CN110032768A - A kind of four pulse-orbits intersection optimization method using precise kinetic model - Google Patents
A kind of four pulse-orbits intersection optimization method using precise kinetic model Download PDFInfo
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Abstract
Four pulse-orbits that the invention discloses a kind of using precise kinetic model intersect optimization method, are adapted to optimize there are the multi-turn multiple-pulse precise kinetic orbital rendezvous of long term drift and calculate.Impulse orbit transfer policy optimization for given initial and end state and fixed transfer time calculates.Since other perturbing term magnitudes are much smaller than J2 perturbing term, it can be considered that the optimal solution of the analytic optimum solution and numerical value group shot movable model of J2 perturbation is closer to, can be approached by analytic solutions to numerical solution.The present invention devises a kind of reasonable approach method, finds out the deviation of analytic optimum solution and numerical value optimal solution, so that the SOT state of termination meets intersection constraint.It is computationally intensive that the present invention solves pulse existing in the prior art transfer optimization method, the slow problem of optimal speed.
Description
Technical field
The invention belongs to technical field of aerospace control, and in particular to a kind of four pulse-orbits using precise kinetic model
Intersect optimization method.
Background technique
Orbital rendezvous for middle Low Earth Orbit up to dozens of days controls, and floats naturally if rationally utilized caused by perturbation
It moves, will greatly reduce fuel consumption.The transfer optimization method of majority pulse at present is all directly to establish numerical optimization model, using essence
Positive motion mechanical model is integrated to solve.Since circle number is more, there are a large amount of locally optimal solution, cause it is computationally intensive, it is excellent
It is slow to change speed.Since other perturbing term magnitudes are much smaller than J2 perturbing term, it can be considered that the analytic optimum solution and number of J2 perturbation
The optimal solution of value group shot movable model is closer to, and can be approached by analytic solutions to numerical solution.But because inter-orbital transfer time is very long,
Even the state that small model difference also results in after integrating completely offsets from target.Therefore need to design the reasonable side of approaching
Method finds out the deviation of analytic optimum solution and numerical value optimal solution, so that the SOT state of termination meets intersection constraint.
Summary of the invention
The object of the present invention is to provide a kind of four pulse-orbits using precise kinetic model to intersect optimization method, solves
Pulse transfer optimization method existing in the prior art is computationally intensive, optimal speed slow problem.
The technical scheme adopted by the invention is that a kind of four pulse-orbits using precise kinetic model intersect optimization side
Method is specifically implemented according to the following steps:
Step 1 is established and shifts calculating analytic modell analytical model with the lambert of the perturbation containing J2 of six element representation of orbital tracking, uses
Become the speed increment of rail pulse between any two in calculating；
Step 2 is established containing the J2 pulse optimization analytic modell analytical model to perturb and is solved；
Step 3 establishes the dynamic lambert transfer mathematical calculation model of group shot；
Step 4, establish analytic modell analytical model to group shot movable model transformation model and solution obtain optimal transfer.
The features of the present invention also characterized in that
Step 1 is specifically implemented according to the following steps:
Step 1.1, the analytical dynamics equation to perturb containing J2 indicated with orbital tracking hexa-atomic plain [a, e, i, Ω, ω, M]
Are as follows:
Wherein, J2For terrestrial gravitation second order term, Re is earth radius,For orbit averaging angular speed；
Step 1.2 solves end positions under analytical dynamics model, the lambert transfer calculating that the moment is fixed first, fixed
Adopted lambertJ2_M indicates calculating process:
[vin,vout]=lambertJ2_M (rin,rout,t) (2)
Wherein, rin,routThe start-stop position vector respectively inputted, t are transfer time, vin,voutRespectively to be exported
Start-stop velocity vector, i.e. solution [vin,vout], so that state [rin,vin] according to formula (1) extrapolate t time after be equal to [rout,
vout]；
Step 1.3 calculates the first end of lambert transfer for only considering earth disome gravitation model and tip speed:
Then by vinAs variable is solved, useAs initial value, solve so that [r0, vin] according to formula (1) extrapolation t
Position vector is r after timefInitial velocity vin, it may be assumed that
[r, v]=f (r0,vin,t)
J=| r-rf|=0 (4)
In formula, f indicates the parsing extrapolation process according to formula (1), solves vinAnd vout。
Original state is set in step 2 as [A0,e0,i0,Ω0,ω0,M0], corresponding position speed is [r0,v0], dbjective state
For [Af,ef,if,Ωf,ωf,Mf], corresponding position speed is [rf,vf], initial time is fixed as T0, the end moment is TfIt is fixed,
Umber of pulse is fixed as 4, applies postimpulse orbit computation using formula (1), i.e., spacecraft orbit is pushed into the first pulse first
Moment is pushed into the second pulse time after applying pulse again, applies pulse pusher to third pulse time, then according to space flight at this time
The position of device and terminal position constraint, go out spacecraft in third by the dipulse lambert branching algorithm inverse of J2 analytic modell analytical model
Pulse time applies postimpulse speed and terminal juncture applies the speed before pulse, then third pulse and the 4th impulse magnitude
It can thus calculate, be specifically implemented according to the following steps:
Step 2.1, solution variable x have 9 dimensions:
For first pulsion phase to the duration of initial time, i.e. coasting-flight phase is as follows:
t1=(Tf-T0)x[0] (5)
First impulse magnitude, direction are as follows:
Second pulsion phase is as follows to the duration of first pulse, is limited to less than 1 orbital period:
t2=(Tf-T0)(1-x[0])x[4] (7)
Second impulse magnitude, direction are as follows:
Interval of the third between the 4th pulse is as follows, is limited to less than 1 orbital period, the 4th pulse time
The moment is intersected for terminal:
t3=(Tf-T0)(1-x[0])(1-x[4])x[8] (9)
Step 2.2 sets [r3,v3] it is the shape obtained according to second postimpulse Orbit extrapolation to third pulse time
State, then according to the dipulse lambert branching algorithm of J2 analytic modell analytical model, [vin,vout]=lambertJ2_M (rin,rout, t) and letter
Number calculates the speed increment of third and the 4th pulse, it may be assumed that
[v3 in,v4 out]=lambertJ2_M (r3,rf,t3) (10)
In formula, v3 in,v4 outSpeed after respectively third pulse applies and before the 4th pulse application, then pulse is big
It is small are as follows:
Step 2.3, total optimizing index are to keep 4 subpulse general speed increments minimum:
J=| dv1|+|dv2|+|dv3|+|dv4| (12)
Step 2.4 is solved using differential evolution algorithm, and solution procedure includes being initialized first；Then to population into
Row variation, intersection, selection operation are with Population Regeneration；And renewal process is repeated until meeting the condition of convergence.
Step 3 is specifically implemented according to the following steps:
Step 3.1, the numerical value kinetics equation comprising perturbing term are as follows:
Wherein: r is satellite position vectors, and v is velocity vector, and μ is Gravitational coefficient of the Earth, apFor perturbation acceleration；
Step 3.2 defines lambertJ2_H expression calculating process:
[vin,vout]=lambertJ2_H (rin,rout,t) (14)
Wherein, rin,routThe start-stop position vector respectively inputted, t are transfer time, vin,voutRespectively to be exported
Start-stop velocity vector, i.e. solution [vin,vout], so that state [rin,vin] according to formula (13) extrapolate t time after be equal to [rout,
vout]；
Step 3.3, using the speed solved in step 2 as initial value, then by vinAs solution variable, it may be assumed that
[r, v]=g (r0,vin,t)
J=| r-rf|=0 (15)
In formula, g indicates the numerical integration extrapolation process according to formula (13), solves vinAnd vout。
Step 4 is specifically implemented according to the following steps:
Step 4.1 defines normalized optimized variable x=[x0,x1,x2,x3,x4,x5] have 6 dimensions, respectively second and
The position r of third pulse time2,r3Adjustment amount, r1,rfIt is constant:
In formula, r2'、r3' be respectively lower second of numerical value kinetic model and third pulse time position；
Step 4.2, the difference converted according to flat wink, k=10km, the then speed that 4 pulses apply front and back spacecraft are pressed
It shifts according to multi-turn lambert and is calculated by position vector:
In formula,WithSpacecraft is respectively indicated from r1It is transferred to r2' place initial velocity and tip speed,WithSpacecraft is respectively indicated from r2' it is transferred to r3' place initial velocity and tip speed,WithRespectively indicate spacecraft from
r3' it is transferred to rfThe initial velocity and tip speed at place；
Step 4.3, then four pulses speed increment dvi, i=1,2,3,4 is respectively
Step 4.4, optimizing index and constraint are expressed as:
J=| dv1|+|dv2|+|dv3|+|dv4| (19)
It can be obtained the optimal transfer of four pulses using differential evolution algorithm solution.
The invention has the advantages that a kind of four pulse-orbits using precise kinetic model intersect optimization method, fit
There are the optimizations of the multi-turn multiple-pulse precise kinetic orbital rendezvous of long term drift to calculate by Ying Yu.For given initial and end state
And the impulse orbit transfer policy optimization of fixed transfer time calculates.Since other perturbing term magnitudes are much smaller than J2 perturbing term,
It, can be by analytic solutions to numerical value it is considered that the optimal solution of analytic optimum solution and numerical value group shot movable model of J2 perturbation is closer to
Solution is approached.The present invention devises a kind of reasonable approach method, finds out the deviation of analytic optimum solution and numerical value optimal solution, so that eventually
End state meets intersection constraint.
Detailed description of the invention
Fig. 1 is a kind of flow chart of the four pulse-orbits intersection optimization method using precise kinetic model of the present invention.
Fig. 2 is that a kind of analytic perturbation of the four pulse-orbits intersection optimization method using precise kinetic model of the present invention is excellent
Change model schematic.
Fig. 3 is that a kind of parsing initial value of the four pulse-orbits intersection optimization method using precise kinetic model of the present invention arrives
The transformation model of numerical value optimal solution.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
A kind of four pulse-orbits using precise kinetic model of the present invention intersect optimization method, flow chart as shown in Figure 1,
It is specifically implemented according to the following steps:
Step 1 is established and shifts calculating analytic modell analytical model with the lambert of the perturbation containing J2 of six element representation of orbital tracking, uses
Become the speed increment of rail pulse between any two in calculating, be specifically implemented according to the following steps:
Step 1.1, the analytical dynamics equation to perturb containing J2 indicated with orbital tracking hexa-atomic plain [a, e, i, Ω, ω, M]
Are as follows:
Wherein, J2For terrestrial gravitation second order term, Re is earth radius,For orbit averaging angular speed；
Step 1.2 solves end positions under analytical dynamics model, the lambert transfer calculating that the moment is fixed first, fixed
Adopted lambertJ2_M indicates calculating process:
[vin,vout]=lambertJ2_M (rin,rout,t) (2)
Wherein, rin,routThe start-stop position vector respectively inputted, t are transfer time, vin,voutRespectively to be exported
Start-stop velocity vector, i.e. solution [vin,vout], so that state [rin,vin] according to formula (1) extrapolate t time after be equal to [rout,
vout]；
Step 1.3 calculates the first end of lambert transfer for only considering earth disome gravitation model and tip speed:
Then by vinAs variable is solved, useAs initial value, solve so that [r0, vin] according to formula (1) extrapolation t
Position vector is r after timefInitial velocity vin, it may be assumed that
[r, v]=f (r0,vin,t)
J=| r-rf|=0 (4)
In formula, f indicates the parsing extrapolation process according to formula (1), solves vinAnd vout。
Step 2 is established containing the J2 pulse optimization analytic modell analytical model to perturb and is solved:
Original state is set in step 2 as [A0,e0,i0,Ω0,ω0,M0], corresponding position speed is [r0,v0], dbjective state
For [Af,ef,if,Ωf,ωf,Mf], corresponding position speed is [rf,vf], initial time is fixed as T0, the end moment is TfIt is fixed,
Umber of pulse is fixed as 4, applies postimpulse orbit computation using formula (1), i.e., spacecraft orbit is pushed into the first pulse first
Moment is pushed into the second pulse time after applying pulse again, applies pulse pusher to third pulse time, then according to space flight at this time
The position of device and terminal position constraint, go out spacecraft in third by the dipulse lambert branching algorithm inverse of J2 analytic modell analytical model
Pulse time applies postimpulse speed and terminal juncture applies the speed before pulse, then third pulse and the 4th impulse magnitude
It can thus calculate, be specifically implemented according to the following steps:
Step 2.1, solution variable x have 9 dimensions, as shown in Figure 2:
For first pulsion phase to the duration of initial time, i.e. coasting-flight phase is as follows:
t1=(Tf-T0)x[0] (5)
First impulse magnitude, direction are as follows:
Second pulsion phase is as follows to the duration of first pulse, is limited to less than 1 orbital period:
t2=(Tf-T0)(1-x[0])x[4] (7)
Second impulse magnitude, direction are as follows:
|dv2|=dvmaxx[5]
dv2x=| dv2|cos(2πx[6])
dv2y=| dv2|sin(2πx[6])cos(2πx[7])
dv2z=| dv2|sin(2πx[6])sin(2πx[7]) (8)
Interval of the third between the 4th pulse is as follows, is limited to less than 1 orbital period, the 4th pulse time
The moment is intersected for terminal:
t3=(Tf-T0)(1-x[0])(1-x[4])x[8] (9)
Step 2.2 sets [r3,v3] it is the shape obtained according to second postimpulse Orbit extrapolation to third pulse time
State, then according to the dipulse lambert branching algorithm of J2 analytic modell analytical model, [vin,vout]=lambertJ2_M (rin,rout, t) and letter
Number calculates the speed increment of third and the 4th pulse, it may be assumed that
[v3 in,v4 out]=lambertJ2_M (r3,rf,t3) (10)
In formula, v3 in,v4 outSpeed after respectively third pulse applies and before the 4th pulse application, then pulse is big
It is small are as follows:
Step 2.3, total optimizing index are to keep 4 subpulse general speed increments minimum:
J=| dv1|+|dv2|+|dv3|+|dv4| (12)
Step 2.4 is solved using differential evolution algorithm, and solution procedure includes being initialized first；Then to population into
Row variation, intersection, selection operation are with Population Regeneration；And renewal process is repeated until meeting the condition of convergence.
Step 3 establishes the dynamic lambert transfer mathematical calculation model of group shot, is specifically implemented according to the following steps:
Step 3.1, the numerical value kinetics equation comprising perturbing term are as follows:
Wherein: r is satellite position vectors, and v is velocity vector, and μ is Gravitational coefficient of the Earth, apFor perturbation acceleration；It is (main
It is the function of satellite position, speed including perturbation of earths gravitational field, atmospheric drag, solar light pressure, lunisolar attraction etc., has
Mature calculation method).
Step 3.2 defines lambertJ2_H expression calculating process:
[vin,vout]=lambertJ2_H (rin,rout,t) (14)
Wherein, rin,routThe start-stop position vector respectively inputted, t are transfer time, vin,voutRespectively to be exported
Start-stop velocity vector, i.e. solution [vin,vout], so that state [rin,vin] according to formula (13) extrapolate t time after be equal to [rout,
vout]；
Step 3.3, using the speed solved in step 2 as initial value, then use Minpack kit
By vinAs solution variable, it may be assumed that
[r, v]=g (r0,vin,t)
J=| r-rf|=0 (15)
In formula, g indicates the numerical integration extrapolation process according to formula (13), solves vinAnd vout。
Step 4, establish analytic modell analytical model to group shot movable model transformation model and solution obtain optimal transfer, specifically according to
Lower step is implemented:
Step 4.1, due to other perturbing term magnitudes be less than J2 perturbing term, it can be considered that J2 perturbation analytic optimum solution
It is closer to the optimal solution of numerical value group shot movable model.Numerical value optimal solution can be set compared with analytic optimum solution, turned between pulse
Shift time is constant, and there is an amount trimmed in the position that intermediate two pulses apply the moment, sees attached drawing 3, defines normalized optimization
Variable x=[x0,x1,x2,x3,x4,x5] there are 6 dimensions, the position r of respectively second and third pulse time2,r3Adjustment amount,
r1,rfIt is constant:
In formula, r2'、r3' be respectively lower second of numerical value kinetic model and third pulse time position；
Step 4.2, the difference converted according to flat wink, k=10km, the then speed that 4 pulses apply front and back spacecraft are pressed
It shifts according to multi-turn lambert and is calculated by position vector:
In formula,WithSpacecraft is respectively indicated from r1It is transferred to r2' place initial velocity and tip speed,With
Spacecraft is respectively indicated from r2' it is transferred to r3' place initial velocity and tip speed,WithSpacecraft is respectively indicated from r3'
It is transferred to rfThe initial velocity and tip speed at place；
Step 4.3, then four pulses speed increment dvi, i=1,2,3,4 is respectively
Step 4.4, optimizing index and constraint are expressed as:
J=| dv1|+|dv2|+|dv3|+|dv4| (19)
It can be obtained the optimal transfer of four pulses using differential evolution algorithm solution.
Embodiment
In specific application example, used tracking star orbital road and target satellite track come from (the 9th world GTOC9
Orbit Optimized contest) data file.
Known tracking star and target satellite track are shown in Table 1 respectively, start time (unit MJD2000, TfIt together) is T0=
24111.63 the intersection moment is Tf=24114.51, when transfer, is T=2.88 days a length of.
Table 1 tracks star and target satellite orbital tracking
Initial position and speed and target position speed are then calculated first.
[r0,v0]=[522053.631, -1114330.156, -6901285.848, -4424.105, -6071.874,
638.533]
[rf,vf]=[4740455.489,4037622.516, -3516701.059, -1932.103, -3298.295, -
6419.572]
According to attached drawing 2, the Optimized model under the analytical dynamics equation of 4 pulses is established.Process is that umber of pulse is fixed as 4
It is a, apply postimpulse orbit computation using formula (1), i.e., spacecraft orbit is pushed into the first pulse time first, applies pulse
It is pushed into the second pulse time again afterwards, applies pulse pusher to third pulse time, then according to the position and end of spacecraft at this time
End position constraint goes out spacecraft by the dipulse lambert branching algorithm inverse of J2 analytic modell analytical model and applies in third pulse time
Postimpulse speed and terminal juncture apply the speed before pulse, then thus third pulse and the 4th impulse magnitude can calculate.
Therefore solving variable x has 9 dimensions, and total optimizing index is to keep 4 subpulse general speed increments minimum.
It is calculated using differential evolution algorithm and obtains analytic optimum solution:
The dimension that differential evolution algorithm is arranged is 9, and population number is 100.It is initialized, population is carried out first then
Variation, intersection, selection operation repeat renewal process until meeting the condition of convergence, optimal solution with Population Regeneration are as follows:
Xopt[9]=[0.0081254,0.7172128, -0.409457,0.0197869,0.4598666,
0.00027222897,-0.708910,0.543359,0.00739929].Corresponding speed increment and moment are shown in Table 2, and general speed increases
Amount is 102.4m/s:
2 optimal velocity increment of table
Establish analytic modell analytical model to group shot movable model Optimized model:
Formula (11) are arrived according to formula (5), the position arrow for parsing optimal transfer orbit at the 1st, 2,3 pulse applications is calculated
Amount are as follows:
r1=[4969597.813050483,3916697.428043888, -3013178.929439275] m
r2=[4888736.738673554,3782212.216964675, -3302647.922404093] m
r3=[- 4169891.907243956, -3208239.320903509,4667574.196774956] m
The optimal transfer orbit of numerical value is set according to formula (16)Wherein k=1 000m.
X [6] is 6 dimension optimized amounts of transformation model, and optimizing index is formula (19).
It is calculated using differential evolution algorithm and obtains numerical value optimal solution:
The dimension that differential evolution algorithm is arranged is 3, and population number is 20, solves optimal solution are as follows:
X=[0.1309456, -0.106957, -0.10677567, -0.86676, -0.540467,0.89727].It is then right
The optimal transfer orbit answered can calculate acquisition according to formula (16) to formula (18), be shown in Table 3.General speed increment is 104.3m/s.
3 numerical solution optimal velocity increment of table
Compare jet propulsion laboratory JPL in the 9th international Orbit Optimized contest as a result, identical in design conditions
In the case where, the optimum results that provide are 105.2m/s, it was demonstrated that effect of optimization of the invention is more preferable.
Claims (5)
1. a kind of four pulse-orbits using precise kinetic model intersect optimization method, which is characterized in that specifically according to following
Step is implemented:
Step 1 is established and shifts calculating analytic modell analytical model with the lambert of the perturbation containing J2 of six element representation of orbital tracking, based on
It calculates and becomes the speed increment of rail pulse between any two；
Step 2 is established containing the J2 pulse optimization analytic modell analytical model to perturb and is solved；
Step 3 establishes the dynamic lambert transfer mathematical calculation model of group shot；
Step 4, establish analytic modell analytical model to group shot movable model transformation model and solution obtain optimal transfer.
2. a kind of four pulse-orbits using precise kinetic model according to claim 1 intersect optimization method, special
Sign is that the step 1 is specifically implemented according to the following steps:
Step 1.1, the analytical dynamics equation to perturb containing J2 indicated with orbital tracking hexa-atomic plain [a, e, i, Ω, ω, M] are as follows:
Wherein, J2For terrestrial gravitation second order term, Re is earth radius,For orbit averaging angular speed；
Step 1.2 solves end positions under analytical dynamics model, the lambert transfer calculating that the moment is fixed first, definition
LambertJ2_M indicates calculating process:
[vin,vout]=lambertJ2_M (rin,rout,t) (2)
Wherein, rin,routThe start-stop position vector respectively inputted, t are transfer time, vin,voutThe start-stop respectively to be exported
Velocity vector, i.e. solution [vin,vout], so that state [rin,vin] according to formula (1) extrapolate t time after be equal to [rout,vout]；
Step 1.3 calculates the first end of lambert transfer for only considering earth disome gravitation model and tip speed:
Then by vinAs variable is solved, useAs initial value, solve so that [r0,vin] extrapolate the t time according to formula (1)
Position vector is r afterwardsfInitial velocity vin, it may be assumed that
[r, v]=f (r0,vin,t)
J=| r-rf|=0 (4)
In formula, f indicates the parsing extrapolation process according to formula (1), solves vinAnd vout。
3. a kind of four pulse-orbits using precise kinetic model according to claim 2 intersect optimization method, special
Sign is, original state is set in the step 2 as [A0,e0,i0,Ω0,ω0,M0], corresponding position speed is [r0,v0], target-like
State is [Af,ef,if,Ωf,ωf,Mf], corresponding position speed is [rf,vf], initial time is fixed as T0, the end moment is TfGu
Fixed, umber of pulse is fixed as 4, applies postimpulse orbit computation using formula (1), i.e., spacecraft orbit is pushed into the first arteries and veins first
It rushes the moment, is pushed into the second pulse time again after applying pulse, apply pulse pusher to third pulse time, then basis is navigated at this time
The position of its device and terminal position constraint go out spacecraft the by the dipulse lambert branching algorithm inverse of J2 analytic modell analytical model
Three pulse times apply postimpulse speed and terminal juncture applies the speed before pulse, then third pulse and the 4th pulse are big
It is small thus to calculate, it is specifically implemented according to the following steps:
Step 2.1, solution variable x have 9 dimensions:
For first pulsion phase to the duration of initial time, i.e. coasting-flight phase is as follows:
t1=(Tf-T0)x[0] (5)
First impulse magnitude, direction are as follows:
Second pulsion phase is as follows to the duration of first pulse, is limited to less than 1 orbital period:
t2=(Tf-T0)(1-x[0])x[4] (7)
Second impulse magnitude, direction are as follows:
|dv2|=dvmaxx[5]
dv2x=| dv2|cos(2πx[6])
dv2y=| dv2|sin(2πx[6])cos(2πx[7])
dv2z=| dv2|sin(2πx[6])sin(2πx[7]) (8)
Interval of the third between the 4th pulse is as follows, is limited to less than 1 orbital period, and the 4th pulse time is eventually
The end intersection moment:
t3=(Tf-T0)(1-x[0])(1-x[4])x[8] (9)
Step 2.2 sets [r3,v3] it is the state obtained according to second postimpulse Orbit extrapolation to third pulse time, then
According to the dipulse lambert branching algorithm of J2 analytic modell analytical model, [vin,vout]=lambertJ2_M (rin,rout, t) and function, meter
Calculate the speed increment of third and the 4th pulse, it may be assumed that
[v3 in,v4 out]=lambertJ2_M (r3,rf,t3) (10)
In formula, v3 in,v4 outAfter respectively third pulse applies and the 4th pulse apply before speed, then impulse magnitude are as follows:
Step 2.3, total optimizing index are to keep 4 subpulse general speed increments minimum:
J=| dv1|+|dv2|+|dv3|+|dv4| (12)
Step 2.4 is solved using differential evolution algorithm, and solution procedure includes being initialized first；Then population is become
Different, intersection, selection operation are with Population Regeneration；And renewal process is repeated until meeting the condition of convergence.
4. a kind of four pulse-orbits using precise kinetic model according to claim 3 intersect optimization method, special
Sign is that the step 3 is specifically implemented according to the following steps:
Step 3.1, the numerical value kinetics equation comprising perturbing term are as follows:
Wherein: r is satellite position vectors, and v is velocity vector, and μ is Gravitational coefficient of the Earth, apFor perturbation acceleration；
Step 3.2 defines lambertJ2_H expression calculating process:
[vin,vout]=lambertJ2_H (rin,rout,t) (14)
Wherein, rin,routThe start-stop position vector respectively inputted, t are transfer time, vin,voutThe start-stop respectively to be exported
Velocity vector, i.e. solution [vin,vout], so that state [rin,vin] according to formula (13) extrapolate t time after be equal to [rout,vout]；
Step 3.3, using the speed solved in step 2 as initial value, then by vinAs solution variable, it may be assumed that
[r, v]=g (r0,vin,t)
J=| r-rf|=0 (15)
In formula, g indicates the numerical integration extrapolation process according to formula (13), solves vinAnd vout。
5. a kind of four pulse-orbits using precise kinetic model according to claim 4 intersect optimization method, special
Sign is that the step 4 is specifically implemented according to the following steps:
Step 4.1 defines normalized optimized variable x=[x0,x1,x2,x3,x4,x5] there are 6 dimensions, respectively second and third
The position r of a pulse time2,r3Adjustment amount, r1,rfIt is constant:
In formula, r2'、r3' be respectively lower second of numerical value kinetic model and third pulse time position；
Step 4.2, the difference converted according to flat wink, k=10km, then 4 pulses apply the speed of front and back spacecraft according to more
Circle lambert transfer is calculated by position vector:
In formula,WithSpacecraft is respectively indicated from r1It is transferred to r2' place initial velocity and tip speed,WithRespectively
Indicate spacecraft from r2' it is transferred to r3' place initial velocity and tip speed,WithSpacecraft is respectively indicated from r3' transfer
To rfThe initial velocity and tip speed at place；
Step 4.3, then four pulses speed increment dvi, i=1,2,3,4 is respectively
Step 4.4, optimizing index and constraint are expressed as:
J=| dv1|+|dv2|+|dv3|+|dv4| (19)
It can be obtained the optimal transfer of four pulses using differential evolution algorithm solution.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110765504A (en) * | 2019-10-29 | 2020-02-07 | 北京空间技术研制试验中心 | Orbit design method for rendezvous and docking of spacecraft orbits around the moon |
| CN111090941A (en) * | 2019-12-17 | 2020-05-01 | 哈尔滨工业大学 | Spacecraft optimal Lambert orbit rendezvous method based on multi-objective optimization algorithm |
| CN111268176A (en) * | 2020-01-17 | 2020-06-12 | 中国人民解放军国防科技大学 | Perturbation track four-pulse intersection rapid optimization method |
| CN113060306A (en) * | 2021-03-31 | 2021-07-02 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Multi-pulse intersection iterative guidance method and device for limited thrust and electronic equipment |
| CN113968361A (en) * | 2021-10-28 | 2022-01-25 | 中国西安卫星测控中心 | Analytic calculation method suitable for geosynchronous satellite fixed-point control planning |
| CN114368493A (en) * | 2021-12-01 | 2022-04-19 | 北京航天飞行控制中心 | Orbit-changing control method and device for spacecraft, electronic equipment and medium |
| CN115465475A (en) * | 2022-11-02 | 2022-12-13 | 哈尔滨工业大学 | Inverse orbit intersection detection method and device for large-scale constellation and storage medium |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017005052A1 (en) * | 2015-07-09 | 2017-01-12 | 北京航空航天大学 | Optimization and design method for gradient segmentation of intervals of spacecraft pulse rendezvous trajectory |
| CN107526368A (en) * | 2017-09-12 | 2017-12-29 | 北京理工大学 | A kind of multiple-pulse ring moon satellites formation initial method for considering error |
| CN107992682A (en) * | 2017-12-05 | 2018-05-04 | 北京理工大学 | A kind of optimal multiple-pulse transfer method of interplanetary multi-body system asteroid detection |
-
2019
- 2019-03-15 CN CN201910199227.6A patent/CN110032768B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017005052A1 (en) * | 2015-07-09 | 2017-01-12 | 北京航空航天大学 | Optimization and design method for gradient segmentation of intervals of spacecraft pulse rendezvous trajectory |
| CN107526368A (en) * | 2017-09-12 | 2017-12-29 | 北京理工大学 | A kind of multiple-pulse ring moon satellites formation initial method for considering error |
| CN107992682A (en) * | 2017-12-05 | 2018-05-04 | 北京理工大学 | A kind of optimal multiple-pulse transfer method of interplanetary multi-body system asteroid detection |
Non-Patent Citations (2)
| Title |
|---|
| 童科伟等: "广义多圈Lambert算法求解多脉冲最优交会问题", 《北京航空航天大学学报》 * |
| 荆武兴等: "摄动椭圆参考轨道上的最优精确交会", 《中国空间科学技术》 * |
Cited By (11)
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|---|---|---|---|---|
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| CN111090941A (en) * | 2019-12-17 | 2020-05-01 | 哈尔滨工业大学 | Spacecraft optimal Lambert orbit rendezvous method based on multi-objective optimization algorithm |
| CN111268176A (en) * | 2020-01-17 | 2020-06-12 | 中国人民解放军国防科技大学 | Perturbation track four-pulse intersection rapid optimization method |
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| CN113060306B (en) * | 2021-03-31 | 2022-02-08 | 中国空气动力研究与发展中心设备设计与测试技术研究所 | Multi-pulse intersection iterative guidance method and device for limited thrust and electronic equipment |
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