance pulse according to the pulse avoidance analytic solution to correct the trajectory of the spacecraft, so that error interference in an actual task is avoided, the spacecraft is ensured to keep more relatively stable working states in the avoidance stage, and the effective task running time of the spacecraft is prolonged.
When earth shadow needs to be avoided, an active control strategy is designed to apply pulse control to the spacecraft. Two constraints are assumed here: the first constraint condition is that the magnitude and the opportunity of applying the speed pulse are searched one month before the orbit spacecraft enters the shadow, and the spacecraft is given enough time to perform orbit change to avoid the shadow. The second constraint condition is that a safe distance is set between the corrected orbit and the earth shadow region, so that errors caused in simulation are avoided.
Before the spacecraft enters the earth shadow
Figure 68310DEST_PATH_IMAGE028
At the moment, the corresponding initial state is
Figure 702553DEST_PATH_IMAGE029
And
Figure 737505DEST_PATH_IMAGE030
to which a velocity pulse is applied
Figure 508015DEST_PATH_IMAGE031
Performing track correction, wherein the corrected track is closest to the geocentric point
Figure 868590DEST_PATH_IMAGE075
Just controlled at the boundary of the earth shadow, and the corresponding time is
Figure 724550DEST_PATH_IMAGE076
At this time, the spacecraft state quantity is
Figure 284232DEST_PATH_IMAGE077
(ii) a Track distance and geocentric closest point before correction
Figure 174828DEST_PATH_IMAGE078
Corresponding to a time of
Figure 440724DEST_PATH_IMAGE079
At this time, the spacecraft state quantity is
Figure 518401DEST_PATH_IMAGE037
. The schematic view is shown in fig. 2.
When the correction amount is small, the deviation amount is:
Figure 410003DEST_PATH_IMAGE038
（8）
wherein
Figure 155105DEST_PATH_IMAGE039
，
Figure 591902DEST_PATH_IMAGE040
，
Figure 422455DEST_PATH_IMAGE041
Then (8) write to
Figure 602901DEST_PATH_IMAGE080
And
Figure 451777DEST_PATH_IMAGE081
including state transition matrices
Figure 325055DEST_PATH_IMAGE044
Wherein the state transition matrix is derived from a state space form of a state differential equation;
Figure 377325DEST_PATH_IMAGE045
（9）
because the original track and the corrected track both meet the requirements
Figure 95882DEST_PATH_IMAGE082
And (3) under the plane near-location condition, neglecting high-order small quantity to obtain the formula (10):
Figure 815576DEST_PATH_IMAGE083
（10）
the formula (9) is substituted for the formula (10) and the corrected orbit can be obtained by calculation
Figure 843444DEST_PATH_IMAGE082
State quantity of plane near-point position
Figure 648589DEST_PATH_IMAGE084
（11）
Wherein the content of the first and second substances,
Figure 170837DEST_PATH_IMAGE085
when the track is corrected
Figure 745038DEST_PATH_IMAGE082
Plane near point position
Figure 960119DEST_PATH_IMAGE086
Located at the boundary of the earth shadow, it is required to satisfy
Figure 721401DEST_PATH_IMAGE087
（12）
Finally, the speed pulse applied by the active avoiding shadow area can be deduced
Figure 45677DEST_PATH_IMAGE088
Analytic solution of (2):
Figure 474384DEST_PATH_IMAGE089
（13）
wherein the content of the first and second substances,
Figure 594787DEST_PATH_IMAGE090
through analysis of the earth shadow rule, the first event that the spacecraft enters the earth shadow occurs about 301 th day of the space mission, and the shadow duration lasts about 1.25h. The directional components of the corrected speed pulse required for this avoidance are shown in table 1.
Figure 92634DEST_PATH_IMAGE091
Step three: after the spacecraft reaches a division point, double-pulse track design with minimum fuel consumption cost is carried out aiming at a return stage, and active control is carried out through the double-pulse track design to ensure that the spacecraft is prevented from entering a shadow area in the process of returning to an original orbit, so that the spacecraft can be ensured to keep more relatively stable working states in the return stage, and the effective task running time of the spacecraft is prolonged.
The design variable of the double-pulse motor-driven application strategy is the departure time of the correction track
Figure 956684DEST_PATH_IMAGE092
. Transfer time to return to track
Figure 974319DEST_PATH_IMAGE093
Time of arrival at the original track
Figure 531202DEST_PATH_IMAGE094
. The initial state of the spacecraft leaving the correction orbit is
Figure 516345DEST_PATH_IMAGE095
The target state of the spacecraft to the original orbit is
Figure 918507DEST_PATH_IMAGE096
Calculating the amount of applied pulse velocity using a differential correction strategy
Figure 56227DEST_PATH_IMAGE097
。
In the geocentric inertial system, the kinetic equation of the sun, earth and moon spacecraft four-body system is deduced and the state quantity is used
Figure 49591DEST_PATH_IMAGE095
Integrating step by step to obtain end state
Figure 7183DEST_PATH_IMAGE098
And corresponding state transition matrix
Figure 993462DEST_PATH_IMAGE099
At the calculation of the amount of end position deviation
Figure 985689DEST_PATH_IMAGE100
And whether the accuracy requirement is met is judged.
Figure 884375DEST_PATH_IMAGE101
Then it is calculated by end state velocity matching. In said step, the optimization is also carried out with the minimum transfer burnup as the optimum target, i.e.
Figure 594842DEST_PATH_IMAGE102
And minimum.
The data relating to the two track pulses are calculated and shown in table 2. A schematic diagram of single-pass tracking control is shown in fig. 4.
TABLE 2 correlation data for two track corrections
Figure 869966DEST_PATH_IMAGE103
After the shadow detection of the original orbit, the spacecraft enters the shadow area for 11 times in total in a space mission of six years, namely, the evasive measures are required to be applied for eleven times in total. All the avoidance pulse data of the six-year orbit inter-mission spacecraft are obtained through calculation of pulse quantity and are shown in the table 3.
TABLE 3 orbital control data for avoiding six-year mission spacecraft
Figure 703317DEST_PATH_IMAGE104
The above detailed description is further intended to illustrate the objects, technical solutions and advantages of the present invention, and it should be understood that the above detailed description is only an example of the present invention and should not be used 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 (3)

1. A spacecraft illumination shadow avoidance control method in a terrestrial-lunar system is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: analyzing the earth natural illumination rule and the shadow condition of the spacecraft through the earth-moon system shadow constraint condition under a circular restrictive three-body model; analyzing the shadow condition according to the spacecraft orbit of the appointed orbit initial value, judging the ground shadow constraint critical state aiming at the orbit of the spacecraft on the orbit, and preliminarily judging whether the orbit enters a shadow area;
step two: when the spacecraft trajectory prediction interval is detected to be located in a shadow area in the first step, setting a safety distance by taking a closest point of a corrected orbit to the ground center as a dividing point, and dividing the shadow avoidance problem into two stages of avoidance and return according to the dividing point; deriving a pulse avoidance analytic solution with minimum fuel consumption cost in an avoidance stage, and actively applying an avoidance pulse according to the pulse avoidance analytic solution to correct the trajectory of the spacecraft, so as to avoid error interference in an actual task and ensure that the spacecraft keeps more relatively stable working states in the avoidance stage;
the second step is realized by the method that,
continuously detecting whether the next state of the spacecraft enters a shadow area along with the operation of the spacecraft on the original orbit, and setting forward prediction time length to prevent incomplete operation caused by overlong orbital transfer time; when the spacecraft enters the earth shadow within the future preset time, applying pulse control to the spacecraft in advance;
before the spacecraft enters the earth shadow
Figure 70628DEST_PATH_IMAGE001
At the moment, the corresponding initial state is
Figure 736096DEST_PATH_IMAGE002
And
Figure 21583DEST_PATH_IMAGE003
to which a velocity pulse is applied
Figure 912923DEST_PATH_IMAGE004
Performing track correction, wherein the corrected track is closest to the geocentric point
Figure 233046DEST_PATH_IMAGE005
Just controlled at the boundary of the earth shadow, and the corresponding time is
Figure 69414DEST_PATH_IMAGE006
At this time, the spacecraft state quantity is
Figure 779882DEST_PATH_IMAGE007
(ii) a Track distance and geocentric closest point before correction
Figure 851743DEST_PATH_IMAGE008
Corresponding to a time of
Figure 151006DEST_PATH_IMAGE009
At this time, the spacecraft state quantity is
Figure 282910DEST_PATH_IMAGE010
，
When the correction amount is a small amount, the deviation amount is:
Figure 418356DEST_PATH_IMAGE011
（8）
wherein
Figure 762750DEST_PATH_IMAGE012
，
Figure 417984DEST_PATH_IMAGE013
，
Figure 127314DEST_PATH_IMAGE014
Then (8) is written as
Figure 874691DEST_PATH_IMAGE015
And
Figure 412988DEST_PATH_IMAGE016
including state transition matrices
Figure 296631DEST_PATH_IMAGE017
Wherein the state transition matrix is derived from a state space form of a state differential equation;
Figure 973600DEST_PATH_IMAGE018
（9）
will be provided with
Figure 818059DEST_PATH_IMAGE019
Merging into a 1 × 42 dimensional matrix, converting the final state value obtained by corresponding to the original unit matrix into a 6 × 6 matrix after state equation integration
Figure 35414DEST_PATH_IMAGE020
Then, the corresponding state transition matrix is obtained:
Figure 679889DEST_PATH_IMAGE021
（10）
because the original track and the corrected track both meet the requirements
Figure 58917DEST_PATH_IMAGE022
And (3) under the plane near-location condition, neglecting high-order small quantity to obtain the formula (11):
Figure 718569DEST_PATH_IMAGE023
（11）
substituting equation (9) into equation (11) and calculating the corrected track plane perigee position state quantity:
Figure 349401DEST_PATH_IMAGE024
（12）
wherein the content of the first and second substances,
Figure 207636DEST_PATH_IMAGE025
when the position of the track plane near the place is corrected
Figure 944517DEST_PATH_IMAGE026
And if the position is located at the boundary of the earth shadow, the following requirements are met:
Figure 91464DEST_PATH_IMAGE027
（13）
deducing to obtain the velocity pulse applied by the active avoiding shadow region
Figure 57146DEST_PATH_IMAGE028
Analytic solution of (2):
Figure 973150DEST_PATH_IMAGE029
（14）
wherein, the first and the second end of the pipe are connected with each other,
Figure 585659DEST_PATH_IMAGE030
；
according to a pulse avoidance analytic solution shown as a formula (14), actively correcting the orbit originally in the shadow region, preventing the spacecraft from entering the shadow region, and ensuring that the spacecraft keeps more relatively stable working states in an avoidance stage;
step three: after the spacecraft reaches a division point, double-pulse track design with minimum fuel consumption cost is carried out aiming at a return stage, and the spacecraft is actively controlled by the double-pulse track design to avoid entering a shadow area in the process of returning to an original orbit, so that the spacecraft can be ensured to keep more relatively stable working states in the return stage.
2. The method for avoiding the illumination shadow of the spacecraft in the earth-moon system as claimed in claim 1, wherein: the first implementation method comprises the following steps of,
the spacecraft dynamics equation of the earth-moon rotation coordinate system under the circular restrictive three-system is expressed as follows:
Figure 16640DEST_PATH_IMAGE031
（1）
in the formula (I), the compound is shown in the specification,
Figure 254855DEST_PATH_IMAGE032
represents the acceleration vector of the spacecraft in the earth-moon rotation system,
Figure 822102DEST_PATH_IMAGE033
represents the acceleration vector of the spacecraft in the earth-moon rotation system,
Figure 104048DEST_PATH_IMAGE034
representing a position vector of the spacecraft under the earth-moon rotation system;
Figure 22325DEST_PATH_IMAGE035
the potential energy of the system is represented,
Figure 533072DEST_PATH_IMAGE036
represents the effective potential energy of the system:
Figure 423668DEST_PATH_IMAGE037
in the earth-moon system,
Figure 751881DEST_PATH_IMAGE038
in order to be a constant of the attractive force,
Figure 515044DEST_PATH_IMAGE039
representing the distances of the particles to the main celestial body 1 and 2, respectively, by the expression:
Figure 485274DEST_PATH_IMAGE040
in order to investigate the illumination shadow relation of the original track, the relation conversion is carried out on the coordinate system of the defined track; firstly, translating the origin of coordinates of the Earth-moon rotation system to the Earth-moon rotation system through coordinate translation, and translating vectors
Figure 902480DEST_PATH_IMAGE041
For the earth-centered earth-moon rotation system and the earth-centered earth-sun rotation system, the transformation matrix between the coordinate systems is:
Figure 604857DEST_PATH_IMAGE042
（2）
wherein
Figure 232148DEST_PATH_IMAGE043
The rotation angle of the earth-moon rotation system to the earth center inertia system is a time variable,
Figure 130702DEST_PATH_IMAGE044
the angle between the original orbit plane of the earth-moon system and the sunlight incident angle is shown; the position coordinates of the original spacecraft are set as
Figure 667994DEST_PATH_IMAGE045
The coordinate system being rotated by time and place
Figure 338010DEST_PATH_IMAGE046
In-plane, spacecraft position coordinates
Figure 78695DEST_PATH_IMAGE047
The following steps are changed:
Figure 62831DEST_PATH_IMAGE048
（3）
the center-to-ground distance of the spacecraft is
Figure 579263DEST_PATH_IMAGE049
When the center distance of the spacecraft is smaller than the radius of the earth
Figure 295547DEST_PATH_IMAGE050
And is located atxWhen the axle is positive, the spacecraft is judged to enter the earth shadow area;
for the original orbit of the spacecraft, a projection matrix is defined
Figure 897429DEST_PATH_IMAGE051
Sum matrix
Figure 606628DEST_PATH_IMAGE052
Respectively as follows:
Figure 243146DEST_PATH_IMAGE053
（4）
defining a spacecraft intThe orbital parameter at a time is
Figure 130330DEST_PATH_IMAGE054
(ii) a The condition that the spacecraft enters the earth shadow is an equation (5), the condition that the spacecraft leaves the earth shadow range is an equation (6), and the flight trajectoryClosest point to the geocentricCThe formula (7) is required to be satisfied; preliminarily judging whether the track enters a shadow area or not through the ground shadow constraint of the original orbit of the spacecraft;
Figure 953930DEST_PATH_IMAGE055
（5）
Figure 545448DEST_PATH_IMAGE056
（6）
Figure 399922DEST_PATH_IMAGE057
（7）。
3. the method for avoiding the illumination shadow of the spacecraft in the earth-moon system as claimed in claim 1, wherein: after the spacecraft reaches the division point, the spacecraft needs to be timely subjected to pulse control to return to the original orbit; aiming at the double-pulse track design with minimum fuel consumption cost in the return stage, the implementation method of the double-pulse track design is as follows,
the design variable designed by the double-pulse track is
Figure 582641DEST_PATH_IMAGE058
，
Figure 34482DEST_PATH_IMAGE058
To correct the track departure time; transfer time to return to track
Figure 226429DEST_PATH_IMAGE059
Then arrive at the time of the original track
Figure 165435DEST_PATH_IMAGE060
(ii) a The initial state of the spacecraft leaving the correction orbit is
Figure 784635DEST_PATH_IMAGE061
The target state from the spacecraft to the original orbit is that the applied pulse velocity is calculated by adopting a differential correction strategy
Figure 458193DEST_PATH_IMAGE062
；
In the geocentric inertial system, the kinetic equation of the sun-earth-moon spacecraft four-body system is deduced and the state quantity is used for calculating the state quantity
Figure 922673DEST_PATH_IMAGE063
Integrating step by step to obtain the final state
Figure 748809DEST_PATH_IMAGE064
And corresponding state transition matrix
Figure 804489DEST_PATH_IMAGE065
At the time of calculating the amount of deviation of the end position
Figure 699764DEST_PATH_IMAGE066
Judging whether the precision requirement is met; if the precision requirement is met, terminating the iteration; otherwise, continuing to perform differential correction; calculating pulse velocity through end state velocity matching
Figure 233514DEST_PATH_IMAGE067
；
Based on the obtained pulse velocity quantity
Figure 491320DEST_PATH_IMAGE068
Pulse velocity volume
Figure 108115DEST_PATH_IMAGE067
The active control ensures that the spacecraft avoids the shadow area and can return to the original orbit, thereby ensuring that the spacecraft can also keep more relatively stable working states in the return stage.
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