CN112231943B - Multi-star fly-over sequence searching method and system containing 'one stone and multiple birds' fly-over segments - Google Patents

Multi-star fly-over sequence searching method and system containing 'one stone and multiple birds' fly-over segments Download PDF

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CN112231943B
CN112231943B CN202011490325.4A CN202011490325A CN112231943B CN 112231943 B CN112231943 B CN 112231943B CN 202011490325 A CN202011490325 A CN 202011490325A CN 112231943 B CN112231943 B CN 112231943B
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朱阅訸
罗亚中
杨震
张进
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National University of Defense Technology
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Abstract

The method and the system for searching the multi-satellite flying sequence containing the 'one stone and multiple birds' flying fragment give the number of targets and applied pulses in the flying sequence and give a pulse and target arrangement mode; designing a single-pulse double-star and two-pulse three-star target search strategy; establishing a single-pulse double-star and two-pulse triple-star fly-over trajectory planning model, and designing a corresponding multi-star fly-over trajectory planning method; selecting a corresponding target search strategy according to the type of the first fly-over segment, finding out a potential target combination, and obtaining the fly-over segment; and repeating the process of selecting a corresponding target search strategy according to the type of the next flying segment, finding out a potential target combination and obtaining the flying segments until all the flying segments are searched. The method can find out a target combination meeting the multi-satellite flying condition from a large number of candidate targets, plan out a corresponding pulse flying track and obtain a multi-satellite flying sequence containing a 'one stone and multiple birds' flying fragment.

Description

Multi-star fly-over sequence searching method and system containing 'one stone and multiple birds' fly-over segments
Technical Field
The invention belongs to the field of spacecraft flight mission planning, and particularly relates to a multi-pulse multi-satellite flying sequence searching method and system.
Background
Multi-star fly-by sequence planning is a typical type of problem in multi-objective access mission planning. The method comprises a multi-satellite approaching reconnaissance task, a multi-asteroid flying observation task and the like, and can be considered as a multi-satellite flying sequence planning problem.
In the conventional multi-pulse, multi-star fly-by sequence planning problem, the number of pulses that can be applied is typically greater than the number of targets visited. At least one pulse may be applied to target the next target after the previous target has flown. The mathematical characteristics of the problem are similar to the multi-star rendezvous sequence planning problem, and the difficulty in solving the problem mainly lies in the optimization of the access sequence. However, when the number of movements is limited and the number of applicable pulses is less than the number of targets visited, the fly-by sequence may have no pulses between two adjacent targets visited, i.e. one pulse needs to aim at two or more targets at the same time. In this case, the difficulty in solving is not optimization of the access sequence, but how to search out a target combination satisfying the single-pulse multi-star flying condition from large-scale candidate targets, and further obtain a flying sequence containing a 'one stone and multiple birds' flying fragment. The flying segment is defined as a flying track formed by the spacecraft flying over one or more targets by one to two pulses from the current target.
The multi-satellite flying sequence search containing the 'one stone and multiple birds' flying fragment needs to firstly solve the problem of multi-satellite flying trajectory planning. The traditional pulse fly-by trajectory planning method usually finds a pulse intersection solution first, and then releases the pulse of the intersection terminal to obtain a corresponding fly-by solution. The method can only be used for planning the flying track of a single target, and can not realize the simultaneous flying of a plurality of targets through one pulse. In addition, no effective method for quickly finding out the target combination meeting the multi-satellite flying condition exists at present.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a multi-star fly-over sequence searching method and system containing a 'one stone and multiple birds' fly-over segment. The method can quickly find out a target combination meeting the multi-satellite flying condition from a large number of candidate targets, and plan out a corresponding pulse flying track, thereby obtaining a multi-satellite flying sequence containing a 'one stone and multiple birds' flying fragment. The method can provide effective technical support for searching the multi-satellite flying sequence for large-scale targets.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
the multi-star fly-over sequence searching method containing the 'one stone and multiple birds' fly-over segment comprises the following steps:
s1: giving the number of access targets and applied pulses in the multi-satellite flying sequence searched at this time;
s2: giving pulses and an arrangement mode of the targets according to the number of the targets and the number of the pulses, and determining a multi-satellite flying sequence according to the arrangement mode of the targets, wherein the multi-satellite flying sequence comprises the number of flying fragments in the multi-satellite flying sequence, the type and the arrangement sequence of each flying fragment;
s3: selecting a corresponding flying target searching strategy according to the type of a first flying fragment in a multi-satellite flying sequence by taking the position and the speed of a starting target of the spacecraft as a current initial state, finding out a potential target combination, and obtaining the flying fragment meeting the constraint by adopting a corresponding multi-satellite flying track planning method;
s4: selecting a corresponding flying target searching strategy according to the type of the next flying fragment in the multi-satellite flying sequence determined in S2 by taking the position and the speed of the last target in the last flying fragment when the spacecraft flies over as the current initial state, finding out a potential target combination, and obtaining the flying fragment meeting the constraint by adopting a corresponding multi-satellite flying trajectory planning method;
s5: s4 is repeated until a complete multi-satellite fly-through sequence is obtained.
In the present invention S1, the number of targets is greater than the number of pulses but not greater than twice the number of pulses.
In the preferred embodiment of the present invention, in S2, the arrangement of the given pulse and the target should satisfy the following two constraints: 1) the number of targets between any two adjacent pulses is not more than 3; 2) if there are 3 consecutive targets, at least two consecutive pulses are scheduled before flying over the 3 consecutive targets.
As a preferred scheme of the invention, the flying target search strategy of the invention is divided into a flying target search strategy of a single-pulse double-star flying fragment and a flying target search strategy of a two-pulse three-star flying fragment, if the flying target search strategy is the single-pulse double-star flying fragment, the flying target search strategy of the single-pulse double-star flying fragment is selected, and a potential target combination is found out; and if the two-pulsar flying fragment is the two-pulsar flying fragment, selecting a flying target search strategy of the two-pulsar flying fragment, and finding out a potential target combination.
As a preferred scheme of the present invention, a method for searching a flying target search strategy of a single-pulse double-star flying segment is as follows:
(1): randomly giving a sliding time
Figure 52803DEST_PATH_IMAGE001
Bringing the spacecraft from an initial state(r 0,v 0) Report onr 1,v 1) Wherein (a)r 0,v 0) For initial spacecraft position and velocity, (r 1,v 1) For the spacecraft to pass through a period of taxiing time
Figure 441059DEST_PATH_IMAGE001
The latter position and velocity;
(2): randomly giving a pulse
Figure 400925DEST_PATH_IMAGE002
And a period of time of coasting
Figure 318065DEST_PATH_IMAGE003
From the current state of the spacecraft (r 1,v 1) Report onr 2,v 2)，(r 2,v 2) For spacecraft from a current state (r 1,v 1) Time of sliding
Figure 628961DEST_PATH_IMAGE003
The latter position and velocity;
(3): computing
Figure 289749DEST_PATH_IMAGE004
Collecting the closest distances between the spacecraft and all the access targets in the time period, wherein all the closest distances are less than a given upper limit valued maxAnd counting the number of the objects asn；
(4): if it is
Figure 369701DEST_PATH_IMAGE005
Returning to (1);
(5): will be provided with
Figure 723322DEST_PATH_IMAGE006
And two targets with the minimum closest distance to the spacecraft in the time period are taken as potential flying target combinations.
As a preferred embodiment of the present invention, a method for searching a flying target search strategy of a two-pulse three-star flying segment is as follows:
(1): randomly giving a sliding time
Figure 754469DEST_PATH_IMAGE007
Bringing the spacecraft from an initial state (r 0,v 0) Report onr 1,v 1) Wherein (a)r 0,v 0) For initial spacecraft position and velocity, (r 1,v 1) For the spacecraft to pass through a period of taxiing time
Figure 484528DEST_PATH_IMAGE007
The latter position and velocity;
(2): randomly giving a pulse
Figure 153407DEST_PATH_IMAGE008
And a period of time of coasting
Figure 677929DEST_PATH_IMAGE009
From the current state of the spacecraft (r 1,v 1) Report onr 2,v 2)，(r 2,v 2) For spacecraft from a current state (r 1,v 1) Time of sliding
Figure 697838DEST_PATH_IMAGE009
The latter position and velocity;
(3): randomly giving a pulse
Figure 966008DEST_PATH_IMAGE010
And a period of time of coasting
Figure 754972DEST_PATH_IMAGE011
From the current state of the spacecraft (r 2,v 2) Report onr 3,v 3)，(r 3,v 3) For spacecraft from a current state (r 2,v 2) Time of sliding
Figure 450396DEST_PATH_IMAGE011
The latter position and velocity;
(4): computing
Figure 957601DEST_PATH_IMAGE011
Collecting the closest distances between the spacecraft and all the access targets in the time period, wherein all the closest distances are less than a given upper limit valued maxAnd counting the number of the objects asn；
(5): if it is
Figure 763883DEST_PATH_IMAGE012
Returning to (1);
(6): will be provided with
Figure 938512DEST_PATH_IMAGE013
And three targets with the minimum closest distance to the spacecraft in the time period are taken as potential flying target combinations.
As a preferred scheme of the invention, the multi-satellite flying track planning method is divided into a single-pulse double-satellite flying track planning method and a two-pulse triple-satellite flying track planning method, if the multi-satellite flying track planning method is a single-pulse double-satellite flying track fragment, the single-pulse double-satellite flying track planning method is selected to obtain a flying fragment meeting the constraint, and if the multi-satellite flying track planning method is a two-pulse triple-satellite flying fragment, the two-pulse triple-satellite flying track planning method is selected to obtain a flying fragment meeting the constraint.
As a preferred scheme of the invention, the single-pulse double-star fly-by trajectory planning method comprises the following steps:
(1): constructing a four-pulse double-satellite intersection track optimization model;
the design variables of the four-pulse double-star rendezvous trajectory optimization model are as follows:
Figure 539258DEST_PATH_IMAGE014
Figure 35223DEST_PATH_IMAGE015
wherein the content of the first and second substances,dt 1the time for the spacecraft to wait on the initial orbit;dt 2the time for the spacecraft to transfer from the initial orbit to the first access target by two pulses;dt 3the time for the spacecraft to transfer from a first target to a second target by two pulses; the spacecraft does not stay on the first target of access, so the two pulses in the middle are applied at the same time; is provided witht 0At the initial moment, the moment when the spacecraft applies the first pulset 1The moment of application of the second and third pulsest 2And the moment of application of the fourth pulset 3Comprises the following steps:
Figure 379617DEST_PATH_IMAGE016
Figure 143174DEST_PATH_IMAGE017
the four-pulse double-star rendezvous trajectory optimization model comprises three types of constraints, wherein the first type of constraint is pulse velocity increment constraint:
Figure 180400DEST_PATH_IMAGE018
Figure 662197DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,
Figure 810281DEST_PATH_IMAGE020
the first pulse to be applied for the spacecraft,
Figure 693924DEST_PATH_IMAGE021
the upper limit of the single pulse speed increment.
The second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
Figure 167630DEST_PATH_IMAGE022
Figure 871144DEST_PATH_IMAGE023
in the formula (I), the compound is shown in the specification,r 0(t 2) Andr 1(t 2) Respectively for the spacecraft and the first access targett 2A position vector of a time;r 0(t 3) Andr 2(t 3) Respectively for the spacecraft and the second access targett 3A position vector of time of day.
The third type of constraint is the relative velocity constraint between the spacecraft at the meeting time and the access target:
Figure 822920DEST_PATH_IMAGE024
Figure 561068DEST_PATH_IMAGE025
in the formula (I), the compound is shown in the specification,v 0(t 2) Andv 1(t 2) Respectively for the spacecraft and the first access targett 2A velocity vector of a time of day;v 0(t 3) Andv 2(t 3) Respectively for the spacecraft and the second access targett 3A velocity vector of a time of day;
Figure 438632DEST_PATH_IMAGE026
a fourth pulse applied to the spacecraft for an encounter with a second access target,dv maxthe maximum relative velocity allowed when the spacecraft flies over the target.
The objective function of the four-pulse two-star rendezvous trajectory optimization model is a model for minimizing the sum of two pulse vectors in the middle:
Figure 629442DEST_PATH_IMAGE027
Figure 119329DEST_PATH_IMAGE028
in the formula (I), the compound is shown in the specification,
Figure 977564DEST_PATH_IMAGE029
and
Figure 527494DEST_PATH_IMAGE030
are respectively spacecraftst 2Two pulses are applied at a time to meet and aim at a first accessed target.
(2): adopting a rendezvous trajectory optimization transition method to transition the four-pulse double-star rendezvous trajectory to a single-pulse double-star flying trajectory;
in the flight process of a spacecraft intersecting two targets through four pulses, the spacecraft, a first access target and a second access target are at the initial momentt 0Are in the state of [ 2 ]r 0(t 0), v 0(t 0)]、[r 1(t 0), v 1(t 0)]And 2r 2(t 0), v 2(t 0)]，[r 0(t 0), v 0(t 0)]、[r 1(t 0), v 1(t 0)]And 2r 2(t 0), v 2(t 0)]Respectively representing the spacecraft, the first access target and the second access target at the initial momentt 0A position vector and a velocity vector.
For any given set of design variables
Figure 205600DEST_PATH_IMAGE031
First, it is necessary to navigateThe states of the celestial body and two visiting objects are defined byr 0(t 0), v 0(t 0)]、[r 1(t 0), v 1(t 0)]And 2r 2(t 0), v 2(t 0)]Respectively predict the value of [ 2 ]r 0(t 1), v 0(t 1)]、[r 1(t 2), v 1(t 2)]And 2r 2(t 3), v 2(t 3)]Then adopting Lambert algorithm to respectively solver 0(t 1) Tor 1(t 2) Andr 1(t 2) Tor 2(t 3) Two sections of two pulses between the two pulse crossing tracks obtain 4 pulses required by the crossing
Figure 233599DEST_PATH_IMAGE032
~
Figure 946340DEST_PATH_IMAGE033
(ii) a Optimizing and adjusting the value of the design variable through an evolutionary algorithm to continuously reduce the formula (6) to 0 and cancel
Figure 932751DEST_PATH_IMAGE034
~
Figure 98153DEST_PATH_IMAGE035
The four-pulse two-star rendezvous trajectory can be successfully transited into a single-pulse two-star flying trajectory.
As a preferred scheme of the invention, the two-pulse three-star fly-over trajectory planning method comprises the following steps:
(1): constructing a seven-pulse three-star rendezvous trajectory optimization model;
the design variables of the seven-pulse three-star rendezvous trajectory optimization model are as follows:
Figure 195422DEST_PATH_IMAGE036
Figure 497090DEST_PATH_IMAGE037
wherein the content of the first and second substances,dt 1the time for the spacecraft to wait on the initial orbit;dt 2time of flight after application of the first pulse to the spacecraft;dt 3the time for the spacecraft to transition from the transition orbit to the first access target by two pulses;dt 4the time for the spacecraft to transfer from a first target to a second target by two pulses;dt 5the time for the spacecraft to transition from the second access target to the third access target by two pulses;
Figure 890288DEST_PATH_IMAGE038
is the first pulse; the spacecraft does not stay on the first access target and the second access target, so that the third pulse and the fourth pulse are applied at the same time, and the fifth pulse and the sixth pulse are also applied at the same time; is provided witht 0The initial time is the time when the spacecraft applies each pulse as follows:
Figure 808565DEST_PATH_IMAGE039
Figure 178366DEST_PATH_IMAGE040
wherein the content of the first and second substances,t 1andt 2first and second pulse application times, respectively;t 3a third and fourth pulse application time;t 4a fifth, sixth pulse application time;t 5the seventh pulse application time.
The seven-pulse three-star rendezvous trajectory optimization model comprises three types of constraints. The first type is the pulse velocity increment constraint:
Figure 600120DEST_PATH_IMAGE041
Figure 928334DEST_PATH_IMAGE042
in the formula (I), the compound is shown in the specification,
Figure 802749DEST_PATH_IMAGE043
and
Figure 507400DEST_PATH_IMAGE044
first and second pulses respectively.
The second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
Figure 783660DEST_PATH_IMAGE045
Figure 17195DEST_PATH_IMAGE046
in the formula (I), the compound is shown in the specification,r 0(t 3) Andr 1(t 3) Respectively for the spacecraft and the first access targett 3A position vector of a time;r 0(t 4) Andr 2(t 4) Respectively for the spacecraft and the second access targett 4A position vector of a time;r 0(t 5) Andr 3(t 5) Respectively for the spacecraft and the third access targett 5A position vector of time of day.
The third type of constraint is the relative velocity constraint between the spacecraft at the meeting time and the access target:
Figure 378907DEST_PATH_IMAGE047
Figure 356090DEST_PATH_IMAGE048
in the formula (I), the compound is shown in the specification,v 0(t 3) Andv 1(t 3) Respectively for the spacecraft and the first access targett 3A velocity vector of a time of day;v 0(t 4) Andv 2(t 4) Respectively for the spacecraft and the second access targett 4A velocity vector of a time of day;v 0(t 5) Andv 3(t 5) Respectively for the spacecraft and the third access targett 5A velocity vector of a time of day;
Figure 752436DEST_PATH_IMAGE049
a seventh pulse applied to the spacecraft for an encounter with a third access target.
The objective function of the seven-pulse three-star intersection trajectory optimization model is a model for minimizing the sum of the third and fourth pulse vectors and the sum of the fifth and sixth pulse vectors:
Figure 491345DEST_PATH_IMAGE050
Figure 605932DEST_PATH_IMAGE051
in the formula (I), the compound is shown in the specification,
Figure 121227DEST_PATH_IMAGE052
and
Figure 637659DEST_PATH_IMAGE053
are respectively spacecraftst 3Two pulses applied at a time to meet and aim at a first accessed target;
Figure 212997DEST_PATH_IMAGE054
and
Figure 549300DEST_PATH_IMAGE055
are respectively spacecraftst 4Applied at a timeTwo pulses for meeting and targeting a second access target and a third access target.
(2): adopting a rendezvous trajectory optimization transition method to transition the rendezvous trajectory of the seven-pulse three-star to a two-pulse three-star flying trajectory;
for any given set of design variablesdt 1, dt 2, dt 3, dt 4, dt 5]First, it is necessary to predict the spacecraft and the three access targets from the initial states separatelyr 0(t 2), v 0(t 2)]、[r 1(t 3), v 1(t 3)]、[r 2(t 4), v 2(t 4)]And 2r 3(t 5), v 3(t 5)]Then adopting Lambert algorithm to respectively solver 0(t 2) Tor 1(t 3)、r 1(t 3) Tor 2(t 4) Andr 2(t 4) Tor 3(t 5) Three-section two-pulse intersection track between the two pulses to obtain six pulses required by intersection
Figure 868286DEST_PATH_IMAGE056
~
Figure 239224DEST_PATH_IMAGE057
(ii) a Optimizing and adjusting the value of the design variable through an evolutionary algorithm to continuously reduce the value of the formula (12) to 0 and cancel
Figure 985464DEST_PATH_IMAGE058
~
Figure 543484DEST_PATH_IMAGE059
And successfully transitioning the seven-pulse three-star rendezvous trajectory into a two-pulse three-star flying trajectory.
The invention also provides a multi-satellite flying sequence searching system containing the 'one stone and multiple birds' flying fragment, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the following steps when executing the computer program:
s1: giving the number of access targets and applied pulses in the multi-satellite flying sequence searched at this time;
s2: giving pulses and an arrangement mode of the targets according to the number of the targets and the number of the pulses, and determining a multi-satellite flying sequence according to the arrangement mode of the targets, wherein the multi-satellite flying sequence comprises the number of flying fragments in the multi-satellite flying sequence, the type and the arrangement sequence of each flying fragment;
s3: selecting a corresponding flying target searching strategy according to the type of a first flying fragment in a multi-satellite flying sequence by taking the position and the speed of a starting target of the spacecraft as a current initial state, finding out a potential target combination, and obtaining the flying fragment meeting the constraint by adopting a corresponding multi-satellite flying track planning method;
s4: selecting a corresponding flying target searching strategy according to the type of the next flying fragment in the multi-satellite flying sequence determined in S2 by taking the position and the speed of the last target in the last flying fragment when the spacecraft flies over as the current initial state, finding out a potential target combination, and obtaining the flying fragment meeting the constraint by adopting a corresponding multi-satellite flying trajectory planning method;
s5: s4 is repeated until a complete multi-satellite fly-through sequence is obtained.
A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, carries out the steps of:
s1: giving the number of access targets and applied pulses in the multi-satellite flying sequence searched at this time;
s2: giving pulses and an arrangement mode of the targets according to the number of the targets and the number of the pulses, and determining a multi-satellite flying sequence according to the arrangement mode of the targets, wherein the multi-satellite flying sequence comprises the number of flying fragments in the multi-satellite flying sequence, the type and the arrangement sequence of each flying fragment;
s3: selecting a corresponding flying target searching strategy according to the type of a first flying fragment in a multi-satellite flying sequence by taking the position and the speed of a starting target of the spacecraft as a current initial state, finding out a potential target combination, and obtaining the flying fragment meeting the constraint by adopting a corresponding multi-satellite flying track planning method;
s4: selecting a corresponding flying target searching strategy according to the type of the next flying fragment in the multi-satellite flying sequence determined in S2 by taking the position and the speed of the last target in the last flying fragment when the spacecraft flies over as the current initial state, finding out a potential target combination, and obtaining the flying fragment meeting the constraint by adopting a corresponding multi-satellite flying trajectory planning method;
the conventional fly-by sequence planning method is only suitable for the fly-by sequence planning problem that at least one pulse is contained between adjacent targets. According to the method and the system for searching the multi-satellite flying sequence containing the 'one stone and multiple bird' flying fragments, the flying targets are searched section by section according to the arrangement mode of the given pulse and the access targets, the maneuvering time and the maneuvering amount of the pulse are planned, the flying fragments meeting the constraint are obtained, and then the final multi-satellite flying sequence is obtained in a section-by-section accumulation mode of the flying fragments. The method overcomes the defects of the traditional fly-over sequence planning method, can effectively support the condition that no pulse exists between two or three adjacent targets, and realizes large-scale global search of the fly-over sequence containing 'one stone and a plurality of birds'.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is an exemplary illustration of a fly-by fragment;
FIG. 3 is a diagram of the flight of a spacecraft through a four-pulse intersection of two targets;
FIG. 4 is a diagram of the flight of a spacecraft by seven-pulse intersection with three targets;
FIG. 5 is a diagram of a search process for a single-pulse two-star fly-through segment;
FIG. 6 is a diagram of a search process for a two-pulse, three-star fly-through segment;
FIG. 7 is a diagram of a search process for a "222" multi-star fly-by sequence;
FIG. 8 shows a flight path diagram of a spacecraft flying over 6 stars in sequence from the solar system;
fig. 9 shows a flight path diagram of the spacecraft flying over 5 stars in sequence from the solar system.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1:
as shown in fig. 1, the method for searching a multi-star fly-over sequence containing a "one-stone multi-bird" fly-over segment provided in this embodiment includes the following steps:
s1: the number of targets visited and pulses applied in the multi-satellite fly-through sequence for this search is given. Wherein the number of access targets is greater than the number of pulses but not greater than twice the number of pulses.
S2: and giving the pulse and the arrangement mode of the target according to the number of the target and the pulse, and determining the multi-satellite flying sequence according to the arrangement mode of the target. The number of flying fragments in the sequence searched at this time, the type and the arrangement sequence of each flying fragment are determined by the arrangement mode of the target;
the invention defines a flight track formed by a spacecraft flying over one or a plurality of targets simultaneously through one to two pulses from a current target as a flying segment. Wherein, the starting time of the flying segment is the time of flying the last target in the last flying segment, and the terminal time of the flying segmentThe moment of flight over the last target of the one or more targets. Fig. 2 shows an example of a fly-by sequence with a target number of 7 and a pulse number of 4, comprising 3 fly-by segments. Wherein the content of the first and second substances,
Figure 931740DEST_PATH_IMAGE060
to
Figure 891606DEST_PATH_IMAGE061
Is a single-pulse single-star flying segment,
Figure 310211DEST_PATH_IMAGE062
to
Figure 621106DEST_PATH_IMAGE063
Is a single-pulse double-star flying segment,
Figure 281895DEST_PATH_IMAGE064
to
Figure 361846DEST_PATH_IMAGE065
Is a two-pulse three-star fly-over segment.
The arrangement of the pulse and the target given in the step needs to satisfy the following two constraints: 1) the number of targets between any two adjacent pulses is not more than 3; 2) if there are 3 consecutive targets, at least two consecutive pulses are scheduled before flying over the 3 consecutive targets.
S3: respectively designing a flying target search strategy of a single-pulse double-star flying fragment and a flying target search strategy of a two-pulse three-star flying fragment.
S301: designing a flying target searching strategy of a single-pulse double-star flying fragment;
the searching process of the flying target searching strategy of the single-pulse double-star flying segment is as follows:
s30101: randomly giving a sliding time
Figure 715467DEST_PATH_IMAGE066
Bringing the spacecraft from an initial state (r 0,v 0) Report onr 1,v 1) Wherein (a)r 0,v 0) For initial spacecraft position and velocity, (r 1,v 1) For the spacecraft to pass through a period of taxiing time
Figure 248080DEST_PATH_IMAGE066
The latter position and velocity.
S30102: randomly giving a pulse
Figure 712559DEST_PATH_IMAGE067
And a period of time of coasting
Figure 647017DEST_PATH_IMAGE068
From the current state of the spacecraft (r 1,v 1) Report onr 2,v 2)，(r 2,v 2) For spacecraft from a current state (r 1,v 1) Time of sliding
Figure 171539DEST_PATH_IMAGE068
The latter position and velocity.
S30103: computing
Figure 925869DEST_PATH_IMAGE068
Collecting the closest distances between the spacecraft and all the access targets in the time period, wherein all the closest distances are less than a given upper limit valued maxAnd counting the number of the objects asn；
S30104: if it isn< 2, return to S30101;
s30105: will be provided with
Figure 459618DEST_PATH_IMAGE069
And two targets with the minimum closest distance to the spacecraft in the time period are taken as potential flying target combinations.
S302: designing a flying target searching strategy of a two-pulse three-star flying fragment;
the process of the flying target searching strategy of the two-pulse three-star flying fragment is as follows:
s30201: randomly giving a sliding time
Figure 248583DEST_PATH_IMAGE070
Bringing the spacecraft from an initial state (r 0,v 0) Report onr 1,v 1) Wherein (a)r 0,v 0) For initial spacecraft position and velocity, (r 1,v 1) For the spacecraft to pass through a period of taxiing time
Figure 678427DEST_PATH_IMAGE070
The latter position and velocity.
S30202: randomly giving a pulse
Figure 949746DEST_PATH_IMAGE071
And a period of time of coasting
Figure 756028DEST_PATH_IMAGE072
From the current state of the spacecraft (r 1,v 1) Report onr 2,v 2)，(r 2,v 2) For spacecraft from a current state (r 1,v 1) Time of sliding
Figure 399499DEST_PATH_IMAGE073
The latter position and velocity.
S30203: randomly giving a pulse
Figure 265824DEST_PATH_IMAGE074
And a period of time of coasting
Figure 994746DEST_PATH_IMAGE075
From the current state of the spacecraft (r 2,v 2) Report onr 3,v 3)，(r 3,v 3) For spacecraft from a current state (r 2,v 2) Time of sliding
Figure 870298DEST_PATH_IMAGE076
The latter position and velocity.
S30204: computing
Figure 633854DEST_PATH_IMAGE076
Collecting the closest distances between the spacecraft and all the access targets in the time period, wherein all the closest distances are less than a given upper limit valued maxAnd counting the number of the objects asn。
S30205: if it isn< 3, return to S30201.
S30206: will be provided with
Figure 405501DEST_PATH_IMAGE077
And three targets with the minimum closest distance to the spacecraft in the time period are taken as potential flying target combinations.
S4: and designing a single-pulse double-star fly-over trajectory planning method and a two-pulse three-star fly-over trajectory planning method.
S401: and designing a single-pulse double-star fly-over trajectory planning method.
S40101: constructing a four-pulse double-satellite intersection track optimization model;
the design variables of the four-pulse double-star rendezvous trajectory optimization model are as follows:
Figure 887298DEST_PATH_IMAGE078
Figure 300962DEST_PATH_IMAGE079
wherein the content of the first and second substances,dt 1the time for the spacecraft to wait on the initial orbit;dt 2the time for the spacecraft to transfer from the initial orbit to the first access target by two pulses;dt 3the time for the spacecraft to transfer from a first target to a second target by two pulses; the spacecraft does not stay on the first target of access, so the two pulses in the middle are applied at the same time; is provided witht 0At the initial moment, the moment when the spacecraft applies the first pulset 1The moment of application of the second and third pulsest 2And the moment of application of the fourth pulset 3Comprises the following steps:
Figure 919025DEST_PATH_IMAGE080
Figure 861573DEST_PATH_IMAGE081
the four-pulse two-star rendezvous trajectory optimization model needs to consider the following three types of constraints. The first type of constraint is the pulse velocity delta constraint:
Figure 332131DEST_PATH_IMAGE082
Figure 283907DEST_PATH_IMAGE083
in the formula (I), the compound is shown in the specification,
Figure 756476DEST_PATH_IMAGE084
the first pulse to be applied for the spacecraft,
Figure 401084DEST_PATH_IMAGE085
the upper limit of the single pulse speed increment.
The second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
Figure 591894DEST_PATH_IMAGE086
Figure 81781DEST_PATH_IMAGE087
in the formula (I), the compound is shown in the specification,r 0(t 2) Andr 1(t 2) Respectively for the spacecraft and the first access targett 2A position vector of a time;r 0(t 3) Andr 2(t 3) Respectively for the spacecraft and the second access targett 3A position vector of time of day.
The third type of constraint is the relative velocity constraint between the spacecraft at the meeting time and the access target:
Figure 940016DEST_PATH_IMAGE088
Figure 489946DEST_PATH_IMAGE089
in the formula (I), the compound is shown in the specification,v 0(t 2) Andv 1(t 2) Respectively for the spacecraft and the first access targett 2A velocity vector of a time of day;v 0(t 3) Andv 2(t 3) Respectively for the spacecraft and the second access targett 3A velocity vector of a time of day;
Figure 902473DEST_PATH_IMAGE090
a fourth pulse applied to the spacecraft for an encounter with a second access target,dv maxthe maximum relative velocity allowed when the spacecraft flies over the target.
The objective function of the four-pulse two-star rendezvous trajectory optimization model is a model for minimizing the sum of two pulse vectors in the middle:
Figure 461630DEST_PATH_IMAGE091
Figure 908792DEST_PATH_IMAGE092
in the formula (I), the compound is shown in the specification,
Figure 629623DEST_PATH_IMAGE093
and
Figure 795025DEST_PATH_IMAGE094
are respectively spacecraftst 2Two pulses are applied at a time to meet and aim at a first accessed target.
S40102: adopting an intersection track optimization transition method to transition the four-pulse intersection solution to a single-pulse fly-by solution;
the flight of a spacecraft by four pulses meeting two targets is shown in figure 3. Wherein the content of the first and second substances,O 0is the flight trajectory of the spacecraft before the pulse is applied,O 1andO 2flight trajectories for a first 1 and a second 2 access object, respectively. The spacecraft, the first access object 1 and the second access object 2 are at an initial moment
Figure 390830DEST_PATH_IMAGE095
Are in the state of [ 2 ]r 0(t 0), v 0(t 0)]、[r 1(t 0), v 1(t 0)]And 2r 2(t 0), v 2(t 0)]. For any given set of design variablesdt 1, dt 2, dt 3]First, it is necessary to set the states of the spacecraft and the two access targets to the values of [ 2 ]r 0(t 0), v 0(t 0)]、[r 1(t 0), v 1(t 0)]And 2r 2(t 0), v 2(t 0)]Respectively predict the value of [ 2 ]r 0(t 1), v 0(t 1)]、[r 1(t 2), v 1(t 2)]And 2r 2(t 3), v 2(t 3)]Then adopting Lambert algorithm to respectively solver 0(t 1) Tor 1(t 2) Andr 1(t 2) Tor 2(t 3) Two sections of two pulses between the two pulse crossing tracks obtain 4 pulses required by the crossing
Figure 692498DEST_PATH_IMAGE096
. Optimizing and adjusting the value of the design variable through an evolutionary algorithm to continuously reduce the formula (6) to 0 and cancel
Figure 584231DEST_PATH_IMAGE096
The four-pulse two-star rendezvous trajectory can be successfully transited into a single-pulse two-star flying trajectory.
S402: designing a two-pulse three-star fly-over trajectory planning method.
S40201: constructing a seven-pulse three-star rendezvous trajectory optimization model;
the design variables of the seven-pulse three-star rendezvous trajectory optimization model are as follows:
Figure 971350DEST_PATH_IMAGE097
Figure 872309DEST_PATH_IMAGE098
wherein the content of the first and second substances,dt 1the time for the spacecraft to wait on the initial orbit;dt 2time of flight after application of the first pulse to the spacecraft;dt 3the time for the spacecraft to transition from the transition orbit to the first access target by two pulses;dt 4the time for the spacecraft to transfer from a first target to a second target by two pulses;dt 5the time for the spacecraft to transition from the second access target to the third access target by two pulses;
Figure 294064DEST_PATH_IMAGE099
is the first pulse; the spacecraft does not dwell on the first and second targets, so the third and fourth pulses are applied at the same time, and the fifth and sixth pulses are applied at the same time. Is provided witht 0The initial time is the time when the spacecraft applies each pulse as follows:
Figure 356697DEST_PATH_IMAGE100
Figure 231113DEST_PATH_IMAGE101
wherein the content of the first and second substances,t 1andt 2first and second pulse application times, respectively;t 3a third and fourth pulse application time;t 4a fifth, sixth pulse application time;t 5the seventh pulse application time.
The requirements of the seven-pulse three-star rendezvous trajectory optimization model consider the following three types of constraints. The first type is the pulse velocity increment constraint:
Figure 404605DEST_PATH_IMAGE102
Figure 946445DEST_PATH_IMAGE103
in the formula (I), the compound is shown in the specification,
Figure 179980DEST_PATH_IMAGE104
and
Figure 807270DEST_PATH_IMAGE105
first and second pulses respectively.
The second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
Figure 285918DEST_PATH_IMAGE106
Figure 682265DEST_PATH_IMAGE107
in the formula (I), the compound is shown in the specification,r 0(t 3) Andr 1(t 3) Respectively for the spacecraft and the first access targett 3A position vector of a time;r 0(t 4) Andr 2(t 4) Respectively for the spacecraft and the second access targett 4A position vector of a time;r 0(t 5) Andr 3(t 5) Respectively for the spacecraft and the third access targett 5A position vector of time of day.
The third type of constraint is the relative velocity constraint between the spacecraft at the meeting time and the access target:
Figure 86701DEST_PATH_IMAGE108
Figure 935709DEST_PATH_IMAGE109
in the formula (I), the compound is shown in the specification,v 0(t 3) Andv 1(t 3) Respectively for the spacecraft and the first access targett 3A velocity vector of a time of day;v 0(t 4) Andv 2(t 4) Respectively for the spacecraft and the second access targett 4A velocity vector of a time of day;v 0(t 5) Andv 3(t 5) Respectively for the spacecraft and the third access targett 5A velocity vector of a time of day;
Figure 716583DEST_PATH_IMAGE110
a seventh pulse applied to the spacecraft for an encounter with a third access target.
The objective function of the seven-pulse three-star intersection trajectory optimization model is a model for minimizing the sum of the third and fourth pulse vectors and the sum of the fifth and sixth pulse vectors:
Figure 967436DEST_PATH_IMAGE111
Figure 542773DEST_PATH_IMAGE112
in the formula (I), the compound is shown in the specification,
Figure 879077DEST_PATH_IMAGE113
and
Figure 198063DEST_PATH_IMAGE114
are respectively spacecraftst 3Two pulses applied at a time for meeting with the access target 1 and aiming at the access target 2;
Figure 303422DEST_PATH_IMAGE115
and
Figure 49661DEST_PATH_IMAGE116
are respectively spacecraftst 4Two pulses are applied at a time for meeting with the access target 2 and aiming at the access target 3.
S40202: adopting an intersection track optimization transition method to transition the seven-pulse intersection solution to a two-pulse fly-over solution;
the flight process of a spacecraft intersecting three targets with seven pulses is shown in fig. 4. Wherein the content of the first and second substances,
Figure 138840DEST_PATH_IMAGE117
is the flight trajectory of the spacecraft before the pulse is applied,O 1、O 2andO 3respectively, the flight trajectories of the three access targets. For any given set of design variablesdt 1, dt 2, dt 3, dt 4, dt 5]First, it is necessary to predict the spacecraft and the three access targets from the initial states separatelyr 0(t 2), v 0(t 2)]、[r 1(t 3), v 1(t 3)]、[r 2(t 4), v 2(t 4)]And 2r 3(t 5), v 3(t 5)]Then adopting Lambert algorithm to respectively solver 0(t 2) Tor 1(t 3)、r 1(t 3) Tor 2(t 4) Andr 2(t 4) Tor 3(t 5) Three-section two-pulse intersection track between the two pulses to obtain six pulses required by intersection
Figure 995937DEST_PATH_IMAGE118
~
Figure 985497DEST_PATH_IMAGE119
(ii) a Optimizing and adjusting the value of the design variable through an evolutionary algorithm to continuously reduce the value of the formula (12) to 0 and cancel
Figure 902637DEST_PATH_IMAGE120
~
Figure 479112DEST_PATH_IMAGE121
And successfully transitioning the seven-pulse three-star rendezvous trajectory into a two-pulse three-star flying trajectory.
S5: and taking the position speed of the starting target of the spacecraft as the current initial state, selecting a corresponding flying target search strategy in S3 according to the type of the first flying segment in the given multi-satellite flying sequence in S2, finding out a potential target combination, and obtaining the flying segment meeting the constraint by adopting a corresponding multi-satellite flying trajectory planning method in S4.
The steps can be summarized into two stages of 'injection and fine adjustment'. Here, "shooting" is a search process of finding a potential target combination that can fly through simultaneously from a large number of targets, i.e., S3. The "fine tuning" is to adjust the "shooting" trajectory by an optimization method, so that the spacecraft can fly over the searched potential target combination at the same time, i.e. the optimization process of S4. The search process of the single-pulse two-star flying segment is shown in fig. 5, and the search process of the two-pulse three-star flying segment is shown in fig. 6.
S6: and taking the position speed of the last star in the last fragment when the spacecraft flies over as the current initial state, selecting a corresponding flying target search strategy in the S3 according to the type of the next flying fragment in the multi-star flying sequence determined in the S2, finding out a potential target combination, and obtaining the flying fragment meeting the constraint by adopting a corresponding multi-star flying track planning method in the S4.
S7: s6 is repeated until a complete multi-satellite fly-through sequence is obtained.
The process of repeating S6 is a process of continuously accumulating the fly-over segments when searching for the fly-over sequence. For ease of description, the present invention employs a string of numbers to characterize the type of fly-by sequence. The length (number of bits) of the digital string represents the total number of pulses applied, and the number in the digital string represents the number of targets flying after each pulse is applied. For example, "222" indicates that the spacecraft has applied 3 pulses in total, flying 6 targets, each pulse flying two targets separately. "0322" indicates that the spacecraft has applied 4 pulses in total, flying over 7 targets, the first two pulses flying over three targets, and the last two pulses flying over two targets each. The search process for the "222" fly-by sequence is shown in FIG. 7.
So far, the multi-star fly-over sequence searching process containing the 'one stone and multi-bird' fly-over segment is completely finished based on the fly-over segment accumulation method.
Example 2:
this example will be described by taking a galaxy multi-sidereal fly-over sequence search as an example. In this example, the starting target is a solar system, and the position and velocity at the initial time are [8.34 kpc, 0, 0] and [0, -256.41 km/s, 0], respectively. Where 1 kpc = 30856775814671900 km. The initial position and speed of the spacecraft is the same as the solar system.
The multi-star fly-over sequence searching method containing the 'one stone and multiple birds' fly-over segment in the embodiment comprises the following steps:
s1: giving the number of accessed targets and applied pulses in the flying sequence of the search;
the fly-by sequence of this search is given by 6 accessed targets and 3 pulses.
S2: giving a pulse and a target arrangement mode according to the number of accessed targets and pulses, wherein the arrangement mode determines the number of the flying fragments in the sequence, the types of the flying fragments and the arrangement sequence;
the fly-by sequence for this search is given a type "222". Therefore, the number of flying segments in the sequence is 3, and the flying segments are all single-pulse double-star flying segments.
S3: a single-pulse two-star target search strategy and a two-pulse three-star target search strategy are respectively designed according to the method in S3 in embodiment 1.
S4: respectively establishing single-pulse double-star and two-pulse three-star fly-over trajectory planning models according to the method in S4 in embodiment 1, and designing a corresponding multi-star fly-over trajectory planning method.
S5: selecting a corresponding target search strategy in S3 according to the type of a given first flying fragment in S2 by taking the position and the speed of a starting target of the spacecraft as a current initial state, finding out a potential target combination, and obtaining a flying fragment meeting the constraint by adopting a corresponding multi-satellite flying trajectory planning method in S4;
the first flight segment given in this embodiment S2 is a single-pulse two-star flight segment, so the single-pulse two-star target search strategy in S3 is selected, two potential stars numbers 10672 and 9880 capable of simultaneously flying are obtained through the single-pulse two-star target search strategy, and ephemeris data can be obtained by accessing https:// gtocx. And then, a single-pulse double-star flying track planning method is adopted to obtain the flying tracks of synchronously flying over No. 10672 stars and No. 9880 stars.
S6: the position and the speed of the last star in the last fragment of the flying of the spacecraft are in the current initial state, the corresponding target search strategy in S3 is selected according to the type of the next fragment of the flying determined in S2, a potential target combination is found out, and the fragment of the flying meeting the constraint is obtained by adopting the corresponding multi-star flying trajectory planning method in S4;
s7: s6 is repeated until a complete multi-satellite fly-through sequence is obtained.
And (3) taking the position and the speed of the spacecraft when flying over the 9880 # star as the current position and speed, selecting a single-pulse double-star target search strategy in S3, obtaining the numbers of two potential stars capable of flying over simultaneously as 40977 and 99421 through the steps (1) to (5), and then obtaining the flying tracks of stars flying over 40977 and 99421 simultaneously by adopting a single-pulse double-star flying track planning method. And then taking the position and the speed of the spacecraft when the spacecraft flies over the 99421 # sidereal as the current position and speed, selecting a single-pulse double-star target search strategy in S3, obtaining two potential sidereal numbers 13002 and 12384 which can fly over simultaneously through the steps (1) to (5), and then obtaining the flying tracks of the sidereal which fly over 13002 and 12384 simultaneously by adopting a single-pulse double-star flying track planning method. At this point, a complete "222" multi-star fly-by sequence search is completed.
Fig. 8 shows the flight path of the spacecraft from the solar system to fly over 6 stars in sequence. Table 1 gives the information about the fly-through sequence of this example "222". It can be seen from the table that the relative distances of the spacecraft flying over the 6 stars are less than 10-4 kpc, the relative speed is less than 300 km/s, which satisfies the constraint of flying state. Thus, the "222" fly-through sequence given in Table 1 is a multi-star fly-through sequence containing a "woodruff" fly-through segment that satisfies the fly-through state constraint.
TABLE 1 "222" fly-by sequence related information
Figure 405480DEST_PATH_IMAGE122
Example 3:
in this embodiment, the starting target is a solar system, and the position and the velocity at the initial time are [8.34 kpc, 0, 0] and [0, -256.41 km/s, 0], respectively. Where 1 kpc = 30856775814671900 km. The initial position and speed of the spacecraft is the same as the solar system.
The multi-star fly-over sequence searching method containing the 'one stone and multiple birds' fly-over segment in the embodiment comprises the following steps:
s1: the number of targets visited and pulses applied in the fly-by sequence for this search is given.
The fly-by sequence of this search is given by 5 accessed targets and 3 pulses.
S2: giving a pulse and a target arrangement mode according to the number of accessed targets and pulses, wherein the arrangement mode determines the number of the flying fragments in the sequence, the types of the flying fragments and the arrangement sequence;
the fly-by sequence of this search is given the type "032". Thus, the number of fly-through segments in the sequence is 2, the first being a two-pulse, three-star fly-through segment and the second being a single-pulse, two-star fly-through segment.
S3: a single-pulse two-star target search strategy and a two-pulse three-star target search strategy are respectively designed according to the method in S3 in embodiment 1.
S4: respectively establishing single-pulse double-star and two-pulse three-star fly-over trajectory planning models according to the method in S4 in embodiment 1, and designing a corresponding multi-star fly-over trajectory planning method.
S5: selecting a corresponding target search strategy in S3 according to the type of a given first flying fragment in S2 by taking the position and the speed of a starting target of the spacecraft as a current initial state, finding out a potential target combination, and obtaining a flying fragment meeting the constraint by adopting a corresponding multi-satellite flying trajectory planning method in S4;
the first flight segment given in S2 is a two-pulse three-star flight segment, so the two-pulse three-star target search strategy in S3 is selected to obtain three potential stars with numbers 2097, 49164, and 4478, and then the two-pulse three-star flight trajectory planning method is adopted to obtain the flight trajectories of stars with numbers 2097, 49164, and 4478.
S6: selecting a corresponding target search strategy in S3 according to the type of the next flying segment determined in S2 by taking the position and the speed of the last star in the last flying segment of the spacecraft as the current initial state, finding out a potential target combination, and obtaining the flying segment meeting the constraint by adopting a corresponding multi-star flying trajectory planning method in S4;
s7: s6 is repeated until a complete multi-satellite fly-through sequence is obtained.
And (3) taking the position and the speed of the spacecraft when flying through the 4478 # stars as the current position and speed, selecting a single-pulse double-star target search strategy in S3 to obtain two potential stars with numbers of 4855 and 36794 which can fly through simultaneously, and then obtaining the flying tracks of the stars with numbers of 4855 and 36794 simultaneously by adopting a single-pulse double-star flying track planning method. At this point, a complete "032" multi-satellite flyover sequence is searched.
Fig. 9 shows the flight path of the spacecraft from the solar system to the 5 stars in sequence. Table 2 shows the information related to the fly-through sequence of "032" in this example. It can be seen from the table that the relative distances of the spacecraft flying over the 5 stars are less than 10-4 kpc, the relative speed is less than 300 km/s, which satisfies the constraint of flying state. Thus, the "032" fly-through sequence given in Table 2 is a multi-star fly-through sequence containing a "rock-two bird" and a "rock-three bird" fly-through segment that satisfies the constraints of the fly-through state.
TABLE 2 "032" fly-by sequence related information
Figure 485431DEST_PATH_IMAGE123
In summary, although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made by those skilled in the art without departing from the spirit and scope of the invention.

Claims (10)

1. The method for searching the multi-star fly-over sequence containing the 'one stone and multiple birds' fly-over segment is characterized by comprising the following steps of:
s1: giving the number of access targets and applied pulses in the multi-satellite flying sequence searched at this time;
s2: giving pulses and an arrangement mode of the targets according to the number of the targets and the number of the pulses, and determining a multi-satellite flying sequence according to the arrangement mode of the targets, wherein the multi-satellite flying sequence comprises the number of flying fragments in the multi-satellite flying sequence, the type and the arrangement sequence of each flying fragment;
s3: selecting a corresponding flying target searching strategy according to the type of a first flying fragment in a multi-satellite flying sequence by taking the position and the speed of a starting target of the spacecraft as a current initial state, finding out a potential target combination, and obtaining a flying fragment by adopting a corresponding multi-satellite flying track planning method;
s4: selecting a corresponding flying target searching strategy according to the type of the next flying fragment in the multi-satellite flying sequence determined in S2 by taking the position and the speed of the last target in the last flying fragment when the spacecraft flies over as the current initial state, finding out a potential target combination, and obtaining the flying fragment by adopting a corresponding multi-satellite flying trajectory planning method;
s5: s4 is repeated until a complete multi-satellite fly-through sequence is obtained.
2. The method for searching the multi-star fly-over sequence containing the "one stone and multiple birds" fly-over segments according to claim 1, wherein in S1, the number of targets is greater than the number of pulses but not greater than twice the number of pulses.
3. The method for searching the multi-satellite flying sequence containing the 'one stone and multiple birds' flying fragment according to claim 1 or 2, wherein in S2, the given arrangement of the pulse and the target satisfies the following two constraints: 1) the number of targets between any two adjacent pulses is not more than 3; 2) if there are 3 consecutive targets, at least two consecutive pulses are scheduled before flying over the 3 consecutive targets.
4. The method for searching the multi-satellite flying sequence containing the 'one stone and multiple birds' flying fragment according to claim 3, wherein the flying target search strategy is divided into a single-pulse and double-satellite flying fragment flying target search strategy and a two-pulse and three-satellite flying fragment flying target search strategy, and if the flying target search strategy is the single-pulse and double-satellite flying fragment, the single-pulse and double-satellite flying fragment flying target search strategy is selected to find out a potential target combination; and if the two-pulsar flying fragment is the two-pulsar flying fragment, selecting a flying target search strategy of the two-pulsar flying fragment, and finding out a potential target combination.
5. The method for searching the multi-satellite flying sequence containing the 'one stone and multiple birds' flying fragment according to claim 4, wherein the method for searching the flying target search strategy of the single pulse and double-satellite flying fragment is as follows:
(1): randomly giving a sliding time
Figure 155865DEST_PATH_IMAGE001
Bringing the spacecraft from an initial state (r 0,v 0) Report onr 1,v 1) Wherein (a)r 0,v 0) For initial spacecraft position and velocity, (r 1,v 1) For the spacecraft to pass through a period of taxiing time
Figure 338585DEST_PATH_IMAGE002
The latter position and velocity;
(2): randomly giving a pulse
Figure 649480DEST_PATH_IMAGE003
And a period of time of coasting
Figure 310269DEST_PATH_IMAGE004
From the current state of the spacecraft (r 1,v 1) Report onr 2,v 2)，(r 2,v 2) For spacecraft from a current state (r 1,v 1) Time of sliding
Figure 390220DEST_PATH_IMAGE005
The latter position and velocity;
(3): computing
Figure 478262DEST_PATH_IMAGE006
Spacecraft and all access targets in a time periodAll the closest distances are collected to be less than a given upper limit valued maxAnd counting the number of the objects asn；
(4): if it isn< 2, return to (1);
(5): will be provided with
Figure 798426DEST_PATH_IMAGE007
And two targets with the minimum closest distance to the spacecraft in the time period are taken as potential flying target combinations.
6. The method for searching the multi-satellite flying sequence containing the 'one-stone multi-bird' flying fragment according to claim 4, wherein the method for searching the flying target of the two-pulse three-satellite flying fragment comprises the following steps:
(1): randomly giving a sliding time
Figure 528485DEST_PATH_IMAGE008
Bringing the spacecraft from an initial state (r 0,v 0) Report onr 1,v 1) Wherein (a)r 0,v 0) For initial spacecraft position and velocity, (r 1,v 1) For the spacecraft to pass through a period of taxiing time
Figure 728522DEST_PATH_IMAGE008
The latter position and velocity;
(2): randomly giving a pulse
Figure 987465DEST_PATH_IMAGE009
And a period of time of coasting
Figure 272953DEST_PATH_IMAGE010
From the current state of the spacecraft (r 1,v 1) Report onr 2,v 2)，(r 2,v 2) For spacecraft from a current state (r 1,v 1) Time of sliding
Figure 275544DEST_PATH_IMAGE010
The latter position and velocity;
(3): randomly giving a pulse
Figure 64508DEST_PATH_IMAGE011
And a period of time of coasting
Figure 759932DEST_PATH_IMAGE012
From the current state of the spacecraft (r 2,v 2) Report onr 3,v 3)，(r 3,v 3) For spacecraft from a current state (r 2,v 2) Time of sliding
Figure 532716DEST_PATH_IMAGE012
The latter position and velocity;
(4): computing
Figure 73419DEST_PATH_IMAGE012
Collecting the closest distances between the spacecraft and all the access targets in the time period, wherein all the closest distances are less than a given upper limit valued maxAnd counting the number of the objects asn；
(5): if it isn< 3, return to (1);
(6): will be provided with
Figure 982469DEST_PATH_IMAGE013
And three targets with the minimum closest distance to the spacecraft in the time period are taken as potential flying target combinations.
7. The method for searching the multi-satellite fly-over sequence containing the 'one stone and multiple birds' fly-over segment according to claim 4, 5 or 6, wherein the multi-satellite fly-over trajectory planning method is divided into a single-pulse two-satellite fly-over trajectory planning method and a two-pulse three-satellite fly-over trajectory planning method, if the multi-satellite fly-over trajectory planning method is the single-pulse two-satellite fly-over segment, the single-pulse two-satellite fly-over trajectory planning method is selected to obtain the fly-over segment satisfying the constraint, and if the multi-satellite fly-over trajectory planning method is the two-pulse three-satellite fly-over segment, the two-pulse three-satellite fly-over trajectory planning method is selected to obtain the fly.
8. The method for searching the multi-satellite flying sequence containing the 'one stone and multiple birds' flying fragment according to claim 7, wherein the method for planning the single-pulse and double-satellite flying trajectory comprises the following steps:
(1): constructing a four-pulse double-satellite intersection track optimization model;
the design variables of the four-pulse double-star rendezvous trajectory optimization model are as follows:
Figure 350258DEST_PATH_IMAGE014
Figure 344759DEST_PATH_IMAGE015
wherein the content of the first and second substances,dt 1the time for the spacecraft to wait on the initial orbit;dt 2the time for the spacecraft to transfer from the initial orbit to the first access target by two pulses;dt 3the time for the spacecraft to transfer from a first target to a second target by two pulses; the spacecraft does not stay on the first target of access, so the two pulses in the middle are applied at the same time; is provided witht 0At the initial moment, the moment when the spacecraft applies the first pulset 1The moment of application of the second and third pulsest 2And the moment of application of the fourth pulset 3Comprises the following steps:
Figure 689153DEST_PATH_IMAGE016
Figure 718289DEST_PATH_IMAGE017
the four-pulse double-star rendezvous trajectory optimization model comprises three types of constraints, wherein the first type of constraint is pulse velocity increment constraint:
Figure 21094DEST_PATH_IMAGE018
Figure 237312DEST_PATH_IMAGE019
in the formula (I), the compound is shown in the specification,
Figure 385396DEST_PATH_IMAGE020
the first pulse to be applied for the spacecraft,
Figure 3460DEST_PATH_IMAGE021
an upper limit for single pulse speed increment;
the second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
Figure 477166DEST_PATH_IMAGE022
Figure 180680DEST_PATH_IMAGE023
in the formula (I), the compound is shown in the specification,r 0(t 2) Andr 1(t 2) Respectively for the spacecraft and the first access targett 2A position vector of a time;r 0(t 3) Andr 2(t 3) Respectively for the spacecraft and the second access targett 3A position vector of a time;
the third type of constraint is the relative velocity constraint between the spacecraft at the meeting time and the access target:
Figure 866876DEST_PATH_IMAGE024
Figure 870604DEST_PATH_IMAGE025
in the formula (I), the compound is shown in the specification,v 0(t 2) Andv 1(t 2) Respectively for the spacecraft and the first access targett 2A velocity vector of a time of day;v 0(t 3) Andv 2(t 3) Respectively for the spacecraft and the second access targett 3A velocity vector of a time of day;
Figure 13748DEST_PATH_IMAGE026
a fourth pulse applied to the spacecraft for an encounter with a second access target,dv maxthe maximum relative speed allowed when the spacecraft flies over the target;
the objective function of the four-pulse two-star rendezvous trajectory optimization model is a model for minimizing the sum of two pulse vectors in the middle:
Figure 204557DEST_PATH_IMAGE027
Figure 694445DEST_PATH_IMAGE028
in the formula (I), the compound is shown in the specification,
Figure 287100DEST_PATH_IMAGE029
and
Figure 837030DEST_PATH_IMAGE030
are respectively spacecraftst 2Two pulses applied at a time to meet and aim at a first accessed target;
(2): adopting a rendezvous trajectory optimization transition method to transition the four-pulse double-star rendezvous trajectory to a single-pulse double-star flying trajectory;
in the flight process of a spacecraft intersecting two targets through four pulses, the spacecraft, a first access target and a second access target are at the initial momentt 0Are in the state of [ 2 ]r 0(t 0),v 0(t 0)]、[r 1(t 0),v 1(t 0)]And 2r 2(t 0),v 2(t 0)]，[r 0(t 0),v 0(t 0)]、[r 1(t 0),v 1(t 0)]And 2r 2(t 0),v 2(t 0)]Respectively representing the spacecraft, the first access target and the second access target at the initial momentt 0A position vector and a velocity vector of;
for any given set of design variablesdt 1,dt 2,dt 3]First, it is necessary to set the states of the spacecraft and the two access targets to the values of [ 2 ]r 0(t 0),v 0(t 0)]、[r 1(t 0),v 1(t 0)]And 2r 2(t 0),v 2(t 0)]Respectively predict the value of [ 2 ]r 0(t 1),v 0(t 1)]、[r 1(t 2),v 1(t 2)]And 2r 2(t 3),v 2(t 3)]Then adopting Lambert algorithm to respectively solver 0(t 1) Tor 1(t 2) Andr 1(t 2) Tor 2(t 3) Two sections of two pulses between the two pulse crossing tracks obtain 4 pulses required by the crossing
Figure 780715DEST_PATH_IMAGE031
~
Figure 74293DEST_PATH_IMAGE032
(ii) a Optimizing and adjusting the value of the design variable through an evolutionary algorithm to continuously reduce the formula (6) to 0 and cancel
Figure 521455DEST_PATH_IMAGE033
~
Figure 242287DEST_PATH_IMAGE034
The four-pulse two-star rendezvous trajectory can be successfully transited into a single-pulse two-star flying trajectory.
9. The method for searching the multi-satellite flying sequence containing the 'one stone and multiple birds' flying fragment according to claim 8, wherein the two-pulse three-satellite flying trajectory planning method comprises:
(1): constructing a seven-pulse three-star rendezvous trajectory optimization model;
the design variables of the seven-pulse three-star rendezvous trajectory optimization model are as follows:
Figure 407689DEST_PATH_IMAGE035
Figure 239378DEST_PATH_IMAGE036
wherein the content of the first and second substances,dt 1the time for the spacecraft to wait on the initial orbit;dt 2time of flight after application of the first pulse to the spacecraft;dt 3the time for the spacecraft to transition from the transition orbit to the first access target by two pulses;dt 4the time for the spacecraft to transfer from a first target to a second target by two pulses;dt 5the time for the spacecraft to transition from the second access target to the third access target by two pulses;
Figure 839249DEST_PATH_IMAGE037
is the first pulse; the spacecraft does not stay on the first access target and the second access target, so that the third pulse and the fourth pulse are applied at the same time, and the fifth pulse and the sixth pulse are also applied at the same time; is provided witht 0The initial time is the time when the spacecraft applies each pulse as follows:
Figure 465403DEST_PATH_IMAGE038
Figure 383680DEST_PATH_IMAGE039
wherein the content of the first and second substances,t 1andt 2first and second pulse application times, respectively;t 3a third and fourth pulse application time;t 4a fifth, sixth pulse application time;t 5a seventh pulse application time;
the seven-pulse three-star rendezvous trajectory optimization model comprises three types of constraints; the first type is the pulse velocity increment constraint:
Figure 19061DEST_PATH_IMAGE040
Figure 440815DEST_PATH_IMAGE041
in the formula (I), the compound is shown in the specification,
Figure 503449DEST_PATH_IMAGE042
and
Figure 643443DEST_PATH_IMAGE043
first and second pulses, respectively;
the second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
Figure 82515DEST_PATH_IMAGE044
Figure 624355DEST_PATH_IMAGE045
in the formula (I), the compound is shown in the specification,r 0(t 3) Andr 1(t 3) Respectively for the spacecraft and the first access targett 3A position vector of a time;r 0(t 4) Andr 2(t 4) Respectively for the spacecraft and the second access targett 4A position vector of a time;r 0(t 5) Andr 3(t 5) Respectively for the spacecraft and the third access targett 5A position vector of a time;
the third type of constraint is the relative velocity constraint between the spacecraft at the meeting time and the access target:
Figure 857890DEST_PATH_IMAGE046
Figure 219601DEST_PATH_IMAGE047
in the formula (I), the compound is shown in the specification,v 0(t 3) Andv 1(t 3) Respectively for the spacecraft and the first access targett 3A velocity vector of a time of day;v 0(t 4) Andv 2(t 4) Respectively for the spacecraft and the second access targett 4A velocity vector of a time of day;v 0(t 5) Andv 3(t 5) Respectively for the spacecraft and the third access targett 5A velocity vector of a time of day;
Figure 960899DEST_PATH_IMAGE048
a seventh pulse applied to the spacecraft for intersecting the third access target;
the objective function of the seven-pulse three-star intersection trajectory optimization model is a model for minimizing the sum of the third and fourth pulse vectors and the sum of the fifth and sixth pulse vectors:
Figure 91666DEST_PATH_IMAGE049
Figure 496102DEST_PATH_IMAGE050
in the formula (I), the compound is shown in the specification,
Figure 610689DEST_PATH_IMAGE051
and
Figure 125984DEST_PATH_IMAGE052
are respectively spacecraftst 3Two pulses applied at a time to meet and aim at a first accessed target;
Figure 376836DEST_PATH_IMAGE053
and
Figure 217754DEST_PATH_IMAGE054
are respectively spacecraftst 4Two pulses applied at a time to meet and aim at a second accessed target;
(2): adopting a rendezvous trajectory optimization transition method to transition the rendezvous trajectory of the seven-pulse three-star to a two-pulse three-star flying trajectory;
for any given set of design variablesdt 1,dt 2,dt 3,dt 4,dt 5]First, it is necessary to predict the spacecraft and the three access targets from the initial states separatelyr 0(t 2),v 0(t 2)]、[r 1(t 3),v 1(t 3)]、[r 2(t 4),v 2(t 4)]And 2r 3(t 5),v 3(t 5)]Then adopting Lambert algorithm to respectively solver 0(t 2) Tor 1(t 3)、r 1(t 3) Tor 2(t 4) Andr 2(t 4) Tor 3(t 5) Three-section two-pulse intersection track between the two pulses to obtain six pulses required by intersection
Figure 554057DEST_PATH_IMAGE055
~
Figure 873043DEST_PATH_IMAGE056
(ii) a Optimizing and adjusting the value of the design variable through an evolutionary algorithm to continuously reduce the value of the formula (12) to 0 and cancel
Figure 243981DEST_PATH_IMAGE057
~
Figure 990220DEST_PATH_IMAGE058
And successfully transitioning the seven-pulse three-star rendezvous trajectory into a two-pulse three-star flying trajectory.
10. The multi-satellite flying sequence search system comprising a "stone and multi-bird" flying segment comprises a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to realize the steps of the multi-satellite flying sequence search method comprising the "stone and multi-bird" flying segment according to claim 1.
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