CN112231943A - Multi-star fly-over sequence searching method and system containing 'one stone and multiple birds' fly-over segments - Google Patents

Abstract

Multi-star flyby sequence search method and system including "one stone, many birds" flyby segment, given the number of targets and applied pulses in the flyby sequence, and given an arrangement of pulses and targets; design single-pulse double stars and two-pulse triple stars Target search strategy; establish single-pulse double-star and two-pulse three-star flyby trajectory planning models, and design the corresponding multi-star flyby trajectory planning method; select the corresponding target search strategy according to the type of the first flyby segment to find out potential target combinations, And obtain the fly-by segment; repeat the process of selecting the corresponding target search strategy according to the type of the next fly-by segment, find out potential target combinations, and obtain the fly-by segment until all the fly-by segments are searched. This method can find out the target combination that meets the conditions of multi-star flyby from a large number of candidate targets, plan the corresponding pulse flyby trajectory, and obtain the multi-star flyby sequence including the flyby segment of "one stone, many birds".

Description

Multi-star flyby sequence search method and system including "one stone, many birds" flyby segment

technical field

The invention belongs to the field of spacecraft flight mission planning, and in particular relates to a method and a system for searching for a multi-pulse multi-star flyby sequence.

Background technique

Multi-satellite flyby sequence planning is a typical problem in multi-objective access mission planning. Including multi-satellite approaching reconnaissance missions and multi-asteroid flyby observation missions, etc. can be considered for the multi-satellite flyby sequence planning problem.

In the traditional multi-pulse multi-star flyby sequence planning problem, the number of pulses that can be applied is usually larger than the number of visited targets. After completing the flyover of the previous target, at least one pulse can be applied to target the next target. The mathematical properties of this kind of problem are similar to the multi-satellite rendezvous sequence programming problem, and the difficulty of solving it mainly lies in the optimization of the access order. However, when the number of maneuvers is limited and the number of pulses that can be applied is less than the number of access targets, there will be no pulses between two adjacent access targets in the flyover sequence, that is, one pulse needs to be aimed at two or more targets at the same time. Happening. In this case, the difficulty of solving is no longer the optimization of the access order, but how to search for the target combination that satisfies the conditions of single-pulse multi-star flyby from the large-scale candidate targets, and then obtain the flyby sequence with the flyby segment of "multiple birds with one stone". . Among them, the flyover segment is defined as the flight trajectory formed by the spacecraft starting from the current target and flying over one or multiple targets at the same time through one or two pulses.

The multi-satellite fly-by sequence search with fly-by segments of "one stone, many birds" needs to solve the multi-satellite fly-by trajectory planning problem first. The traditional pulse flyover trajectory planning method is usually to first obtain a pulse intersection solution, and then release the pulse at the intersection terminal to obtain the corresponding flyover solution. This method can only be used for the flyover trajectory planning of a single target, and cannot achieve simultaneous flyover of multiple targets with one pulse. In addition, there is no effective method to quickly find out the target combination that satisfies the multi-star flyby conditions.

SUMMARY OF THE INVENTION

In view of the defects existing in the prior art, the present invention provides a method and system for searching a multi-star flyby sequence containing "one stone, many birds" flyby segments. This method can quickly find out the target combination that satisfies the conditions of multi-star flyby from a large number of candidate targets, plan the corresponding pulse flyby trajectory, and then obtain the multi-star flyby sequence containing the flyby segment of "one stone, many birds". This method can provide effective technical support for multi-star flyby sequence search for large-scale targets.

For realizing the above-mentioned technical purpose, the technical scheme of the present invention is:

The multi-star flyby sequence search method with flyby fragments of "one stone, many birds" includes the following steps:

S1: The number of visited targets and applied pulses in the multi-satellite flyby sequence given this search;

S2: The arrangement of pulses and targets is given according to the number of targets and pulses, and the multi-satellite flyby sequence is determined by the arrangement of the targets, including the number of flyby segments in the multi-satellite flyby sequence, the type and arrangement order of each flyby segment;

S3: Take the position and speed of the departure target of the spacecraft as the current initial state, select the corresponding fly-by target search strategy according to the type of the first fly-by segment in the multi-star fly-by sequence, find out potential target combinations, and use the corresponding multi-star fly-by sequence. Star flyby trajectory planning method obtains flyby segments satisfying constraints;

S4: Take the position and speed of the last target in the last flyby segment of the spacecraft as the current initial state, select the corresponding flyby target search strategy according to the type of the next flyby segment in the multi-star flyby sequence determined in S2, and find out Potential target combinations, and use the corresponding multi-star flyby trajectory planning method to obtain flyby segments that meet the constraints;

S5: Repeat S4 until a complete multi-star flyby sequence is obtained.

As a preferred solution of the present invention, 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.

As a preferred solution of the present invention, in S2 of the present invention, the arrangement of a given pulse and target must satisfy the following two constraints: 1) the number of targets between any two adjacent pulses does not exceed 3; 2) if If there are 3 consecutive targets, at least two consecutive pulses are scheduled before flying over the 3 consecutive targets.

As a preferred solution of the present invention, the fly-by target search strategy of the present invention is divided into a fly-by target search strategy of a single-pulse double-star fly-by segment and a fly-by target search strategy of a two-pulse three-star fly-by segment. The fly-by target search strategy of the fly-by segment is used to find potential target combinations; if it is a two-pulse three-star fly-by segment, the fly-by target search strategy of the two-pulse three-star fly-by segment is selected to find potential target combinations.

As a preferred solution of the present invention, the search method of the fly-by target search strategy of the single-pulse double-star fly-by segment is as follows:

，将航天器从初始状态(r ₀,v ₀)预报到(r ₁,v ₁)，其中(r ₀,v ₀)为航天器初始位置和速度，(r ₁,v ₁)为航天器经过一段滑行时间

后的位置和速度；(1): Randomly give a taxiing time

, predict the spacecraft from the initial state ( r ₀ , v ₀ ) to ( r ₁ , v ₁ ), where ( r ₀ , v ₀ ) is the initial position and velocity of the spacecraft, and ( r ₁ , v ₁ ) is the spacecraft after a glide time

rear position and velocity;

和一段滑行时间

，将航天器从当前状态(r ₁,v ₁)预报到(r ₂,v ₂)，(r ₂,v ₂)为航天器从当前状态(r ₁,v ₁)经过滑行时间

后的位置和速度；(2): Randomly give a pulse

and a glide time

, predicts the spacecraft from the current state ( r ₁ , v ₁ ) to ( r ₂ , v ₂ ), and ( r ₂ , v ₂ ) is the taxiing time of the spacecraft from the current state ( r ₁ , v ₁ )

rear position and velocity;

时间段内航天器与所有访问目标的最近距离，收集所有最近距离小于给定上限值d _max的目标并统计这些目标的个数记为n；(3): Calculation

The shortest distance between the spacecraft and all the visited targets in the time period, collect all the targets whose shortest distance is less than the given upper limit value d _max and count the number of these targets as n ;

，返回（1）；(4): If

, return (1);

时间段内与航天器最近距离最小的两个目标作为潜在飞越目标组合。(5): will

The two targets with the shortest distance to the spacecraft in the time period are used as a combination of potential overflight targets.

As a preferred solution of the present invention, the search method of the fly-by target search strategy of the two-pulse three-star fly-by segment is as follows:

，将航天器从初始状态(r ₀,v ₀)预报到(r ₁,v ₁)，其中(r ₀,v ₀)为航天器初始位置和速度，(r ₁,v ₁)为航天器经过一段滑行时间

后的位置和速度；(1): Randomly give a taxiing time

, predict the spacecraft from the initial state ( r ₀ , v ₀ ) to ( r ₁ , v ₁ ), where ( r ₀ , v ₀ ) is the initial position and velocity of the spacecraft, and ( r ₁ , v ₁ ) is the spacecraft after a glide time

rear position and velocity;

和一段滑行时间

，将航天器从当前状态(r ₁,v ₁)预报到(r ₂,v ₂)，(r ₂,v ₂)为航天器从当前状态(r ₁,v ₁)经过滑行时间

后的位置和速度；(2): Randomly give a pulse

and a glide time

, predicts the spacecraft from the current state ( r ₁ , v ₁ ) to ( r ₂ , v ₂ ), and ( r ₂ , v ₂ ) is the taxiing time of the spacecraft from the current state ( r ₁ , v ₁ )

rear position and velocity;

和一段滑行时间

，将航天器从当前状态(r ₂,v ₂)预报到(r ₃,v ₃)，(r ₃,v ₃)为航天器从当前状态(r ₂,v ₂)经过滑行时间

后的位置和速度；(3): Randomly give a pulse

and a glide time

, predicts the spacecraft from the current state ( r ₂ , v ₂ ) to ( r ₃ , v ₃ ), and ( r ₃ , v ₃ ) is the taxiing time of the spacecraft from the current state ( r ₂ , v ₂ )

rear position and velocity;

时间段内航天器与所有访问目标的最近距离，收集所有最近距离小于给定上限值d _max的目标并统计这些目标的个数记为n；(4): Calculation

The shortest distance between the spacecraft and all the visited targets in the time period, collect all the targets whose shortest distance is less than the given upper limit value d _max and count the number of these targets as n ;

，返回（1）；(5): If

, return (1);

时间段内与航天器最近距离最小的三个目标作为潜在飞越目标组合。(6): will

The three targets with the shortest distance to the spacecraft in the time period are used as a combination of potential overflight targets.

As a preferred solution of the present invention, the multi-star flyby trajectory planning method is divided into a single-pulse double-star flyby trajectory planning method and a two-pulse three-star flyby trajectory planning method. For the constrained flyover segment, if it is a two-pulse three-star flyby segment, select the two-pulse three-star flyby trajectory planning method to obtain a flyby segment that satisfies the constraint.

As a preferred solution of the present invention, the single-pulse binary star flyby trajectory planning method includes:

(1): Construct a four-pulse binary star rendezvous trajectory optimization model;

The design variables of the four-pulse binary star rendezvous trajectory optimization model are:

Among them, dt ₁ is the waiting time of the spacecraft on the initial orbit; dt ₂ is the time when the spacecraft transfers from the initial orbit to the first visiting target through two pulses; dt ₃ is the time when the spacecraft passes two pulses from the first visiting target Time to transfer to the second visit target; the spacecraft does not stop on the first visit target, so the two pulses in the middle are applied at the same time; let t ₀ be the initial time, the time when the spacecraft applies the first pulse t ₁ , time t ₂ when the second and third pulses are applied, and time t ₃ when the fourth pulse is applied are:

The four-pulse binary star rendezvous trajectory optimization model includes three types of constraints. The first type of constraints is the pulse velocity increment constraint:

为航天器施加的第一个脉冲，

为单个脉冲速度增量上限。In the formula,

the first pulse applied to the spacecraft,

It is the upper limit of single pulse speed increment.

The second type of constraint is the relative position constraint between the spacecraft at the moment of rendezvous and the visiting target:

In the formula, r ₀ ( t ₂ ) and r ₁ ( t ₂ ) are the position vectors of the spacecraft and the first visited target at time t ₂ , respectively; r ₀ ( t ₃ ) and r ₂ ( t ₃ ) are the aerospace The position vector _of the controller and the second access target at time t3 .

The third type of constraint is the relative velocity constraint between the spacecraft at the moment of rendezvous and the visiting target:

为航天器施加的用于与第二个访问目标交会的第四个脉冲，dv _max为航天器飞越目标时允许的最大相对速度。where v ₀ ( t ₂ ) and v ₁ ( t ₂ ) are the velocity vectors of the spacecraft and the first visiting target at time t ₂ , respectively; v ₀ ( t ₃ ) and v ₂ ( t ₃ ) are the the velocity vector of the controller and the second visiting target at time t3 _;

The fourth pulse applied to the spacecraft for rendezvous with the second visiting target, dv _max is the maximum relative velocity allowed for the spacecraft to fly over the target.

The objective function of the four-pulse binary star rendezvous trajectory optimization model is to minimize the modulus of the vector sum of the two intermediate pulses:

和

分别为航天器在t ₂时刻施加的用于与第一个访问目标交会和瞄准第二个访问目标的两个脉冲。In the formula,

and

are the two pulses applied by the spacecraft at time t ₂ for rendezvous with the first visiting target and aiming at the second visiting target, respectively.

(2): Using the rendezvous trajectory optimization transition method to transition the four-pulse binary star rendezvous trajectory to the single-pulse double star flyby trajectory;

During the flight of the spacecraft to meet the two targets through four pulses, the states of the spacecraft, the first visiting target and the second visiting target at the initial time t ₀ are [ r ₀ ( t ₀ ), v ₀ ( t ₀ )], [ r ₁ ( t ₀ ), v ₁ ( t ₀ )] and [ r ₂ ( t ₀ ), v ₂ ( t ₀ )], [ r ₀ ( t ₀ ), v ₀ ( t ₀ )] , [ r ₁ ( t ₀ ), v ₁ ( t ₀ )] and [ r ₂ ( t ₀ ), v ₂ ( t ₀ )] represent the spacecraft, the first visit target and the second visit target at the initial The position vector and velocity vector at time t ₀ .

，首先需要将航天器和两个访问目标的状态由[r ₀(t ₀), v ₀(t ₀)]、[r ₁(t ₀), v ₁(t ₀)]和[r ₂(t ₀), v ₂(t ₀)]分别预报到[r ₀(t ₁), v ₀(t ₁)]、[r ₁(t ₂), v ₁(t ₂)]和[r ₂(t ₃), v ₂(t ₃)]，然后采用Lambert算法分别求解r ₀(t ₁)至r ₁(t ₂)和r ₁(t ₂)至r ₂(t ₃)之间的两段两脉冲交会轨迹，获得交会所需的4个脉冲

~

；通过进化算法优化调整设计变量的取值使式（6）不断减小直至降为0并取消

~

，则四脉冲双星交会轨迹可成功过渡为单脉冲双星飞越轨迹。For any given set of design variables

, the state of the spacecraft and the two visiting targets needs to be divided by [ r ₀ ( t ₀ ), v ₀ ( t ₀ )], [ r ₁ ( t ₀ ), v ₁ ( t ₀ )] and [ r ₂ ( t ₀ ), v ₂ ( t ₀ )] respectively predict [ r ₀ ( t ₁ ), v ₀ ( t ₁ )], [ r ₁ ( t ₂ ), v ₁ ( t ₂ )] and [ r ₂ ( t ₃ ), v ₂ ( t ₃ )], and then use Lambert's algorithm to solve the two segments between r ₀ ( t ₁ ) to r ₁ ( t ₂ ) and r ₁ ( t ₂ ) to r ₂ ( t ₃ ), respectively The two pulses intersect the trajectory to obtain the 4 pulses required for the intersection

~

; Optimize and adjust the value of the design variables through the evolutionary algorithm, so that the formula (6) is continuously reduced until it is reduced to 0 and canceled

~

, then the rendezvous trajectory of the four-pulse binary star can be successfully transitioned to the flyby trajectory of the single-pulse binary star.

As a preferred solution of the present invention, the two-pulse three-star flyover trajectory planning method includes:

(1): Build a seven-pulse Samsung rendezvous trajectory optimization model;

The design variables of the seven-pulse Samsung rendezvous trajectory optimization model are:

为第一个脉冲；航天器在第一个访问目标和第二个访问目标上都不作停留，因而第三、第四个脉冲在同一时刻施加，第五、第六个脉冲也在同一时刻施加；设t ₀为初始时刻，则航天器施加各次脉冲的时刻为：Among them, dt ₁ is the waiting time of the spacecraft on the initial orbit; dt ₂ is the flight time after the spacecraft applies the first pulse; dt ₃ is the time when the spacecraft transfers from the transition orbit to the first access target through two pulses ; dt ₄ is the time for the spacecraft to transfer from the first access target to the second access target by two pulses; dt ₅ is the time for the spacecraft to transfer from the second access target to the third access target by two pulses;

is the first pulse; the spacecraft does not stop on the first visit target and the second visit target, so the third and fourth pulses are applied at the same time, and the fifth and sixth pulses are also applied at the same time ; Let t ₀ be the initial moment, then the moment when the spacecraft applies each pulse is:

Among them, t ₁ and t ₂ are the moment of applying the first and second pulses respectively; t ₃ is the moment of applying the third and fourth pulses; t ₄ is the moment of applying the fifth and sixth pulses; t ₅ is the moment of applying the seventh pulse pulse application time.

The seven-pulse Samsung rendezvous trajectory optimization model includes three kinds of constraints. The first type is the pulse velocity increment constraint:

和

分别为第一个和第二个脉冲。In the formula,

and

are the first and second pulses, respectively.

The second type of constraint is the relative position constraint between the spacecraft at the moment of rendezvous and the visiting target:

In the formula, r ₀ ( t ₃ ) and r ₁ ( t ₃ ) are the position vectors of the spacecraft and the first visited target at time t ₃ , respectively; r ₀ ( t ₄ ) and r ₂ ( t ₄ ) are the aerospace are the position vectors of the spacecraft and the second visiting target at time t ₄ ; r ₀ ( t ₅ ) and r ₃ ( t ₅ ) are the position vectors of the spacecraft and the third visiting target at time t ₅ , respectively.

The third type of constraint is the relative velocity constraint between the spacecraft at the moment of rendezvous and the visiting target:

为航天器施加的用于与第三个访问目标交会的第七个脉冲。In the formula, v ₀ ( t ₃ ) and v ₁ ( t ₃ ) are the velocity vectors of the spacecraft and the first visiting target at time t ₃ , respectively; v ₀ ( t ₄ ) and v ₂ ( t ₄ ) are the the velocity vectors of the spacecraft and the second visiting target at time t ₄ ; v ₀ ( t ₅ ) and v ₃ ( t ₅ ) are the velocity vectors of the spacecraft and the third visiting target at time t ₅ , respectively;

The seventh pulse applied to the spacecraft for rendezvous with the third visiting target.

The objective function of the seven-pulse three-star intersection trajectory optimization model is to minimize the modulo of the third and fourth pulse vector sums and the fifth and sixth pulse vector sums:

和

分别为航天器在t ₃时刻施加的用于与第一个访问目标交会和瞄准第二个访问目标的两个脉冲；

和

分别为航天器在t ₄时刻施加的用于与第二个访问目标交会和瞄准第三个访问目标的两个脉冲。In the formula,

and

are the _two pulses applied by the spacecraft at time t3 for rendezvous with the first visiting target and aiming at the second visiting target;

and

are the two pulses applied by the spacecraft at time t4 for _rendezvous with the second visit target and aiming at the third visit target, respectively.

(2): Using the rendezvous trajectory optimization transition method to transition the seven-pulse three-star intersection trajectory to the two-pulse three-star flyover trajectory;

~

；通过进化算法优化调整设计变量的取值使式（12）的值不断减小直至降为0并取消

~

，则七脉冲三星交会轨迹成功过渡为两脉冲三星飞越轨迹。For any given set of design variables [ dt ₁ , dt ₂ , dt ₃ , dt ₄ , dt ₅ ], it is necessary to first predict the spacecraft and the three visit targets from the initial state to [ r ₀ ( t ₂ ), v ₀ ( t ₂ )], [ r ₁ ( t ₃ ), v ₁ ( t ₃ )], [ r ₂ ( t ₄ ), v ₂ ( t ₄ )], and [ r ₃ ( t ₅ ), v ₃ ( t ₅ )], and then use the Lambert algorithm to solve r ₀ ( t ₂ ) to r ₁ ( t ₃ ), r ₁ ( t ₃ ) to r ₂ ( t ₄ ) and r ₂ ( t ₄ ) to r ₃ ( t ₅ ) The three-segment two-pulse rendezvous trajectory between the three segments to obtain the six pulses required for the rendezvous

~

; Optimize and adjust the value of design variables through evolutionary algorithm to make the value of formula (12) decrease continuously until it drops to 0 and cancel

~

, then the seven-pulse three-star intersection trajectory successfully transitions to the two-pulse three-star flyover trajectory.

The present invention also provides a multi-satellite fly-by sequence search system with fly-by segments of "one stone, many birds", comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the following steps when executing the computer program :

S1: The number of visited targets and applied pulses in the multi-satellite flyby sequence given this search;

S2: The arrangement of pulses and targets is given according to the number of targets and pulses, and the multi-satellite flyby sequence is determined by the arrangement of the targets, including the number of flyby segments in the multi-satellite flyby sequence, the type and arrangement order of each flyby segment;

S3: Take the position and speed of the departure target of the spacecraft as the current initial state, select the corresponding fly-by target search strategy according to the type of the first fly-by segment in the multi-star fly-by sequence, find out potential target combinations, and use the corresponding multi-star fly-by sequence. Star flyby trajectory planning method obtains flyby segments satisfying constraints;

S4: Take the position and speed of the last target in the last flyby segment of the spacecraft as the current initial state, select the corresponding flyby target search strategy according to the type of the next flyby segment in the multi-star flyby sequence determined in S2, and find out Potential target combinations, and use the corresponding multi-star flyby trajectory planning method to obtain flyby segments that meet the constraints;

S5: Repeat S4 until a complete multi-star flyby sequence is obtained.

A computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented:

S1: The number of visited targets and applied pulses in the multi-satellite flyby sequence given this search;

S2: The arrangement of pulses and targets is given according to the number of targets and pulses, and the multi-satellite flyby sequence is determined by the arrangement of the targets, including the number of flyby segments in the multi-satellite flyby sequence, the type and arrangement order of each flyby segment;

S3: Take the position and speed of the departure target of the spacecraft as the current initial state, select the corresponding fly-by target search strategy according to the type of the first fly-by segment in the multi-star fly-by sequence, find out potential target combinations, and use the corresponding multi-star fly-by sequence. Star flyby trajectory planning method obtains flyby segments satisfying constraints;

S4: Take the position and speed of the last target in the last flyby segment of the spacecraft as the current initial state, select the corresponding flyby target search strategy according to the type of the next flyby segment in the multi-star flyby sequence determined in S2, and find out Potential target combinations, and use the corresponding multi-star flyby trajectory planning method to obtain flyby segments that meet the constraints;

Traditional fly-by sequence planning methods are only suitable for fly-by sequence planning problems that contain at least one pulse between adjacent targets. The method and system for searching a multi-satellite fly-by sequence with fly-by segments of "one stone, many birds" provided by the present invention, according to a given arrangement of pulses and access targets, search for fly-by targets segment by segment, plan pulse maneuver time and maneuver amount, and obtain satisfactory results. Constrained flyby segments, and then the final multi-star flyby sequence is obtained by accumulating the flyby segments segment by segment. The invention overcomes the shortcomings of the traditional fly-by sequence planning method, can effectively support the situation that there is no pulse between two or three adjacent targets, and realizes a large-scale global search for the fly-by sequence with "one stone, many birds".

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to the structures shown in these drawings without creative efforts.

1 is a flowchart of an embodiment of the present invention;

Figure 2 is an example diagram of a flyover segment;

Figure 3 is a flight process diagram of the spacecraft crossing two targets through four pulses;

Figure 4 is a flight process diagram of the spacecraft crossing three targets through seven pulses;

Fig. 5 is a search process diagram of a single-pulse binary star flyby segment;

Fig. 6 is the search process diagram of the two-pulse Samsung flyover segment;

Fig. 7 is the search process diagram of "222" multi-star flyby sequence;

Figure 8 shows the flight trajectories of the spacecraft flying over 6 stars in sequence from the solar system;

Figure 9 shows the flight trajectories of the spacecraft flying over five stars in sequence from the solar system.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Example 1:

As shown in FIG. 1 , the method for searching a multi-star flyby sequence with a flyby segment of “multiple birds with one stone” provided by this embodiment includes the following steps:

S1: The number of targets visited and pulses applied in the multi-satellite flyby sequence for a given search. Wherein, the number of access targets is greater than the number of pulses but not more than twice the number of pulses.

S2: The arrangement of pulses and targets is given according to the number of targets and pulses, and the multi-satellite flyby sequence is determined by the arrangement of targets. The arrangement of the targets determines the number of flyover segments, the type and arrangement order of each flyover segment in the sequence of this search;

至

为单脉冲单星飞越片段，

至

为单脉冲双星飞越片段，

至

为两脉冲三星飞越片段。The present invention defines the flight trajectory formed by the spacecraft starting from the current target and flying over one or multiple targets simultaneously through one to two pulses as a flying segment. The start time of the flyover segment is the time of flying over the last target in the previous flyover segment, and the terminal time of the flyover segment is the time of flying over the last target of one or more targets. Figure 2 shows an example of a fly-by sequence with 7 targets and 4 pulses, including 3 fly-by segments. in,

to

is the single-pulse single-star flyby segment,

to

for the flyby segment of a monopulse binary star,

to

For the two-pulse three-star flyby segment.

The arrangement of pulses and targets given in this step must meet the following two constraints: 1) The number of targets between any two adjacent pulses does not exceed 3; 2) If there are 3 consecutive targets, fly over 3 At least two consecutive pulses are scheduled before each consecutive target.

S3: Design the flyby target search strategy of the single-pulse double-star flyby segment and the flyby target search strategy of the two-pulse three-star flyby segment.

S301: Design a fly-by target search strategy for a single-pulse double-star fly-by segment;

The search process of the flyby target search strategy of the flyby segment of the single-pulse binary star is as follows:

，将航天器从初始状态(r ₀,v ₀)预报到(r ₁,v ₁)，其中(r ₀,v ₀)为航天器初始位置和速度，(r ₁,v ₁)为航天器经过一段滑行时间

后的位置和速度。S30101: Randomly give a taxiing time

, predict the spacecraft from the initial state ( r ₀ , v ₀ ) to ( r ₁ , v ₁ ), where ( r ₀ , v ₀ ) is the initial position and velocity of the spacecraft, and ( r ₁ , v ₁ ) is the spacecraft after a glide time

position and speed.

和一段滑行时间

，将航天器从当前状态(r ₁,v ₁)预报到(r ₂,v ₂)，(r ₂,v ₂)为航天器从当前状态(r ₁,v ₁)经过滑行时间

后的位置和速度。S30102: Randomly give a pulse

and a glide time

, predicts the spacecraft from the current state ( r ₁ , v ₁ ) to ( r ₂ , v ₂ ), and ( r ₂ , v ₂ ) is the taxiing time of the spacecraft from the current state ( r ₁ , v ₁ )

position and speed.

时间段内航天器与所有访问目标的最近距离，收集所有最近距离小于给定上限值d _max的目标并统计这些目标的个数记为n；S30103: Calculation

The shortest distance between the spacecraft and all the visited targets in the time period, collect all the targets whose shortest distance is less than the given upper limit value d _max and count the number of these targets as n ;

S30104: If n < 2, return to S30101;

时间段内与航天器最近距离最小的两个目标作为潜在飞越目标组合。S30105: Will

The two targets with the shortest distance to the spacecraft in the time period are used as a combination of potential overflight targets.

S302: Design a flyover target search strategy for two-pulse three-star flyover segments;

The flow of the overflight target search strategy of the two-pulse three-star flyover segment is as follows:

，将航天器从初始状态(r ₀,v ₀)预报到(r ₁,v ₁)，其中(r ₀,v ₀)为航天器初始位置和速度，(r ₁,v ₁)为航天器经过一段滑行时间

后的位置和速度。S30201: Randomly give a taxiing time

, predict the spacecraft from the initial state ( r ₀ , v ₀ ) to ( r ₁ , v ₁ ), where ( r ₀ , v ₀ ) is the initial position and velocity of the spacecraft, and ( r ₁ , v ₁ ) is the spacecraft after a glide time

position and speed.

和一段滑行时间

，将航天器从当前状态(r ₁,v ₁)预报到(r ₂,v ₂)，(r ₂,v ₂)为航天器从当前状态(r ₁,v ₁)经过滑行时间

后的位置和速度。S30202: Randomly give a pulse

and a glide time

, predicts the spacecraft from the current state ( r ₁ , v ₁ ) to ( r ₂ , v ₂ ), and ( r ₂ , v ₂ ) is the taxiing time of the spacecraft from the current state ( r ₁ , v ₁ )

position and speed.

和一段滑行时间

，将航天器从当前状态(r ₂,v ₂)预报到(r ₃,v ₃)，(r ₃,v ₃)为航天器从当前状态(r ₂,v ₂)经过滑行时间

后的位置和速度。S30203: Randomly give a pulse

and a glide time

, predicts the spacecraft from the current state ( r ₂ , v ₂ ) to ( r ₃ , v ₃ ), and ( r ₃ , v ₃ ) is the taxiing time of the spacecraft from the current state ( r ₂ , v ₂ )

position and speed.

时间段内航天器与所有访问目标的最近距离，收集所有最近距离小于给定上限值d _max的目标并统计这些目标的个数记为n。S30204: Calculation

The shortest distance between the spacecraft and all the visited targets in the time period, collect all targets whose shortest distance is less than the given upper limit value d _max and count the number of these targets as n .

S30205: If n <3, return to S30201.

时间段内与航天器最近距离最小的三个目标作为潜在飞越目标组合。S30206: Will

The three targets with the shortest distance to the spacecraft in the time period are used as a combination of potential overflight targets.

S4: Design a single-pulse double-star flyby trajectory planning method and a two-pulse three-star flyby trajectory planning method.

S401: Design a single-pulse binary star flyby trajectory planning method.

S40101: Construct a four-pulse binary star rendezvous trajectory optimization model;

The design variables of the four-pulse binary star rendezvous trajectory optimization model are:

Among them, dt ₁ is the waiting time of the spacecraft on the initial orbit; dt ₂ is the time when the spacecraft transfers from the initial orbit to the first visiting target through two pulses; dt ₃ is the time when the spacecraft passes two pulses from the first visiting target Time to transfer to the second visit target; the spacecraft does not stop on the first visit target, so the two pulses in the middle are applied at the same time; let t ₀ be the initial time, the time when the spacecraft applies the first pulse t ₁ , time t ₂ when the second and third pulses are applied, and time t ₃ when the fourth pulse is applied are:

The following three types of constraints need to be considered in the optimization model of the rendezvous trajectory of the four-pulse binary star. The first type of constraint is the pulse velocity increment constraint:

为航天器施加的第一个脉冲，

为单个脉冲速度增量上限。In the formula,

the first pulse applied to the spacecraft,

It is the upper limit of single pulse speed increment.

The second type of constraint is the relative position constraint between the spacecraft at the moment of rendezvous and the visiting target:

In the formula, r ₀ ( t ₂ ) and r ₁ ( t ₂ ) are the position vectors of the spacecraft and the first visited target at time t ₂ , respectively; r ₀ ( t ₃ ) and r ₂ ( t ₃ ) are the aerospace The position vector _of the controller and the second access target at time t3 .

The third type of constraint is the relative velocity constraint between the spacecraft at the moment of rendezvous and the visiting target:

为航天器施加的用于与第二个访问目标交会的第四个脉冲，dv _max为航天器飞越目标时允许的最大相对速度。where v ₀ ( t ₂ ) and v ₁ ( t ₂ ) are the velocity vectors of the spacecraft and the first visiting target at time t ₂ , respectively; v ₀ ( t ₃ ) and v ₂ ( t ₃ ) are the the velocity vector of the controller and the second visiting target at time t3 _;

The fourth pulse applied to the spacecraft for rendezvous with the second visiting target, dv _max is the maximum relative velocity allowed for the spacecraft to fly over the target.

The objective function of the four-pulse binary star rendezvous trajectory optimization model is to minimize the modulus of the vector sum of the two intermediate pulses:

和

分别为航天器在t ₂时刻施加的用于与第一个访问目标交会和瞄准第二个访问目标的两个脉冲。In the formula,

and

are the two pulses applied by the spacecraft at time t ₂ for rendezvous with the first visiting target and aiming at the second visiting target, respectively.

S40102: Transition the four-pulse intersection solution to the single-pulse flyover solution by using the intersection trajectory optimization transition method;

的状态分别为[r ₀(t ₀), v ₀(t ₀)]、[r ₁(t ₀), v ₁(t ₀)]和[r ₂(t ₀), v ₂(t ₀)]。对于任给的一组设计变量[dt ₁, dt ₂, dt ₃]，首先需要将航天器和两个访问目标的状态由[r ₀(t ₀), v ₀(t ₀)]、[r ₁(t ₀), v ₁(t ₀)]和[r ₂(t ₀), v ₂(t ₀)]分别预报到[r ₀(t ₁), v ₀(t ₁)]、[r ₁(t ₂), v ₁(t ₂)]和[r ₂(t ₃), v ₂(t ₃)]，然后采用Lambert算法分别求解r ₀(t ₁)至r ₁(t ₂)和r ₁(t ₂)至r ₂(t ₃)之间的两段两脉冲交会轨迹，获得交会所需的4个脉冲

。通过进化算法优化调整设计变量的取值使式（6）不断减小直至降为0并取消

，则四脉冲双星交会轨迹可成功过渡为单脉冲双星飞越轨迹。The flight process of the spacecraft through the four-pulse rendezvous with two targets is shown in Figure 3. in,O ₀is the trajectory of the spacecraft before applying the pulse,O ₁andO ₂The flight trajectories of the first visit target 1 and the second visit target 2, respectively. The spacecraft, the first visit target 1 and the second visit target 2 at the initial moment

The statuses are [r ₀(t ₀),v ₀(t ₀)], [r ₁(t ₀), v ₁(t ₀)]and[r ₂(t ₀),v ₂(t ₀)]. For any given set of design variables [dt ₁,dt ₂,dt ₃], the state of the spacecraft and the two access targets needs to be converted by [r ₀(t ₀),v ₀(t ₀)], [r ₁(t ₀),v ₁(t ₀)]and[r ₂(t ₀),v ₂(t ₀)] respectively predicted to [r ₀(t ₁),v ₀(t ₁)], [r ₁(t ₂),v ₁(t ₂)]and[r ₂(t ₃),v ₂(t ₃)], and then use the Lambert algorithm to solve ther ₀(t ₁)tor ₁(t ₂)andr ₁(t ₂)tor ₂(t ₃) between the two segments of the two-pulse rendezvous trajectory to obtain the 4 pulses required for the rendezvous

. By optimizing and adjusting the value of design variables through evolutionary algorithm, formula (6) is continuously reduced until it is reduced to 0 and canceled

, then the rendezvous trajectory of the four-pulse binary star can be successfully transitioned to the flyby trajectory of the single-pulse binary star.

S402: Design a two-pulse three-star flyover trajectory planning method.

S40201: Build a seven-pulse Samsung rendezvous trajectory optimization model;

The design variables of the seven-pulse Samsung rendezvous trajectory optimization model are:

为第一个脉冲；航天器在第一个访问目标和第二个访问目标上都不作停留，因而第三、第四个脉冲在同一时刻施加，第五、第六个脉冲也在同一时刻施加。设t ₀为初始时刻，则航天器施加各次脉冲的时刻为：Among them, dt ₁ is the waiting time of the spacecraft on the initial orbit; dt ₂ is the flight time after the spacecraft applies the first pulse; dt ₃ is the time when the spacecraft transfers from the transition orbit to the first access target through two pulses ; dt ₄ is the time for the spacecraft to transfer from the first access target to the second access target by two pulses; dt ₅ is the time for the spacecraft to transfer from the second access target to the third access target by two pulses;

is the first pulse; the spacecraft does not stop on the first visit target and the second visit target, so the third and fourth pulses are applied at the same time, and the fifth and sixth pulses are also applied at the same time . Let t ₀ be the initial moment, then the moment when the spacecraft applies each pulse is:

Among them, t ₁ and t ₂ are the moment of applying the first and second pulses respectively; t ₃ is the moment of applying the third and fourth pulses; t ₄ is the moment of applying the fifth and sixth pulses; t ₅ is the moment of applying the seventh pulse pulse application time.

The optimization model of the seven-pulse three-star intersection trajectory needs to consider the following three kinds of constraints. The first type is the pulse velocity increment constraint:

和

分别为第一个和第二个脉冲。In the formula,

and

are the first and second pulses, respectively.

The second type of constraint is the relative position constraint between the spacecraft at the moment of rendezvous and the visiting target:

In the formula, r ₀ ( t ₃ ) and r ₁ ( t ₃ ) are the position vectors of the spacecraft and the first visited target at time t ₃ , respectively; r ₀ ( t ₄ ) and r ₂ ( t ₄ ) are the aerospace are the position vectors of the spacecraft and the second visiting target at time t ₄ ; r ₀ ( t ₅ ) and r ₃ ( t ₅ ) are the position vectors of the spacecraft and the third visiting target at time t ₅ , respectively.

The third type of constraint is the relative velocity constraint between the spacecraft at the moment of rendezvous and the visiting target:

为航天器施加的用于与第三个访问目标交会的第七个脉冲。In the formula, v ₀ ( t ₃ ) and v ₁ ( t ₃ ) are the velocity vectors of the spacecraft and the first visiting target at time t ₃ , respectively; v ₀ ( t ₄ ) and v ₂ ( t ₄ ) are the the velocity vectors of the spacecraft and the second visiting target at time t ₄ ; v ₀ ( t ₅ ) and v ₃ ( t ₅ ) are the velocity vectors of the spacecraft and the third visiting target at time t ₅ , respectively;

The seventh pulse applied to the spacecraft for rendezvous with the third visiting target.

The objective function of the seven-pulse three-star intersection trajectory optimization model is to minimize the modulo of the third and fourth pulse vector sums and the fifth and sixth pulse vector sums:

和

分别为航天器在t ₃时刻施加的用于与访问目标1交会和瞄准访问目标2的两个脉冲；

和

分别为航天器在t ₄时刻施加的用于与访问目标2交会和瞄准访问目标3的两个脉冲。In the formula,

and

are the two pulses applied by the spacecraft at time t ₃ for rendezvous with visiting target 1 and aiming at visiting target 2;

and

are the two pulses applied by the spacecraft at time t ₄ to rendezvous with visit target 2 and to aim at visit target 3, respectively.

S40202: Transition the seven-pulse intersection solution to the two-pulse flyover solution by using the rendezvous trajectory optimization transition method;

为航天器在施加脉冲前的飞行轨道，O ₁、O ₂和O ₃分别为三个访问目标的飞行轨道。对于任给的一组设计变量[dt ₁, dt ₂, dt ₃, dt ₄, dt ₅]，需要首先将航天器和三个访问目标由初始状态分别预报到[r ₀(t ₂), v ₀(t ₂)]、[r ₁(t ₃), v ₁(t ₃)]、[r ₂(t ₄), v ₂(t ₄)]和[r ₃(t ₅), v ₃(t ₅)]，然后采用Lambert算法分别求解r ₀(t ₂)至r ₁(t ₃)、r ₁(t ₃)至r ₂(t ₄)和r ₂(t ₄)至r ₃(t ₅)之间的三段两脉冲交会轨迹，获得交会所需的六个脉冲

~

；通过进化算法优化调整设计变量的取值使式（12）的值不断减小直至降为0并取消

~

，则七脉冲三星交会轨迹成功过渡为两脉冲三星飞越轨迹。The flight process of the spacecraft through the seven-pulse rendezvous with three targets is shown in Figure 4. in,

O ₁ , O ₂ and O ₃ are the flight trajectories of the three visiting targets, respectively. For any given set of design variables [ dt ₁ , dt ₂ , dt ₃ , dt ₄ , dt ₅ ], it is necessary to first predict the spacecraft and the three visit targets from the initial state to [ r ₀ ( t ₂ ), v ₀ ( t ₂ )], [ r ₁ ( t ₃ ), v ₁ ( t ₃ )], [ r ₂ ( t ₄ ), v ₂ ( t ₄ )], and [ r ₃ ( t ₅ ), v ₃ ( t ₅ )], and then use the Lambert algorithm to solve r ₀ ( t ₂ ) to r ₁ ( t ₃ ), r ₁ ( t ₃ ) to r ₂ ( t ₄ ) and r ₂ ( t ₄ ) to r ₃ ( t ₅ ) The three-segment two-pulse rendezvous trajectory between the three segments to obtain the six pulses required for the rendezvous

~

; Optimize and adjust the value of design variables through evolutionary algorithm to make the value of formula (12) decrease continuously until it drops to 0 and cancel

~

, then the seven-pulse three-star intersection trajectory successfully transitions to the two-pulse three-star flyover trajectory.

S5: Take the position and speed of the spacecraft's departure target as the current initial state, select the corresponding fly-by target search strategy in S3 according to the type of the first fly-by segment in the multi-star fly-by sequence given in S2, and find out potential target combinations , and use the corresponding multi-star flyby trajectory planning method in S4 to obtain flyby segments that satisfy the constraints.

This step can be summarized as two stages of "test firing + fine-tuning". Among them, the "test firing" is to find out potential target combinations that can be flown over at the same time from a large number of targets, that is, the search process of S3. The "fine-tuning" is to adjust the "test-fire" trajectory through an optimization method, so that the spacecraft can fly over the potential target combination found at the same time, that is, the optimization process of S4. The search process of the single-pulse double-star flyby segment is shown in Figure 5, and the search process of the two-pulse three-star flyby segment is shown in Figure 6.

S6: Take the position and speed of the spacecraft flying over the last star in the previous segment as the current initial state, select the corresponding fly-by target search strategy in S3 according to the type of the next fly-by segment in the multi-star fly-by sequence determined in S2, and find The potential target combination is obtained, and the corresponding multi-satellite flyby trajectory planning method in S4 is used to obtain the flyby segment that meets the constraints.

S7: Repeat S6 until a complete multi-star flyby sequence is obtained.

The process of repeating S6 is the process of continuously accumulating the flyover segments when searching for the flyover sequence. For the convenience of description, the present invention adopts a number string to represent the type of flyover sequence. Among them, the length (number of digits) of the digital string represents the total number of pulses applied, and the number in the digital string represents the number of targets to fly over after each pulse is applied. For example, "222" means that the spacecraft applied a total of 3 pulses and flew over 6 targets, with each pulse flying over two targets separately. "0322" means that the spacecraft applied a total of 4 pulses and flew over 7 targets. The first two pulses flew over three targets, and the last two pulses flew over two targets each. The search process of the "222" flyover sequence is shown in Figure 7.

So far, the search process of multi-star flyby sequences containing flyby fragments of "multiple birds with one stone" based on the flyby fragment accumulation method has been completed.

Example 2:

This embodiment is described by taking the multi-star flyby sequence search in the Milky Way as an example. In this embodiment, the starting target is the solar system, and its initial position and velocity are [8.34 kpc, 0, 0] and [0, -256.41 km/s, 0] respectively. where 1kpc = 30856775814671900 km. The initial position and velocity of the spacecraft are the same as in the solar system.

The multi-star flyby sequence search method containing the flyby segment of "one stone, many birds" in this embodiment includes the following steps:

S1: The number of visited targets and applied pulses in the flyover sequence given this search;

The flyover sequence of this search is given as the number of visited targets is 6 and the number of pulses is 3.

S2: According to the number of visited targets and pulses, an arrangement of pulses and targets is given, which determines the number of flyover segments in the sequence, the type and arrangement order of each flyover segment;

The flyover sequence for this search is given the "222" type. Therefore, the number of flyby segments in this sequence is 3, all of which are single-pulse binary flyby segments.

S3: According to the method in S3 in Embodiment 1, a single-pulse double-star target search strategy and a two-pulse three-star target search strategy are respectively designed.

S4: According to the method in S4 in Embodiment 1, respectively establish a single-pulse double-star and two-pulse three-star flyby trajectory planning model, and design a corresponding multi-star flyby trajectory planning method.

S5: Take the position and speed of the departure target of the spacecraft as the current initial state, select the corresponding target search strategy in S3 according to the type of the first flyover segment given in S2, find out potential target combinations, and use the corresponding target in S4. The multi-satellite flyby trajectory planning method based on the method obtains flyby segments that satisfy the constraints;

The first flyby segment given in S2 in this embodiment is a single-pulse double-star flyby segment. Therefore, the single-pulse-binary star target search strategy in S3 is selected, and the numbers of two potential stars that can fly by at the same time are obtained through the single-pulse-binary star target search strategy. For 10672 and 9880, ephemeris data is available by visiting https://gtocx.jpl.nasa.gov/gtocx/data/. Then, the flyby trajectories of the stars 10672 and 9880 at the same time are obtained by using the single-pulse binary flyby trajectory planning method.

S6: The position and speed of the last star in the previous segment of the spacecraft is the current initial state. According to the type of the next segment determined in S2, the corresponding target search strategy in S3 is selected to find out potential target combinations, and Use the corresponding multi-satellite flyby trajectory planning method in S4 to obtain flyby segments that satisfy the constraints;

S7: Repeat S6 until a complete multi-star flyby sequence is obtained.

Taking the position and speed of the spacecraft when flying over the star 9880 as the current position and speed, select the single-pulse binary star target search strategy in S3, and obtain two potential stars that can fly by at the same time through steps (1)~(5). 40977 and 99421, and then use the single-pulse binary flyby trajectory planning method to obtain the flyby trajectories of the stars 40977 and 99421 at the same time. Then take the position and speed of the spacecraft when flying over the star 99421 as the current position and speed, select the single-pulse binary star target search strategy in S3, and obtain the numbers of two potential stars that can fly by at the same time through steps (1)~(5). are 13002 and 12384, and then the flyby trajectories of the stars 13002 and 12384 at the same time are obtained by using the single-pulse binary flyby trajectory planning method. So far, a complete "222" multi-star flyby sequence has been searched.

Figure 8 shows the flight trajectories of the spacecraft starting from the solar system and flying over six stars in sequence. Table 1 gives the relevant information of the "222" flyover sequence in this example. It can be seen from the table that the relative distance and relative velocity of the spacecraft are all less than 10 ^-4 kpc when flying over these six stars, and the relative speed is all less than 300 km/s, which satisfies the constraints of the flyby state. Therefore, the "222" fly-by sequence given in Table 1 is a multi-star fly-by sequence with a fly-by segment of "two birds with one stone" that satisfies the fly-by state constraint.

Table 1 "222" flyover sequence related information

Example 3:

In this embodiment, the starting target is the solar system, and its initial position and velocity are [8.34 kpc, 0, 0] and [0, -256.41 km/s, 0] respectively. where 1 kpc = 30856775814671900 km. The initial position and velocity of the spacecraft are the same as in the solar system.

The multi-star flyby sequence search method containing the flyby segment of "one stone, many birds" in this embodiment includes the following steps:

S1: The number of targets visited and applied pulses in the flyover sequence given this search.

The flyover sequence of this search is given as, the number of visited targets is 5, and the number of pulses is 3.

S2: According to the number of visited targets and pulses, an arrangement of pulses and targets is given, which determines the number of flyover segments in the sequence, the type and arrangement order of each flyover segment;

The flyover sequence for this search is given the "032" type. Therefore, the number of flyby segments in this sequence is 2, the first is a two-pulse three-star flyby segment, and the second is a single-pulse double-star flyby segment.

S3: According to the method in S3 in Embodiment 1, a single-pulse double-star target search strategy and a two-pulse three-star target search strategy are respectively designed.

S4: According to the method in S4 in Embodiment 1, respectively establish a single-pulse double-star and two-pulse three-star flyby trajectory planning model, and design a corresponding multi-star flyby trajectory planning method.

S5: Take the position and speed of the departure target of the spacecraft as the current initial state, select the corresponding target search strategy in S3 according to the type of the first flyover segment given in S2, find out potential target combinations, and use the corresponding target in S4. The multi-satellite flyby trajectory planning method obtains flyby segments that satisfy the constraints;

The given first flyby segment in S2 is a two-pulse three-star flyby segment, so the two-pulse three-star target search strategy in S3 is selected to obtain three potential simultaneous flyby stars numbered 2097, 49164 and 4478, and then two The pulsing three-star flyby trajectory planning method obtains the flyby trajectories of the stars 2097, 49164 and 4478 at the same time.

S6: Take the position and speed of the last star in the last segment of the spacecraft as the current initial state, select the corresponding target search strategy in S3 according to the type of the next segment determined in S2, and find out potential target combinations, And use the corresponding multi-star flyby trajectory planning method in S4 to obtain flyby segments that satisfy the constraints;

S7: Repeat S6 until a complete multi-star flyby sequence is obtained.

Taking the position and speed of the spacecraft when flying over the star 4478 as the current position and speed, select the target search strategy for single-pulse binary stars in S3, and obtain two potential stars that can be flown by at the same time. The flyby trajectory planning method obtained the flyby trajectories of the stars 4855 and 36794 at the same time. So far, a complete "032" multi-star flyby sequence has been searched.

Figure 9 shows the flight trajectories of the spacecraft flying over five stars in sequence from the solar system. Table 2 gives the relevant information of the "032" flyover sequence in this example. It can be seen from the table that the relative distance and relative velocity of the spacecraft are all less than 10 ^-4 kpc when flying over the five stars, and the relative speed is all less than 300 km/s, which satisfies the constraints of the flyby state. Therefore, the "032" fly-by sequence given in Table 2 is a multi-star fly-by sequence that satisfies the fly-by state constraint and contains one fly-by segment of "two birds with one stone" and one fly-by segment of "three birds with one stone".

Table 2 "032" flyover sequence related information

In summary, although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person of ordinary skill in the art, without departing from the spirit and scope of the present invention, can make various modifications. Therefore, the protection scope of the present invention shall be subject to the scope defined by the claims.

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

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

The latter position and velocity;

(2): randomly giving a pulse

And a period of time of coasting

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

The latter position and velocity;

(3): computing

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 isn< 2, return to (1);

(5): will be provided with

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

Bringing 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 time

The latter position and velocity;

(2): randomly giving a pulse

And a period of time of coasting

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

The latter position and velocity;

(3): randomly giving a pulse

And a period of time of coasting

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

The latter position and velocity;

(4): computing

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

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:

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,

and

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

~

(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:

in the formula,

and

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:

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,

and

are respectively spacecraftst ₃Two for meeting a first access target and aiming a second access target applied at a timePulsing;

and

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

~

(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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