CN107589756B - Method for initializing lunar-rushing satellite formation - Google Patents

Method for initializing lunar-rushing satellite formation Download PDF

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CN107589756B
CN107589756B CN201710814705.0A CN201710814705A CN107589756B CN 107589756 B CN107589756 B CN 107589756B CN 201710814705 A CN201710814705 A CN 201710814705A CN 107589756 B CN107589756 B CN 107589756B
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CN107589756A (en
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乔栋
李翔宇
胡勃钦
杜燕茹
孙超
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Beijing Institute of Technology BIT
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Abstract

The invention discloses an initialization method for a lunar-running satellite formation, and belongs to the technical field of aerospace. The specific implementation method of the invention is as follows: respectively establishing satellite kinetic equations under the earth and moon inertial systems; through multiple times of multi-target orbit correction, formation initialization of multiple satellites is guaranteed; by adding midway correction in the earth-moon transfer, the orbit inclination angles of the satellites are ensured, the heights of the near-moon points are the same, and the time for reaching the near-moon points is close; applying maneuver at the moonpoint to ensure that the heights of the moonpoints of the satellites are the same; determining a reference star, wherein the other satellites are tracking stars, and ensuring that the phase angle of the tracking star is the same as that of the reference star by utilizing twice lunar point phase modulation maneuvers; and finally, optimal two-pulse or multi-pulse intersection is adopted, so that the speed position of each tracking satellite and the reference satellite meet the formation constraint, and the formation initialization of the lunar satellites is realized. The invention provides an orbit formation initialization method for forming a moon formation after a plurality of satellites are separated and run for the month, which has the advantages of high efficiency and low fuel consumption.

Description

Method for initializing lunar-rushing satellite formation
Technical Field
The invention relates to an initialization method for a lunar-rushing satellite formation, in particular to a method for forming a satellite formation suitable for satellites which reach the moon through earth-moon transfer, and belongs to the technical field of aerospace.
Background
The lunar exploration has important scientific value and engineering significance, and multiple satellites are adopted to form a formation to develop a lunar formation to carry out scientific exploration, so that more scientific data can be obtained, and tasks which cannot be completed by a single satellite, such as gravity field measurement, ultralong wave exploration and the like, can be completed. The satellite can carry the same carrier rocket for launching, earth and moon transfer is independently carried out after the satellite is separated from the rocket, the separation states of the satellite and the rocket are different, the orbit formed after the satellite arrives at the moon for capture is also different, errors can exist in the maneuvering process, the satellite orbit state difference is larger, the distance difference is longer, and formation cannot be directly formed. The formation initialization needs to be completed through maneuvering, the relative distance between the satellites is ensured to be small, and preparation for final formation is completed.
In the prior art [1] in the developed design of the formation of the satellites (see initialization simulation of coplanar formation of small satellites based on the Hill equation [ C ]. system simulation technology and academic seminar of application thereof, cunning crystal, great strength, 2007) an initialization scheme for applying impulse in the flight direction of the tracking satellites and realizing formation of the small satellites in the reference orbital plane is provided based on the Hill equation.
In the prior art [2] (see initialization conditions and simulation analysis [ J ] maintained by satellite formation computer simulation, wuweihua, houming, liu yong, 2009, 26(10)), an analytic solution of a relative motion equation is derived based on a T-H equation, and initialization conditions satisfying periodic motion of the satellite formation are derived. The above technologies are all suitable for formation of earth satellites, and are difficult to apply to formation of satellites which reach the moon through earth-moon transfer.
Disclosure of Invention
The invention discloses an initialization method for a lunar formation satellite, aiming at solving the technical problem of providing an initialization method for an orbit formation which forms a lunar formation after a plurality of satellites are separated for a lunar formation, and the method has the advantages of high efficiency and low fuel consumption.
The purpose of the invention is realized by the following technical scheme.
The invention discloses an initialization method for a lunar-rushing satellite formation, which comprises the steps of respectively establishing satellite kinetic equations under the earth and lunar inertial systems; through multiple times of multi-target orbit correction, formation initialization of multiple satellites is guaranteed; by adding midway correction in the earth-moon transfer, the orbit inclination angles of the satellites are ensured, the heights of the near-moon points are the same, and the time for reaching the near-moon points is close; applying maneuver at the moonpoint to ensure that the heights of the moonpoints of the satellites are the same; determining a reference star, wherein the other satellites are tracking stars, and ensuring that the phase angle of the tracking star is the same as that of the reference star by utilizing twice lunar point phase modulation maneuvers; and finally, optimal two-pulse or multi-pulse intersection is adopted, so that the speed position of each tracking satellite and the reference satellite meet the formation constraint, and the formation initialization of the lunar satellites is realized.
And performing round-the-moon orbit formation on the satellites with the given emission window by the method for initializing the formation of the lunar satellites, thereby realizing a detection task.
The invention discloses an initialization method for a lunar-running satellite formation, which comprises the following steps:
the method comprises the following steps: satellite kinetic equations are respectively established under the earth and moon inertial systems.
The satellite adopts a geocentric inertial system in the earth-moon transfer and correction process, and adopts a lunar-center inertial system in the lunar capture and transfer section.
Considering the influence of the gravity of the earth, the moon and the sun and the non-spherical perturbation, the kinetic equation of the satellite in the geocentric inertial system is written as follows:
Figure BDA0001404798070000021
wherein r, v are the position vector and velocity vector of the satellite relative to the earth, respectively, ANEFor non-spherical gravitational perturbation of the earth, ASPerturbation of the sun's third body's gravitational force, AMIs the third body gravity perturbation of the moon, mueIs the earth's gravitational constant.
The kinetic equation of the satellite under the lunar center inertial system is written as:
Figure BDA0001404798070000022
wherein r isM,vMRespectively the position vector and the velocity vector of the satellite with respect to the moon, ANMFor non-spherical gravitational perturbation of the moon, ASPerturbation of the sun's third body's gravitational force, AEPerturbation of the third body's gravity of the earth, mumIs the moon gravitational constant.
rM,vMAnd r, v satisfy:
Figure BDA0001404798070000023
wherein R isM,VMThe position and velocity vectors of the moon under the geocentric inertial system.
Step two: selecting an orbital inclination i of the satellite relative to the moonTAnd a height r of the point of the moonpTAnd time T to the point of the near moonTAnd adding midway correction to make the orbital inclination angle of each satellite be identical to the height of the moonpoint, and make the arrival time be close. The arrival time is close to the arrival time, and the arrival time meets the preset time precision requirement.
After the satellite and the rocket are separated for several hours, the midway correction is carried out, and the corresponding position speed is r0,v0]The inclination angle of the orbit at the moon near moon point is i0Height r of the near moon pointp0Time to near moon point T0. And (3) performing midway correction by adopting a differential correction algorithm to apply a speed increment delta v, wherein the midway correction refers to: correcting the inclination angle of the orbit at the time of reaching the moon near moon point to iTCorrection of the height of the near-moon point to rpTThe time to the near moon point is corrected to TT。
And step two, applying a speed increment by adopting a differential correction algorithm to perform midway correction, wherein the specific implementation method is as follows:
respectively giving each component of the satellite velocity a small disturbance delta, obtaining the response to the disturbance at the time of reaching the moonpoint after the integration of equation (1), and obtaining a state transition matrix K of the terminal state relative to the initial state:
Figure BDA0001404798070000031
i.e. the change of the initial speed to the change of the end state should satisfy the following relation:
Figure BDA0001404798070000032
calculating the deviation between the actual terminal state and the target state of the satellite:
Figure BDA0001404798070000033
obtaining the velocity increment delta v ═ delta v needed for the intermediate correctionx,Δvy,Δvz]：
Figure BDA0001404798070000034
Through multiple iterations, a correction speed increment Δ v ═ Δ v satisfying the end constraint can be obtainedx,Δvy,Δvz]. Respectively carrying out midway correction on each satellite, wherein the orbital inclination i of the target moon is correctedTAnd a height r of the point of the moonpTSimilarly, to ensure safety, the time T to the point of near-moon is reachedTWith a slight difference. After correction, the orbit inclination angle of each satellite reaching the moon is the same as the height of the moon point, and the arrival time is close. The arrival time is close to the arrival time, and the arrival time meets the preset time precision requirement.
Step three: orbital eccentricity e of selected satelliteTAnd a semi-major axis aTApplying maneuvers to the satellites as they approach the near-moon point to cause the orbital eccentricity e of each satelliteTAnd a semi-major axis aTAnd (5) the consistency is achieved.
When the satellite reaches the near moon point, the eccentricity of the orbit is different from the semimajor axis due to the difference in the satellite velocity, and the eccentricity e of each satellite needs to be adjusted by applying a maneuverTAnd a semi-major axis aTThe same is true. Defining the eccentricity e of the satellite with respect to the moon at the point of the near moon0And a semi-major axis of a0Then the corresponding near-moon point velocity is
Figure BDA0001404798070000041
The near-moon point velocity of the target orbit is
Figure BDA0001404798070000042
Then an incremental velocity Δ v needs to be appliedp＝vpT-vp0The direction is the satellite velocity reversal.
Step four: and selecting one satellite in the required satellite formation as a reference satellite, and defining the rest satellites as tracking satellites. And applying two pulses through the near-moon point, and adjusting the time when the other tracking stars pass through the near-moon point to enable the phase of the tracking star to be consistent with that of the reference star.
Defining the time difference of two satellites passing through the near-moon point as delta T and the orbit period of the reference satellite as TperAnd the satellite completes phase modulation through at least one orbit period, and the phase difference of the corresponding period needing to be adjusted is delta t. According to the relationship between the orbit period and the semimajor axis, the following steps are obtained:
Figure BDA0001404798070000043
Figure BDA0001404798070000044
a′Tthe phase modulation orbit is a semi-long axis corresponding to the phase modulation orbit, the phase modulation maneuver is applied at a lunar point, and the speed of the lunar point of the original orbit is as follows:
Figure BDA0001404798070000045
the phase modulation orbit has a moonpoint speed of:
Figure BDA0001404798070000046
then two maneuvers need to be applied with the maneuver size Δ v separatelypha＝|v′pT-vpTI, direction is the same or opposite to speed.
The phase-modulated tracks have the same track inclination angle iTSemi-major axis aTEccentricity eTAngle f of true approach pointTAnd the tracking star phase is consistent with the reference star.
Step five: and adjusting the distance between the satellite and the reference satellite by adopting an optimal two-pulse or multi-pulse orbit to complete formation initialization.
And step five, adjusting the distance between the satellite and the reference satellite by adopting the optimal two-pulse orbit to complete formation initialization, wherein the specific implementation method is the step 5.1.
The tracks after the phase modulation in the step four have the same track inclination angle iTSemi-major axis aTEccentricity eTAngle f of true approach pointTThere may be some error in consideration of measurement and control and execution errors. Amplitude angle omega of near-moon point of simultaneous satellitenAnd the right ascension omeganThere is also a slight difference in the time of arrival at the near moon point. Therefore, the optimal two pulses are adopted to solve the Lambert problem, so that the number of the orbits of the tracking satellite and the reference satellite is consistent, close-distance intersection is realized, the relative position and the speed between the satellites are close to 0, and formation initialization is completed.
The step 5.1 is realized by the following method:
defining the position and velocity vector of the tracking satellite after phase modulation as r1,v1]The position velocity vector of the reference star is [ r ]0,v0]Setting an optimized variable parking time tparkAnd a transfer time ttransfer. Time t is integrated for satellite 1 position velocity state using equation (2)parkObtaining a pre-convergence speed position vector r'1,v′1]Integrating time t with equation (2) for reference star position velocity statepark+ttransferObtaining a pre-convergence speed position vector r'0,v′0]. Solving from the initial point P1(r1') to the target point P2(r0') transition time ttransferSolving the corresponding initial velocity v1+' and terminal velocity v0-'. Selecting a target function J ═ v'1-v′1+|+|v′0-v′0-I represents the speed increment required by the transfer of the two pulses, and the optimization function is adopted to optimize the objective function to obtain the parking time t corresponding to the minimum speed incrementparkAnd a transfer time ttransferAnd corresponding speed increment, the tracking satellite applies corresponding maneuver to realize the intersection with the reference satellite, and after the intersection is finishedThe distance and the speed of the satellite relative to the reference satellite are close to 0, the formation condition of the satellite is met, and the formation initialization of the satellite when the satellite runs the moon is realized.
Solving for the corresponding initial velocity v as described in step 5.11+' and terminal velocity v0-' preferably using Gauss algorithm or global variational method.
And step five, adjusting the distance between the satellite and the reference satellite by adopting the optimal multi-pulse orbit to complete formation initialization, wherein the specific implementation method is step 5.2.
The optimal two-pulse orbit is solved and optimized, the first rendezvous maneuver is executed, then the satellite state is updated according to conditions, the next optimal two-pulse optimization is carried out, and the formation initialization of the tracking satellite and the reference satellite is realized until the result of the last rendezvous pulse is smaller than the preset constraint.
Further comprises the following steps: and performing lunar orbit formation on a plurality of satellites with given emission windows through the first step to the fifth step to realize a detection task.
The satellite formation initialization method for the satellite rushing to the moon is preferably suitable for micro-satellite formation.
Has the advantages that:
1. the invention discloses a method for initializing a lunar-running satellite formation, which comprises the steps of applying midway correction maneuver in the second step, applying a near-moon maneuver in the third step, applying a phase modulation maneuver in the fourth step, applying optimal two pulses or multiple pulses in the fifth step, and applying multiple maneuvers layer by layer, so that satellites in different launching states can complete the initialization of the lunar formation, and the application range is wide.
2. According to the initialization method for formation of the satellite capable of running the moon, disclosed by the invention, the formation reliability is good by selecting the reference satellite as a target and applying mobility to the other satellites to approach the reference satellite.
3. According to the method for initializing the formation of the lunar-running satellite, disclosed by the invention, the formation initialization speed increment is low and the fuel consumption is low by optimizing the rendezvous orbit by two pulses or more.
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FIG. 1 is a schematic flow chart of a scheme of an initialization method for formation of a satellite lunar-rushing satellite according to the present invention;
fig. 2 is a schematic diagram of a lunar satellite two-pulse optimization process of an initialization method for a satellite formation for a satellite rushing to the moon.
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:
in the initialization method for the formation of the lunar-rushing satellite disclosed by the embodiment, satellite kinetic equations are respectively established under the earth and the lunar inertial system; and through multiple times of multi-target orbit correction, formation initialization of multiple satellites is guaranteed. By adding midway correction in the earth-moon transfer, the orbit inclination angles of the satellites are ensured, the heights of the near-moon points are the same, and the time for reaching the near-moon points is close; applying maneuver at the moonpoint to ensure that the heights of the moonpoints of the satellites are the same; determining a reference star, wherein the other satellites are tracking stars, and ensuring that the phase angle of the tracking star is the same as that of the reference star by utilizing twice lunar point phase modulation maneuvers; and finally, optimal two-pulse or multi-pulse intersection is adopted, so that the velocity position of each tracking satellite and the reference satellite meet formation constraint, and formation initialization of the satellite is realized.
The method for initializing a march satellite formation disclosed in this embodiment takes a two-star ring-moon formation as an example, and includes the following steps:
the method comprises the following steps: satellite kinetic equations are respectively established under the earth and moon inertial systems.
The satellite adopts a geocentric inertial system in the earth-moon transfer and correction process, and adopts a lunar-center inertial system in the lunar capture and transfer section.
Considering the influence of the gravity of the earth, the moon and the sun and the non-spherical perturbation, the kinetic equation of the satellite in the geocentric inertial system is written as follows:
Figure BDA0001404798070000061
wherein r, v are the position vector and velocity vector of the satellite relative to the earth, respectively, ANEFor non-spherical gravitational perturbation of the earth, ASPerturbation of the sun's third body's gravitational force, AMIs the third body gravity perturbation of the moon, mueIs the earth's gravitational constant.
The kinetic equation of the satellite under the lunar center inertial system is written as:
Figure BDA0001404798070000071
wherein r isM,vMRespectively the position vector and the velocity vector of the satellite with respect to the moon, ANMFor non-spherical gravitational perturbation of the moon, ASPerturbation of the sun's third body's gravitational force, AEPerturbation of the third body's gravity of the earth, mumIs the moon gravitational constant.
rM,vMAnd r, v satisfy
Figure BDA0001404798070000072
Wherein R isM,VMThe position and velocity vectors of the moon under the geocentric inertial system.
Step two: selecting an orbital inclination i of the satellite relative to the moonTAnd a height r of the point of the moonpTAnd time T to the point of the near moonTAnd adding midway correction to make the orbital inclination angle of each satellite be identical to the height of the moonpoint, and make the arrival time be close. The arrival time is close to the arrival time, and the arrival time meets the preset time precision requirement.
After the satellite and the rocket are separated for several hours, the midway correction is carried out, and the corresponding position speed is r0,v0]The inclination angle of the orbit at the moon near moon point is i0Height r of the near moon pointp0Time to near moon point T0. And (3) performing midway correction by adopting a differential correction algorithm to apply a speed increment delta v, wherein the midway correction refers to: correcting the inclination angle of the orbit at the time of reaching the moon near moon point to iTCorrection of the height of the near-moon point to rpTThe time to the near moon point is corrected to TT。
And step two, applying a speed increment by adopting a differential correction algorithm to perform midway correction, wherein the specific implementation method is as follows:
respectively giving each component of the satellite velocity a small disturbance delta, obtaining the response to the disturbance at the time of reaching the moonpoint after the integration of equation (1), and obtaining a state transition matrix K of the terminal state relative to the initial state:
Figure BDA0001404798070000073
i.e. the change of the initial speed to the change of the end state should satisfy the following relation:
Figure BDA0001404798070000081
calculating the deviation between the actual terminal state and the target state of the satellite:
Figure BDA0001404798070000082
obtaining the velocity increment delta v ═ delta v needed for the intermediate correctionx,Δvy,Δvz]：
Figure BDA0001404798070000083
Through multiple iterations, a correction speed increment Δ v ═ Δ v satisfying the end constraint can be obtainedx,Δvy,Δvz]. Respectively carrying out midway correction on each satellite, wherein the orbital inclination i of the target moon is correctedTAnd a height r of the point of the moonpTSimilarly, to ensure safety, the time T to the point of near-moon is reachedTWith a slight difference. After correction, the orbit inclination angle of each satellite reaching the moon is the same as the height of the moon point, and the arrival time is close. The arrival time is close to the arrival time, and the arrival time meets the preset time precision requirement.
The orbit inclination angle of the satellite when the satellite reaches the near moon point is 15 degrees, the height of the near moon point is 300km, the satellite A is separated from a carrier rocket 2 minutes before B, the separation speed is 1.5m/s, the time difference of reaching the near moon point is 10 minutes, half-way correction is carried out for 22 hours of A, half-way correction is carried out for 25 hours of B, the half-way correction speed increment of A is 11.04m/s, and the half-way correction speed increment of B is 11.15 m/s.
Step three: orbital eccentricity e of selected satelliteTAnd a semi-major axis aTApplying maneuvers to the satellites as they approach the near-moon point to cause the orbital eccentricity e of each satelliteTAnd a semi-major axis aTAnd (5) the consistency is achieved.
When the satellite reaches the near moon point, the eccentricity of the orbit is different from the semimajor axis due to the difference in the satellite velocity, and the eccentricity e of each satellite needs to be adjusted by applying a maneuverTAnd a semi-major axis aTThe same is true. Defining the eccentricity e of the satellite with respect to the moon at the point of the near moon0And a semi-major axis of a0Then the corresponding near-moon point velocity is
Figure BDA0001404798070000084
The near-moon point velocity of the target orbit is
Figure BDA0001404798070000085
Then an incremental velocity Δ v needs to be appliedp＝vpT-vp0The direction is the satellite velocity reversal.
Selecting the orbit eccentricity e of the satellite to be 0.683, the orbit semi-major axis a to be 6440km, and applying maneuver 369.04km/s to the moon point of the A star; the B star moons applied maneuver 370.24 km/s.
Step four: and selecting one satellite in the required satellite formation as a reference satellite, and defining the rest satellites as tracking satellites. And applying two pulses through the near-moon point, and adjusting the time when the other tracking stars pass through the near-moon point to enable the phase of the tracking star to be consistent with that of the reference star.
Defining the time difference of two satellites passing through the near-moon point as delta T and the orbit period of the reference satellite as TperAnd the satellite completes phase modulation through at least one orbit period, and the phase difference of the corresponding period needing to be adjusted is delta t. According to the relationship between the orbit period and the semimajor axis, the following steps are obtained:
Figure BDA0001404798070000091
Figure BDA0001404798070000092
a′Tthe phase modulation orbit is a semi-long axis corresponding to the phase modulation orbit, the phase modulation maneuver is applied at a lunar point, and the speed of the lunar point of the original orbit is as follows:
Figure BDA0001404798070000093
the phase modulation orbit has a moonpoint speed of:
Figure BDA0001404798070000094
then two maneuvers need to be applied with the maneuver size Δ v separatelypha＝|v′pT-vpTI, direction is the same or opposite to speed.
The phase-modulated tracks have the same track inclination angle iTSemi-major axis aTEccentricity eTAngle f of true approach pointTNamely, the tracking star phase is consistent with the reference star.
The phase-modulated tracks have the same track inclination angle, semimajor axis, eccentricity and true paraxial point angle. And taking the star A as a reference star, performing phase modulation on the star B for 10 minutes, and increasing the required speed by 2.05 m/s.
Step five: and adjusting the distance between the satellite and the reference satellite by adopting an optimal two-pulse or multi-pulse orbit to complete formation initialization.
Step 5.1: and adjusting the distance between the satellite and the reference satellite by adopting the optimal two-pulse orbit to complete formation initialization.
The tracks after the phase modulation in the step four have the same track inclination angle iTSemi-major axis aTEccentricity eTAngle f of true approach pointTThere may be some error in consideration of measurement and control and execution errors. Amplitude angle omega of near-moon point of simultaneous satellitenAnd the right ascension omeganThere is also a slight difference in the time of arrival at the near moon point. Therefore, the optimal two pulses are adopted to solveAnd the lambert problem enables the number of the orbits of the tracking satellite and the reference satellite to be consistent, close-range intersection is realized, the relative position and the speed between the satellites are close to 0, and formation initialization is completed.
The step 5.1 is realized by the following method:
defining the position and velocity vector of the tracking satellite after phase modulation as r1,v1]The position velocity vector of the reference star is [ r ]0,v0]Setting an optimized variable parking time tparkAnd a transfer time ttransfer. Time t is integrated for satellite 1 position velocity state using equation (2)parkObtaining a pre-convergence speed position vector r'1,v′1]Integrating time t with equation (2) for reference star position velocity statepark+ttransferObtaining a pre-convergence speed position vector r'0,v′0]. Solving from the initial point P1(r1') to the target point P2(r0') transition time ttransferSolving the corresponding initial velocity v1+' and terminal velocity v0-'. Selecting a target function J ═ v'1-v′1+|+|v′0-v′0-I represents the speed increment required by the transfer of the two pulses, and the optimization function is adopted to optimize the objective function to obtain the parking time t corresponding to the minimum speed incrementparkAnd a transfer time ttransferAnd corresponding speed increment, the tracking satellite can realize the rendezvous with the reference satellite by applying corresponding maneuver, the distance and the speed of the satellite relative to the reference satellite are close to 0 after the rendezvous is finished, the formation condition of the satellite is met, and the formation initialization of the satellite by the satellite rushing to the moon is realized.
Optimized, the optimal mooring time is tpark13504s, transfer time ttransfer48060s, the optimal crossing speed increment is 2.816m/s, the relative distance between the two stars after the completion of the optimal two pulses varies between 1.5 km and 8.5km, and the formation initialization condition can be met.
Solving for the corresponding initial velocity v as described in step 5.11+' and terminal velocity v0-' preferably using Gauss algorithm or global variational method.
Step 5.2: and adjusting the distance between the satellite and the reference satellite by adopting the optimal multi-pulse orbit to complete formation initialization.
The optimal two-pulse orbit is solved and optimized, the first rendezvous maneuver is executed, then the satellite state is updated according to conditions, the next optimal two-pulse optimization is carried out, and the formation initialization of the tracking satellite and the reference satellite is realized until the result of the last rendezvous pulse is smaller than the preset constraint.
Further comprises the following steps: and performing lunar orbit formation on a plurality of satellites with given emission windows through the first step to the fifth step to realize a detection task.
The satellite formation initialization method for the satellite rushing to the moon is preferably suitable for micro-satellite formation.
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 (8)

1. A method for initializing a lunar-running satellite formation is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: respectively establishing satellite kinetic equations under the earth and moon inertial systems;
the satellite adopts a geocentric inertial system in the earth-moon transfer and correction process, and adopts a lunar-centered inertial system in the lunar capture and transfer section;
considering the influence of the gravity of the earth, the moon and the sun and the non-spherical perturbation, the kinetic equation of the satellite in the geocentric inertial system is written as follows:
Figure FDA0002359238230000011
wherein r, v are the position vector and velocity vector of the satellite relative to the earth, respectively, ANEFor non-spherical gravitational perturbation of the earth, ASPerturbation of the sun's third body's gravitational force, AMIs the third body gravity perturbation of the moon, mueIs the constant of the earth's gravity;
the kinetic equation of the satellite under the lunar center inertial system is written as:
Figure FDA0002359238230000012
wherein r isM，vMRespectively the position vector and the velocity vector of the satellite with respect to the moon, ANMFor non-spherical gravitational perturbation of the moon, ASPerturbation of the sun's third body's gravitational force, AEPerturbation of the third body's gravity of the earth, mumIs the moon gravitational constant;
rM，vMand r, v satisfy:
Figure FDA0002359238230000013
wherein R isM，VMThe position and the velocity vector of the moon under the geocentric inertial system are obtained;
step two: selecting an orbital inclination i of the satellite relative to the moonTAnd a height r of the point of the moonpTAnd time T to the point of the near moonTAdding midway correction to ensure that the orbit inclination angle of each satellite is the same as the height of the moonpoint and the arrival time is close; the arrival time is close to the arrival time and meets the preset time precision requirement;
after the satellite and the rocket are separated for several hours, the midway correction is carried out, and the corresponding position speed is r0，v0]The inclination angle of the orbit at the moon near moon point is i0Height r of the near moon pointp0Time to near moon point T0(ii) a And (3) performing midway correction by adopting a differential correction algorithm to apply a speed increment delta v, wherein the midway correction refers to: correcting the inclination angle of the orbit at the time of reaching the moon near moon point to iTCorrection of the height of the near-moon point to rpTThe time to the near moon point is corrected to TT；
Step three: is selected byOrbital eccentricity e of satelliteTAnd a semi-major axis aTApplying maneuvers to the satellites as they approach the near-moon point to cause the orbital eccentricity e of each satelliteTAnd a semi-major axis aTThe consistency is achieved;
when the satellite reaches the near moon point, the eccentricity of the orbit is different from the semimajor axis due to the difference in the satellite velocity, and the eccentricity e of each satellite needs to be adjusted by applying a maneuverTAnd a semi-major axis aTThe same; defining the eccentricity e of the satellite with respect to the moon at the point of the near moon0And a semi-major axis of a0Then the corresponding near-moon point velocity is
Figure FDA0002359238230000021
The near-moon point velocity of the target orbit is
Figure FDA0002359238230000022
Then an incremental velocity Δ v needs to be appliedp＝vpT-vp0The direction is the satellite speed reversal;
step four: selecting a certain satellite in the required satellite formation as a reference satellite, and defining other satellites as tracking satellites; applying two pulses through the near-moon point, and adjusting the time when the other tracking stars pass through the near-moon point to make the phase of the tracking star consistent with that of the reference star;
defining the time difference of two satellites passing through the near-moon point as delta T and the orbit period of the reference satellite as TperThe satellite completes phase modulation through at least one orbit period, and the difference of the orbit periods of the two satellites is the time difference delta t; according to the relationship between the orbit period and the semimajor axis, the following steps are obtained:
Figure FDA0002359238230000023
Figure FDA0002359238230000024
a′Tthe phase modulation orbit is a semi-long axis corresponding to the phase modulation orbit, the phase modulation maneuver is applied at a lunar point, and the speed of the lunar point of the original orbit is as follows:
Figure FDA0002359238230000025
the phase modulation orbit has a moonpoint speed of:
Figure FDA0002359238230000026
then two maneuvers need to be applied with the maneuver size Δ v separatelypha＝|v′pT-vpTThe direction and the speed are the same or opposite;
the phase-modulated tracks have the same track inclination angle iTSemi-major axis aTEccentricity eTAngle f of true approach pointTThe tracking star phase is consistent with the reference star;
step five: and adjusting the distance between the satellite and the reference satellite by adopting an optimal two-pulse or multi-pulse orbit to complete formation initialization.
2. The method for initializing a march satellite formation according to claim 1, wherein: further comprises the following steps: and performing lunar orbit formation on a plurality of satellites with given emission windows through the first step to the fifth step to realize a detection task.
3. The method for initializing a march satellite formation according to claim 1 or 2, wherein: a method for initializing formation of satellites rushing to the moon is characterized in that the satellites are suitable for formation of micro satellites.
4. The method for initializing a march satellite formation according to claim 3, wherein: step two, the differential correction algorithm is adopted to apply the speed increment for midway correction, the specific realization method is as follows,
respectively giving each component of the satellite velocity a small disturbance delta, obtaining the response to the disturbance at the time of reaching the moonpoint after the integration of equation (1), and obtaining a state transition matrix K of the terminal state relative to the initial state:
Figure FDA0002359238230000031
wherein v isx，vy，vzFor the satellite velocity in the three directions of the inertial system X, Y, Z, the velocity change should satisfy the following relationship to the change of the terminal state:
Figure FDA0002359238230000032
calculating the deviation between the actual terminal state and the target state of the satellite:
Figure FDA0002359238230000033
obtaining the velocity increment delta v ═ delta v needed for the intermediate correctionx，Δvy，Δvz]：
Figure FDA0002359238230000034
Through multiple iterations, a correction speed increment Δ v ═ Δ v satisfying the end constraint can be obtainedx，Δvv，Δvz](ii) a Respectively carrying out midway correction on each satellite, wherein the orbital inclination i of the target moon is correctedTAnd a height r of the point of the moonpTSimilarly, to ensure safety, the time T to the point of near-moon is reachedTSlightly different; after correction, the orbit inclination angle of each satellite reaching the moon is the same as the height of the moon point, and the reaching time is close; the arrival time is close to the arrival time, and the arrival time meets the preset time precision requirement.
5. The method for initializing a march satellite formation according to claim 4, wherein: step five, the optimal two-pulse orbit is adopted to adjust the distance between the satellite and the reference satellite to complete formation initialization, and the specific implementation method is the step 5.1,
track after four phase modulationHaving the same track inclination iTSemi-major axis aTEccentricity eTAngle f of true approach pointTCertain errors may exist under the condition of considering measurement and control and execution errors; amplitude angle omega of near-moon point of simultaneous satellitenAnd the right ascension omeganSlight differences exist due to differences in the time of reaching the near-moon point; therefore, the optimal two pulses are adopted to solve the Lambert problem, so that the number of the orbits of the tracking satellite and the reference satellite is consistent, close-distance intersection is realized, the relative position and the speed between the satellites are close to 0, and formation initialization is completed.
6. The method for initializing a march satellite formation according to claim 5, wherein: the specific implementation method of step 5.1 is as follows,
defining the position and velocity vector of the tracking satellite after phase modulation as r1，v1]The position velocity vector of the reference star is [ r ]0，v0]Setting an optimized variable parking time tparkAnd a transfer time ttransfer(ii) a Time t is integrated for satellite 1 position velocity state using equation (2)parkObtain the velocity position vector [ r ] before intersection1′，v1′]Integrating time t with equation (2) for reference star position velocity statepark+ttransferObtaining a pre-convergence speed position vector r'0，v′0](ii) a Solving from the initial point P1(r1') to the target point P2(r0') transition time ttransferSolving the corresponding initial velocity v1+' and terminal velocity v0-'; selecting a target function J ═ v'1-v′1+|+|v′0-v′0I represents the speed increment required by the transfer of the two pulses, and the optimization function is adopted to optimize the objective function to obtain the parking time t corresponding to the minimum speed incrementparkAnd a transfer time ttransferAnd corresponding speed increment, the intersection with the reference satellite can be realized by tracking the satellite and applying corresponding maneuver, the distance and the speed of the satellite relative to the reference satellite are close to 0 after the intersection is finished, the formation condition of the satellite is met, and the satellite can rush to the moonAnd initializing the satellite formation.
7. The method for initializing a march satellite formation according to claim 6, wherein: solving for the corresponding initial velocity v as described in step 5.11+' and terminal velocity v0-' solve using Gauss algorithm or global variational method.
8. The method for initializing a march satellite formation according to claim 4, wherein: fifthly, adjusting the distance between the satellite and the reference satellite by adopting the optimal multi-pulse orbit to complete formation initialization, wherein the specific implementation method is step 5.2;
the optimal two-pulse orbit is solved and optimized, the first rendezvous maneuver is executed, then the satellite state is updated according to conditions, the next optimal two-pulse optimization is carried out, and the formation initialization of the tracking satellite and the reference satellite is realized until the result of the last rendezvous pulse is smaller than the preset constraint.
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