阅读说明：本技术 一种多天体飞越探测轨道设计方法 (Design method of multi-celestial-body flying detection track ) 是由 刘磊 陈明 刘勇 张尧 马传令 陈莉丹 梁伟光 曹鹏飞 于 2021-06-08 设计创作，主要内容包括：本发明公开一种多天体飞越探测轨道设计方法,该方法包括：首先,基于飞越探测任务的能量、时间等约束或者对目标物理特征、轨道特征的探测需求,定义初步筛选参数,从包含海量天体的数据库中筛选出初步待飞越探测的天体目标；其次,对于待飞越探测目标,结合现有转移轨道计算方法,设置多个目标确定门限条件,基于各门限条件逐层优选天体目标,最终确定多天体飞越探测的目标序列,同时得到相应的飞越探测轨道。本发明有效解决了海量天体目标搜索空间大、探测飞行轨道计算时间长、多目标序列优化难等问题,降低了多天体飞越探测轨道设计难度,提高了多目标任务轨道设计的效率。(The invention discloses a design method of a multi-celestial-body flying detection track, which comprises the following steps: firstly, defining preliminary screening parameters based on the constraints of energy, time and the like of a flying detection task or the detection requirements of target physical characteristics and track characteristics, and screening out a preliminary celestial body target to be subjected to flying detection from a database containing massive celestial bodies; secondly, for the object to be detected flying over, combining the existing transfer orbit calculation method, setting a plurality of object determination threshold conditions, optimizing celestial objects layer by layer based on each threshold condition, finally determining the object sequence of the multi-celestial-body flying over detection, and obtaining the corresponding flying over detection orbit. The method effectively solves the problems of large search space of mass celestial body targets, long calculation time of the detection flight track, difficult multi-target sequence optimization and the like, reduces the design difficulty of the multi-celestial body flying detection track, and improves the efficiency of multi-target task track design.)

1. A design method of a multi-celestial body flying detection track is characterized by comprising the following steps: preliminarily screening celestial body targets, and combining with layer-by-layer preferred search design calculated by transfer orbit,

firstly, primarily screening celestial body targets;

based on the constraint conditions of the flying detection task, selecting one constraint condition or a combination of a plurality of constraint conditions as a primary screening parameter, and screening a primary celestial object to be subjected to flying detection from a small celestial object database provided by a minor planet center subordinate to the international astronomical union; the constraint conditions of the flying detection task comprise total energy constraint, total task time constraint, physical characteristics of a celestial body target or orbit characteristics of the celestial body target, wherein the physical characteristics of the celestial body target comprise the size of a small celestial body, the size of a small celestial body star and the like or the type of the small celestial body, and the orbit characteristics of the celestial body target comprise a semi-major axis of an orbit, an orbit eccentricity or a distance from the earth;

secondly, carrying out layer-by-layer preferential search;

and setting a plurality of target determination threshold conditions aiming at the screened preliminary targets to be detected by flying, optimizing the celestial body targets layer by layer based on each threshold condition, finally determining a target sequence of the multi-celestial body flying detection, and simultaneously obtaining corresponding flying detection tracks.

2. The method for designing a multi-celestial-body flight detection orbit of claim 1, wherein in the first step, the method for defining the preliminary screening parameters based on the total energy constraint of the flight detection mission is as follows:

1.1, calculating the energy J of the lunar center two-body ellipse orbit entering after the detector escapes from the moon or the earth by using a formula (1);

wherein v is₀The speed of the detector entering the sun center orbit at the initial moment, r is the sun center distance of the detector, a is the semimajor axis of the orbit, and mu is the gravitational constant of the sun center; Δ v is the detector's speed increment, "+" corresponds to acceleration, "-" corresponds to deceleration;

1.2 velocity increment of Deltav under all propellant action of the probe_mReplacing Δ v in the formula (1) with Δ v_mAnd taking "+" to calculate out a ═ a₁Taking "-" to calculate out a ═ a₂Thus obtaining the corresponding semimajor axis range a of the sun center orbit under the action of all propellants of the detector_sIs [ a ]₁,a₂]And using the threshold as a threshold to screen the small celestial bodies by using the semimajor axis of the track.

3. The method for designing a multi-celestial-body flying probe orbit according to claim 1, wherein in the first step, the method for defining the preliminary screening parameters based on the total mission time constraint of the flying probe mission is as follows:

calculating the flight time delta t under the elliptical orbit of the centrosolar two bodies after the detector enters the centrosolar orbit by using a formula (2), estimating the position which can be reached by the detector in the given task time by using the flight time delta t, and screening the small celestial bodies by using the position of the centrosolar orbit as a threshold;

wherein M is a mean and near point angle, M₀The azimuth angle corresponding to the initial time of the detector is the mean azimuth angle of the sun, a is the semimajor axis of the track, and mu is the gravitational constant of the sun.

4. The method for designing a multi-celestial-body flying detection orbit according to claim 1, wherein in the first step, the method for defining the preliminary screening parameters of the small celestial body target star and the like is as follows:

estimating absolute star and the like H of the small celestial body by using a formula (3), taking the absolute star and the like as a threshold, and screening the small celestial body suitable for flying detection by using the star and the like;

wherein alpha is the geometric albedo and D is the size of the small celestial body.

5. The method of claim 1, wherein the second step further comprises:

2.1 after the detector enters the orbit of the sunset, firstly carrying out first target preferential calculation;

1) within the task time constraint range, performing accurate orbit prediction calculation on the detector and the n detected targets to be flown over to obtain respective accurate orbits;

2) based on the accurate orbit obtained by the calculation, calculating the shortest distances dm and the corresponding moments tm between the detector and all the n detection targets to be overflown one by one;

3) setting a target determination threshold condition C1 formed by a plurality of layers of preferred screening conditions, and carrying out target preferred calculation;

4) after the first time of target preferential calculation is finished, obtaining a preferential screening result under a target determination threshold condition C1, and recording the number of the preferential screening targets as n 1;

2.2 after n1 preferential screening targets are obtained, continuing to perform second-time target preferential calculation;

1) carrying out intersection track design on n1 preferred screening targets one by one, and acquiring intersection tracks, required optimal speed increment delta v, intersection time and target characteristics of the detector for the preferred screening targets;

2) setting a target determination threshold condition C2 consisting of a plurality of preferential screening conditions; setting the preferential screening conditions as speed increment, meeting time or star and the like, and setting the respective corresponding preferential quantities as k 2; performing second preferential screening on all n1 preferential screening targets and intersection tracks thereof according to a target determination threshold condition C2, selecting the targets according to each preferential screening condition, and only 1 repeated target is reserved;

3) after the second time of target preferential calculation is finished, obtaining a preferential screening result under the target determination threshold condition C2, namely n2 preferential screening targets and intersection tracks thereof;

2.3, after n2 preferential screening targets and the intersection tracks thereof are obtained, continuing to perform the third target preferential calculation;

1) for n2 preferential screening targets and the intersection tracks thereof, calculating parameters corresponding to each preferential screening condition one by one according to a plurality of preferential screening conditions;

2) setting a target determination threshold condition C3 consisting of a plurality of preferential screening conditions; carrying out secondary preferential screening on all n2 preferential screening targets and intersection tracks thereof according to a target determination threshold condition C3, setting the preferential quantity respectively corresponding to each preferential screening condition as k3, selecting the targets according to each preferential screening condition, and only keeping 1 repeated target;

3) and after the third time of target preferential calculation is finished, obtaining a preferential screening result under a target determination threshold condition C3, and obtaining j intersection track schemes, wherein each scheme comprises small celestial body targets with different numbers, each intersection time, the speed increment required by each intersection and the total speed increment.

2.4 search termination

And repeating the steps 2.1-2.3 until the total speed increment required by all the track schemes exceeds the maximum speed increment which can be provided by the propellant of the detector, namely the propellant is completely used up, or the total flight time required by all the track schemes obtained by searching is larger than the task time constraint, or the target number of the required intersections is obtained, and ending the searching.

6. The method as claimed in claim 5, wherein in the first target preferential calculation, a target determination threshold condition C1 is set, and the target preferential calculation is performed by the following method:

firstly, setting 2 layers of preferential screening conditions, and setting the 1 st layer as a maximum distance threshold d; the 2 nd layer is set as a closest distance corresponding time tm, a closest distance dm, a star and the like, and the respective corresponding preferred quantities are set as k 1;

selecting small celestial bodies with the shortest distance dm smaller than the maximum distance threshold d as a primary screening target according to the layer 1 preferred screening condition;

and thirdly, carrying out secondary preferential screening on the primary screening target obtained in the second step according to the layer 2 preferential screening condition, wherein only 1 repeated target is reserved.

7. The method for designing a multi-celestial-body flying detection orbit as claimed in claim 5, wherein in the first target preferential calculation, the method for performing accurate orbit prediction calculation on the detector and the n targets to be detected by flying comprises the following steps:

performing orbit integration by using a detector accurate orbit dynamics model to obtain a detector accurate orbit;

the detector precise orbit dynamics equation is as follows:

wherein r is the sun center position vector of the detector, a_NFor the detector to receiveA great planet perturbation of_solarPerturbation for sunlight pressure;

performing orbit integration by using a small celestial object accurate orbit dynamics model to obtain a small celestial object accurate orbit;

the precise orbit dynamics equation of the small celestial body target is as follows:

wherein r is the sun center position vector of the small celestial body, a_NIs perturbed by the great planet gravitation borne by the small celestial body.

8. The method as claimed in claim 5, wherein in the second target optimization calculation, the rendezvous orbit design is performed one by one for n1 optimized screening targets, and the method for obtaining the rendezvous orbit, the required optimal velocity increment Δ v, the rendezvous time and the target characteristics of the detector for each optimized screening target is as follows:

the design constraint of the rendezvous orbit is set as the orbit measurement and control condition and the transfer time, and the optimization design is that the optimal value delta v of the speed increment required by solving the rendezvous small celestial body target can be expressed as the following constraint optimization problem

In formula (8), σ₁And σ₂Orbit parameters, t, for the detector and the small celestial object, respectively₀、t₁And t₂Respectively, the track epoch time, the departure time and the crossing time, R (t)₂) To meet the moment of the heart-distance, dt and R_mRespectively as a departure time constraint and a maximum measurement and control range; the corresponding departure time t is obtained by solving the delta v by using the formula (8)₁And meeting time t₂At t₁Adding delta v to the velocity vector of the moment, and performing orbit by using a detector accurate orbit dynamics model formula (6)Trace integral to t₂And obtaining the corresponding rendezvous orbit.

9. The method as claimed in claim 5, wherein in step 2.3, the plurality of preferential screening conditions constituting the target determination threshold condition C3 include a plurality of conditions selected from total velocity increment, total flight time, star, etc., target number, geocentric distance at meeting time, and time that the measurement and control network in China can track and measure.

Technical Field

The invention belongs to the technical field of deep space exploration, and particularly relates to a multi-celestial body flying exploration track design method based on multilayer preferential search.

Background

The deep space exploration flight distance is generally far, the flight time is long, if a plurality of celestial body targets can be simultaneously explored by a single task, the cost-to-efficiency ratio of the whole task can be greatly reduced, and the value and the benefit of the obtained engineering task can be greatly improved. In addition, from the practice of lunar exploration tasks in China, after the lunar exploration tasks are finished, the detector often has more propellant residues, the detector is quite good in each state, and if the lunar exploration tasks can be used for planning the expansion flight tasks of a plurality of celestial bodies, more valuable exploration targets can be expected to be achieved, so that the maximization of task resource values is achieved. The planning of these tasks involves a problem of multi-celestial fly-by exploration track design techniques.

The design of the multi-celestial-body flying detection orbit is that an orbit scheme which can be launched once and fly a plurality of celestial bodies one by one is designed, the distribution of the celestial bodies in the universe is considered, and the small celestial bodies such as the asteroid and the comet are generally selected as flying detection targets. However, there are many small celestial bodies, and the latest database provided by the asteroid center (http:// www.minorplanetcenter.org) under the international astronomical association (International astronomical Commission) contains over 103 ten thousand small celestial bodies, and if the orbit is calculated for all targets, the calculation amount is too large, and taking the scheme of intersecting 5 small celestial bodies as an example, about 10 small celestial bodies will be obtained by adopting the permutation and combination method³⁰The orbit scheme, which is a one-to-one calculation analysis for such a huge solution space, obviously exceeds the capability of general calculation conditions.

Therefore, a design method of a multi-celestial-body flying detection track needs to be researched, so that the problems of large search space of massive celestial body targets, long calculation time of the detection flight track, difficulty in multi-target sequence optimization and the like are effectively solved, the design difficulty of the multi-celestial-body flying detection track is reduced, and the efficiency of multi-target task track design is improved.

Disclosure of Invention

The technical problems to be solved by the invention are as follows: the method for designing the multi-target flying-over detection track can screen flying-over detection feasible targets from mass celestial body target data, is reasonable and feasible in flying-over detection sequence and high in track design efficiency.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows:

the invention provides a design method of a multi-celestial-body flying detection track, which comprises the following steps: primarily screening celestial body targets, and calculating layer-by-layer preferred search design by combining transfer orbits.

Preliminarily screening celestial body targets, namely defining preliminary screening parameters based on the constraint conditions of the flying detection tasks, such as total energy constraint or total task time constraint, or based on the detection requirements of the flying detection tasks on the physical characteristics or the orbital characteristics of the celestial body targets, such as target size, star and the like, types, small planets near the ground and the like, and screening preliminary celestial body targets to be subjected to flying detection from a database containing massive celestial bodies;

combining with layer-by-layer preferred search design of transfer orbit calculation, setting a plurality of target determination threshold conditions for the detected target to be flown obtained by preliminary screening and combining with the existing transfer orbit calculation method, such as accurate orbit prediction, intersection interception orbit design and the like, preferably selecting celestial objects layer by layer based on each threshold condition, finally determining a target sequence of multi-celestial object flying detection, and simultaneously obtaining a corresponding flying detection orbit.

The specific scheme is as follows:

a design method of a multi-celestial body flying detection track comprises the following steps: preliminarily screening celestial body targets, combining with layer-by-layer preferred search design calculated by a transfer orbit,

firstly, primarily screening celestial body targets;

based on the constraint conditions of the flying detection task, selecting one constraint condition or a combination of a plurality of constraint conditions as a primary screening parameter, and screening a primary celestial object to be subjected to flying detection from a small celestial object database provided by a minor planet center belonging to the international astronomical union; the constraint conditions of the flying detection task comprise total energy constraint, total task time constraint, physical characteristics of a celestial body target or orbit characteristics of the celestial body target, wherein the physical characteristics of the celestial body target comprise the size of a small celestial body, the size of a small celestial body star and the like or the type of the small celestial body, and the orbit characteristics of the celestial body target comprise an orbit semi-major axis, orbit eccentricity or the distance from the earth;

secondly, carrying out layer-by-layer preferential search;

and setting a plurality of target determination threshold conditions aiming at the screened preliminary targets to be detected by flying, optimizing the celestial body targets layer by layer based on each threshold condition, finally determining a target sequence of the multi-celestial body flying detection, and simultaneously obtaining corresponding flying detection tracks.

Further, in the first step, the method for defining the preliminary screening parameters based on the total energy constraint of the flying probe task is as follows:

1.1, calculating the energy J of the lunar center two-body ellipse orbit entering after the detector escapes from the moon or the earth by using a formula (1);

wherein v is₀The speed of the detector entering the sun center orbit at the initial moment, r is the sun center distance of the detector, a is the semimajor axis of the orbit, and mu is the gravitational constant of the sun center; Δ v is the detector's speed increment, "+" corresponds to acceleration, "-" corresponds to deceleration;

1.2 velocity increment of Deltav under all propellant action of the probe_mReplacing Δ v in the formula (1) with Δ v_mAnd taking "+" to calculate out a ═ a₁Taking "-" to calculate out a ═ a₂Thus obtaining the semimajor axis range a of the sun center orbit corresponding to the detector under the action of all the propellant_sIs [ a ]₁,a₂]And using the threshold as a threshold to screen the small celestial bodies by using the semimajor axis of the track.

Further, in the first step, the method for defining the preliminary screening parameters based on the total task time constraint of the fly-by probe task is as follows:

calculating the flight time delta t under the elliptical orbit of the centrosolar two bodies after the detector enters the centrosolar orbit by using a formula (2), estimating the position which can be reached by the detector in the given task time by using the flight time delta t, and screening the small celestial bodies by using the position of the centrosolar orbit as a threshold;

wherein M is a mean and near point angle, M₀The azimuth angle corresponding to the initial time of the detector is the mean azimuth angle of the sun, a is the semimajor axis of the track, and mu is the gravitational constant of the sun.

Further, in the first step, the method for defining the preliminary screening parameters by the small celestial object star and the like is as follows:

estimating absolute star and the like H of the small celestial body by using a formula (3), and screening the small celestial body suitable for flying over detection by using the star and the like as a threshold;

wherein alpha is the geometric albedo and D is the size of the small celestial body.

Further, the second step further comprises:

2.1 after the detector enters the orbit of the sunset, firstly carrying out first target preferential calculation;

1) within the task time constraint range, performing accurate orbit prediction calculation on the detector and the n detection targets to be flown over to obtain respective accurate orbits;

2) based on the accurate orbit obtained by the calculation, calculating the shortest distances dm and the corresponding moments tm between the detector and all the n detection targets to be overflown one by one;

3) setting a target determination threshold condition C1 formed by a plurality of layers of preferred screening conditions, and carrying out target preferred calculation;

4) after the first time of target preferential calculation is finished, obtaining a preferential screening result under a target determination threshold condition C1, and recording the number of the preferential screening targets as n 1;

2.2 after n1 preferential screening targets are obtained, continuing to perform second-time target preferential calculation;

1) carrying out intersection track design on n1 preferred screening targets one by one, and acquiring intersection tracks, required optimal speed increment delta v, intersection time and target characteristics of the detector for the preferred screening targets;

2) setting a target determination threshold condition C2 consisting of a plurality of preferential screening conditions; setting the preferential screening conditions as speed increment, meeting time or star and the like, and setting the respective corresponding preferential quantities as k 2; performing second preferential screening on all n1 preferential screening targets and intersection tracks thereof according to a target determination threshold condition C2, selecting the targets according to each preferential screening condition, and only keeping 1 repeated target;

3) after the second time of target preferential calculation is finished, obtaining a preferential screening result under the target determination threshold condition C2, namely n2 preferential screening targets and intersection tracks thereof;

2.3, after n2 preferential screening targets and the intersection tracks thereof are obtained, continuing to perform third-time target preferential calculation;

1) for n2 preferential screening targets and the intersection tracks thereof, calculating parameters corresponding to each preferential screening condition one by one according to a plurality of preferential screening conditions;

2) setting a target determination threshold condition C3 consisting of a plurality of preferential screening conditions; carrying out secondary preferential screening on all n2 preferential screening targets and the intersection tracks thereof according to a target determination threshold condition C3, setting the preferential quantity respectively corresponding to each preferential screening condition as k3, selecting the targets according to each preferential screening condition, and only reserving 1 repeated target;

3) and after the third time of target preferential calculation is finished, obtaining a preferential screening result under a target determination threshold condition C3, and obtaining j intersection track schemes, wherein each scheme comprises small celestial body targets with different numbers, each intersection time, the speed increment required by each intersection and the total speed increment.

2.4 search termination

And repeating the steps 2.1-2.3 until the total speed increment required by all the track schemes exceeds the maximum speed increment which can be provided by the propellant of the detector, namely the propellant is completely used up, or the total flight time required by all the track schemes obtained by searching is larger than the task time constraint, or the target number of required intersections is obtained, and terminating the searching.

Further, in the first time of the target preferential calculation, a target determination threshold condition C1 formed by a plurality of layers of preferential screening conditions is set, and the method for performing the target preferential calculation is as follows:

firstly, setting 2 layers of preferential screening conditions, and setting the 1 st layer as a maximum distance threshold d; the 2 nd layer is set as the closest distance corresponding time tm, the closest distance dm, the star and the like, and the preferred number corresponding to each layer is set as k 1;

selecting small celestial bodies with the shortest distance dm smaller than the maximum distance threshold d as primary screening targets according to the layer 1 preferred screening conditions;

and thirdly, carrying out secondary preferential screening on the primary screening target obtained in the second step according to the layer 2 preferential screening condition, wherein only 1 repeated target is reserved.

Further, in the first target preferential calculation, the method for performing accurate orbit prediction calculation on the detector and the n targets to be detected flying over comprises the following steps:

performing orbit integration by using a detector accurate orbit dynamics model to obtain a detector accurate orbit;

the detector precise orbit dynamics equation is as follows:

wherein r is the sun center position vector of the detector, a_NIs the perturbation of the detector by the great planet gravity, a_solarPerturbation for sunlight pressure;

performing orbit integration by using a small celestial object accurate orbit dynamics model to obtain a small celestial object accurate orbit;

the precise orbit dynamics equation of the small celestial body target is as follows:

wherein r is the sun center position vector of the small celestial body, a_NIs perturbed by the great planet gravitation borne by the small celestial body.

Further, in the second target preferential calculation, the design of the rendezvous orbit is developed one by one for n1 preferential screening targets, and the method for obtaining the rendezvous orbit, the required optimal velocity increment Δ v, the rendezvous time and the target characteristics of each preferential screening target by the detector is as follows:

the design constraint of the rendezvous orbit is set as the orbit measurement and control condition and the transfer time, and the optimization design is that the optimal value delta v of the speed increment required by solving the rendezvous small celestial body target can be expressed as the following constraint optimization problem

In formula (8), σ₁And σ₂Orbit parameters, t, for the detector and the small celestial object, respectively₀、t₁And t₂Respectively, a track epoch time, a departure time and a rendezvous time, R (t)₂) To meet the moment of the heart-distance, dt and R_mRespectively as a departure time constraint and a maximum measurement and control range; the corresponding sending time t is obtained by solving the delta v by using the formula (8)₁And meeting time t₂At t₁Adding delta v to the velocity vector at the moment, and performing orbit integration to t by using a detector accurate orbit dynamics model formula (6)₂And obtaining the corresponding rendezvous orbit.

Further, in the step 2.3, the plurality of preferential screening conditions constituting the target determination threshold condition C3 include a plurality of times of total velocity increment, total flight time, star, etc., target number, geocentric distance at the meeting time, or time that the national measurement and control network can track and measure.

The invention has the beneficial effects that:

the design method of the multi-celestial-body flying detection track based on the multilayer preferred search fully utilizes the advantages of good screening effect of the track and physical characteristics on the number of celestial bodies and maturity and reliability of the conventional transfer track calculation method, effectively solves the problems of large search space of mass celestial body targets, long calculation time of the detection flight track, difficulty in multi-target sequence optimization and the like, reduces the design difficulty of the multi-celestial-body flying detection track, and improves the efficiency of multi-target task track design. The invention can be used for the special small celestial body exploration task and can also be used for the small celestial body exploration and expansion task after the lunar exploration and deep space exploration tasks.

Drawings

FIG. 1 is a multi-layer preferred search algorithm for multi-celestial objects and orbits in accordance with the present invention;

fig. 2 shows the multi-celestial body flying detection orbit obtained by the invention, (a) scheme 1, (b) scheme 2, (c) scheme 3 and (d) scheme 4.

Description of the attached tables

Table 1 shows the search results of the multi-celestial-body fly-over detection obtained by the present invention;

table 2 shows the multi-celestial-body fly-over detection transfer flight parameters and multi-celestial-body parameters obtained by the present invention.

Detailed Description

The present invention will be described in further detail with reference to fig. 1.

The invention provides a multi-celestial body flying detection track design method based on multilayer preferential search, which mainly comprises the steps of celestial body target primary screening, layer-by-layer preferential search design combined with transfer track calculation and the like.

Step one, primarily screening celestial body targets

In the step, based on the constraint conditions of the flying detection task, one condition or a combination of a plurality of constraint conditions is selected as a primary screening parameter, a primary celestial object to be subjected to flying detection is screened from a database containing a large number of celestial objects, the constraint conditions of the flying detection task comprise total energy constraint, total task time constraint, physical characteristics of the celestial object and orbit characteristics of the celestial object, the physical characteristics of the celestial object comprise the size of a small celestial object, the type of the small celestial object and the like, and the orbit characteristics of the celestial object comprise orbit radius, orbit eccentricity, distance from the earth and the like.

1.1 celestial data reading

Dat is a file name of the small celestial body data provided by a minor planet center belonging to international astronomical association, wherein the file name includes orbital root, star and the like of about 103 ten thousand small celestial bodies and observation related parameters, and the small celestial body data needs to be read strictly according to the format.

1.2 Primary screening parameter determination

And selecting one constraint condition or a combination of a plurality of constraint conditions as a primary screening parameter, wherein the flight detection task constraint conditions comprise total energy constraint, total task time constraint, celestial object physical characteristics and celestial object orbit characteristics. Celestial object physical characteristics include size, star, etc., celestial type, etc. Orbital characteristics of celestial objects include orbital radius, orbital eccentricity, distance from the earth, etc.

(1) Energy confinement

The energy J of the sun-center two-body ellipse orbit of the detector entering behind the escape moon or the earth is calculated by using the formula (1)

Wherein v is₀The speed of the detector entering the sun center orbit at the initial moment, r is the sun center distance of the detector, a is the semimajor axis of the orbit, and mu is the gravitational constant of the sun center; Δ v is the probe speed increment, the "+" sign corresponds to acceleration, and the "-" corresponds to deceleration.

The increment of velocity obtained under the action of all propellant in the detector is delta v_mReplacing Δ v in the formula (1) by Δ v_mAnd taking "+" to calculate out a ═ a₁Taking "-" to calculate out a ═ a₂Thus obtaining the semimajor axis range a of the sun orbit after the detector is fully acted by the propellant_sIs [ a ]₁,a₂]Using the semi-major axis of the orbit as a threshold to screen the small celestial bodies, i.e. selecting the semi-major axis of the orbit to be in the range a_sInner celestial body as primary screeningAnd (4) a target.

(2) Total task time constraints

Calculating the flight time delta t under the orbit of the lunar center two-body ellipse after the detector enters the orbit of the lunar center by using a formula (2);

wherein M is₀The mean-near-point angle of the centroid corresponding to the initial moment of the detector, M is the mean-near-point angle, a is the semimajor axis of the track, and mu is the gravitational constant of the centroid.

Estimation of detector at given mission time t using time of flight Δ t₁,t₂]Inner reachable orbital position of the sun [ M ]₁,M₂]The small celestial bodies are screened by taking the position as a threshold, namely the position of the orbit of the centroid is selected to be within the range [ M₁,M₂]The small celestial bodies in the inner part are used as primary screening targets.

(3) Analysis of celestial object stars

The larger the size of a small celestial object, the greater the probability of acquiring a clear image thereof, based on the imaging device capabilities carried by the detector. Estimation of Absolute Star, etc. H of celestial bodies using equation (3)

Wherein alpha is the geometric albedo and D is the size of the small celestial body. Screening small celestial bodies suitable for flying detection by taking star class H as threshold, namely selecting star class in range H₁,H₂]The small celestial bodies in the inner part are used as primary screening targets.

1.3 preliminary screening

Based on the preliminary screening parameters, most of small celestial objects which do not meet the conditions are excluded, and a limited number (set as n) of detection objects to be flown over are obtained, so that the calculation amount of subsequent object searching and track design is greatly reduced.

Step two, layer-by-layer preferred search calculation

Aiming at the screened preliminary targets to be detected by flying over, combining the existing transfer orbit calculation method such as accurate orbit prediction, intersection interception orbit design and the like, setting a plurality of target determination threshold conditions, optimizing celestial body targets layer by layer based on each threshold condition, finally determining a target sequence of multi-celestial body flying over detection, and obtaining corresponding flying over detection orbits.

This step involves the following multi-level preferential search calculation:

(1) aiming at the screened detection target to be flown over, performing accurate track forecast to obtain the accurate tracks of the detector and the small celestial body;

in the design of a small celestial body flying detection task, accurate orbit prediction is required to analyze the distance between a transfer orbit and a target celestial body. After the detector enters the centrosolar orbit, the accurate orbit dynamics equation is as follows:

wherein, mu is a constant of the sun gravity, r is a vector of the sun position of the detector, and the magnitude is r, a_NFor perturbation of the detector by the great planetary attraction, a_solarPerturbation for sunlight pressure.

And (3) performing orbit integration by using a detector accurate orbit dynamics model in the formula (6) and adopting a numerical method such as a single-step method Runge-Kutta method, a linear multi-step method Adams method, a Cowell method and the like to obtain the detector accurate orbit.

As for the accurate orbit prediction of the small celestial body target, the orbit dynamics model only needs to consider the perturbation of the great planet attraction and the solar gravity, and the accurate orbit dynamics equation is as follows:

wherein r is the sun center position vector of the small celestial body with the size of r, a_NIs perturbed by the great planet gravitation borne by the small celestial body.

The orbit integration method of the small celestial body is the same as that of the detector, namely, the orbit integration is carried out by using a small celestial body orbit dynamics model in the formula (7) and adopting numerical methods such as a single-step method Runge-Kutta method, a linear multi-step method Adams method, a Cowell method and the like, so that the accurate orbit of the small celestial body target is obtained.

(2) Rendezvous track design

On the premise that the initial orbit of the detector and the small celestial body target are determined, the design of the rendezvous orbit can be simplified into a centroid two-body interception orbit, namely a classical Gaussian problem of a given departure epoch and a transfer time. The design constraint of the rendezvous orbit is the orbit measurement and control condition and the transfer time, and the optimization design is that the optimal value delta v of the speed increment required for solving the rendezvous small celestial body target can be expressed as the following constraint optimization problem

In formula (6), σ₁And σ₂Orbit parameters, t, for the detector and the small celestial object, respectively₀、t₁And t₂Respectively, the track epoch time, the departure time and the crossing time, R (t)₂) To meet the moment of the heart-distance, dt and R_mRespectively a departure time constraint and a maximum measurement and control range. The formula (6) can be used for solving the delta v by directly using a quadratic programming method, and can also be used for solving the delta v by using intelligent optimization algorithms such as a genetic algorithm after being converted into an unconstrained optimization problem.

While solving for Δ v, a corresponding departure time t is obtained₁And meeting time t₂At t₁Adding delta v to the velocity vector at the moment, and performing orbit integration to t by using a detector accurate orbit dynamics model formula (6)₂And obtaining the corresponding rendezvous orbit.

The layer-by-layer optimization searching process comprises the following steps:

1. first time target preferential calculation

After the detector enters the solar orbit, first target preferential calculation is carried out, namely

1) Within the task time constraint range, performing accurate orbit prediction calculation on the detector and the n detection targets to be flown over to obtain respective accurate orbits;

2) based on the accurate orbit obtained by the calculation, calculating the shortest distances dm and the corresponding moments tm between the detector and all the n detection targets to be overflown one by one;

3) and setting a target determination threshold condition C1 consisting of a plurality of layers of preferred screening conditions to perform target preferred calculation.

Taking a 2-layer preferred screening condition as an example, setting a 1 st layer as a maximum distance threshold d; setting the layer 2 as a closest distance corresponding time tm, a closest distance dm, a star and the like H, and setting the corresponding preferred number as k 1;

selecting small celestial bodies with the shortest distance dm smaller than the maximum distance threshold d as primary screening targets according to the layer 1 preferred screening condition, wherein the number of the targets is not limited;

and thirdly, carrying out secondary preferential screening on the primary screening target in the second step according to the layer 2 preferential screening condition.

Preferably, selecting k1 targets according to the sequence of tm from small to large, selecting k1 targets according to the sequence of dm from small to large, and selecting k1 targets according to the sequence of H from small to large, wherein only 1 repeated target is reserved in all 3k1 targets;

4) after the first time of target preferential calculation is finished, a preferential screening result under the condition of a target determination threshold C1 is obtained, the number of the preferential screening targets is recorded as n1, and obviously n1 is less than or equal to 3k 1.

2. Second target preferential calculation

After n1 preferential screening targets are obtained, continuing to perform the second target preferential calculation, namely

1) And (3) carrying out intersection track design on the n1 preferred screening targets one by one, and acquiring intersection tracks, required optimal speed increment delta v, intersection time and target characteristics of the detector for the preferred screening targets.

2) Setting a target determination threshold condition C2 composed of a plurality of preferred screening conditions, and carrying out preferred screening again on all n1 preferred screening targets and intersection tracks thereof according to the target determination threshold condition C2.

For example, C2 is composed of 3 preferential screening conditions, such as speed increment, meeting time, and star, and the number of corresponding preferential selections is k 2. Preferably, selecting k2 targets according to the sequence of the speed increment from small to large, selecting k2 targets according to the sequence of the meeting time from near to far, selecting k2 targets according to the sequence of the star and the like from small to large, and only keeping 1 repeated target in all 3k2 targets;

3) after the second time of the target preferential calculation is completed, the preferential screening result under the condition of the target determination threshold C2 is obtained, namely n2 preferential screening targets and the intersection tracks thereof obviously have n2 less than or equal to 3k 2.

3. Third time target preferential calculation

After n2 preferential screening targets and the intersection tracks thereof are obtained, the third target preferential calculation is carried out continuously, namely

1) For n2 preferential screening targets and the rendezvous orbit thereof, calculating corresponding total speed increment, total flight time and rendezvous target quantity one by one;

2) setting a target determination threshold condition C3 composed of a plurality of preferred screening conditions, and carrying out preferred screening again on all n2 preferred screening targets and intersection tracks thereof according to the target determination threshold condition C3.

For example, C3 is composed of 3 preferential screening conditions, and the respective preferential numbers are k3, such as total velocity increment, total flight time, and star. Preferentially, selecting k3 targets according to the sequence of the speed increment from small to large, selecting k3 targets according to the sequence of the rendezvous time from near to far, selecting k3 targets according to the sequence of the stars and the like from small to large, and only keeping 1 repeated target in all 3k3 targets;

3) and after the third time of target preferential calculation is finished, obtaining a preferential screening result under a target determination threshold condition C3, and without setting j crossing track schemes, wherein each scheme comprises small celestial body targets with different numbers, each crossing time, the speed increment required by each crossing and the total speed increment, and j is obviously less than or equal to 3k 3.

In order to further preferentially screen the targets, a fourth target preferential calculation can be performed.

And (3) a fourth target preferential calculation process:

after j preferential screening targets and the intersection tracks thereof are obtained, the fourth target preferential calculation is carried out continuously, namely

1) Analyzing and calculating the geocentric distance of each intersection time, the measurement and control time of the ground measuring station and the illumination condition of the intersection time one by one for the j preferred screening targets and the intersection tracks thereof;

2) and setting a target determination threshold condition C4 consisting of a plurality of preferential screening conditions, and performing fourth target preferential calculation.

3) And carrying out preferential screening again on all j preferential screening targets and the intersection tracks thereof according to a target determination threshold condition C4.

For example, C4 is composed of 2 preferential screening conditions, and for example, the geocentric distance at the meeting time and the measurement and control time of the measurement and control network in China are selected, and the respective corresponding preferential quantities are set to be k 4. Preferably, k4 targets are selected according to the sequence of the geocentric distance at the meeting time from small to large, k4 targets are selected according to the sequence of the measurement and control time of the measurement and control network in China from long to short, and only 1 repeated target is reserved in all 2k4 targets;

4) after the fourth time of target preferential calculation is completed, a preferential screening result under a target determination threshold condition C4 is obtained, and m crossing track schemes are not set to be obtained, each scheme comprises small celestial body targets with different numbers, each crossing time, the speed increment required by each crossing and the total speed increment, and obviously, m is less than or equal to 2k 4.

4. Search termination

And (3) repeating the steps 1-3 until the total speed increment required by all the track schemes exceeds the maximum speed increment which can be provided by the propellant of the detector, namely the propellant is completely used up, or the total flight time required by all the track schemes obtained by searching is larger than the task time constraint, or the target number of required encounters is obtained, and ending the searching.

In addition, some calculation accidental termination conditions should be considered, such as iteration exceeding a certain number of times, too long search calculation time, failure to continue searching due to target screening or 0 preferred result, and the like.

Numerical verification

The method is verified by taking the task of designing the CE-5 orbiter to fly over and detect a plurality of small celestial bodies as an example. When CE-5 sampling returns to the vicinity of the earth, the detector consists of a returning device and an orbiter, the returning device returns to a landing field after the two are separated at a preset position, the height of the near place of the orbiter is too low, and in order to ensure the safety of the orbiter, the near place of the orbiter needs to be lifted by applying orbit control. Taking the elevation of the near place to 135km as an example, the orbiter enters a geocentric large elliptical orbit with a period of about 17.8 days, and analysis shows that the speed increment of 37.8m/s needs to be applied to the near place when the orbiter escapes under a high-precision force model.

The method is adopted to search and calculate feasible small celestial bodies and corresponding transfer tracks of the flying detection, the gravitational influence of the sun and each large celestial body is considered during track calculation, and the celestial body position adopts JPL DE 430.

Firstly, numbered celestial bodies, about 54.7 ten thousand targets, are extracted from the minor planet data files, and by adopting the first step of the method, the minor celestial bodies with the near-day distance smaller than 1.2AU, about 2.2 ten thousand targets are screened out.

Secondly, by adopting the second step of the method, feasible small celestial body targets are searched under the constraint of total energy and flight time, transfer tracks of the small celestial body targets are obtained at the same time, 19 track schemes are obtained through initial search, and parameters of each scheme are shown in the attached table 1. In the attached table 1, N is the number of small celestial bodies to be intersected, Δ t is the total number of days of the detection task, i.e., the total flight time of the last small celestial body to be intersected, Δ V is the total velocity increment required by the detection task, and Rs is the geocentric distance range when each small celestial body is intersected.

The parameters of the transfer flight and the parameters of the small celestial bodies of the first 4 schemes given in the attached table 1 are shown in the attached table 2, t, R and Δ V are respectively the time, the geocentric distance and the required speed increment for meeting each small celestial body, ID, H and D are the number, star and the like and the size of each small celestial body in sequence, and the definitions of Δ t and Δ V are the same as those in the attached table 1.

The transfer orbit of 4 schemes in the attached table 2 is shown in the attached fig. 2(a) to (d), wherein the departure time position CE of the orbiter is given, the transfer flight stage and the intersection position for intersecting each small celestial body are marked by different colors, and the number and the orbit of the small celestial body are given at the same time.

Table 119 track plan parameters

TABLE 2 Multi-celestial fly-over detection transfer flight parameters and Multi-celestial parameters