CN110096069A - II surpass the optimization method of breadth imaging satellite formation configuration based on NSGA - Google Patents
II surpass the optimization method of breadth imaging satellite formation configuration based on NSGA Download PDFInfo
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Abstract
The invention discloses the optimization methods for II surpassing breadth imaging satellite formation configuration based on NSGA, are related to the satellites formation configuration design of super breadth imaging, belong to the technical field of control, adjusting.The algorithm models the relative motion of formation spacecrafts first with relative eccentric ratio/dip vector method；Then, consider the earthJ 2The influence perturbed to formation Relative Orbit Elements, fuel consumption needed for deriving compensation Perturbation Effect；Later by discretization Satellite Formation Flying observation process, Satellite Formation Flying observation mission sequence is planned, further construction evaluates the objective function of super breadth imaging effect；Obtain considering the satellites formation configuration of fuel consumption and super breadth imaging effect eventually by II algorithm of NSGA.Inventive algorithm is effective, for reducing fuel consumption needed for flight pattern is kept and improving the multi-objective optimization question of super breadth imaging observation effect, realizes the optimization design of satellites formation configuration.
Description
Technical field
The invention discloses the optimization method based on the super breadth imaging satellite formation configuration of NSGA II, be related to super breadth at
The satellites formation configuration of picture designs, and belongs to the technical field of control, adjusting.
Background technique
As big data handles the fast development with space technology, satellite remote sensing technology is each in human society production, life
The application scale in field constantly expands, and global commerce remote sensing satellite enters versatility and updates and industrialized development period.Tradition
Single earth observation satellite imaging breadth is limited, even if being increased using the method for image mosaic by limited side-sway automotive
Breadth, it is also difficult to guarantee the resolution ratio and the uniformity of time of every earth observation image.With the development of satellite Development Techniques,
It is gradually attracted attention using the technology of satellites formation collaboration earth observation.
The earth observation task of big breadth may be implemented using the advantage of satellites formation spatial distribution, wherein how right
It is main difficult point that satellites formation, which optimizes, and on the one hand due to the influence of earth perturbation, most of satellites formations need
Guarantee the stabilization of configuration by active control, however, satellite is motor-driven at this stage still relies primarily on chemical fuel, but satellite carries
Chemical fuel be limited, so design when need consider reduce the earth perturbation influence；And another aspect flight pattern
Design also to consider that observation mission can be efficiently accomplished, guarantee the stabilization of observation swath.Existing Spacecraft formation configuration is set
Meter is theoretical main to consider how formation configuration keeps stable for a long time, application also focus primarily upon the interference of SAR satellite over the ground at
Picture, and about also less using the earth observation task study of the big breadth of Satellite Formation Flying.
Entitled " the satellites formation implementation method towards super breadth imaging over the ground " patent application proposes a kind of based on J2
The super breadth imaging pattern of the Distributed Satellite Formation of stability is designed in orbital plane using keeping formation stable configuration as target
Relative elliptical movement, corresponding orbital tracking is obtained by desired elliptical shape, though be able to solve satellite stare range it is small, at
The problems such as film size width, earth rotation make satellite that can not realize continuous imaging to ground adjacent area, but the satellites formation is real
Existing scheme considers fuel consumption and does not measure ultra-wide imaging effect to stable influence is kept rank, that is, the satellites formation
Implementation cannot meet fuel consumption minimum simultaneously and efficiently accomplish the two requirements of observation mission.
Summary of the invention
Goal of the invention of the invention is the deficiency for above-mentioned background technique, is provided based on the super breadth imaging of NSGA II
The optimization method of satellites formation configuration considers that formation configuration is protected in the case where given single satellite observation swath and side-sway angle
Hold fuel consumption and earth observation breadth ballast, realize Spacecraft formation configuration in track normal orientation super breadth at
The optimization design of picture, solve existing Spacecraft formation cannot meet simultaneously fuel consumption minimum and efficiently accomplish observation mission this
Two the technical issues of requiring.
The present invention adopts the following technical scheme that for achieving the above object
Surpass the optimization method of breadth imaging satellite formation configuration based on NSGAII, comprising the following steps:
1) the fuel consumption function of formation configuration is kept by relative eccentric ratio/dip vector drift calculation
The design of formation configuration uses median orbital elements, need to only consider J in this way2Shadow of the secular term of perturbation to formation configuration
It rings.Classical J2Constant track can guarantee that relative orbit is only considering J2It is steady in a long-term when perturbation, but its constraint is excessively harsh.
The present invention take partially restrained reduce maintain formation configuration fuel consumption, for perturbation caused by form into columns along mark to drift
It moves, can be eliminated by changing semi-major axis deviation, can specifically be expressed as formula (1):
Wherein, δ a is formation spacecrafts track and the semi-major axis deviation with reference to spacecraft orbit, J2For earth J2Perturbation,
a0For the semi-major axis with reference to spacecraft orbit, ReFor earth radius, η0With reference to the orthogonal chord length of spacecraft orbit,δ η=- e0δe/η0, δ η is formation spacecrafts and the orthogonal string deviation of reference spacecraft orbit, e0For with reference to space flight
The eccentricity of device track, i0For the orbit inclination angle with reference to spacecraft, δ i is formation spacecrafts track and reference spacecraft orbit
Inclination deviation.
Fuel consumption caused by drifting about for relative eccentric ratio vector, shown in calculation method such as formula (2):
Wherein, T is the orbital period,Eccentricity for form into columns p-th of spacecraft orbit and reference spacecraft orbit is inclined
Difference, v are the speed with reference to spacecraft, tcFor the Perturbation Effect duration.Since breadth super in present invention imaging is along orbital method
To on direction, do not need Satellite Formation Flying along mark to and radial motion, therefore settable identical eccentricity, then for relatively partially
Fuel consumption caused by heart rate vector drifts about is negligible.
Fuel consumption caused by drifting about for relative inclination vector, shown in calculation method such as formula (3), whereinTo compile
The relative inclination deviation of p-th of spacecraft in team:
The fuel of relative inclination vector drift consumption is directed to for p-th of spacecraft,For p-th of spacecraft orbit
With the inclination deviation of reference spacecraft orbit, by formula (3) it is found that reference orbit inclination angle size and relative inclination vector drift
Fuel consumption is positively correlated, and is not easy to select excessive.Comprehensively consider above-mentioned analysis, excludes the combustion that can be eliminated by amendment or certain constraint
After material consumption, for the formation with n spacecraft, fuel consumption evaluation function can be expressed as formula (4):
Wherein, n is the spacecraft number shared in Spacecraft formation,It is sweared for p-th of spacecraft for relative inclination
The fuel of amount drift consumption.
2) discretization formation motion process construction evaluates the objective function of super breadth imaging effect
According to relative eccentric ratio/dip vector model, after being simplified by linearisation, Satellite Formation Flying is upward in orbital method
Movement can be approximately sinusoidal motion, such as formula (5), shown in (6):
Wherein, rNFor relative position of the formation spacecrafts in reference spacecraft orbit normal direction, δ i is formation spacecrafts rail
The inclination deviation in road and reference spacecraft orbit, i0For the inclination angle with reference to space-flight trajectory, Φ is that formation spacecrafts are opposite with reference to boat
The initial phase of its device track normal direction movement, δ Ω are that formation spacecrafts track and the right ascension of ascending node with reference to spacecraft orbit are inclined
Difference, u are the independent variable about the time.In order to realize super breadth imaging task, it is ensured that each moment is imaged along track normal direction
Breadth is stablized, and therefore, suitable observation can be chosen in track normal orientation perpendicular to the reference star substar direction of motion
Point guarantees that all observation points of each moment can be observed by Satellite Formation Flying.The selection of observation point and its can be observed
To the condition that need to meet, such as formula (7) and (8) are shown respectively:
Wherein, W is wide along track normal direction assembly film size, and m is observation point number, and H is between observation point along track normal direction
Distance, φ0For the angle of visibility of single satellite,For pth satellite t moment along track normal direction away from formation reference center away from
From LjDistance for j-th of observation point along track normal direction away from reference center substar, apIt is the half of p-th of spacecraft orbit of forming into columns
Long axis,The lateral swinging angle along track normal direction allowed for satellite.
Building Satellite Formation Flying observation sequence specifically includes step following six.
Step 1: suitable time interval is chosen, to Satellite Formation Flying along the fortune that orbital method is upward within half of orbital period
The dynamic sliding-model control that carries out obtains distance of each moment Satellite Formation Flying with respect to reference star.
First be that each observation point creates a list step 2: for the k moment, according to formula (8) to each satellite and
Observation point is judged, if meeting observation condition, satellite number is added among the list of corresponding observation point, if not defending
Star can observe Current observation point, then is stored in default flag position, upward in orbital method according to observation point and reference satellite later
The observation satellite list for each observation point that distance from small to large establishes the k moment is ranked up.
Step 3: using recursive algorithm from the observation satellite list for each observation point that the k moment establishes for each sight
Measuring point chooses an observation satellite and obtains all observation sequences at k moment, recurrence will calculate that process is each observation point each time
An observation sequence of the number of the observation satellite of selection as the k moment, and the satellite number being selected is stored in new list, if
It was found that there is repetition satellite number to appear in an observation sequence, then only retain one, remaining repeatable position is changed to default flag
Position, each observation sequence that recursive algorithm each in new list is obtained according to considerable measuring point the descending sequence of quantity.
Step 4: judging the considerable measuring point of k-1 moment observation sequence if there are the observation sequences at k-1 moment in new list
Whether number is less than the observation sequence (i.e. the maximum observation sequence of k moment Observable point quantity) of list first place, if so, will column
Observation sequence of the observation sequence of heading position as the k moment, if it is not, then k moment observation sequence is still the observation sequence at k-1 moment
Column directly select sight of the observation sequence of list first place as the k moment if the observation sequence at k-1 moment is not present in list
Sequencing column.
Step 5: saving the observation sequence at k moment, second step planning subsequent time is returned until whole cycle terminates.
Step 6: the observation sequence sequence according to Satellite Formation Flying, constructs corresponding super breadth imaging effect evaluation function,
Shown in circular such as formula (9):
Obj2=(x α1+y·α2+z·α3)/N (9),
Wherein, x is the number that Satellite Formation Flying observation sequence default value occurs in an orbital period, and N is a track week
The time interval number that phase includes, it is not that empty but observation point is seen without entirely capped Satellite Formation Flying that y, which is in an orbital period,
Column number is sequenced, z is the number that front and back changes close to moment Satellite Formation Flying observation sequence in an orbital period, α1, α2,
α3Respectively its corresponding penalty coefficient.
3) super breadth imaging formation configuration is optimized using NSGAII algorithm
Step 1: population and parameter in initialization NSGAII algorithm, in the application, each of population individual is average
The corresponding orbital method of relative light intensity upward amplitude and phase, are denoted as 2n dimensional vector (A1, A2... An, Φ1, Φ2...
Φn), objective function vector is [Obj1 Obj2], initial parameter includes that the range matrix of population, population scale, most is randomly generated
Big genetic algebra, crossover probability, mutation probability etc..
Step 2: random initializtion starts population P0 and carries out non-dominated ranking to P0, initializes the rank of each individual
Value.
Step 3: filial generation kind is obtained by three algorithm of tournament selection of genetic algorithm, two-point crossover, variation basic operations
Group.
Step 4: carrying out quick non-dominated ranking after parent population is merged with progeny population, meanwhile, to each non-dominant
Individual in layer carries out crowding calculating, shown in calculation method such as formula (10):
Wherein,It indicates to press first of objective function ObjlThe l calculated after sequence according to the latter position individual of the individual
The value of a objective function,It indicates to press first of objective function ObjlIt is calculated after sequence according to the previous position individual of the individual
The value of first of objective function,Respectively first of objective function Obj of the individual same levellMaximum value
And minimum value.
Step 5: corresponding individual is selected from merging population by exclusion and elite retention strategy and forms population of new generation
P1。
Step 6: skipping to step 3, until reaching maximum genetic algebra.
4) average Relative Orbit Elements are converted by the population at individual that optimization obtains
Population at individual after optimization is still 2n dimensional vector (A1, A2... An, Φ1, Φ2...Φn), for Pareto optimality
For the average relative light intensity of p-th of spacecraft in solution, ifThen corresponding average relative orbit is wanted
Element can be derived by by formula (5), (6), as shown by the equation:
δΩp=tan Φp·δip/sini0(12),
δwp+δMp=-δ Ωpcos(i0) (13),
If Φp=± pi/2, then δ ip=0,Shown in average semi-major axis deviation such as formula (1), average phase
To eccentricity deviation be 0, for compensation Satellite Formation Flying because the red diameter deviation of ascending node cause Satellite Formation Flying along mark to offset, can pass through
The sum of the average argument of perigee deviation δ w and average mean anomaly deviation δ M of Satellite Formation Flying are adjusted to realize, such as formula (13) institute
Show.
The present invention by adopting the above technical scheme, has the advantages that
(1) it considers in J2Formation Formation keeping fuel consumption and the super breadth imaging effect of completion are to formation under Perturbation Effect
The influence of configuration design, using fuel consumption evaluation function and super breadth imaging effect evaluation function as multiple-objection optimization object,
Two targets are obtained by using NSGAII algorithm and mutually restrict the Pareto optimality disaggregation under situation, realize minimum fuel consumption
The formation configuration of effectively super breadth imaging optimizes in rail normal direction under constraint.
(2) for the super breadth imaging task along track normal orientation, the application passes through discretization formation earth observation
Journey, definition judge the stable auxiliary sighting point of observation swath, go out formation earth observation task sequence according to algorithmic rule, and thus
Corresponding formation earth observation evaluation goal function is devised, is given a kind of for the logical of the stable observation swath effect of holding of forming into columns
Use appraisal procedure.
Detailed description of the invention
Fig. 1 is that the present invention realizes that the schematic diagram of Spacecraft formation is imaged in super breadth.
Fig. 2 is the flow chart of the super breadth imaging satellite formation configuration optimization method based on NSGAII.
Fig. 3 is the flow chart of super breadth imaging satellite formation observation sequence planning algorithm.
Fig. 4 is that the Pareto forward position that formation configuration optimizes is imaged to super breadth using NSGA II algorithm
Solution.
Fig. 5 is the schematic diagram of observation point observation sequence in an orbital period.
Fig. 6 is the change curve that total breadth is observed in present invention design formation within an orbital period.
Specific embodiment
The technical solution of invention is described in detail with reference to the accompanying drawing.
It is excellent that the present invention for Spacecraft formation shown in FIG. 1 proposes a kind of design of the configuration that detailed process is as shown in Figure 2
Change method, it is contemplated that earth J2Formation Formation keeping fuel consumption and the super breadth imaging effect of completion are to formation structure under Perturbation Effect
The influence of type design, by discretization Spacecraft formation normal direction motion process planning and designing formation observation sequence, using shown in Fig. 3
Flow layout formation observation sequence calculates the function for assessing super breadth imaging effect, acquires the problem using NSGAII algorithm
Pareto disaggregation realizes the optimization design of Spacecraft formation.
Embodiment
Given formation observation swath requires to be 410km, and reference orbit is circular orbit, orbit altitude 630km, single satellite
Imaging breadth is 90km over the ground, along the distance of normal orientation is 80km between observation point, using reference star substar position as origin
O, being perpendicularly to the direction of movement observation point coordinate is respectively [- 160, -80,0,80,160].By the super breadth based on NSGAII at
As satellites formation configuration designing method obtains the Pareto optimization disaggregation of the problem, the opposite rail that the suitable solution construction of selection is formed into columns
Road radical realizes the optimization design of formation configuration.
Initial parameter required for emulating is as shown in table 1, wherein S is population scale, and which determine the optimizing of algorithm effects
Fruit is generally the bigger the better, but its calculation amount that will increase algorithm, is set as 50 here.MAXGEN is the maximum number of iterations of algorithm.
α1, α2, α3Respectively its corresponding penalty coefficient, the scheme bigger to super breadth Imaging, penalty coefficient is accordingly bigger,
It can change according to actual needs.For satellite allow the lateral swinging angle along track normal direction, in order to which image quality pivot angle should not be set
It is excessive.N is the time interval number for an orbital period including, and value is generally by allowing interval time to determine, the orbital period
Longer, satellite maneuvering frequency is about high, and corresponding value is bigger.Fig. 4 show the Pareto forward position solution of the problem obtained after optimization,
Abscissa is super breadth evaluation function, and it is better to be worth smaller observation effect；Ordinate is to form into columns in the time in order to keep structure
Fuel consumed by type, unit m/s.Ordinate is begun to ramp up at Obj2=15, is comprehensively considered imaging effect and is disappeared with fuel
Two factors are consumed, choose Obj2=8.5, the solution at Obj1=0.8 is as optimal solution.Fig. 5 is formation one acquired by optimal solution
The observation sequence of orbital period, synteny does not represent different satellites, and having solid line covering to represent the point can be observed.Fig. 6 is
The change curve of the total observation swath of formation in one orbital period.
The initial setup parameter of 1 analogue simulation of table
Table 2 is formation reference orbit median orbital elements after optimization and Satellite Formation Flying with respect to median orbital elements value.By
For table 2 it is found that in obtained formation median orbital elements, the satellite relative orbit inclination angle that number is 5 is 0, does not need fuel
Consumption can be maintained for a long time stabilization, but due to the requirement of super breadth observation, other number satellites are relative to reference orbit
There are relative orbit inclination angles.Illustrate proposed method really while considering fuel consumption and observation requires two factors.Meanwhile table 3
Give preceding 20 minutes observation sequence schemes of forming into columns in an orbital period, it is seen that observation program is to change over time and change
, observation point is able to satisfy preferable covering, illustrates the validity of observation program planing method.
Formation configuration median orbital elements after table 2 optimizes
Table 3 is preceding ten minutes observation sequence schemes of forming into columns in an orbital period."-", indicates that the point cannot be observed.
The preceding 20 minutes observation sequence schemes of formation in 3 one orbital periods of table
Claims (10)
1. II surpassing the optimization method of breadth imaging satellite formation configuration based on NSGA, which is characterized in that for Satellite Formation Flying along ginseng
The satellites formation for examining the imaging of satellite orbit normal direction ultra-wide ignores fuel consumption caused by eccentricity vector drifts about, considers the earth
J2The fuel consumption building fuel caused by the influence to formation Relative Orbit Elements and meter and the drift of relative inclination vector that perturbs disappears
Evaluation function is consumed, observation point is chosen along track normal direction on perpendicular to the reference satellite substar direction of motion and is surpassed with discretization formation
Breadth observation process determines the Observable satellite of each observation point of each moment using planning algorithm and then constructs the observation sequence at each moment
Column meet number structure motor-driven needed for the duration for stablizing observation swath and Satellite Formation Flying with Satellite Formation Flying in an orbital period
Super breadth imaging effect evaluation function is made, fuel consumption needed for keeping Satellite Formation Flying configuration with reduction and the super breadth imaging of raising
Effect is that optimization aim constructs multi-objective optimization question, solves the Pareto of the multi-objective optimization question most using II algorithm of NSGA
Pareto optimality disaggregation is finally converted to the average Relative Orbit Elements of satellites formation by excellent disaggregation.
2. to surpass the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 1, which is characterized in that
The fuel consumption evaluation function is Obj1,N is the spacecraft number shared in Spacecraft formation
Mesh, X indicate Spacecraft formation set,The fuel of relative inclination vector drift consumption is directed to for p-th of spacecraft,T is orbital period, ReFor earth radius, a0For half with reference to spacecraft orbit
Long axis, J2For earth J2Perturbation, i0For with reference to spacecraft orbit inclination angle,For p-th of spacecraft orbit and refer to space flight
The inclination deviation of device track, v are the speed with reference to spacecraft, tcFor the Perturbation Effect duration.
3. to surpass the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 1, which is characterized in that
Consider earth J2Fuel consumption structure caused by influence and meter and the drift of relative inclination vector perturbed to formation Relative Orbit Elements
During building fuel consumption evaluation function, firstly, drift tangential between formation spacecrafts is eliminated by semi-major axis deviation,
Expression is as follows:So
Afterwards, ignore J2The perigee rotation differential that perturbation generates influences, and derivation calculates formation and only considering J2In the case where perturbation
Eliminate J2The fuel consumed by influence to relative inclination vector that perturbs isWherein, δ
A is the semi-major axis deviation of formation spacecrafts track and reference orbit, J2For earth J2Perturbation, a0For with reference to spacecraft orbit
Semi-major axis, ReFor earth radius, η0With reference to the orthogonal chord length of spacecraft orbit,δ η=- e0δe/η0, e0For
With reference to the eccentricity of spacecraft orbit, i0For the orbit inclination angle with reference to spacecraft, δiFor formation spacecrafts track and refer to spacecraft
The inclination deviation of track, T are the orbital period, and Δ i is that relative inclination Vector Mode is long.
4. II surpassing the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 1, which is characterized in that
The Simplified Motion Equation that Satellite Formation Flying is imaged along reference satellite track normal direction ultra-wide are as follows:Wherein, rNIt is formation spacecrafts in reference spacecraft orbit normal direction
On relative position, δ i be formation spacecrafts track and with reference to spacecraft orbit inclination deviation, δ Ω be formation spacecrafts track
And the right ascension of ascending node deviation of reference spacecraft orbit, i0For the inclination angle with reference to space-flight trajectory, u is the independence change about the time
Amount, Φ are the opposite initial phase for referring to the movement of spacecraft orbit normal direction of formation spacecrafts,
5. II surpassing the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 1, which is characterized in that
The Observable satellite of each observation point of each moment is determined using planning algorithm and then constructs the specific method of the observation sequence at each moment
Are as follows:
Sliding-model control is carried out along orbital method upward movement within half of orbital period to Satellite Formation Flying and obtains each moment volume
Team satellite with respect to reference satellite distance,
The observation satellite list that current time is constructed for each observation point, upward in orbital method according to observation point and reference satellite
Distance is from small to large ranked up the observation satellite list of current time each observation point,
Recurrence each time is calculated that process is the sight of the observation satellite that each observation point is chosen numbered as current time
Sequencing arranges, and has repetition satellite number only to retain one when occurring in an observation sequence, remaining duplicates the column of satellite number
Table data are changed to default flag position, each observation sequence that recurrence each in new list is calculated according to considerable measuring point quantity
Descending sequence,
It, will when the considerable measuring point number of previous moment observation sequence is less than the maximum considerable measuring point number of current time observation sequence
Observation sequence of the current time maximum observation sequence of Observable point quantity as current time, previous moment observation sequence can
When observation point number is greater than the maximum considerable measuring point number of current time observation sequence, then current time observation sequence is still previous
The observation sequence at moment, the observation sequence of previous moment, then it is maximum to directly select current time Observable point quantity if it does not exist
Observation sequence of the observation sequence as current time,
Current time observation sequence is saved, planning subsequent time is until whole cycle terminates.
6. the super breadth imaging satellite formation configuration designing method based on NSGA II according to claim 1, which is characterized in that
The super breadth imaging effect evaluation function of construction is Obj2, Obj2=(x α1+y·α2+z·α3)/N, N are an orbital period
The time interval number for including, x are the number that Satellite Formation Flying observation sequence default value occurs in an orbital period, and y is one
Be not empty but observation point in orbital period without entirely capped observation sequence number, z be in an orbital period before and after close to
The number that the observation sequence at moment changes, α1, α2, α3The respectively corresponding penalty coefficient of x, y, z.
7. II surpassing the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 1, which is characterized in that
The Pareto optimality disaggregation of the multi-objective optimization question is solved using II algorithm of NSGA method particularly includes: by each formation space flight
The be averaged upward amplitude of the corresponding orbital method of relative light intensity and phase mapping of device is each individual in population, using basis
Fuel consumption evaluation function and super breadth imaging effect evaluation function solve the crowding of each individual, retain plan in conjunction with elite
Slightly screening individual optimization population.
8. II surpassing the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 5, which is characterized in that
During the observation satellite list for constructing current time for each observation point, according to expression formula
Judge whether satellite meets observation condition at current time, the observation at the satellite number write-in current time of observation condition will be met
Satellite list defends the observation at default flag position deposit current time if meeting observation condition at current time without satellite
Star,Distance for pth satellite in t moment along track normal direction away from formation reference center, LjIt is j-th of observation point along track
Distance of the normal direction away from reference center substar, apFor form into columns p-th of satellite orbit semi-major axis,It is satellite permission along rail
Dow process to lateral swinging angle.
9. II surpassing the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 7, which is characterized in that
The expression formula of each individual crowding is solved according to fuel consumption evaluation function and super breadth imaging effect evaluation function are as follows: It indicates to press first of objective function ObjlIt is latter according to the individual after sequence
The value for first of objective function that position individual calculates,It indicates to press first of objective function ObjlAfter sequence according to the individual before
The value for first of objective function that one individual calculates, Objl max、Objl minRespectively first of objective function of individual same level
ObjlMaximum value and minimum value.
10. II surpassing the optimization method of breadth imaging satellite formation configuration based on NSGA according to claim 7, which is characterized in that will
Pareto optimality disaggregation is converted to the average Relative Orbit Elements of satellites formation method particularly includes: is pth in Pareto optimal solution
When the range value Ap and phase value Φ p of a spacecraft, if Φ p is not equal to
δΩp=tan Φp·δip/sin i0, δ wp+δMp=-δ Ωpcos(i0), otherwise, δ ip=0,δipIt is p-th
The inclination deviation of spacecraft orbit and reference spacecraft orbit, δ ΩpFor p-th of spacecraft orbit and with reference to spacecraft orbit
Right ascension of ascending node deviation, δ ωpFor p-th of spacecraft and with reference to the average argument of perigee deviation of spacecraft, δ MpIt navigates for p-th
The average mean anomaly deviation of its device and reference spacecraft.
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