CN114148548B - Small-thrust track rapid optimization method for three-system periodic orbital phase modulation - Google Patents

Small-thrust track rapid optimization method for three-system periodic orbital phase modulation Download PDF

Info

Publication number
CN114148548B
CN114148548B CN202210123115.4A CN202210123115A CN114148548B CN 114148548 B CN114148548 B CN 114148548B CN 202210123115 A CN202210123115 A CN 202210123115A CN 114148548 B CN114148548 B CN 114148548B
Authority
CN
China
Prior art keywords
thrust
phase modulation
orbit
convex
optimization
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210123115.4A
Other languages
Chinese (zh)
Other versions
CN114148548A (en
Inventor
乔栋
贾飞达
韩宏伟
李翔宇
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Original Assignee
Beijing Institute of Technology BIT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT filed Critical Beijing Institute of Technology BIT
Priority to CN202210123115.4A priority Critical patent/CN114148548B/en
Publication of CN114148548A publication Critical patent/CN114148548A/en
Application granted granted Critical
Publication of CN114148548B publication Critical patent/CN114148548B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/242—Orbits and trajectories

Landscapes

  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a small-thrust trajectory fast optimization method for three-system periodic orbital phase modulation, and belongs to the technical field of aerospace. The implementation method of the invention comprises the following steps: establishing a dynamic model of the detector considering thrust in a three-system; giving a specific form of a three-system low-thrust phase modulation optimization problem according to phase modulation track constraints and dynamic characteristics, wherein the specific form refers to a specific form of the phase modulation optimization problem which considers the equality constraints of the starting state and the ending state, the equality constraints of thrust components and the inequality constraints of thrust sizes of three-system phase modulation tracks corresponding to the starting time and the ending time, and takes the maximum quality of the tail end of a detector as a performance index; carrying out linearization processing on the established three-system dynamic model, and carrying out relaxation processing on the obtained thrust equality constraint, namely realizing the convexity of the three-system small thrust phase modulation optimization problem; and (3) fast iterative solution is carried out through numerical integration and a successive approximation strategy to obtain the three-system periodic orbit optimal phase modulation orbit, so that the three-system low-thrust orbit fast optimization is realized.

Description

Small-thrust track fast optimization method for periodic orbital phase modulation of three systems
Technical Field
The invention relates to a method for quickly optimizing a low-thrust orbit of periodic orbit phase modulation of a three-system, which is particularly suitable for quickly optimizing a low-thrust phase modulation orbit considering initial and final phase constraints of a periodic orbit in the three-system and belongs to the technical field of aerospace.
Background
The lagrange point has been extensively addressed in recent years due to its particular dynamic characteristics. Combining the inherent advantages of trisomy with advanced propulsion technology can produce richer mission revenue. The large thrust-weight ratio of the small-thrust engine greatly reduces the consumption of the propellant in the task, so that the small-thrust rail designed in the three-system has excellent application prospect. Phase modulation of a Lagrange point periodic orbit is an indispensable technology in tasks such as Lagrange point formation, manifold transfer of a specific window and the like, however, the phase modulation of the periodic orbit has the problems of difficult convergence, low solving efficiency and the like due to strong nonlinearity of Lagrange point dynamics. In the developed prior art on Three-system small-Thrust-orbit Optimization [1] (see [1] Zhang C, Topputo F, Bernelli-Zazzera F, et al, Low-Thrust Minimum-Fuel Optimization in the Circular controlled Three-Body protocol [ J ]. Journal of guide Control and Dynamics, 2015, 38(8): 1501 1509.), a small-Thrust-orbit Optimization method in a limiting Three-system based on the homotopic method is proposed, although the method can solve the transfer Problem of Minimum Fuel consumption, the optimal solution needs to be screened from multiple sets of initial values of covariates in the solving process, so the method has general efficiency.
Disclosure of Invention
In order to solve the phase modulation problem of the periodic orbit in the three-system of strong nonlinear dynamics, the invention mainly aims to provide a small-thrust orbit fast optimization method of the periodic orbit phase modulation of the three-system, which considers the period of the periodic orbit phase modulation during the initial and tail end phase constraints and realizes the small-thrust orbit fast optimization problem of the three-system through sequence convex programming. The invention has the advantages of high phase modulation efficiency and high precision.
The purpose of the invention is realized by the following technical scheme: the invention discloses a small-thrust orbit fast optimization method of periodic orbit phase modulation of a three-system, which comprises the steps of establishing a dynamic model of a detector considering thrust in the three-system; giving a specific form of a three-system small-thrust phase modulation optimization problem according to phase modulation track constraints and dynamic characteristics, wherein the specific form refers to a specific form of the phase modulation optimization problem which takes the starting and ending state equality constraints, the thrust component equality constraints and the thrust size inequality constraints of a three-system phase modulation track corresponding to the starting and ending moments into consideration, and takes the mass of the tail end of a detector as the maximum performance index; carrying out linearization processing on the established three-system dynamic model, and carrying out relaxation processing on the obtained thrust equality constraint, namely realizing the convexity of the three-system small thrust phase modulation optimization problem; and (3) obtaining the three-system periodic orbit optimal phase modulation orbit through numerical integration and successive approximation strategy fast iterative solution, namely realizing the three-system low-thrust orbit fast optimization.
The invention discloses a small-thrust orbit fast optimization method of three-system periodic orbit phase modulation, which comprises the following steps: the method comprises the following steps: and establishing a dynamic model of the detector considering thrust in a three-system.
In the three-body problem, the detector state is recorded as
Figure DEST_PATH_IMAGE002
The position vector is
Figure DEST_PATH_IMAGE004
The velocity vector is
Figure DEST_PATH_IMAGE006
Wherein the superscript "T" is a transposed symbol; the dynamic model considering the thrust in the three-system is
Figure DEST_PATH_IMAGE007
（1）
Wherein mu is a three-system coefficient of attraction,
Figure DEST_PATH_IMAGE009
the distance from the detector to the main celestial body and the secondary celestial body respectively, T is the thrust of the detector,
Figure DEST_PATH_IMAGE011
the thrust in three directions is large and small,
Figure 100002_DEST_PATH_IMAGE013
is the specific impulse of the power generated by the detector,
Figure DEST_PATH_IMAGE015
is the sea level gravitational acceleration.
Step two: giving a specific form of the three-system small-thrust phase modulation optimization problem according to phase modulation track constraints and dynamic characteristics, wherein the specific form refers to a specific form of the phase modulation optimization problem which considers the initial and final state equality constraints, the thrust component equality constraints and the thrust size inequality constraints of the three-system phase modulation track corresponding to the initial and final moments, and takes the maximum quality of the tail end of the detector as a performance index.
The detector states of the beginning and end states of the phase modulation track are:
Figure DEST_PATH_IMAGE016
Figure DEST_PATH_IMAGE017
wherein
Figure DEST_PATH_IMAGE018
And
Figure DEST_PATH_IMAGE019
respectively the beginning time and the end time; and initial mass
Figure 100002_DEST_PATH_IMAGE021
Fixation, end mass
Figure DEST_PATH_IMAGE023
No constraint; thrust component of the probe satisfies
Figure DEST_PATH_IMAGE024
And is
Figure DEST_PATH_IMAGE025
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE027
is the maximum thrust of the probe.
In order to obtain a fuel-optimal three-system low-thrust phase modulation orbit, the performance index of an optimization problem is set as
Figure DEST_PATH_IMAGE028
The mass of the tail end of the detector is maximum, namely, the fuel consumption is minimized;
thereby obtaining the fuel optimal three-system phase-modulated orbit low thrust optimization problem which is marked as P1, and the concrete form is
Figure DEST_PATH_IMAGE029
Constraint equation: formulae (2) to (5).
Step three: and (3) carrying out linearization processing on the three-system dynamics model established in the step one, and carrying out relaxation processing on the thrust equality constraint obtained in the step two, namely realizing the convexity of the three-system small thrust phase modulation optimization problem obtained in the step two.
The problem is solved by adopting a successive convex optimization method, and the problem P1 needs to be subjected to convex processing. Separate the state term and the control term in the kinetic equation and write as
Figure DEST_PATH_IMAGE030
Wherein
Figure DEST_PATH_IMAGE031
Matrix of control vector coefficients
Figure DEST_PATH_IMAGE032
The control vector is
Figure DEST_PATH_IMAGE034
；
Carrying out convex processing on the kinetic equation based on a small disturbance continuous linearization method; note the book
Figure 100002_DEST_PATH_IMAGE036
Are respectively the first
Figure DEST_PATH_IMAGE037
And a first step of
Figure 100002_DEST_PATH_IMAGE038
The solution of the sub-iteration is that the linearized kinetic equation is
Figure DEST_PATH_IMAGE040
（10）
Wherein
Figure DEST_PATH_IMAGE042
（11）
Figure DEST_PATH_IMAGE043
Figure DEST_PATH_IMAGE044
Figure DEST_PATH_IMAGE045
Figure DEST_PATH_IMAGE046
Figure DEST_PATH_IMAGE047
Figure DEST_PATH_IMAGE048
Figure DEST_PATH_IMAGE049
Figure DEST_PATH_IMAGE050
Figure DEST_PATH_IMAGE051
Figure DEST_PATH_IMAGE052
In addition to this, the non-linear constraint of equation (4) is non-convex, so the equal sign in equation (4) is changed to an unequal sign, the problem is equivalent, and the constraint thus translates into a convex constraint:
Figure DEST_PATH_IMAGE054
（13）
thus, non-convex problem P1 translates into convex problem P2; and (3) wherein the convex dynamic model is expressed by the formula (10), and the convex constraints are expressed by the formulas (2), (3), (5) and (13), namely, the convexity is realized on the three-system low-thrust phase modulation optimization problem obtained in the step (II).
Step four: and (3) obtaining the three-system periodic orbit optimal phase modulation orbit through numerical integration and successive approximation strategy fast iterative solution, namely realizing the three-system low-thrust orbit fast optimization.
The numerical integration in equation (10) is transformed using the trapezoidal equation to transform the problem P2 into a convex optimization problem form. Then continuously approximating the convex problem so as to obtain the optimal three-system low-thrust phase modulation orbit by iterative solution,
until the solution of the problem P2 converges to the solution of P1.
For the first
Figure DEST_PATH_IMAGE056
A second iteration of selecting
Figure DEST_PATH_IMAGE057
Solutions for sub-iterations
Figure DEST_PATH_IMAGE059
As guess initial value of the state vector, corresponding to
Figure DEST_PATH_IMAGE060
The solution pair of the sub-iteration is
Figure DEST_PATH_IMAGE061
Checking whether a convergence condition is satisfied:
Figure DEST_PATH_IMAGE062
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE063
is a convergence accuracy requirement; if equation (14) is not satisfied, the iterative solution is required to be continued, and if equation (14) is satisfied, the solution of the problem P1 is obtained
Figure DEST_PATH_IMAGE064
；
The solution of the problem of the fast optimization of the small-thrust orbit phase modulation of the three-system periodic orbit is obtained,
Figure DEST_PATH_IMAGE065
in order to optimize the phase-modulated track,
Figure DEST_PATH_IMAGE066
the corresponding optimal control direction is obtained;
namely, the three-body system small thrust orbit is rapidly optimized through the sequential convex programming.
Further comprises the following steps: and D, performing high-precision phase modulation orbit transfer according to the three-system low-thrust phase modulation orbit obtained by optimization in the step four.
Has the advantages that:
1. the invention discloses a small-thrust orbit fast optimization method for periodic orbit phase modulation of a three-system, which considers the initial and final phase constraints, the transfer duration constraint and the maximum thrust constraint of the periodic orbit in the three-system and can optimize with high precision and high efficiency to obtain a phase modulation orbit with optimal fuel.
2. The invention discloses a small-thrust orbit fast optimization method of three-system periodic orbit phase modulation, which is not only suitable for the optimization of the periodic orbit phase modulation orbit in the three-system, but also suitable for the optimization of long-distance transfer orbits and the like in the three-system due to the establishment of a dynamic model with thrust in the three-system, and has wide application range.
3. The invention discloses a small-thrust orbit rapid optimization method of three-system periodic orbit phase modulation, which is characterized in that the initial optimization value only needs to be selected as a point on the original periodic orbit without carrying out a large amount of complex initial search, so that the problem of lower initial value guessing efficiency is obviously improved compared with the traditional small-thrust orbit optimization method, and the robustness is strong.
4. The invention discloses a small-thrust orbit fast optimization method for periodic orbital phase modulation of a three-system, which solves the problem of the nonlinear small-thrust phase modulation orbit optimization of the three-system after the three-system is embossed by a sequence convex programming method, generally only needs second-level operation, obviously improves the efficiency compared with a homotopy method, and further ensures that the phase modulation and the orbit transfer efficiency are high.
5. The invention discloses a method for quickly optimizing a low-thrust orbit of three-system periodic orbit phase modulation.
Drawings
FIG. 1 is a flow chart of a method for rapidly optimizing a low-thrust orbit by three-system periodic orbital phase modulation disclosed by the invention;
FIG. 2 is an optimal low-thrust transfer orbit obtained by solving a three-system periodic orbit phase modulation fast optimization method for a low-thrust orbit disclosed by the invention;
FIG. 3 is an optimal thrust magnitude change curve obtained by solving a three-system periodic orbital phase modulation fast optimization method for low thrust orbits disclosed by the invention;
fig. 4 is an optimal radial, tangential and normal thrust component variation curve obtained by solving the small thrust orbit fast optimization method of the three-system periodic orbit phase modulation disclosed by the invention.
Detailed Description
To better illustrate the objects and advantages of the present invention, the following detailed explanation of the invention is made in conjunction with specific implementation examples.
Example 1: two phase points of 0 degree and 180 degree on a Halo orbit in a geostationary three-body system are selected as starting and ending positions, and the corresponding orbit states are shown in table 1. The initial mass of the detector is 100kg, and the maximum thrust of the engine is Tmax90mN, specific impact of
Figure DEST_PATH_IMAGE067
3100 s. The phase modulation process is set for 27 days, whereas a 0 degree shift to 180 degrees on the Halo orbit would require about 7 days, and lag phase modulation is implemented.
TABLE 1 phase modulation track initial, terminal states (normalization)
Status of state x y z Vx Vy Vz
Initial value 1.1087 0 0.0390 0 0.2093 0
End value 1.0353 0 0.0185 0.4202 0.3735 -0.0124
As shown in fig. 1, the present embodiment discloses a method for fast optimizing a low-thrust orbit phase modulation by three-system periodic orbits,
as shown in fig. 1, the specific implementation steps are as follows:
the method comprises the following steps: and establishing a dynamic model of the detector considering thrust in a three-system.
In the restrictive trisomy problem, the detector state is recorded as
Figure DEST_PATH_IMAGE068
The position vector is
Figure DEST_PATH_IMAGE069
The velocity vector is
Figure DEST_PATH_IMAGE070
Wherein the superscript "T" is a transposed symbol; the dynamic model considering the thrust in the three-system is
Figure 667019DEST_PATH_IMAGE007
（15）
Wherein mu is a three-system coefficient of attraction,
Figure DEST_PATH_IMAGE071
the distance from the detector to the main celestial body and the secondary celestial body respectively, T is the thrust of the detector,
Figure DEST_PATH_IMAGE072
the thrust in three directions is large and small,
Figure DEST_PATH_IMAGE073
is the specific impulse of the power generated by the detector,
Figure DEST_PATH_IMAGE074
is the sea level gravitational acceleration.
Step two: and giving a specific form of the three-system low-thrust phase modulation optimization problem according to phase modulation track constraints and dynamic characteristics, wherein the specific form refers to a specific form of the phase modulation optimization problem which considers the equality constraints of the starting state and the ending state, the equality constraints of thrust components and the inequality constraints of thrust sizes of the three-system phase modulation tracks corresponding to the starting time and the ending time, and takes the maximum quality of the tail end of the detector as a performance index.
The detector states of the beginning and end states of the phase modulation track are:
Figure DEST_PATH_IMAGE075
Figure DEST_PATH_IMAGE076
wherein
Figure DEST_PATH_IMAGE077
And
Figure DEST_PATH_IMAGE078
respectively the beginning time and the end time; and initial mass
Figure DEST_PATH_IMAGE079
Fixation, end mass
Figure DEST_PATH_IMAGE080
No constraint; thrust component of the probe satisfies
Figure DEST_PATH_IMAGE081
And is
Figure DEST_PATH_IMAGE082
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE083
is the maximum thrust of the probe.
In order to obtain the fuel optimal three-body system low-thrust phase modulation track, the performance indexes of the optimization problem are set as follows:
Figure DEST_PATH_IMAGE084
i.e. the probe tip mass is maximal, i.e. the fuel consumption is minimized.
Therefore, the fuel-optimal three-body system phase modulation orbit low-thrust optimization problem is obtained and recorded as P1, and the specific form is as follows:
Figure DEST_PATH_IMAGE085
constraint equation: formulae (16) to (19).
Step three: and (3) carrying out linearization processing on the three-system dynamics model established in the step one, and carrying out relaxation processing on the thrust equality constraint obtained in the step two, namely realizing the convexity of the three-system small thrust phase modulation optimization problem obtained in the step two.
The problem is solved by adopting a successive convex optimization method, and the problem P1 needs to be subjected to convex processing. Separate the state term and the control term in the kinetic equation and write into
Figure DEST_PATH_IMAGE086
Wherein
Figure DEST_PATH_IMAGE087
Matrix of control vector coefficients
Figure DEST_PATH_IMAGE088
The control vector is
Figure DEST_PATH_IMAGE089
。
Carrying out convex processing on the kinetic equation based on a small disturbance continuous linearization method; note the book
Figure DEST_PATH_IMAGE090
,
Figure DEST_PATH_IMAGE091
Are respectively the first
Figure DEST_PATH_IMAGE092
And a first
Figure DEST_PATH_IMAGE093
The solution of the sub-iteration is that the linearized kinetic equation is
Figure DEST_PATH_IMAGE094
Wherein
Figure DEST_PATH_IMAGE095
Figure DEST_PATH_IMAGE096
Figure DEST_PATH_IMAGE097
Figure DEST_PATH_IMAGE098
Figure 261177DEST_PATH_IMAGE046
Figure 696706DEST_PATH_IMAGE047
Figure 91915DEST_PATH_IMAGE048
Figure DEST_PATH_IMAGE099
Figure DEST_PATH_IMAGE100
Figure DEST_PATH_IMAGE101
Figure DEST_PATH_IMAGE102
In addition to this, the non-linear constraint of equation (18) is non-convex, so the equal sign in equation (18) is changed to an unequal sign, the problem is equivalent, and the constraint thus translates into a convex constraint:
Figure DEST_PATH_IMAGE103
thus, non-convex problem P1 translates into convex problem P2. Wherein the convex dynamical model is formula (24), and the convex constraints are formulae (16), (17), (19) and (27).
Step four: and (3) obtaining the three-system periodic orbit optimal phase modulation orbit through numerical integration and successive approximation strategy fast iterative solution, namely realizing the three-system low-thrust orbit fast optimization.
The numerical integral in equation (24) is transformed using the trapezoidal equation, thereby transforming the problem P2 into a convex optimization problem form. And then continuously approximating the convex problem so as to obtain an optimal three-system low-thrust phase modulation orbit by iterative solution until the solution converges to the solution of P1.
For the first
Figure DEST_PATH_IMAGE093A
Iteration, selecting
Figure DEST_PATH_IMAGE104
Solution of sub-iteration
Figure DEST_PATH_IMAGE105
As guess initial value of the state vector, corresponding to
Figure DEST_PATH_IMAGE093AA
The solution pair of the sub-iteration is
Figure DEST_PATH_IMAGE106
Checking whether a convergence condition is satisfied:
Figure DEST_PATH_IMAGE107
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE108
is a convergence accuracy requirement; if equation (28) is not satisfied, the iterative solution is continued, and if equation (28) is satisfied, the solution of the problem P1 is obtained
Figure DEST_PATH_IMAGE109
。
So that the solution of the problem of fast optimization of the small-thrust orbit of the periodic orbital phase modulation of the three systems is obtained,
Figure DEST_PATH_IMAGE110
in order to optimally phase-modulate the track,
Figure DEST_PATH_IMAGE111
is the corresponding optimal control direction.
Through optimization, the convergence condition (28) is met after 8 iterations, the fuel consumption of the detector in the transfer process is 337.5kg, and the detector can accurately reach the state of the tail end constraint phase position. The optimal low thrust phase modulation orbit is shown in fig. 2, the corresponding optimal thrust amplitude variation curve is shown in fig. 3, and the optimal thrust x, y and z direction variation curve is shown in fig. 4.
The method also comprises the following five steps: and (4) performing high-precision phase modulation orbit transfer according to the three-system low-thrust phase modulation orbit obtained by optimization in the fourth step.
The above detailed description further details the objects, aspects and advantages of the present invention. It should be understood that the above description is only exemplary of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A method for quickly optimizing a low-thrust orbit of three-system periodic orbit phase modulation is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
the method comprises the following steps: establishing a dynamic model of the detector considering thrust in a three-system;
the first implementation method comprises the following steps of,
in the three-body problem, the detector state is recorded as
Figure 534847DEST_PATH_IMAGE001
The position vector is
Figure 186409DEST_PATH_IMAGE002
Velocity vector of
Figure 966146DEST_PATH_IMAGE003
Wherein the superscript "T" is a transposed symbol; the dynamic model considering the thrust in the three-system is
Figure 158093DEST_PATH_IMAGE004
Wherein mu is a three-system coefficient of attraction,
Figure 706886DEST_PATH_IMAGE005
the distance from the detector to the main celestial body and the secondary celestial body respectively, T is the thrust of the detector,
Figure 699987DEST_PATH_IMAGE006
the thrust in three directions is large and small,
Figure 967021DEST_PATH_IMAGE007
is the specific impulse of the power generated by the detector,
Figure 900342DEST_PATH_IMAGE008
is sea level gravitational acceleration;
step two: giving a specific form of a three-system low-thrust phase modulation optimization problem according to phase modulation track constraints and dynamic characteristics, wherein the specific form refers to a specific form of the phase modulation optimization problem which takes the starting and ending state equality constraints, the thrust equality constraints and the thrust size inequality constraints of a three-system phase modulation track corresponding to the starting and ending moments into consideration, and takes the mass of the tail end of a detector as the maximum performance index;
the second step is realized by the method that,
the detector states of the beginning and end states of the phase modulation track are:
Figure 365958DEST_PATH_IMAGE009
Figure 93742DEST_PATH_IMAGE010
whereint 0Andt f respectively the beginning time and the end time; and initial massm(t 0) Fixation, end massm(t f ) No constraint; thrust component of the probe satisfies
Figure 520176DEST_PATH_IMAGE011
And is
Figure 257188DEST_PATH_IMAGE012
Wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE013
is the maximum thrust of the detector;
in order to obtain a low thrust phase modulation orbit of a fuel-optimal three-body system, the performance index of an optimization problem is set as
Figure 311731DEST_PATH_IMAGE014
The mass of the tail end of the detector is maximum, namely, the fuel consumption is minimized;
thereby obtaining the fuel optimal three-system phase-modulated orbit low thrust optimization problem which is marked as P1, and the concrete form is
Figure 741576DEST_PATH_IMAGE015
Constraint equation: formulas (2) to (5);
step three: carrying out linearization processing on the three-system dynamics model established in the step one, and carrying out relaxation processing on the thrust equality constraint obtained in the step two, namely realizing the convexity on the three-system small thrust phase modulation optimization problem obtained in the step two;
the third step is realized by the method that,
solving the problem by adopting a successive convex optimization method, wherein the problem P1 needs to be subjected to convex processing; separate the state term and the control term in the kinetic equation and write as
Figure 717622DEST_PATH_IMAGE016
Wherein
Figure 664849DEST_PATH_IMAGE017
Matrix of control vector coefficients
Figure 42741DEST_PATH_IMAGE018
The control vector is
Figure 377907DEST_PATH_IMAGE019
；
Carrying out convex processing on the kinetic equation based on a small disturbance continuous linearization method; note the book
Figure 903567DEST_PATH_IMAGE020
Are respectively the firstiAnd a firstiThe solution of +1 iteration, the linearized kinetic equation is
Figure DEST_PATH_IMAGE021
Wherein
Figure 716802DEST_PATH_IMAGE022
Figure 886883DEST_PATH_IMAGE023
Figure 392951DEST_PATH_IMAGE024
Figure 140327DEST_PATH_IMAGE025
Figure 22832DEST_PATH_IMAGE026
Figure 109737DEST_PATH_IMAGE027
Figure 222924DEST_PATH_IMAGE028
Figure 660859DEST_PATH_IMAGE029
Figure 815897DEST_PATH_IMAGE030
Figure 85204DEST_PATH_IMAGE031
Figure 933074DEST_PATH_IMAGE032
In addition to this, the non-linear constraint of equation (4) is non-convex, so the equal sign in equation (4) is changed to an unequal sign, the problem is equivalent, and the constraint thus translates into a convex constraint:
Figure 858305DEST_PATH_IMAGE033
thus, non-convex problem P1 translates into convex problem P2; wherein the convex dynamic model is a formula (10), the convex constraints are formulas (2), (3), (5) and (12), and the convexity is realized on the three-system low-thrust phase modulation optimization problem obtained in the step two;
step four: and (3) obtaining the three-system periodic orbit optimal phase modulation orbit through numerical integration and successive approximation strategy fast iterative solution, namely realizing the three-system low-thrust phase modulation orbit fast optimization.
2. The method for fast optimization of small thrust orbits for three-system periodic orbital phasing according to claim 1, characterized in that: and step five, performing high-precision phase modulation orbit transfer according to the three-system low-thrust phase modulation orbit obtained by optimization in the step four.
3. The method for fast optimization of small thrust orbits for three-system periodic orbital phasing according to claim 1, characterized in that: the implementation method of the fourth step is that,
converting the numerical integration in the formula (10) by adopting a trapezoidal formula, and converting the problem P2 into a convex optimization problem form; then continuously approximating the convex problem so as to obtain an optimal three-system low-thrust phase modulation orbit by iterative solution until the solution of the problem P2 converges to the solution of P1;
for the firsti+1 iteration, choose theiSolution of sub-iteration
Figure 754717DEST_PATH_IMAGE034
As a guess initial value of the state vector, it is checked whether the convergence condition is satisfied:
Figure 550635DEST_PATH_IMAGE035
(14)
wherein, the requirements are convergence accuracy; if equation (14) is not satisfied, the iterative solution is required to be continued, and if equation (14) is satisfied, the solution of the problem P1 is obtained
Figure DEST_PATH_IMAGE036
；
Obtaining the low-thrust orbit of the periodic orbit phase modulation of the three systemsThe solution of the problem is optimized quickly,
Figure 631723DEST_PATH_IMAGE037
in order to optimize the phase-modulated track,
Figure DEST_PATH_IMAGE038
the corresponding optimal control direction is obtained;
namely, the three-body system small thrust orbit is rapidly optimized through the sequential convex programming.
CN202210123115.4A 2022-02-10 2022-02-10 Small-thrust track rapid optimization method for three-system periodic orbital phase modulation Active CN114148548B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210123115.4A CN114148548B (en) 2022-02-10 2022-02-10 Small-thrust track rapid optimization method for three-system periodic orbital phase modulation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210123115.4A CN114148548B (en) 2022-02-10 2022-02-10 Small-thrust track rapid optimization method for three-system periodic orbital phase modulation

Publications (2)

Publication Number Publication Date
CN114148548A CN114148548A (en) 2022-03-08
CN114148548B true CN114148548B (en) 2022-06-17

Family

ID=80450128

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210123115.4A Active CN114148548B (en) 2022-02-10 2022-02-10 Small-thrust track rapid optimization method for three-system periodic orbital phase modulation

Country Status (1)

Country Link
CN (1) CN114148548B (en)

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1998033704A2 (en) * 1997-02-04 1998-08-06 Belbruno Edward A Computer implemented procedure for ballistic capture transfer
CN106672266B (en) * 2017-01-04 2019-12-13 北京理工大学 Balance point Halo orbit phase modulation orbit transfer method considering time constraint
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
CN110806212B (en) * 2019-11-12 2021-07-30 北京理工大学 Asteroid detection small thrust transfer trajectory optimization method based on successive convex programming
CN112001029A (en) * 2020-07-28 2020-11-27 清华大学 Rocket online track optimization customized solver based on convex optimization

Also Published As

Publication number Publication date
CN114148548A (en) 2022-03-08

Similar Documents

Publication Publication Date Title
CN111428372B (en) Rocket power failure degradation orbit-entering guidance method based on convex planning and adaptive iteration
Marec Optimal space trajectories
CN110736470B (en) Mixed search method for continuous thrust orbit near small celestial body in irregular shape
Dasso et al. Progressive transformation of a flux rope to an ICME: Comparative analysis using the direct and fitted expansion methods
CN110032768B (en) Four-pulse orbit intersection optimization method using accurate dynamic model
CN108491668B (en) Aircraft system optimization method based on dynamic multi-model fusion
CN110989644B (en) Aircraft trajectory planning method considering target point multi-terminal constraint
CN104536452A (en) Optimization method of relative orbit transfer path of spacecraft based on time-fuel optimum control
CN112084581B (en) Spacecraft low-thrust perturbation intersection trajectory optimization method and system
CN108427289B (en) Hypersonic aircraft tracking control method based on nonlinear function
CN101708780A (en) Method for controlling rigid spacecraft for target attitude tracking
CN110488852B (en) Full-profile self-adaptive control method for hypersonic aircraft
CN110806212B (en) Asteroid detection small thrust transfer trajectory optimization method based on successive convex programming
CN103226631A (en) Method for rapidly designing and optimizing low-thrust transfer orbit
CN114148548B (en) Small-thrust track rapid optimization method for three-system periodic orbital phase modulation
Lan et al. Finite-time control for 6DOF spacecraft formation flying systems
CN103853047B (en) A kind of low thrust homing guidance method based on quantity of state feedback
CN108536009B (en) Orbit maintaining and disturbance inhibiting method for hybrid low-thrust spacecraft
CN105912020A (en) Spacecraft formation flying method in weak-stability boundary area
CN109190155A (en) A kind of continuous low-thrust trajectory design method of mixing promoted using electric propulsion/solar sail
CN112560343A (en) J2 perturbation Lambert problem solving method based on deep neural network and targeting algorithm
CN116880520A (en) Multi-circle pneumatic auxiliary derailment track planning method for Mars detector
CN114154253B (en) Continuous thrust track optimization method considering engine shutdown and strong parameter nonlinearity
CN108984934B (en) Track design method based on circumferential or tangential mixed continuous low thrust
CN112966340B (en) Small deviation quick correction method for carrying capacity of solid binding carrier rocket

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant