CN112084581B - Spacecraft low-thrust perturbation intersection trajectory optimization method and system - Google Patents

Spacecraft low-thrust perturbation intersection trajectory optimization method and system Download PDF

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CN112084581B
CN112084581B CN202011013479.4A CN202011013479A CN112084581B CN 112084581 B CN112084581 B CN 112084581B CN 202011013479 A CN202011013479 A CN 202011013479A CN 112084581 B CN112084581 B CN 112084581B
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罗亚中
黄岸毅
李恒年
张进
杨震
严冰
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Abstract

The invention discloses a low-thrust perturbation intersection track optimization method and a system, which comprises the following steps: the orbit number of the spacecraft and the target at the starting time and the intersection time is given, and four-pulse speed increment is calculated; assuming that the small-thrust switch strategy is on-off-on, and estimating two starting time lengths of small thrust; according to the starting time length of the two small thrusts, the middle point moment of the small thrusts is taken as the equivalent pulse moment, and a new four-pulse speed increment is recalculated; outputting the starting time length with small thrust until the pulse increment size change calculated in the two previous and later times is smaller than a preset value; the estimated small-thrust startup duration is used as a constraint and input into an indirect method optimization model for solving, and the optimal control rate, the transfer track and the mass variation are obtained; and (4) calculating the increment percentage delta of the speed increment and the pulse speed increment corresponding to the optimal control rate, if delta is greater than the threshold value, solving the step 5 again, and if delta is less than the threshold value, outputting the optimal control rate and the transfer track.

Description

Spacecraft low-thrust perturbation intersection trajectory optimization method and system
Technical Field
The invention belongs to the technical field of space navigation control, and particularly relates to a method and a system for optimizing a low-thrust perturbation intersection track of a spacecraft.
Background
On the near-earth orbit, the earth non-spherical gravitational perturbation, the atmospheric resistance and the like are the most main perturbation items. When the small-thrust intersection track optimization is carried out in the space debris clearing task, the influence of the perturbation term must be considered, but the corresponding orbit integral calculation amount is obviously increased compared with a two-body analysis dynamic model. Moreover, when the number of transfer turns is large, the calculation amount is greatly increased, and the efficiency of optimizing the rendezvous trajectory is reduced. Therefore, a new intersection trajectory planning method needs to be found, and planning efficiency is improved.
Disclosure of Invention
The invention aims to solve the technical problem of how to improve the optimization efficiency of a low-thrust intersection track when the influence of a perturbation item is considered, and provides a method and a system for quickly optimizing the low-thrust intersection track.
In order to solve the problem, the technical scheme adopted by the invention is as follows:
a spacecraft low-thrust perturbation intersection track optimization method comprises the following steps:
step 1: given a spacecraft and a target at a starting time t 0 And the number of tracks at the time of the crossing, t f The track transfer time length is delta t, and four-pulse speed increment delta v is calculated 1 ,Δv 2 ,Δv 3 ,Δv 4 The first two pulses in the first and the last two pulses in the last cycle, and the pulse increment of the first cycle is recorded as Deltav 0 And the last pulse increment is recorded as Δ v f ，
Δv 0 ＝Δv 1 +Δv 2
Δv f ＝Δv 3 +Δv 4
Step 2: assuming the low-thrust switching strategy is on-off-on, the first power-on of the low-thrust switching strategy corresponds to a pulse speed increment of Δ v 0 The second start-up corresponds to a pulse velocity increment of Δ v f According to the mass and the thrust of the spacecraft, two equivalent starting time lengths of the small thrust are estimated to be respectively
Figure BDA0002698307390000011
Figure BDA0002698307390000012
Wherein k is the arc segment loss coefficient of the maneuvering effect when expanding the impulse to a small thrust; f is the thrust of the spacecraft, and m is the mass of the spacecraft;
and 3, step 3: according to the estimated two low-thrust equivalent starting-up time lengths, taking the low-thrust midpoint time as the equivalent pulse time, and taking the low-thrust midpoint time as the equivalent pulse time
Figure BDA0002698307390000021
And
Figure BDA0002698307390000022
an equivalent transfer duration of
Figure BDA0002698307390000023
Returning to the step 1 to recalculate a new four-pulse speed increment to obtain a pulse increment delta v of the first circle 0 ' and pulse increment of the last revolution Δ v f '；
And 4, step 4: repeating the steps 1, 2 and 3 until the pulse increment change calculated in two times is smaller than a preset value epsilon, | (delta v) 0 '+Δv f ')-(Δv 0 +Δv f ) If | < epsilon, outputting the corresponding small-thrust starting-up time;
Δ v obtained at this time 0 '+Δv f ' is the speed increment required to meet the estimated small thrust, at this time with the Δ v 0 '+Δv f ' corresponding Delta t 1 And Δ t 2 Starting up time length for two estimated small thrusters;
and 5: the estimated small-thrust starting-up time is used as a constraint and input into an optimization model of an indirect method small-thrust intersection track for solving, and the optimal control rate, the transfer track in the aircraft transfer process and the mass variation are obtained;
step 6: calculating the speed increment delta v corresponding to the optimal control rate according to the mass variation in the aircraft transfer process opt The incremental percentage delta from the pulse velocity increment in step 4,
Figure BDA0002698307390000024
Figure BDA0002698307390000025
if delta is larger than the preset threshold value, solving the step 5 again, and if delta is smaller than the preset threshold valueA set threshold value is set, the optimal control rate and the transfer track are output, wherein I sp Is specific impulse of engine, g is acceleration of gravity, m 0 Mass m at the initial moment of the spacecraft f And (5) meeting time quality for the spacecraft.
The invention also provides a system for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft, which comprises a memory and a processor, wherein the memory stores the method for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft, and the processor realizes the steps of the method when operating the method for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft.
Compared with the prior art, the invention has the following beneficial effects:
according to the method and the system for quickly optimizing the low-thrust perturbation rendezvous trajectory of the spacecraft, the low-thrust rendezvous pulse velocity increment is calculated according to the given initial orbit position and the target orbit position of the spacecraft, and then the low-thrust rendezvous pulse velocity increment is used as an initial value and an optimality criterion for solving and is substituted into an indirect method optimization model to obtain the optimal low-thrust transfer trajectory, so that the problem that the calculation efficiency is low due to the fact that the dynamics recursion calculation amount is large when the transfer time is long in the traditional indirect method low-thrust rendezvous optimization algorithm is solved.
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FIG. 1 is a flow chart of the system of the present invention;
FIG. 2 is a schematic diagram of the power-on and power-off conditions of low thrust under the optimal solution conditions in the embodiment;
FIG. 3 is a trajectory diagram of the spacecraft under optimal solution conditions in the embodiment;
fig. 4 is a schematic diagram of the startup and shutdown conditions of a small thrust under the condition of a locally optimal solution obtained by using a common indirect method trajectory optimization algorithm in the comparative embodiment.
Detailed Description
As shown in fig. 1, a specific embodiment of a method for quickly optimizing a spacecraft small thrust perturbation intersection trajectory according to the present invention is provided, in this embodiment, the number of orbits of a spacecraft and a target at a reference time is shown in table 1:
TABLE 1 reference time spacecraft and target orbit root
Figure BDA0002698307390000031
The initial mass of the spacecraft is 755.32kg, the thrust is 0.5N, and the specific impulse is 1000 s. To be calculated at a relative reference time t 0 Track transfer began on day 154.1, t f 157.8 days of intersection, and Δ t 3.7 days, the optimum control rate for the required small thrust.
Step 1: given spacecraft and target at a starting time t 0 And the number of tracks at the time of the crossing, t f The track transfer time is delta t, and the increment of the four-pulse speed is calculated to be delta v 1 ,Δv 2 ,Δv 3 ,Δv 4 The first two pulses are in the first circle and the last two pulses are in the last circle, and the increment of the first circle is recorded as delta v 0 And the last pulse increment is recorded as Deltav f ，
Figure BDA0002698307390000041
The method for calculating the four-pulse velocity increment comprises a four-pulse perturbation orbit intersection optimization algorithm or a pulse velocity increment estimation method. The pulse velocity increment estimation method is used in the present embodiment.
[Δv 1 ,Δv 2 ,Δv 3 ,Δv 4 ]＝f(Element 0 ,Element f ,t f ,Δt) (2)
Wherein Element 0 And Element f Respectively a starting orbit and a target orbit of the spacecraft, t f At the time of the crossing, Δ t is the track transfer duration, t 0 ＝t f And- Δ t is a departure time, and in this embodiment, a pulse velocity increment estimation method in a J2 perturbation optimal velocity increment fast estimation method under the patent number CN110789739A is adopted as a function f. Will t f Substituting the number of orbits into the function f to obtain Δ v, wherein the number of the orbits is 157.8 days, the number of the Δ t is 3.7 days 0 ＝28.4m/s，Δv f ＝14.7m/s。
And 2, step: assuming that the low-thrust switching strategy is on-off-on, the first start-up of the low-thrust switching strategy corresponds to a pulse speed increment of Δ v 0 The second start-up corresponds to a pulse velocity increment of Δ v f According to the mass and the thrust of the spacecraft, two equivalent starting time lengths of the small thrust are estimated to be respectively
Figure BDA0002698307390000042
Wherein k is the arc segment loss coefficient of the maneuvering effect when the impulse is expanded into small thrust; f is the thrust of the spacecraft, m is the mass of the spacecraft, k is a coefficient less than 1, and k is 0.7 in this embodiment; will be Δ v 0 ＝28.4m/s，Δv f Substituting 14.7m/s into equation 3 to obtain Δ t 1 ＝0.71，Δt 2 Day 0.37. Δ t 1 For the first pulse speed increment at start-up Δ v 0 Corresponding small thrust equivalent start-up duration, Δ t 2 For the second on-time pulse velocity increment Δ v f The corresponding small thrust is equivalent to the starting time.
And step 3: according to the estimated small-thrust starting-up time length, taking the small-thrust midpoint moment as an equivalent pulse moment, namely taking the small-thrust midpoint moment as
Figure BDA0002698307390000043
And
Figure BDA0002698307390000044
then the equivalent transfer duration is
Figure BDA0002698307390000045
Returning to the step 1 to recalculate the new four-pulse speed increment to obtain the pulse increment delta v of the first circle 0 ' and pulse increment of the last revolution Δ v f '；
In this embodiment, t is f (iii) substitution of formula (1) for 157.8-0.37/2-157.615 days and Δ t-3.7-0.71/2-0.37/2-3.16 days to give Δ ν 0 '＝32.07m/s，Δv f '＝16.19m/s。
And 4, step 4: repeating the steps 1, 2 and 3 until the change of the pulse speed increment calculated in the two times is smaller than a preset value epsilon, and outputting the equivalent starting time of the small thrust;
|(Δv 0 '+Δv f ')-(Δv 0 +Δv f )|＜ε (4)
Δ v obtained at this time 0 '+Δv f ' i.e. the pulse velocity increment required for the estimated small thrust intersection, with the Δ v 0 '+Δv f ' corresponding Deltat 1 And Δ t 2 The estimated small-thrust equivalent starting time length is obtained;
in this example, ε is 0.1m/s, and after 3 iterations, the final Δ t is obtained 1 Day 0.82,. DELTA.t 2 0.41 days,. DELTA.v 0 ＝32.69m/s，Δv f ＝16.51m/s。
And 5: and (4) taking the estimated small-thrust startup duration as a constraint input to an optimization model for optimizing a small-thrust intersection track by an indirect method for solving to obtain the optimal control rate, the position speed and the mass variation in the transfer process.
The optimization model for optimizing the low-thrust intersection track by an indirect method refers to the following steps:
let the thrust of the spacecraft be F and the initial mass be m 0 Taking into account the earth's non-spherical gravitational field J 2 Term, in normalized position r ═ X Y Z] T And velocity v ═ v X v Y v Z ] T The finite thrust spacecraft dynamics equation for the state quantity is:
Figure BDA0002698307390000051
Figure BDA0002698307390000052
Figure BDA0002698307390000053
Figure BDA0002698307390000054
the fuel consumption model is:
Figure BDA0002698307390000055
wherein the fundamental dimension unit R Unit Set as the radius of the earth, T Unit Is set as 600s, m Unit Set as initial mass m of spacecraft 0 Then the normalization of other units can be obtained by dimension analysis; alpha ═ alpha X α Y α Z ] T Is a unit vector of thrust direction, alpha X 、α Y 、α Z Respectively representing unit vectors of thrust of the spacecraft in X, Y, Z three-axis coordinate directions, X, Y, Z representing coordinate positions of the spacecraft on three axes in a space coordinate system, v X 、v Y 、v Z Represents the component of the spacecraft velocity in the X, Y, Z three-axis coordinate direction, and u is equal to 0,1]And u is the amplitude of the thrust force,
Figure BDA0002698307390000061
for the maximum amplitude of the normalized thrust force,
Figure BDA0002698307390000062
to specific fuel consumption, I sp Is the engine specific impulse, g is the gravity acceleration, mu is the earth gravity constant, r is the modulus of the vector r; r e Representing the radius of the earth.
For each section of track intersection, the initial time and the final time of the intersection are fixed, the number of the tracks at the corresponding moment is converted into the position speed, and the boundary value conditions are as follows
Figure BDA0002698307390000063
Wherein, m (t) 0 ) I.e. the mass m of the spacecraft at the initial moment 0 ；
The optimal thrust amplitude u (t) and the optimal thrust direction α (t) need to be solved so that the fuel consumption index is minimal:
Figure BDA0002698307390000064
using the principle of minima, first writing the Hamiltonian
Figure BDA0002698307390000065
Wherein
Figure BDA0002698307390000066
To minimize the Hamiltonian, according to (6)
Figure BDA0002698307390000067
Of the expression (b), the optimum thrust direction being such that v A takes the minimum value, i.e.
Figure BDA0002698307390000068
At the same time, the optimum thrust amplitude u should be such that
Figure BDA0002698307390000071
Taking the minimum value, namely:
Figure BDA0002698307390000072
where ρ is defined as the switching function:
Figure BDA0002698307390000073
according to the principle of minima, the covariates have the following relationships:
Figure BDA0002698307390000074
unfolding to obtain:
Figure BDA0002698307390000075
Figure BDA0002698307390000076
Figure BDA0002698307390000077
Figure BDA0002698307390000078
at the same time, as the terminal quality is not constrained, then
λ m (t f )＝0 (17)
If an initial covariant lambda is given r (t 0 )，λ v (t 0 )，λ m (t 0 ) And initial state r (t) 0 )，v(t 0 )，m(t 0 ) Then the state and the covariates of the terminal can be calculated by differential equations. Optimal control problem is equivalent to solving the initial covariate λ r (t 0 )，λ v (t 0 )，λ m (t 0 ) Such that the end state and covariates satisfy the targeting function phi (z):
φ(z)＝[r(t f )-r f ,v(t f )-v f ,λ m (t f )] T ＝0 (18)
that is, the target function has 7 equations in total, and the solution variable is z ═ λ r (t 0 ),λ v (t 0 ),λ m (t 0 )]Also 7 dimensions, corresponding to 7 covariates at the initial instant.
The number of target orbits at the departure time and the number of target orbits at the intersection time are respectively converted into unitized position velocities r 0 ＝[0.425410721120000 0.540281353102000 -0.895982743973000]，v 0 ＝[0.467147840028000 0.316148727267000 0.413824368484000]And r f ＝[-0.167451008984000 0.0699372107820000 -1.10700302437600]，v f ＝[0.497209586529000 0.493710947528000 -0.0434604813910000]。m 0 Is the initial mass. I.e. known r 0 ,v 0 ,m 0 Solving for λ r (t 0 ),λ v (t 0 ),λ m (t 0 ) Let the system of differential equations (6), (7), (15) at t f The time satisfies the terminal condition expression (18).
According to Δ t 1 And Δ t 2 Constraining thrust amplitude u (t) at [ t 0 +Δt 1 ,t f -Δt 2 ]The interval is constantly 0, and a public nonlinear equation system solving and optimizing toolkit Minpack-1 is used for solving by means of a random guess co-modal variable targeting method.
Solving to obtain the optimal solution
[λ r (t 0 ),λ v (t 0 ),λ m (t 0 )]＝[0.283555391709000，-0.0590384733860000，-0.336635442397000，0.625749386435000，-0.148776401651000，0.280129358394000，0.00319735301800000]。
And 6: calculating the corresponding speed increment delta v of the optimal track according to the mass variation in the aircraft transfer process opt The percentage delta from the pulse speed increment in step 4,
according to the optimal solution [ lambda ] r (t 0 ),λ v (t 0 ),λ m (t 0 )]And r (t) 0 )，v(t 0 )，m(t 0 ) Then, t can be obtained by integrating equations (6) and (7) 0 To t f The optimal track between the two, namely the change relation of the position r, the speed v and the mass m along with time, and m is obtained according to the value of the mass m along with the change of time 0 And m f Is m (t) 0 ) And m (t) f ) Equivalent velocity increment corresponding to optimal trajectoryΔv opt ：
Figure BDA0002698307390000091
Calculating to obtain the equivalent velocity increment delta v corresponding to the optimal track opt ＝46.3m/s，
Δ v estimated in step 4 0 '+Δv f '＝32.69+16.51＝49.2
Then the
Figure BDA0002698307390000092
In this embodiment, the preset threshold is 10%, and δ is less than 10%, so the solution obtained in step 5 is the optimal solution, and the optimal solution is output.
The thrust on-off condition of the optimal solution is shown in figure 2, the track is shown in figure 3, and the fuel consumption is 3.4 kg. Optimization takes less than 2 minutes. If the solving strategy designed by the invention is not used, the local optimal solution can be obtained with a higher probability by a common indirect method track optimization algorithm, the thrust on-off condition of the local optimal solution solved at a certain time is shown in figure 4, and the corresponding fuel consumption is 6.4 kg.
The embodiment proves that the method has high optimization speed, can avoid local optimal solution and solves the problem of quick optimization of the low-thrust perturbation intersection track.
The invention also provides a system for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft, which comprises a memory and a processor, wherein the memory stores the method for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft, and the processor realizes the steps of the method when operating the method for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft.
The above-mentioned embodiments only express a certain implementation manner of the present application, and the description is specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent application shall be subject to the appended claims.

Claims (5)

1. A spacecraft low-thrust perturbation intersection trajectory optimization method is characterized by comprising the following steps:
step 1: given a spacecraft and a target at a starting time t 0 And the number of tracks at the time of the crossing, t f The track transfer time length is delta t, and four-pulse velocity increment delta v is calculated 1 ,Δv 2 ,Δv 3 ,Δv 4 The first two pulses in the first turn and the last two pulses in the last turn, and the increment of the first turn is recorded as Deltav 0 And the last pulse increment is recorded as Deltav f ，
Δv 0 ＝Δv 1 +Δv 2
Δv f ＝Δv 3 +Δv 4
Step 2: assuming the low-thrust switching strategy is on-off-on, the first power-on of the low-thrust switching strategy corresponds to a pulse speed increment of Δ v 0 The second start-up corresponds to a pulse velocity increment of Δ v f According to the mass and the thrust of the spacecraft, two equivalent starting time lengths of the small thrust are estimated to be respectively
Figure FDA0002698307380000011
Figure FDA0002698307380000012
Wherein k is the arc segment loss coefficient of the maneuvering effect when expanding the impulse to a small thrust; f is the thrust of the spacecraft, and m is the mass of the spacecraft;
and 3, step 3: according to the estimated starting time length of the two equivalent small thrusts, the middle point moment of the small thrusts is taken as the equivalent pulse moment, and the middle point moment of the small thrusts is taken as the equivalent pulse moment
Figure FDA0002698307380000013
And
Figure FDA0002698307380000014
equivalent transfer duration of
Figure FDA0002698307380000015
Returning to the step 1 to recalculate a new four-pulse speed increment to obtain a pulse increment delta v of the first circle 0 ' and pulse increment of the last revolution Δ v f '；
And 4, step 4: repeating the steps 1, 2 and 3 until the change of the pulse speed increment calculated in two times is less than a preset value epsilon, | (delta v) 0 '+Δv f ')-(Δv 0 +Δv f ) If | < epsilon, outputting the corresponding small-thrust equivalent starting-up duration;
Δ v obtained at this time 0 '+Δv f ' i.e. the pulse velocity increment required for the estimated small thrust intersection, with this Δ v 0 '+Δv f ' corresponding Deltat 1 And Δ t 2 The estimated small-thrust equivalent starting time length is obtained;
and 5: taking the estimated low-thrust equivalent starting time as a constraint input into an optimization model of an indirect low-thrust intersection track to solve, and obtaining the optimal control rate, the transfer track in the aircraft transfer process and the mass variation;
step 6: calculating the corresponding speed increment delta v of the optimal track according to the mass variation in the aircraft transfer process opt The percentage delta from the pulse speed increment in step 4,
Figure FDA0002698307380000021
Figure FDA0002698307380000022
if delta is greater than the preset threshold value, the method is repeatedSolving the step 5, and if delta is smaller than a preset threshold value, outputting the optimal control rate and a transfer track, wherein I sp Is engine specific impulse, g is gravitational acceleration, m 0 Mass m at the initial moment of the spacecraft f And (4) meeting the quality of the spacecraft.
2. The method of claim 1, wherein: the optimization model of the indirect low-thrust intersection trajectory in the step 5 refers to the following steps:
let the thrust of the spacecraft be F and the initial mass be m 0 Taking into account the non-spherical gravitational field J of the earth 2 Term, in normalized position r ═ X Y Z] T And velocity v ═ v X v Y v Z ] T The finite thrust spacecraft dynamics equation for the state quantity is:
Figure FDA0002698307380000023
Figure FDA0002698307380000024
Figure FDA0002698307380000025
Figure FDA0002698307380000026
the fuel consumption model is:
Figure FDA0002698307380000027
wherein the fundamental dimension unit R Unit Set as the radius of the earth, T Unit Is set as 600s, m Unit Set as initial mass m of spacecraft 0 Then the normalization of other units can be obtained by dimension analysis; alpha ═ alpha X α Y α Z ] T Is a unit vector of thrust direction, α X 、α Y 、α Z Respectively representing unit vectors of thrust of the spacecraft in X, Y, Z three-axis coordinate directions, X, Y, Z representing coordinate positions of the spacecraft on three axes in a space coordinate system, v X 、v Y 、v Z Represents the component of the spacecraft velocity in the X, Y, Z three-axis coordinate direction, and u is equal to 0,1]And u is the amplitude of the thrust force,
Figure FDA0002698307380000031
in order to normalize the maximum amplitude of the thrust,
Figure FDA0002698307380000032
mu is the constant of Earth's gravity, R is the modulus of the vector R, R e Represents the radius of the earth;
for each section of track intersection, the initial time and the final time of the intersection are fixed, the number of the tracks at the corresponding moment is converted into the position speed, and the boundary value conditions are as follows
Figure FDA0002698307380000033
The optimal thrust amplitude u (t) and thrust direction α (t) need to be solved so that the fuel consumption index is minimal:
Figure FDA0002698307380000034
using the principle of minima, first writing the Hamiltonian
Figure FDA0002698307380000035
Wherein
Figure FDA0002698307380000036
To minimize the Hamiltonian, according to (6)
Figure FDA0002698307380000039
Of the expression (c), the optimum thrust direction being such that v A takes the minimum value, i.e.
Figure FDA0002698307380000037
At the same time, the optimum thrust amplitude u should be such that
Figure FDA0002698307380000038
Taking the minimum value, namely:
Figure FDA0002698307380000041
where ρ is defined as the switching function:
Figure FDA0002698307380000042
according to the principle of minimum value, the covariates have the following relations:
Figure FDA0002698307380000043
unfolding to obtain:
Figure FDA0002698307380000044
Figure FDA0002698307380000045
Figure FDA0002698307380000046
wherein
Figure FDA0002698307380000047
At the same time, as the terminal quality is not constrained, then
λ m (t f )＝0 (17)
If an initial covariant lambda is given r (t 0 )，λ v (t 0 )，λ m (t 0 ) And initial state r (t) 0 )，v(t 0 )，m(t 0 ) Then the state and the covariates of the terminal can be obtained by calculation through a differential equation, and the optimal control problem is equivalent to solving the initial covariates lambda r (t 0 )，λ v (t 0 )，λ m (t 0 ) Such that the end state and the covariates satisfy the targeting function phi (z):
φ(z)＝[r(t f )-r f ,v(t f )-v f ,λ m (t f )] T ＝0 (18)
that is, the targeting function has 7 equations in total, and the solution variable is z ═ λ r (t 0 ),λ v (t 0 ),λ m (t 0 )]Also 7 dimensions, corresponding to 7 covariates at the initial instant.
3. The method of claim 2, wherein the method of solving the optimization model in step 5 is:
according to Δ t 1 And Δ t 2 Constraining thrust amplitude u (t) at [ t 0 +Δt 1 ,t f -Δt 2 ]The interval is always 0, and a target practice is performed by randomly guessing the covariates using a published nonlinear equation set solution and optimization toolkit Minpack-1.
4. The method of claim 1, wherein: the calculation method of the pulse velocity increment in the step 1 is an optimal four-pulse transfer optimization method or a four-pulse transfer estimation method.
5. The utility model provides a spacecraft low thrust perturbation intersection orbit optimization system which characterized in that: the method comprises a memory and a processor, wherein the memory stores a method for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft, and the processor realizes the steps of the method in any one of claims 1 to 4 when running the method for quickly optimizing the low-thrust perturbation intersection trajectory of the spacecraft.
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