CN103020338A - Low-thrust gravity-assist trajectory solution space pruning method - Google Patents

Abstract

The invention relates to a low-thrust gravity-assist trajectory solution space pruning method and belongs to the field of deep space detection trajectory design. The low-thrust gravity-assist trajectory solution space pruning method comprises the following steps: obtaining a related parameter set for carrying out low-thrust initial design according to the task demands and discretizing design parameters; constructing related constraint conditions and verifying to obtain each group of data in a solution space, rejecting a non-feasible solution, adopting an inverse six-time polynomial approximation low-thrust transfer trajectory in the process and judging related parameter values (speed increment and maximum acceleration value) obtained by a shape approximation technology; and meanwhile, introducing a planet gravity-assist model, splicing all low-thrust arc sections and calculating the speed of a detector after the detector passes through planet gravity to eliminate the speed matching error and improve the calculation accuracy. The method has the beneficial effects that low-thrust gravity-assist transfer trajectories with different task types can be quickly designed according to the given initial and tail end boundary conditions, the calculation precision is effectively improved, and the low-thrust gravity-assist trajectory solution space pruning method is suitable for the transfer trajectory design of intersection type detection tasks, overflight type detection tasks and other various ways of detection tasks.

Description

A kind of low thrust is borrowed power track solution space cutting method

Technical field

The present invention relates to a kind of low thrust and borrow power track solution space cutting method, belong to survey of deep space Track desigh field.

Background technology

In the survey of deep space task, which kind of flight scheme detector takes, and needs to consume how much fuel and could arrive the problem that the target celestial body is the task design first concern.Because the target range earth of survey of deep space is remote, detector usually need to consume huge energy and could realize to the transfer of target celestial body, and the characteristics that traditional chemical propulsion system specific impulse is low, quality is heavy have shown its deficiency.Scientist is seeking new Push Technology and flight theory, the restriction that brings to the survey of deep space task to break through traditional flying method always.Under this demand, high-level efficiency low thrust propulsion system take the sun power electric propulsion as representative arises at the historic moment on the one hand, the low thrust propulsion system has than the advantage of leaping high, quality is light, can effectively reduce the fuel consumption of detector in flight course, and then improves the useful load of detector; On the other hand, along with the deep development of celestial mechanics theory, planet also in succession is found by means of celestial mechanics mechanism such as power and proposes, and the flying method that these novel theories are deep space probe has brought technical renovation.Advanced low thrust propulsion system borrows power mechanism to combine with novel planet, will provide how ingenious efficient detecting strategy for the survey of deep space task, is considered to a kind of branch mode that very efficiently, has broad prospect of application.Yet for borrow the survey of deep space track of power technology in conjunction with low thrust and planet for, its solution space complex distribution, rule difficulty are sought, extreme point is various.Usually be divided into initial designs when carrying out the design of this type of track and accurately design two steps, the purpose of initial designs is to provide feasible track key parameter initial value for accurately designing.An important step is exactly the infeasible region that weeds out in the solution space in the initial designs process, and this link also is to guarantee the correct feasible prerequisite of initial designs result, is present survey of deep space field technology personnel outline problem.

Aspect initial designs, a kind of method commonly used is to adopt pattern curve to approach track, formerly technology [1] is (referring to Petropoulos A E, Longuski J M.Shape-based algorithm forautomated design of low-thrust, gravity-assisttrajectories[J] .Journal of Spacecraft and Rockets, 2004,41 (5): 87-796.), Petropoulos adopts sinusoidal index curve to approach Low-thrust trajectory, and borrow each low thrust segmental arc of power model splicing in conjunction with planet, and then by the feasible preliminary orbit of extensive parameter search, yet the method need to consume a large amount of time when the initial transfer orbit solution space of search.

Technology [2] (Pascale D P formerly, Vasile M.Preliminary Design ofLow-Thrust Multiple Gravity-Assist Trajectories[J] .Journal ofSpacecraft and Rockets, 2006,43 (5): 1065-1076.), Pascale utilizes puppet orbital tracking thought in the first point of Aries, improves a kind of method that Orbit of Rendezvous is analyzed that can be used for that proposes by the offset of sinusoidal index curve.Yet the method has been introduced a plurality of undetermined parameters, has increased the complexity of problem, and the problem solving difficulty is increased.

Technology [3] (Sch ü tzea O formerly, Vasile M, Junge O, Dellnitz M, Izzo D.Designing optimal low-thrust trajectories using space pruning anda multi-objective approach[J], Engineering Optimization, 2009,41 (2): 155-181.), Sch ü tzea etc. are by means of sinusoidal index curve thought, and borrow the solution space of power track to analyze by structure related constraint condition to low thrust.Yet the method borrows power place introducing speeds match error to allow mechanism at planet, and solving precision is had a great impact, and is not suitable for simultaneously the transfer orbit of design intersection type.

Summary of the invention

The objective of the invention is to borrow the problem that power transfer orbit solution space is complicated, extreme point is various for solving in the prior art in conjunction with low thrust and planet, proposed a kind of low thrust and borrowed power track solution space cutting method, can find the solution and obtain in conjunction with low thrust and the efficient solution space of planet by means of the power transfer orbit.

According to mission requirements, problem model is summed up, obtain carrying out the correlation parameter set that low thrust is borrowed the power initial designs, the discretize of design parameter is processed, can obtain the initial solution space that low thrust is intuitively borrowed the power transfer orbit.By structure related constraint condition, and every group of data in the checking gained solution space, to judge whether respectively organize parameter satisfies constraint condition, reject infeasible solution, to adopt in this course contrary six order polynomials to approach Low-thrust trajectory, it can satisfy simultaneously detector and hold boundary constraint and flight time constraint the whole story, and the related parameter values (speed increment, acceleration maximal value) of shape approximation technology gained is judged, then carries out the rejecting of infeasible solution; Also borrow each low thrust segmental arc of power model splicing by introducing planet in addition, borrow speed after the power with calculating detector through planet, but this operation release rate matching error improves computational accuracy.The method can be according to holding the given whole story boundary condition to borrow the power transfer orbit to carry out rapid Design to the low thrust of different task type.

Step 1 is set up solution space

Detector is at t ₀Constantly from celestial body A, arrive target celestial body B after the one or many planet is borrowed power, then the design parameter in the solution space comprises:

(1) time parameter $T_{\mathrm{Launch}},T_{\mathrm{Flyby}}^1,...T_{\mathrm{Flyby}}^i...,T_{\mathrm{Flyby}}^n,T_{\mathrm{End}},$ T wherein _Launch, T _EndThe moment that represents respectively x time and the arrival target celestial body of detector,

The expression detector leaps i the x time of borrowing the power celestial body, i=1, and 2 ..., n, n is for borrowing power celestial body sum;

(2) each low thrust segmental arc is around the rotating cycle of the day heart

(3) speed parameter $V_{\∞}^A,V_{\∞-}^1,...V_{\∞-}^i...,V_{\∞-}^n,V_{\∞}^B,$ Wherein

Be respectively the velocity of escape of fleeing from celestial body A and the relative velocity of target approach celestial body B, For entering i by means of the speed behind the power celestial body;

(4) B plane angle b ₁... b _iB _nWith borrow the power height

B wherein _iBe the i time planet B plane angle when borrowing power,

Be that the i time planet borrowed the height of power.

Set up parameter sets Z:

$Z=\left\{\begin{array}{c}{T}_{\mathrm{Launch}},T_{\mathrm{Flyby}}^1,...T_{\mathrm{Flyby}}^i...,T_{\mathrm{Flyby}}^n,T_{\mathrm{End}},\\ {\mathrm{<figure-callout\; id="1"\; label="n\; rev"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">n</figure-callout>}}_{\mathrm{rev}}^{},...n_{\mathrm{rev}}^i...n_{\mathrm{rev}}^n,V_{\&infin;}^A,V_{\&infin;-}^1,...V_{\&infin;-}^i...,\\ V_{\&infin;-}^n,V_{\&infin;}^B,{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">b</figure-callout>}}_1,...b_i...b_n,{\mathrm{<figure-callout\; id="1"\; label="h\; p"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">h</figure-callout>}}_p^{},...h_p^i...h_p^n\end{array}\right\}$

The process of setting up of solution space is:

Step 1.1 to the time parameter discretize, is set up low thrust and is borrowed the search volume of power track on time domain.

At i section low-thrust trajectory, its initial time is

Wherein

Represent i-1 the lower limit of borrowing power celestial body launching phase,

The expression x time upper limit; Its terminal moment is

By to the initial time of low thrust segmental arc and the discretize in the terminal time range, construct the search volume that is based upon on the time domain.

Step 1.2 is decomposed into tangential velocity and radial velocity with the speed variable, carries out respectively discretize, sets up tangential velocity search volume and radial velocity search volume.The relative i of detector admission velocity of borrowing the power celestial body

Be described as Wherein Be respectively speed tangential component and radial component; Two variation ranges corresponding to component are respectively

With

Variation range is carried out discretize process, have integer

With Satisfy following condition

$d{V}_{\&infin;-\tan }^{i-1}=\frac{{\stackrel{\&OverBar;}{V}}_{\&infin;-\tan }^{i-1}-{\underset{\&OverBar;}{V}}_{\&infin;-\tan }^{i-1}}{N_{\&infin;-\tan }^{i-1}},d{V}_{\&infin;-\mathrm{radial}}^{i-1}=\frac{{\stackrel{\&OverBar;}{V}}_{\&infin;-\mathrm{radial}}^{i-1}-{\underset{\&OverBar;}{V}}_{\&infin;-\mathrm{radial}}^{i-1}}{N_{\&infin;-\mathrm{radial}}^{i-1}}$

With

Be respectively the step sizes that tangential component and radial component are taked for making up the admission velocity search volume.

Step 1.3 borrows force parameter to carry out discretize to each low thrust segmental arc around the number of turns, the planet of the day heart, constructs number of turns search volume, borrows the force parameter search volume.The described force parameter of borrowing comprises by means of power height, B plane angle.

A plurality of search volumes that step 1.1 to step 1.3 obtains are made up, obtain altogether K group discretize parameter, and the composition of every group of parameter comprises time, tangential velocity, radial velocity, the number of turns and borrows force parameter.K group discretize parameter forms design parameter discrete space Ω.

Step 2 is transferred data in the design parameter discrete space that step 1 sets up, and calculates solution space and shears required parameter value.

Step 2.1 determines that detector holds condition the whole story

Extract one group of parameter from parameter space Ω, determine detector at the state at each celestial body place, and the flight time of each low thrust segmental arc.

When carrying out the i time planet by means of power, by time parameter, obtain to hold the whole story Position And Velocity of celestial body, and determine that according to the speed parameter that extracts detector carries out the state before planet is borrowed power:

R, v are that detector is in terminal position and the speed of i section track;

Respectively expression

Constantly borrow the Position And Velocity of power celestial body.

According to the admission velocity in institute's extracting parameter, by means of power height, B plane angle, obtain the relative velocity of detector when borrowing the power celestial body by means of escaping after the power:

$V_{\&infin;+}^i=\left|V_{\&infin;-}^i\right|\left[\begin{array}{ccc}S& T& R\end{array}\right]\left[\begin{array}{c}{\cos \mathrm{\&delta;}}_i\\ -\sin {\mathrm{\&delta;}}_i\cos b_i\\ -\sin {\mathrm{\&delta;}}_i\sin b_i\end{array}\right]$

T=S * h/|S * h|, vector of unit length h=[0,0,1] perpendicular to borrowing power celestial body ecliptic plane, R=S * T, b _iBe the B plane angle, flying out affects speed before the ball by means of the power celestial body With

Between deflection angle δ _iFor

$\sin ({\mathrm{\&delta;}}_i/2)=\frac{1}{1+(h_p^i+r_p^i){\left|V_{\&infin;-}^i\right|}^2/{\mathrm{\&mu;}}_p^i}$

For borrowing the power height,

For borrowing power celestial body radius,

For borrowing power celestial body gravitation constant.

Detector through the i time by means of the flying speed after the power is

Will

With

Respectively as detector initial velocity and the initial position of i+1 section track.

Step 2.2 is calculated thrust acceleration and speed increment

According to the pattern curve approach method, and detector end at the whole story condition that step 2.1 obtains is determined contrary six order polynomial coefficients, the speed increment of finding the solution thrust acceleration scheme and corresponding low thrust segmental arc.

The thrust acceleration of i section is

$F_i=\frac{-\mathrm{\&mu;}}{{2r}^3\cos \mathrm{\&gamma;}}\frac{{6a}_3+24a_4\mathrm{\&theta;}+60a_5{\mathrm{\&theta;}}^2+120a_6{\mathrm{\&theta;}}^3-\left(\tan \mathrm{\&gamma;}\right)/\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">r</figure-callout>}}{1/r+{2a}_2+6a_3\mathrm{\&theta;}+12a_4{\mathrm{\&theta;}}^2+20a_5{\mathrm{\&theta;}}^3+30a_6{\mathrm{\&theta;}}^4}$

I section orbital velocity increment is

${\mathrm{\&Delta;V}}_i={\&Integral;}_0^{{\mathrm{\&theta;}}_f^i}{F}_i\left(\mathrm{\&theta;}\right)/\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\mathrm{d\&theta;}$

A wherein _i(i=0,1 ..., 6) and be the inverse polynomial coefficient, r is the radius vector size of detector track, the transfer phase angle that θ is detector in day heart inertial system, μ is the gravitational constant of the sun, γ is the flight-path angle of detector, initial phase angle theta ₁=0, at the phase angle of i section track end

θ ₂Constantly launch the angle between celestial body and the target celestial body for setting out, n _RevThe number of turns that in transfer process, turns over around the sun for detector.

Step 3, each group parameter that invocation step 1 obtains, and by execution in step 2, obtain detector corresponding to each group parameter and hold state, thrust acceleration and speed increment the whole story, whether 1 call parameters of criterion determination step is feasible according to shearing, but the most remaining all line parameters form final feasible solution space.

Shearing criterion of the present invention has:

1) maximal rate increment constraint

Obtain the speed increment Δ V of each low thrust segmental arc by step 2 _i, when the speed increment that consumes greater than the corresponding low thrust segmental arc that sets

The time, show that one group of parameter calling is infeasible, it is rejected from solution space.

2) peak acceleration constraint

Obtain the acceleration F of each low thrust segmental arc by step 2 _iIf the maximal value of i thrust segmental arc surpasses the maximum thrust acceleration that propulsion system can provide in the i section

Then from solution space, reject corresponding call parameters.

3) forward direction is sheared

According to 1), 2) principle judges: time domain

On T _iWhether be impossible due in constantly.If judge T _iConstantly be impossible due in, then T _iCan not become

X time on the time domain relates to T _iParameter sets be infeasible solution, delete all and relate to T _iParameter sets.

4) backward shearing

According to 1), 2) principle judges: time domain

On

Whether be impossible x time constantly.If judge

Constantly be impossible x time, then

Can not become

On time of arrival, relate to Parameter sets all be infeasible solution, carry out solution space and delete.

Reject infeasible territory in the solution space according to above-mentioned criterion, finally obtain solution space.

If the step-length of choosing during parameter discrete in the step 1 is less, the solution space scale is larger, and the gained solution space is also more accurate.

Beneficial effect

The given low thrust of the present invention is borrowed power transfer orbit solution space cutting method, be used for interplanetary low thrust and borrow the initial designs of power transfer orbit, operation is directly perceived, the precision of can Effective Raise calculating, and the method is applicable to the intersection type, leaps the transfer orbit design of the various ways detection missions such as type.

Description of drawings

Fig. 1 is the process flow diagram of the inventive method;

Fig. 2 is that low thrust is borrowed power transfer orbit synoptic diagram in the embodiment;

Fig. 3 is the solution space on the earth in the embodiment-Mars section time domain;

Fig. 4 is the solution space on Mars in the embodiment-Jupiter section time domain;

Fig. 5 is the earth-Mars in the embodiment-Jupiter transfer orbit;

Fig. 6 is the earth-Mars in the embodiment-Jupiter thrust acceleration.

Embodiment

In order to further specify objects and advantages of the present invention, below in conjunction with drawings and Examples content of the present invention is described further.

Detector is at t ₀Constantly from celestial body A, after the one or many planet is borrowed power, arrive target celestial body B, transfer orbit as shown in Figure 2, at t ₀Constantly, the speed of celestial body A is

The velocity of escape of detector is v _A(t ₀), at t _iConstantly, detector enters i and borrows the power celestial body, and relative velocity is

Process is borrowed power n time, surveys at t _fConstantly arrive target celestial body B.

For the low thrust acting section, the Simplified Motion Equation of detector is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;\&CenterDot;}{r}-r{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}^2+\mathrm{\&mu;}/{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA00002495379900032.png"\; state="\{\{state\}\}">r</figure-callout>}}^2=F\sin \mathrm{\&alpha;}\\ \stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}r+2\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\stackrel{\&CenterDot;}{r}=F\cos \mathrm{\&alpha;}\end{array}\right.$

R is the radius vector size of detector track, the transfer phase angle that θ is detector in day heart inertial system, and μ is the gravitational constant of the sun, and F is the thrust acceleration magnitude, and α is angle of direction of the thrust.

Adopt contrary six order polynomial curves to approach low thrust and shift segmental arc

$r=\frac{1}{a_0+a_1\mathrm{\&theta;}+a_2{\mathrm{\&theta;}}^2+a_3{\mathrm{\&theta;}}^3+a_4{\mathrm{\&theta;}}^4+a_5{\mathrm{\&theta;}}^5+a_6{\mathrm{\&theta;}}^6}$

In the following formula, a _i(i=0,1 ..., 6) be the inverse polynomial coefficient.

The initial phase angle theta of detector ₁=0, in the phase angle theta of track end _f=θ ₂+ 2n _Tevπ, n _TevThe number of turns that in transfer process, turns over around the sun for detector.Can be in the hope of coefficient a according to detector track segment boundary at whole story condition ₀, a ₁, a ₂, a ₄, a ₅, a ₆Unknowm coefficient a ₃Can approach the satisfied constraint of actual flight time of track by order tries to achieve

$f\left(a_3\right)={\&Integral;}_0^{{\mathrm{\&theta;}}_f}(1/\stackrel{\&CenterDot;}{\mathrm{\&theta;}})\mathrm{d\&theta;}-\mathrm{\&Delta;T}=0$

Δ T is the actual flying time of detector.

Adopt the B areal model to describe the i time planet and borrow power, have

$V_{\&infin;+}^i=\left|V_{\&infin;-}^i\right|\left[\begin{array}{ccc}S& T& R\end{array}\right]\left[\begin{array}{c}{\cos \mathrm{\&delta;}}_i\\ -\sin {\mathrm{\&delta;}}_i\cos b_i\\ -\sin {\mathrm{\&delta;}}_i\sin b_i\end{array}\right]$

For detector enters by means of the speed behind the power celestial body,

Vector of unit length h=[0,0,1] perpendicular to borrowing power celestial body ecliptic plane, T=S * h/|S * h|, R=S * T, b _iBe the B plane angle, flying out affects speed before the ball by means of the power celestial body

With

Between deflection angle δ _iCan be expressed as

$\sin ({\mathrm{\&delta;}}_i/2)=\frac{1}{1+(h_p^i+r_p^i){\left|V_{\&infin;-}^i\right|}^2/{\mathrm{\&mu;}}_p^i}$

For borrowing the power height,

For borrowing power celestial body radius, For borrowing power celestial body gravitation constant.

Use the present invention and borrow power track solution space to shear to low thrust, must determine to comprise the parameter that relates to: (1) time parameter, namely detector experiences the moment of each celestial body; (2) each low thrust segmental arc is around the rotating cycle of the day heart; (3) speed parameter comprises velocity of escape and enters the speed of respectively borrowing the power celestial body; (4) planet is borrowed force parameter, i.e. B plane angle and borrow the power height.

$Z=\left\{\begin{array}{c}{T}_{\mathrm{Launch}},{\mathrm{<figure-callout\; id="1"\; label="T\; Flyby"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{Flyby}}^{},...T_{\mathrm{Flyby}}^i...,T_{\mathrm{Flyby}}^n,T_{\mathrm{End}},\\ {\mathrm{<figure-callout\; id="1"\; label="n\; rev"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">n</figure-callout>}}_{\mathrm{rev}}^{},...n_{\mathrm{rev}}^i...n_{\mathrm{rev}}^n,V_{\&infin;}^A,V_{\&infin;-}^1,...V_{\&infin;-}^i...,\\ V_{\&infin;-}^n,V_{\&infin;}^B,{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">b</figure-callout>}}_1,...b_i...b_n,{\mathrm{<figure-callout\; id="1"\; label="h\; p"\; filenames="HDA00002495379900021.png"\; state="\{\{state\}\}">h</figure-callout>}}_p^{},...h_p^i...h_p^n\end{array}\right\}$

Constraint condition has the initial and end-state constraint of detector, and the position constraint when borrowing power is borrowed the constraint of power height and B plane angle.

By the solution space that parameter Z is brought, employing solution space cutting method is rejected the infeasible territory in the solution space, at first will carry out the foundation of track solution space, and concrete operations are:

1) set up the basic search space of preliminary orbit, the basic search space is based upon on the basis to the time parameter discretize.At i section track, its initial time is

Wherein

The lower limit of expression launching phase, The expression x time upper limit; Same, this section track end is constantly

By to initial time and time of arrival scope discretize, can construct the basic search space that is based upon on the time domain.

2) speed parameter is carried out discretize, the speed variable is decomposed into tangential velocity and radial velocity.Borrow the admission velocity of power celestial body to be for the relative i of detector

Be described as

Two variation ranges corresponding to component are respectively With

They are carried out discretize process, have integer

With

Satisfy following condition

$d{V}_{\&infin;-\tan }^{i-1}=\frac{{\stackrel{\&OverBar;}{V}}_{\&infin;-\tan }^{i-1}-{\underset{\&OverBar;}{V}}_{\&infin;-\tan }^{i-1}}{N_{\&infin;-\tan }^{i-1}},d{V}_{\&infin;-\mathrm{radial}}^{i-1}=\frac{{\stackrel{\&OverBar;}{V}}_{\&infin;-\mathrm{radial}}^{i-1}-{\underset{\&OverBar;}{V}}_{\&infin;-\mathrm{radial}}^{i-1}}{N_{\&infin;-\mathrm{radial}}^{i-1}}$

With

Be respectively the step sizes that tangential component and radial component are taked for making up the admission velocity search volume.

3) to the number of turns of each low thrust segmental arc around the day heart, planet is borrowed force parameter to carry out discretize and is processed, structure relevant parameter space.

After setting up solution space, by transferring the data in the parameter space, carry out the correlation computations of preliminary orbit, in order to according to the requirement of task and the parameter area of some physical quantitys the infeasible territory of separating in the search volume is sheared, wherein main shearing criterion has:

1) maximal rate increment constraint

Can obtain the speed increment of each low thrust segmental arc based on the shape approximation technology, when the speed increment that consumes during greater than the maximal rate increment threshold values that sets, just show that one group of parameter calling is infeasible, thereby it is rejected from solution space.

2) peak acceleration constraint

When the low thrust segmental arc acceleration maximal value that obtains by the shape approximation technology surpassed the maximum thrust acceleration threshold values that propulsion system can provide, parameter set also will be rejected from solution space accordingly.

3) forward direction is sheared

In the solution space shear history, by above-mentioned two kinds of shearing means, can obtain such time, if be specifically described as in time domain On, T _iConstantly become impossible due in, can infer T so _iConstantly can not become

X time on the time domain then carries out the relevant parameter collection and deletes.

4) backward shearing

If

Obtaining detector in basic search space and all the other the relevant parameter search spaces can not be constantly Emission can obtain this moment so Can not become

Time of arrival, delete thereby carry out solution space.

Can effectively reject infeasible territory in the solution space by aforesaid operations, the step-length of choosing when parameter discrete is less, and the solution space scale is larger, and acquired results is also more accurate.

In order to verify the technique effect of this invention, the below borrows the solution space of power transfer orbit to shear with the low thrust of the earth-Mars-Jupiter task, the parameter selection range is as shown in table 1, the low thrust that table 1 has provided the earth-Mars-Jupiter task borrows the power transfer orbit to relate to parameter to comprise that detector borrows power, arrives time of Jupiter from earth transmission, Mars, and the speed of detector escape terrestrial time, Mars admission velocity, Jupiter admission velocity, two thrust segmental arcs are around the day heart number of turns, and Mars is borrowed power height and B plane angle.Table 1 has also provided maximal rate increment threshold values and the peak acceleration threshold values of shearing in the criterion simultaneously.Fig. 3, Fig. 4 have provided respectively the solution space on the earth-Mars section, the Mars-Jupiter section time domain, and wherein dash area is the solution space after shearing.Fig. 5, Fig. 6 provide respectively transfer orbit and the accelerating curve of one group of preliminary orbit using gained solution space of the present invention.

Table 1 mathematical simulation parameter

Can find out by table 1, relative velocity when detector arrives Jupiter is 0km/s, can intuitively find out the feasible time range that detector is launched from Fig. 3 and Fig. 4, after rounding, the rotating cycle of day heart is 0 and can observe out each low thrust segmental arc from Fig. 5, satisfy the constraint condition in the table 1, detector (two thrust segmental arcs) in whole flight course all is to satisfy the constraint of peak acceleration threshold values as seen from Figure 6, during to the calculating of acceleration, correlation parameter is value from table 1 given range all.Thereby the method can effectively cut off low thrust by means of the infeasible territory in the power track solution space, can obtain intuitively solution space synoptic diagram, and can design the transfer orbit of intersection type, in addition, the present invention has effectively eliminated the speeds match error that planet is borrowed the power place.

Claims (4)

1. a low thrust is borrowed power track solution space cutting method, it is characterized in that: may further comprise the steps:

Step 1 is set up solution space

Detector is at t ₀Constantly from celestial body A, arrive target celestial body B after the one or many planet is borrowed power, then the design parameter of solution space comprises:

(1) time parameter $T_{\mathrm{Launch}},T_{\mathrm{Flyby}}^1,...T_{\mathrm{Flyby}}^i...,T_{\mathrm{Flyby}}^n,T_{\mathrm{End}},$ T wherein _Launch, T _EndThe moment that represents respectively x time and the arrival target celestial body of detector,

The expression detector leaps i the x time of borrowing the power celestial body, i=1, and 2 ..., n, n is for borrowing power celestial body sum;

(2) each low thrust segmental arc is around the rotating cycle of the day heart

(3) speed parameter $V_{\&infin;}^A,V_{\&infin;-}^1,...V_{\&infin;-}^i...,V_{\&infin;-}^n,V_{\&infin;}^B,$ Wherein

Be respectively the velocity of escape of fleeing from celestial body A and the relative velocity of target approach celestial body B,

For entering i by means of the speed behind the power celestial body;

(4) B plane angle b ₁... b _iB _nWith borrow the power height

B wherein _iBe the i time planet B plane angle when borrowing power,

Be that the i time planet borrowed the height of power;

The process of setting up of solution space is:

Step 1.1 to the time parameter discretize, is set up low thrust and is borrowed the search volume of power track on time domain;

Step 1.2 is decomposed into tangential velocity and radial velocity with the speed variable, carries out respectively discretize, sets up tangential velocity search volume and radial velocity search volume;

Step 1.3 borrows force parameter to carry out discretize to each low thrust segmental arc around the number of turns, the planet of the day heart, constructs number of turns search volume, borrows the force parameter search volume;

A plurality of search volumes that step 1.1 to step 1.3 obtains are made up, obtain altogether K group discretize parameter, and the composition of every group of parameter comprises time, tangential velocity, radial velocity, the number of turns and borrows force parameter; K group discretize parameter forms design parameter discrete space Ω;

Step 2 is transferred data in the design parameter discrete space that step 1 sets up, and calculates solution space and shears required parameter value;

Step 2.1 determines that detector holds condition the whole story

From Ω, extract one group of parameter, determine detector at the state at each celestial body place, and the flight time of each low thrust segmental arc:

When carrying out the i time planet by means of power, by time parameter, obtain to hold the whole story Position And Velocity of celestial body, and determine that according to the speed parameter that extracts detector carries out the state before planet is borrowed power:

R, v are that detector is in terminal position and the speed of i section track;

Respectively expression

Constantly borrow the Position And Velocity of power celestial body;

According to the admission velocity in institute's extracting parameter, by means of power height, B plane angle, obtain the relative velocity of detector when borrowing the power celestial body by means of escaping after the power:

$V_{\&infin;+}^i=\left|V_{\&infin;-}^i\right|\left[\begin{array}{ccc}S& T& R\end{array}\right]\left[\begin{array}{c}{\cos \mathrm{\&delta;}}_i\\ -\sin {\mathrm{\&delta;}}_i\cos b_i\\ -\sin {\mathrm{\&delta;}}_i\sin b_i\end{array}\right]$

T=S * h/|S * h|, vector of unit length h=[0,0,1] perpendicular to borrowing power celestial body ecliptic plane, R=S * T, b _iBe the B plane angle, flying out affects speed before the ball by means of the power celestial body

With

Between deflection angle δ _iFor

$\sin ({\mathrm{\&delta;}}_i/2)=\frac{1}{1+(h_p^i+r_p^i){\left|V_{\&infin;-}^i\right|}^2/{\mathrm{\&mu;}}_p^i}$

For borrowing the power height, For borrowing power celestial body radius,

For borrowing power celestial body gravitation constant;

Detector through the i time by means of the flying speed after the power is

Will

With

Respectively as detector initial velocity and the initial position of i+1 section track;

Step 2.2 is calculated thrust acceleration and speed increment

According to the pattern curve approach method, and detector end at the whole story condition that step 2.1 obtains is determined contrary six order polynomial coefficients, the speed increment of finding the solution thrust acceleration scheme and corresponding low thrust segmental arc;

The thrust acceleration of i section is

$F_i=\frac{-\mathrm{\&mu;}}{{2r}^3\cos \mathrm{\&gamma;}}\frac{{6a}_3+24a_4\mathrm{\&theta;}+60a_5{\mathrm{\&theta;}}^2+120a_6{\mathrm{\&theta;}}^3-\left(\tan \mathrm{\&gamma;}\right)/r}{1/r+{2a}_2+6a_3\mathrm{\&theta;}+12a_4{\mathrm{\&theta;}}^2+20a_5{\mathrm{\&theta;}}^3+30a_6{\mathrm{\&theta;}}^4}$

I section orbital velocity increment is

${\mathrm{\&Delta;V}}_i={\&Integral;}_0^{{\mathrm{\&theta;}}_f^i}{F}_i\left(\mathrm{\&theta;}\right)/\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\mathrm{d\&theta;}$

A wherein _iBe the inverse polynomial coefficient, i=0,1 ..., 6, r is the radius vector size of detector track, the transfer phase angle that θ is detector in day heart inertial system, and μ is the gravitational constant of the sun, γ is the flight-path angle of detector, initial phase angle theta ₁=0, at the phase angle of i section track end

θ ₂Constantly launch the angle between celestial body and the target celestial body for setting out, n _RevThe number of turns that in transfer process, turns over around the sun for detector;

Each group parameter that step 3, invocation step 1 obtain by the described method of step 2, obtains detector corresponding to each group parameter and holds state, thrust acceleration and speed increment the whole story, and whether 1 call parameters of criterion determination step is feasible according to shearing;

The shearing criterion is:

1) maximal rate increment constraint

Obtain the speed increment Δ V of each low thrust segmental arc by step 2 _i, when the speed increment that consumes greater than the corresponding low thrust segmental arc that sets

The time, show that one group of parameter calling is infeasible, it is rejected from solution space;

2) peak acceleration constraint

Obtain the acceleration F of each low thrust segmental arc by step 2 _iIf the maximal value of i thrust segmental arc surpasses the maximum thrust acceleration that propulsion system can provide in the i section

Then from solution space, reject corresponding call parameters;

3) forward direction is sheared

According to 1), 2) principle judges: time domain On T _iWhether be impossible due in constantly; Can not due in, then T if be judged to be _iCan not become

X time on the time domain is deleted all and is related to T _iParameter sets;

4) backward shearing

According to 1), 2) principle judges: time domain

On

Whether be impossible x time constantly; If be judged to be impossible x time, then

Can not become

On time of arrival, delete all and relate to

Parameter sets;

Reject infeasible territory in the solution space according to above-mentioned criterion, finally obtain solution space.

2. a kind of low thrust according to claim 1 is borrowed power track solution space cutting method, and it is characterized in that: the search volume method for building up on the time domain is:

The initial time of i section low-thrust trajectory is

Wherein

Represent i-1 the lower limit of borrowing power celestial body launching phase,

The expression x time upper limit; Its terminal moment is

To initial time and the terminal time range discretize of low thrust segmental arc, structure is based upon the search volume on the time domain.

3. a kind of low thrust according to claim 1 is borrowed power track solution space cutting method, and it is characterized in that: the method for building up of tangential velocity search volume and radial velocity search volume is:

The relative i of detector admission velocity of borrowing the power celestial body

Be described as Wherein

Be respectively speed tangential component and radial component; Two variation ranges corresponding to component are respectively

With

Variation range is carried out discretize process, have integer

With Satisfy following condition

$d{V}_{\&infin;-\tan }^{i-1}=\frac{{\stackrel{\&OverBar;}{V}}_{\&infin;-\tan }^{i-1}-{\underset{\&OverBar;}{V}}_{\&infin;-\tan }^{i-1}}{N_{\&infin;-\tan }^{i-1}},$ ${\mathrm{dV}}_{\&infin;-\mathrm{radial}}^{i-1}=\frac{{\stackrel{\&OverBar;}{V}}_{\&infin;-\mathrm{radial}}^{i-1}-{\underset{\&OverBar;}{V}}_{\&infin;-\mathrm{radial}}^{i-1}}{N_{\&infin;-\mathrm{radial}}^{i-1}}$

With

Be respectively the step sizes that tangential component and radial component are taked for making up the admission velocity search volume.

4. a kind of low thrust according to claim 1 is borrowed power track solution space cutting method, and it is characterized in that: the step-length of choosing during parameter discrete is less, and the solution space scale is larger, and the gained solution space is more accurate.

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