CN109828594A - Electromagnetic spacecraft configuration reconstruction method with low fuel consumption and stable process - Google Patents
Electromagnetic spacecraft configuration reconstruction method with low fuel consumption and stable process Download PDFInfo
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Abstract
The invention belongs to the technical field of electromagnetic spacecrafts, and particularly relates to a configuration reconstruction method of an electromagnetic spacecraft with low fuel consumption and stable process. The method mainly comprises the following steps: (S1) calculating an initial relative equilibrium state configuration and a target relative equilibrium state configuration of the electromagnetic spacecraft formation system, respectively, (S2) designing a time interval as a connection period of the expected initial relative equilibrium unstable manifold and the target relative equilibrium stable manifold; (S3) respectively selecting unstable manifolds in the initial relative equilibrium state configuration global manifolds and a certain number of discrete state points on the target relative equilibrium state configuration global manifolds relative to the stable manifolds in the equilibrium state configuration global manifolds, establishing a scalar optimization objective function related to the deviation between the state points, designing pulse speed increment and electromagnetic magnetic moment to enable the scalar optimization objective function to approach 0, and realizing the reconstruction of the two spacecrafts. The invention introduces electromagnetic force control in configuration reconstruction design, fully utilizes the advantage of not consuming fuel and has better stability.
Description
Technical field
The invention belongs to electromagnetism spacecraft technology fields, and in particular to a kind of low electromagnetism stable with process of fuel consumption navigates
Its device formation reconfiguration method.
Background technique
As micro nano spacecraft carries out the enhancing of in-orbit task ability, single big space flight is realized by micro nano spacecraft cluster
Business or the in-orbit mission requirements of new concept is had a high regard for be increasingly becoming typical module.By micro nano spacecraft cluster and reconstruct to realize configuration
Flexibility, be remarkably improved in-orbit task ability, precision, robustness and upgrading ability.Currently, making for conventional inertia thrust
Spacecraft cluster formation reconfiguration has obtained numerous researchs, proposes some optimum design methods；Spaceborne controllable electromagnetic device
Introducing so that micro nano spacecraft manipulation dynamics shows new characteristic, including do not consume fuel, there are relative equilibrium state and
Stability meets dynamics conservation etc..
The prior art is mainly from Reconstruction Planning method, and (especially micro-nano electromagnetism navigates less consideration control object itself
Its device) intrinsic characteristic, there is insufficient, the disadvantages of being only suboptimum of exploiting potentialities in the reconstruction and optimization scheme of design, comprising: (1) not
Electromagnetism spacecraft is made full use of to manipulate self-characteristic, it is bigger than normal that formation reconfiguration consumes fuel；(2) formation reconfiguration process characteristic is focused on not
Foot, there may be Mechanical instability characteristics in the process.
Summary of the invention
The present invention manipulates kinetic characteristics from micro-nano electromagnetism spacecraft, makes full use of the opposite of electromagnetism cluster spacecraft
Step response is balanced, based on handover optimization control between electromagnetism manipulation dynamics invariant manifold design and unstable-stable manifold
Design, it is low with the stable electromagnetism spacecraft configuation reconstructing method of process to obtain meeting fuel consumption, can meet it is long-term, multiple, can
The formation reconfiguration demand of the multiple types demands such as expansion.Specific technical solution of the present invention is as follows:
A kind of fuel consumption is low with the stable electromagnetism spacecraft configuation reconstructing method of process, is applied to double electromagnetism spacecraft groups
At electromagnetism Spacecraft formation system, key step is as follows:
(S1) initial phase of electromagnetism Spacecraft formation system is calculated separately to equilibrium state configuration and target relative equilibrium state structure
Type, detailed process are as follows:
(S11) using the mass center CM of electromagnetism Spacecraft formation system as origin oCM, establish Dynamic Modeling reference frame
oCMXyz, oCMX-axis is along the earth's core CM far from direction, oCMY-axis is along orbital velocity direction, oCMZ-axis and oCMX-axis, oCMIt is straight that y-axis constitutes the right hand
Angular coordinate system is based on coordinate system oCMXyz establishes translational motion kinetics equation of each spacecraft with respect to CM；
(S12) according to the translational motion kinetics equation of each spacecraft, solve electromagnetism Spacecraft formation system radial direction,
Normal direction and tangential relative equilibrium state condition；
(S13) according to radial direction, normal direction and tangential relative equilibrium state condition, system relative equilibrium state X is obtained*, then according to
According to system relative equilibrium state X*The translational motion kinetic model of opposite CM is linearized to obtain electromagnetism Spacecraft formation position
In system relative equilibrium state X*Inearized model；
(S14) by X*The manifold original state of place's design substitutes into system relative equilibrium state X*Inearized model and integrate
To global manifold, the overall situation manifold includes stable manifold and unstable manifold；
(S2) design time section, the time interval are desired initial phase to unstable equilibrium state manifold and target phase
Period is connected to equilibrium state stable manifold；
(S3) initial phase is chosen respectively to the unstable manifold in equilibrium state configuration overall situation manifold, target relative equilibrium state structure
A certain number of discrete state points in stable manifold in type overall situation manifold, and establish excellent about the scalar of deviation between state point
Change objective function, designing impulse speed increment and electromagnetism magnetic moment makes scalar optimization objective function level off to 0, realizes two space flight
Device is from initial phase away from L1 to the reconstruct it is expected at a distance of L2.
Further, two electromagnetism Spacecraft formations are located at the inearized model of X* in the step (S13) are as follows:
Wherein, δ X (τ)=X (τ)-X*(τ), X (τ) indicate the system mode at τ moment, X*The system phase at (τ) expression τ moment
To equilibrium state；I3×3Indicate 3 × 3 unit matrix, B matrix is according to the difference of radial direction, normal direction and circumferentially opposite equilibrium state mode
It is specific as follows with different form:
Diametrically equilibrium state,
Normal direction relative equilibrium state,
Circumferentially opposite equilibrium state
In formula, meetAnd P=μ1zμ2z-μ1yμ2y；
Wherein L is two electromagnetism spacecraft spacing, M1=m2/(m1+m2), m1And m2For the quality of spacecraft 1,2, nCMFor mass center
CM track angular velocity of satellite motion, μ0For space permeability, (μ1x,μ1y,μ1z)、(μ2x,μ2y,μ2z) it is respectively two spacecraft electromagnetism magnetic
Square μ1、μ2In oCMThe projection components of xyz coordinate system.
Further, detailed process in the step (S14) are as follows:
The invariant feature vector for remembering matrix A is Vs, unstable feature vector be Vu, stable manifold Ws, unstable manifold is
Wu, then
Stable manifold original state is Unstable manifold original state is Wherein ε indicates controling parameter, by original stateSubstitute into inearized model, and to t ∈ [0 ∞) and t
∈ (- ∞ 0] integral, obtain stable manifold；By original stateSubstitute into inearized model, and to t ∈ [0 ∞) and t ∈ (- ∞
0] it integrates, obtains unstable manifold.
Further, the step (S3) has process are as follows:
In initial phase to selection moment point τ in unstable equilibrium state manifoldu, 0≤τu≤0.5τm, τmFor the configuration weight of setting
The structure time chooses moment point τ in target relative equilibrium state stable manifolds, 0≤τs≤0.5τm。
By time interval [0,0.5 τm] N parts are divided into, it is corresponding to calculate separately each moment point stable manifold, unstable manifold
Discrete state Ws(τs)∈Ws、Wu(τu)∈Wu, further calculate the deviation Γ (τ of corresponding statesu,τs)=| | r (τs)-r(τu)1
+1000nCM||v(τs)-v(τu)1, noteAt the time of deviation minimum value corresponds between expression state；
Take control program are as follows: apply impulse speed increment in 2N+1 timing node, 2N stage applies constant electricity
The control of magnetic magnetic moment；Constraint condition are as follows:
Wherein Δ vρIndicate the ρ impulse speed increment, ρ is integer, and ρ=1,2 ..., 2N+1, μkIndicate k-th of electromagnetism
Magnetic moment, k are integer, k=1,2 ..., 2N；U indicates control amount, Δ vmax、μmaxThe respectively capacity threshold of corresponding intrument；
Design synthesis objective function J are as follows:
Using particle swarm optimization algorithm (Particle Swarm Optimization, abbreviation PSO) to integrated objective function
Calculating is optimized, obtains meeting mission requirementsApply the smallest control amount U of summation with impulse speed increment.
To be best understood from technical solution of the present invention, relative theory and derivation process are described further below.
1, Dynamic Modeling and normalization design
It sets two electromagnetism Spacecraft formation system mass centers (with symbol ' CM ' characterization) and runs on circular orbit, Dynamic Modeling ginseng
Examine the Hill system o that coordinate system is chosen at CMCMXyz (as shown in Figure 2): oCMX is along the earth's core CM far from direction, oCMY is along orbital velocity side
To oCMZ and oCMx、oCMY constitutes right hand rectangular coordinate system.Based on oCMXyz coordinate system is derived by spacecraft i (i=1,2) phase
To the translational motion kinetics equation of CM are as follows:
In formula, ri=[xi yi zi]TDistance vector for spacecraft i with respect to CM is in oCMThe projection components of xyz coordinate system,
nCMFor CM track angular velocity of satellite motion, miFor spacecraft i mass, uiIt is inertia thrust suffered by spacecraft i (with impulse speed increment list
Sign), Fi EMFor electromagnetic force suffered by spacecraft i, calculation expression are as follows:
In formula, μ0=4 π × 10-7H/m is space permeability, (μ1,μ2) be respectively spacecraft 1 and spacecraft 2 electromagnetism magnetic
Square, r21=r1-r2For the relative distance vector for being directed toward electromagnetism spacecraft 1 from electromagnetism spacecraft 2, r21=| | r21||2, symbol | | |
|22 norms are sought in expression.
Further, m is defined according to mass center CM1r1+m2r2=0 and r21=r1-r2Definition can obtain:
Formula (3) are substituted into formula (2), the relational expression of the CM distance vector corresponding thereto of electromagnetic force suffered by spacecraft can be obtained are as follows:
In formula, M1=m2/(m1+m2)。
For n in cancelling (1)CMWithThe otherness of magnitude, by τ=nCMt、 Substitution formula (1), can obtain
2, relative equilibrium state and its corresponding manifold solution and Configuration design
It is radial: o for two electromagnetism spacecrafts along track radial direction, normal direction and tangential distributionCMThe direction x, it is tangential: oCMThe side y
To normal direction: oCMThe direction z, if given two electromagnetism spacecraft spacing are L, then corresponding relative equilibrium state condition solves are as follows:
Diametrically equilibrium state
Normal direction relative equilibrium state
Circumferentially opposite equilibrium state
In above formula, (μ1x,μ1y,μ1z)、(μ2x,μ2y,μ2z) it is respectively μ1、μ2In oCMThe projection components of xyz coordinate system.
For general dynamics system, given particular state progress manifold calculating is more complicated, hardly results in manifold
Analytic solutions；The present invention is calculated using the numerical value that approximation method carries out manifold.Based on m1r1+m2r2=0 and m1r′1+m2r′2=0, choosing
Taking system mode is X=[x1 y1 z1 x′1 y′1 z′1]T；(x1,y1,z1) it is spacecraft 1 in oCMIt throws the position of xyz coordinate system
Shadow component, (x '1,y′1,z′1) it is spacecraft 1 in oCMThe velocity projections component of xyz coordinate system.
It can be obtained by above-mentioned two electromagnetism spacecraft at a distance of L, radial direction/normal direction/tangential distribution and corresponding relative equilibrium state condition
Relative equilibrium state X out*.In relative equilibrium state X*Locate lienarized equation (5), obtains two electromagnetism Spacecraft formations and be located at X*It is linear
Change model are as follows:
In formula, δ X (τ)=X (τ)-X*(τ), according to radial direction, normal direction and circumferentially opposite equilibrium state mode, 3 × 3 matrix Bs
With following form:
Diametrically equilibrium state
Normal direction relative equilibrium state
Circumferentially opposite equilibrium state
In formula, meetAnd P=μ1zμ2z-μ1yμ2y。
For the matrix A of formula (9), it is respectively present stable (characteristic value being negative corresponding to real part), unstable
(characteristic value being positive corresponding to real part) and central feature vector (characteristic value for being zero corresponding to real part).Wherein, stablize special
Levy vector VsAnd unstable feature vector VuRespective linear combination be respectively formed invariant feature space EsAnd unstable feature space
Eu.In X*(with a small amount of ε characterizations of multiplying property) in neighbouring certain small space, the stable manifold of nonlinear system (formula (5) characterization)Unstable manifoldRespectively with invariant feature space Es, unstable feature space EuIt is tangent.Therefore, correspond to system phase
To equilibrium state X*, global manifold Ws(or Wu) calculate are as follows: by original stateOrGeneration
Enter formula (9), so respectively toT=∞AndT=- ∞Integral obtains its approximate global manifold.Solution model is shown in Fig. 3, WsFor stable manifold,
WuFor unstable manifold；WithRespectively X*A small range selected by the initial shape tangent with stabilization, unstable manifold
State.Ws-、Ws+Respectively relative to X*Negative sense, positive stable manifold；Wu-、Wu+Respectively relative to X*Negative sense, positive unstable
Constant current shape.
Therefore, the reconstruct of two electromagnetism Spacecraft formation relative equilibrium states can be carried out based on manifold, utilize not unsteady flow to greatest extent
The characteristic and electromagnetism of shape manipulate ability, effectively reduce the use of inertia propulsion, specific mentality of designing is as shown in figure 4, X1 *It is initial
Relative equilibrium state configuration, X2 *It is expected relative equilibrium state configuration；Formation reconfiguration is along X1 *Unstable manifold set out, by or
X is transitioned into without intermediate inertia thrust (application of impulse speed increment)2 *Stable manifold.
3, impulse speed increment and electromagnetism magnetic moment process of optimization
(1) determine that desired stable manifold connect the moment with unstable manifold
Access time 0≤τ of sections≤0.5τmAnd 0≤τu≤0.5τm, calculateThe corresponding discrete state W of stable manifolds
(τs)∈Ws, calculateThe corresponding discrete state W of unstable manifoldu(τu)∈Wu, enable discrete variable Γ (τu,τs)=Ws(τs)-
Wu(τu) characterize deviation between selected state (nearly different place track in other words).
By [0,0.5 τm] N parts (in embodiment, N is according to radial direction or the actual conditions values of normal direction formation design) are divided into,
As shown in figure 5, calculating the corresponding Γ (τ of each node using grid-search methodu,τs) value, Γ (τu,τs)=| | r (τs)-r(τu)|
|1+1000nCM||v(τs)-v(τu)||1, r (τs) indicate stable manifold τsThe position at moment, r (τu) indicate unstable manifold τuWhen
The position at quarter, v (τs) indicate stable manifold τsThe speed at moment, v (τu) indicate unstable manifold τuThe speed at moment.|| ||1Table
Show 1 norm.
By comparing, it obtains corresponding to the smallest timing node of Γ, withIt is characterized.
(2) optimization aim and constraint condition
Desired design target is Γ (τu,τs) gradually it is intended to 0, the control program taken are as follows: 2N+1 moment point applies arteries and veins
Rush speed increment Δ vρ, ρ=1,2 ..., 2N+1；2N stage applies constant electromagnetism magnetic moment control μk, k=1,2 ..., 2N.Then
Corresponding optimization design variable and its constraint condition are as follows:
In formula, Δ vmaxAnd μmaxFor the capacity threshold of corresponding intrument, T indicates transposition symbol.
Consider that impulse speed increment applies summationMinimum, and by desired design target Γ (τu,τs)=0 introduces
Optimization object function obtains integrated objective function J are as follows:
(3) impulse speed increment and electromagnetism magnetic moment numerical optimization
Based on built integrated objective function and control amount threshold value constraint condition, using particle swarm optimization algorithm (Particle
Swarm Optimization, abbreviation PSO) calculating is optimized, it obtains meeting mission requirements Γ (τu,τs)=0 and impulse speed
Increment applies the smallest control amount U of summation Δ V.
Using the present invention obtain the utility model has the advantages that the present invention from micro-nano electromagnetism spacecraft manipulate kinetic characteristics, fill
Divide the relative equilibrium step response using electromagnetism cluster spacecraft, based on electromagnetism manipulation dynamics invariant manifold design and shakiness
It is low with the stable electromagnetism spacecraft configuation of process to obtain meeting fuel consumption for handover optimization control design case between fixed-stable manifold
Reconstructing method.The present invention has the advantages that (1) introduces electromagnetic force manipulation, sufficiently benefit in the design of micro nano spacecraft formation reconfiguration
The advantage of fuel is not consumed with it；(2) by impulse speed increment and electromagnetism magnetic moment optimization design, low micro- of fuel consumption is obtained
Nano spacecraft formation reconfiguration scheme；(3) formation reconfiguration extends along dynamics manifold, the sequence balance for making full use of electromagnetism to manipulate
Step response, stability are preferable；(4) design scheme can meet it is long-term, multiple, task dispatching micro nano spacecraft formation reconfiguration need can be expanded
It asks.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart；
Fig. 2 is that two electromagnetism Spacecraft formations model referential and steric configuration schematic diagram；
Fig. 3 is the global flow shape numerical solution schematic diagram of two electromagnetism Spacecraft formation relative equilibrium states；
Fig. 4 is relative equilibrium state formation reconfiguration process schematic of the two electromagnetism Spacecraft formation systems based on invariant manifold；
Fig. 5 is to determine that desired stable manifold connect moment (τ with unstable manifold using grid-search methodu,τs) signal
Figure；
Fig. 6 is relative equilibrium state overall situation manifold figure when two electromagnetism spacecraft radial direction L=25m, wherein (a) is in implementing
Stable manifold figure (b) is unstable manifold figure；
Fig. 7 is relative equilibrium state overall situation manifold figure when two electromagnetism spacecraft normal direction L=25m, wherein (a) is in implementing
Stable manifold figure (b) is unstable manifold figure；
Fig. 8 is the candidate manifold figure radially reconstructed in embodiment；
Fig. 9 is that optimal reconstruct track and impulse speed increment radial in embodiment apply node；
Figure 10 is radial control variable and time chart, wherein when (a) is impulse speed incremental value and its applies
Between scheme；It (b) is electromagnetism magnetic moment control amount and time chart；
Figure 11 is the candidate manifold figure of normal direction reconstruct in embodiment；
Figure 12 is that the optimal reconstruct track of normal direction and impulse speed increment apply node in embodiment；
Figure 13 is the control variable and time chart of normal direction, wherein when (a) is impulse speed incremental value and its applies
Between scheme；It (b) is electromagnetism magnetic moment control amount and time chart.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples.
If Fig. 1 is the method for the present invention flow chart, a kind of low electromagnetism spacecraft configuation stable with process of fuel consumption is reconstructed
Method is applied to double electromagnetism Spacecraft formations,
(S1) the initial equilibrium state configuration and target equilibrium state configuration of electromagnetism Spacecraft formation system, including step are calculated separately
Suddenly (S11)-(S14):
(S11) Dynamic Modeling reference frame o is establishedCMXyz is based on coordinate system oCMXyz establishes each spacecraft phase
To the translational motion kinetics equation of CM；
(S12) according to the translational motion kinetics equation of each spacecraft, solve electromagnetism Spacecraft formation system radial direction,
Normal direction and tangential relative equilibrium state condition；
(S13) according to radial direction, normal direction and tangential relative equilibrium state condition, system relative equilibrium state X is obtained*, then according to
According to system relative equilibrium state X*It establishes electromagnetism Spacecraft formation and is located at system relative equilibrium state X*Inearized model；
(S14) original state of system is substituted into system relative equilibrium state X*Inearized model and integral obtain global flow
Shape, the overall situation manifold includes stable manifold and unstable manifold；
(S2) design time section, the time interval connect the period with unstable manifold for desired stable manifold；
(S3) unstable manifold in initial equilibrium state configuration overall situation manifold, target equilibrium state configuration global flow are chosen respectively
A certain number of discrete state points on unstable manifold in shape, and establish the scalar optimization target about deviation between state point
Function, design constraint make scalar optimization objective function level off to 0, realize two spacecrafts from initial phase away from L1 to desired phase
Reconstruct away from L2.
Numerical simulation certificate parameter table of the present invention is shown in Table 1.
1 numerical simulation parameter of table
| Parameter | Numerical value | Unit |
| nCM | 7.26×10-5 | rad/s |
| m1 | 150 | kg |
| L | 25/50 | m |
| μ1x(diametrically equilibrium state) | 3587/20292 | Am2 |
| μ1z(normal direction relative equilibrium state) | 2071/11716 | Am2 |
| Δvmax | 1 | mm/s |
| μmax | 30000 | Am2 |
| ε | 0.001 | - |
Wherein electromagnetism magnetic moment (μ1x, μ1z) to correspond to L data be initial phase away from 25m and expectation apart to the "/" both sides data in column
Value in the case of two kinds of 50m.
(1) global manifold
For diametrically equilibrium state, from initial manifold (relative equilibrium state of the corresponding two electromagnetism spacecrafts at a distance of L=25m)
Integrate TCM(mass center orbital period is TCM, TCM=2 π/nCM), corresponding global flow shape is as shown in fig. 6, stable manifold in figure
Symmetrical with unstable manifold, electromagnetism spacecraft 1 and the corresponding manifold of electromagnetism spacecraft 2 are symmetrical.Stable manifold "+branch " is right in figure
Ying Yu " Ws+ ", stable manifold "-branch " corresponds to " Ws-"；Unstable manifold "+branch " corresponds to " Wu+ ", unstable manifold "-
Branch " corresponds to upper right mark " Wu- ".
Similarly, for normal direction relative equilibrium state, from initial manifold (at a distance of the opposite of L=25m between corresponding two electromagnetism spacecrafts
Equilibrium state) integral 3TCM, corresponding global flow shape is as shown in Figure 7.Comparative analysis is radial to be known with normal direction overall situation manifold: radial phase
It is plane configuration to equilibrium state manifold, and normal direction relative equilibrium state manifold is 3-d modelling.
(2) radial reconstruct
For the radial formation reconfiguration mode from relative equilibrium state L=25m to relative equilibrium state L=50m, according to the present invention
It is as shown in Figure 8 to obtain candidate " unstable manifold-stable manifold " switch mode for method；It takesIt obtains
Optimal reconstruct track and impulse speed increment apply node as shown in figure 9, corresponding impulse speed increment and electromagnetism magnetic moment are as schemed
Shown in 10, analyzed by Figure 10 it is found that the radial direction " L=25m → L=50m reconstruct " based on invariant manifold design consumes impulse speed
Increment is about 3.85mm/s.
(3) normal direction reconstructs
It, to the normal direction reconfiguration mode of relative equilibrium state L=50m, is set according to aforementioned theory for from relative equilibrium state L=25m
It is as shown in figure 11 to obtain candidate " unstable manifold-stable manifold " switch mode for meter.It takesIt obtains
Optimal reconstruct track and impulse speed increment application node are as shown in figure 12, and corresponding impulse speed increment and electromagnetism magnetic moment are shown in
Figure 13 is analyzed by Figure 13 it is found that normal direction " L=25m → L=50m reconstruct " the consumption impulse speed based on invariant manifold design increases
Amount is about 5.71mm/s.
The present invention comprehensively utilizes electromagnetism spacecraft and manipulates intrinsic characteristic, is controlled by impulse speed increment and electromagnetism magnetic moment excellent
Change design, so that micro nano spacecraft formation reconfiguration is as often as possible extended along electromagnetism manipulation manifold, there is less consumption fuel, have
The significant advantages such as intrinsic stability.The present invention verifies (radial formation reconfiguration, normal direction formation reconfiguration) by numerical simulation, effect
It is highly desirable, it is consistent with the expection of design.
Claims (4)
1. a kind of fuel consumption is low with the stable electromagnetism spacecraft configuation reconstructing method of process, it is applied to double electromagnetism spacecrafts compositions
Electromagnetism Spacecraft formation system, which is characterized in that
(S1) initial phase of electromagnetism Spacecraft formation system is calculated separately to equilibrium state configuration and target relative equilibrium state configuration, packet
Include step:
(S11) using the mass center CM of electromagnetism Spacecraft formation system as origin oCM, establish Dynamic Modeling reference frame oCMXyz,
oCMX-axis is along the earth's core CM far from direction, oCMY-axis is along orbital velocity direction, oCMZ-axis and oCMX-axis, oCMY-axis constitutes right hand rectangular co-ordinate
System is based on coordinate system oCMXyz establishes translational motion kinetics equation of each spacecraft with respect to CM；
(S12) according to the translational motion kinetics equation of each spacecraft, radial direction, the normal direction of electromagnetism Spacecraft formation system are solved
And tangential relative equilibrium state condition；
(S13) according to radial direction, normal direction and tangential relative equilibrium state condition, system relative equilibrium state X is obtained*, then according to system
Relative equilibrium state X*The translational motion kinetic model of opposite CM is linearized, electromagnetism Spacecraft formation is obtained and is located at system
Relative equilibrium state X*Inearized model；
(S14) by X*The manifold original state of place's design substitutes into system relative equilibrium state X*Inearized model and integral obtain entirely
Office's manifold, the overall situation manifold includes stable manifold and unstable manifold；
(S2) design time section, the time interval are that desired initial phase is relatively flat to unstable equilibrium state manifold and target
The state stable manifold that weighs connects the period；
(S3) it is complete to unstable manifold, the target relative equilibrium state configuration in equilibrium state configuration overall situation manifold that initial phase is chosen respectively
A certain number of discrete state points in stable manifold in office's manifold, and establish the scalar optimization mesh about deviation between state point
Scalar functions, designing impulse speed increment and electromagnetism magnetic moment makes scalar optimization objective function tend to 0, realizes two spacecrafts from first
The reconstruct begun at a distance of L1 to expectation at a distance of L2, L1, L2 indicate distance value.
2. a kind of fuel consumption as described in claim 1 is low with the stable electromagnetism spacecraft configuation reconstructing method of process, special
Sign is that two electromagnetism Spacecraft formations are located at X in the step (S13)*Inearized model are as follows:
Wherein, δ X (τ)=X (τ)-X*(τ), X (τ) indicate the system mode at τ moment, X*(τ) indicates that the system at τ moment is relatively flat
Weigh state；I3×3Indicate that 3 × 3 unit matrix, B matrix have according to the difference of radial direction, normal direction and circumferentially opposite equilibrium state mode
Different form, specific as follows:
Diametrically equilibrium state,
Normal direction relative equilibrium state,
Circumferentially opposite equilibrium state
In formula, meetAnd P=μ1zμ2z-μ1yμ2y；
Wherein L is two electromagnetism spacecraft spacing, M1=m2/(m1+m2), m1,m2The respectively quality of spacecraft 1, spacecraft 2, nCM
For mass center CM track angular velocity of satellite motion, μ0For space permeability, (μ1x,μ1y,μ1z)、(μ2x,μ2y,μ2z) it is respectively two spacecrafts
Electromagnetism magnetic moment μ1、μ2In oCMThe projection components of xyz coordinate system.
3. a kind of fuel consumption as claimed in claim 2 is low with the stable electromagnetism spacecraft configuation reconstructing method of process, special
Sign is, detailed process in the step (S14) are as follows:
The invariant feature vector for remembering matrix A is Vs, unstable feature vector be Vu, stable manifold Ws, unstable manifold Wu, then
Stable manifold original state is Unstable manifold original state is Wherein ε indicates controling parameter, by original stateSubstitute into inearized model, and to t ∈ [0 ∞) and t
∈ (- ∞ 0] integral, obtain stable manifold；By original stateSubstitute into inearized model, and to t ∈ [0 ∞) and t ∈ (- ∞
0] it integrates, obtains unstable manifold.
4. a kind of fuel consumption as claimed in claim 2 is low with the stable electromagnetism spacecraft configuation reconstructing method of process, special
Sign is that the step (S3) has process are as follows:
In initial phase to selection moment point τ in unstable equilibrium state manifoldu, 0≤τu≤0.5τm, τmFor setting formation reconfiguration when
Between, moment point τ is chosen in target relative equilibrium state stable manifolds, 0≤τs≤0.5τm；
By time interval [0,0.5 τm] N parts are divided into, it is corresponding discrete to calculate separately each moment point stable manifold, unstable manifold
State Ws(τs)∈Ws、Wu(τu)∈Wu, further calculate the deviation Γ (τ of corresponding statesu,τs)=| | r (τs)-r(τu)||1+
1000nCM||v(τs)-v(τu)||1, noteAt the time of deviation minimum value corresponds between expression state, wherein r (τs) indicate
Stable manifold τsThe position at moment, r (τu) indicate unstable manifold τuThe position at moment, v (τs) indicate stable manifold τsMoment
Speed, v (τu) indicate unstable manifold τuThe speed at moment, | | | |1Indicate 1 norm；
Take control program are as follows: apply impulse speed increment in 2N+1 timing node, 2N stage applies constant electromagnetism magnetic
Square control；Constraint condition are as follows:
Wherein Δ vρIndicate the ρ impulse speed increment, ρ=1,2 ..., 2N+1, μkIndicate k-th of electromagnetism magnetic moment, k=1,
2,…,2N；U indicates control amount, Δ vmax、μmaxThe respectively capacity threshold of corresponding intrument；
Design synthesis objective function J are as follows:
Calculating is optimized to integrated objective function using particle swarm optimization algorithm, obtains meeting mission requirements Γ=0 and pulse
Speed increment applies the smallest control amount U of summation.
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