CN114148548A - Small-thrust track fast optimization method for periodic orbital phase modulation of three systems - Google Patents
Small-thrust track fast optimization method for periodic orbital phase modulation of three systems Download PDFInfo
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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 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) 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
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
The position vector is
Velocity vector of
Wherein the superscript "T" is a transposed symbol; the dynamic model considering the thrust in the three-system is
Wherein mu is the three-system coefficient of attraction,
the distance from the detector to the main celestial body and the secondary celestial body respectively, T is the thrust of the detector,
the thrust in three directions is large and small,
is the specific impulse of the power generated by the detector,
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:
wherein
And
respectively the beginning time and the end time; and initial mass
Fixation, end mass
No constraint; thrust component of the probe satisfies
And is
Wherein the content of the first and second substances,
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
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
Constraint equation: the 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
Wherein
Matrix of control vector coefficients
The control vector is
；
Carrying out convex processing on the kinetic equation based on a small disturbance continuous linearization method; note the book
Are respectively the first
And a first
The solution of the sub-iteration is that the linearized kinetic equation is
Wherein
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:
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 to the problem P2 converges to the solution to P1.
For the first
A second iteration of selecting
Solutions for sub-iterations
As guess initial value of the state vector, corresponding to
The solution pair of the sub-iteration is
Checking whether a convergence condition is satisfied:
wherein the content of the first and second substances,
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
；
The solution of the problem of the fast optimization of the small-thrust orbit phase modulation of the three-system periodic orbit is obtained,
in order to optimize the phase-modulated track,
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 a low-thrust orbit 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
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
The position vector is
Velocity vector of
Wherein the superscript "T" is a transposed symbol; the dynamic model considering the thrust in the three-system is
Wherein mu is the three-system coefficient of attraction,
the distance from the detector to the main celestial body and the secondary celestial body respectively, T is the thrust of the detector,
the thrust in three directions is large and small,
is the specific impulse of the power generated by the detector,
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:
wherein
And
respectively the beginning time and the end time; and initial mass
Fixation, end mass
No constraint; thrust component of the probe satisfies
And is
Wherein the content of the first and second substances,
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:
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:
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
Wherein
Matrix of control vector coefficients
The control vector is
。
Carrying out convex processing on the kinetic equation based on a small disturbance continuous linearization method; note the book
, 
Are respectively the first
And a first
The solution of the sub-iteration is that the linearized kinetic equation is
Wherein
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:
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
Iteration, selecting
Solutions for sub-iterations
As guess initial value of the state vector, corresponding to
The solution pair of the sub-iteration is
Checking whether a convergence condition is satisfied:
wherein the content of the first and second substances,
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
。
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,
in order to optimize the phase-modulated track,
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.
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.
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 (6)
1. A method for quickly optimizing a low-thrust orbit of periodic orbital phase modulation of a three-system 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;
step two: 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;
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;
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 or 2, characterized in that: the first implementation method is that in the three-body problem, the detector state is recorded as
The position vector is
Velocity vector of
Wherein the superscript "T" is a transposed symbol; the dynamic model considering the thrust in the three-system is
Wherein mu is the three-system coefficient of attraction,
the distance from the detector to the main celestial body and the secondary celestial body respectively, T is the thrust of the detector,
the thrust in three directions is large and small,
is the specific impulse of the power generated by the detector,
is the sea level gravitational acceleration.
4. The method of claim 3 for fast optimization of small thrust orbits for three-system periodic orbital phasing, wherein: the second step is realized by the method that,
the detector states of the beginning and end states of the phase modulation track are:
wherein
And
respectively the beginning and end times(ii) a And initial mass
Fixation, end mass
No constraint; thrust component of the probe satisfies
And is
Wherein the content of the first and second substances,
is the maximum thrust of the detector;
in order to obtain a fuel-optimal three-system low-thrust phase modulation orbit, the performance index of an optimization problem is set as
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
Constraint equation: the formulae (2) to (5).
5. The method of claim 4 for fast optimization of small thrust orbits for three-system periodic orbital phasing, wherein: the third step is to realize the method as follows,
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
Wherein
Matrix of control vector coefficients
The control vector is
；
Carrying out convex processing on the kinetic equation based on a small disturbance continuous linearization method; note the book
, 
Are respectively the first
And a first
The solution of the sub-iteration is that the linearized kinetic equation is
Wherein
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:
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).
6. The method of claim 5 for fast optimization of small thrust orbits for three-system periodic orbital phasing, wherein: 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 is converged to the solution of P1;
for the first
A second iteration of selecting
Solutions for sub-iterations
As guess initial value of the state vector, corresponding to
The solution pair of the sub-iteration is
Checking whether a convergence condition is satisfied:
wherein the content of the first and second substances,
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
；
The solution of the problem of the fast optimization of the small-thrust orbit phase modulation of the three-system periodic orbit is obtained,
in order to optimize the phase-modulated track,
the corresponding optimal control direction is obtained;
namely, the three-body system small thrust orbit is rapidly optimized through the sequential convex programming.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6278946B1 (en) * | 1997-02-04 | 2001-08-21 | Galaxy Development, Llc | Procedure for generating operational ballistic capture transfer using computer implemented process |
| CN106672266A (en) * | 2017-01-04 | 2017-05-17 | 北京理工大学 | Balance point Halo orbit phasing orbit transfer method taking time constraint into consideration |
| 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 |
| CN110806212A (en) * | 2019-11-12 | 2020-02-18 | 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 |
-
2022
- 2022-02-10 CN CN202210123115.4A patent/CN114148548B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6278946B1 (en) * | 1997-02-04 | 2001-08-21 | Galaxy Development, Llc | Procedure for generating operational ballistic capture transfer using computer implemented process |
| CN106672266A (en) * | 2017-01-04 | 2017-05-17 | 北京理工大学 | Balance point Halo orbit phasing orbit transfer method taking time constraint into consideration |
| 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 |
| CN110806212A (en) * | 2019-11-12 | 2020-02-18 | 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 |
Non-Patent Citations (3)
| Title |
|---|
| 尚海滨等: "行星际小推力轨道Lambert解及应用", 《航空学报》 * |
| 王帅等: "利用引力辅助的行星际周期轨道间转移研究", 《中国科学:技术科学》 * |
| 王帅等: "小推力地球卫星圆轨道同轨调相设计方法研究", 《宇航学报》 * |
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