CN112231943A - 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 PDFInfo
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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
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 timeBringing 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 timeThe latter position and velocity;
(2): randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe rear position andspeed;
(3): computingCollecting 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): will be provided withAnd 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 timeBringing 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 timeThe latter position and velocity;
(2): randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe latter position and velocity;
(3): randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe latter position and velocity;
(4): computingCollecting 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;
(6): will be provided withAnd 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:
wherein,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:
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:
in the formula,the first pulse to be applied for the spacecraft,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:
in the formula,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:
in the formula,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;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:
in the formula,andare 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 variablesFirst, 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~(ii) a Optimizing tunes by evolutionary algorithmThe value of the whole design variable continuously reduces the formula (6) until the value is reduced to 0 and is cancelled~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:
wherein,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;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:
wherein,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:
The second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
in the formula,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:
in the formula,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;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:
in the formula,andare respectively spacecraftst 3Two pulses applied at a time to meet and aim at a first accessed target;andare respectively spacecraftst 4Two pulses are 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 sections in betweenThe pulse meeting track obtains six pulses required by meeting~(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~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'.
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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. The starting time of the flying fragment is the time of flying the last target in the last flying fragment, and the terminal time of the flying fragment is the time of flying the last target in 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,toIs a single-pulse single-star flying segment,toIs a single-pulse double-star flying segment,toIs 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 timeBringing 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 timeThe latter position and velocity.
S30102: randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe latter position and velocity.
S30103: computingCollecting 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 withAnd 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 timeBringing 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 timeThe latter position and velocity.
S30202: randomly giving a pulseAnd a period of time of coastingFrom the current state of the spacecraft (r 1,v 1) Report onr 2,v 2),(r 2,v 2) Is composed ofSpacecraft from the current state (r 1,v 1) Time of slidingThe latter position and velocity.
S30203: randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe latter position and velocity.
S30204: computingCollecting 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 withAnd 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:
wherein,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:
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:
in the formula,the first pulse to be applied for the spacecraft,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:
in the formula,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:
in the formula,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;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:
in the formula,andare 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,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 momentAre 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 designsVariable [ 2 ]dt 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. Optimizing and adjusting the value of the design variable through an evolutionary algorithm to continuously reduce the formula (6) to 0 and cancelThe 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:
wherein,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;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:
wherein,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:
The second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
in the formula,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:
in the formula,v 0(t 3) Andv 1(t 3) Respectively for the spacecraft and the first access targett 3Velocity of time of dayA vector;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;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:
in the formula,andare respectively spacecraftst 3Two pulses applied at a time for meeting with the access target 1 and aiming at the access target 2;andare 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,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~(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~Then the seven-pulse three-star rendezvous trajectory is successfully transited intoTwo-pulse three-star fly-over 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
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
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 timeBringing 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 timeThe latter position and velocity;
(2): randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe latter position and velocity;
(3): computingCollecting 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 isn< 2, return to (1);
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 timeBringing the spacecraft from an initial state (r 0,v 0) Report onr 1,v 1) Wherein (a)r 0,v 0) To make voyageInitial antenna position and velocity: (r 1,v 1) For the spacecraft to pass through a period of taxiing timeThe latter position and velocity;
(2): randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe latter position and velocity;
(3): randomly giving a pulseAnd a period of time of coastingFrom 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 slidingThe latter position and velocity;
(4): computingCollecting 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);
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:
wherein,dt 1for spacecraft in initial orbitTime of upper wait;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:
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:
in the formula,the first pulse to be applied for the spacecraft,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:
in the formula,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:
in the formula,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;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:
in the formula,andare 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~(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~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:
wherein,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;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:
wherein,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:
the second type of constraint is a relative position constraint between the spacecraft at the meeting time and the access target:
in the formula,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:
in the formula,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;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:
in the formula,andare respectively spacecraftst 3Two for meeting a first access target and aiming a second access target applied at a timePulsing;andare 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~(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~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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CN115877370A (en) * | 2023-03-08 | 2023-03-31 | 中国西安卫星测控中心 | Method for rapidly calculating spacecraft orbit by using double radar distances and azimuth angles |
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CN118428117A (en) * | 2024-07-02 | 2024-08-02 | 中国人民解放军国防科技大学 | Giant constellation fly-over optimization method and system based on minimum phase adjustment |
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