CN109145391A - A kind of continuous thrust orbit design method of the spacecraft of oriented mission - Google Patents
A kind of continuous thrust orbit design method of the spacecraft of oriented mission Download PDFInfo
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Abstract
The invention discloses a kind of continuous thrust orbit design methods of the spacecraft of oriented mission, the following steps are included: step S1, under two-body gravitational field, kinematical equation of the spacecraft under polar coordinate system is established, assumes that method provides the fitted shapes equation for meeting the spacecraft of spacecraft mission requirements and moving using shape；Step S2 is converted into track variable bound for the task of spacecraft is track restrained, specifically includes the constraint of rail boundary value, point constraint and thrust size constraint in track；Step S3, by the task track of spacecraft it is discrete be several segments, solved using Fourier expansion method and meet the track of the track variable bound.The specific object properties of geometric characteristic parameter and track of overall track are combined, designs and adapts to complicated track restrained hybrid junction track, this method can be good at adapting to complicated orbit maneuver task.
Description
Technical field
The invention belongs to spacecraft thrust orbit design fields；It is continuous more particularly to a kind of spacecraft of oriented mission
Thrust orbit design method.
Background technique
As the development and space tasks of spacecraft propulsion technology become increasingly complex, the motor-driven rail based on continuous low thrust
Road design receives the concern of more and more people.Mainly have two for the space tasks Track desigh under continuous thrust
Kind method, one is the methods based on specific thrust, it is assumed that thus thrust scheme simultaneously calculates the track under thrust, mainly have
Two methods of parsing and numerical value；Another kind is the method based on shape, i.e., the shape letter of errant is characterized by series of parameters
Number, or with the curve of known track characteristic come approximate track, and then realize thrust required for the track of design.The first side
Method is often the Track desigh for being directed to special thrust, does not have generality.Second method is designed compared with first method
Track may not be optimal, but track can be indicated more succinct by this method, can largely reduce calculating
Amount, and there is commonly used characteristic.
For second method Petropoulos et al. using exponential sinusoidal curve come approximate continuous low-thrust trajectory, but
It is that the tangential thrust that this method is assumed is not able to satisfy rail boundary condition.Wall proposes the curve based on six inverse polynomials
Approach method, can be good at meeting terminal position, but when it is applied to LEO and shifts, not be well positioned to meet specific
It is track restrained.M.Vasile et al. proposes a kind of shaped tracks design method based on pseudo- Spring Equinox orbital tracking, this method
It can be good at handling the two_point boundary value problem of Orbit Transformation, however this method is difficult to be adapted to thrust size constraint and track
Path constraint.Ehsan Taheri etc. proposes a kind of approximate method of fourier to handle the Track desigh under thrust constraint
Problem, this method expand the range of parameter selection, however this method in the case where few to constraint condition to a certain extent
In the parameter for determining Fourier space, the selection of discrete point and the hypothesis of original shape have certain randomness, and
When constraining more, all track restrained conditions can not be met simultaneously.
There is many constraints (such as thrust constraint, the interior point constraint of track) in designing in continuous thrust orbit, and these are constrained
It can not convert it into as continuous function.Although the rail design method of fixed shape, the shape of entire track is fixed as
A kind of specific shape constrains orbit parameter using specific function, can greatly reduce the track ginseng for needing to design
Number, but be difficult to meet the interior point constraint of every track section.
Summary of the invention
The present invention provides a kind of continuous thrust orbit design methods of the spacecraft of oriented mission, by the geometry of overall track
Parameters for shape characteristic and the specific object properties of track combine, and design and adapt to complicated track restrained hybrid junction track, should
Method can be good at adapting to complicated orbit maneuver task.
The technical scheme is that a kind of continuous thrust orbit design method of the spacecraft of oriented mission, including it is following
Step: step S1 establishes kinematical equation of the spacecraft under polar coordinate system, using shape hypothesis side under two-body gravitational field
Method provides the fitted shapes equation for meeting the spacecraft movement of spacecraft mission requirements；Step S2, by the task track of spacecraft
Constraint is converted into track variable bound, specifically includes the constraint of rail boundary value, the interior point constraint of track and thrust size constraint；Step
S3, by the task track of spacecraft it is discrete be several segments, using Fourier expansion method solution meet the track variable
The track of constraint.
Further, the features of the present invention also characterized in that:
The tool for meeting the track of the track variable bound is wherein solved in step S3 using Fourier expansion method
Body process is: step S31 designs every section of track using Method On Shape, so that it is met boundary value constraint, while determination changes a section track
Discrete point；Step S32 converts finite term Fu for every section of track in the case where this section of track meets and put constraint in track
In leaf progression form, and determine its coefficient；Step S33 determines every section of track in the case where this section of track meets thrust constraint
Radius vector, polar angle and its finite term fourier function.
Wherein in step S32, certain section of track is unsatisfactory in track in the case where point constraint, step S31 is carried out, until the section
Track meets point constraint in track.
Wherein geometric shape parameters are converted into finite term Fourier space form in step S33 are as follows:
Wherein certain section of track is unsatisfactory for thrust constraint in step S33, step S32 is carried out, until this section of track meets thrust
Constraint.
Wherein in step S1 spacecraft kinematical equation are as follows:Wherein r is spacecraft orbit
Radius vector, θ indicate that spacecraft polar angle in orbit, α are the angles of thrust and track tangential, and β is that spacecraft speed is cut with track
To angle, f be spacecraft thrust acceleration, μ is gravitational constant.
The wherein fitted shapes equation of spacecraft movement are as follows:
9. wherein the task track of spacecraft is separated into n sections in step S3, the geometric shape parameters of every section of track are fi(ri,
θi), the shape of task track are as follows:
Compared with prior art, the beneficial effects of the present invention are: rail design method of the invention by overall track according to
Task restriction is separated into several segments, and every track section is converted to finite term Fourier space form, by adjusting Fourier's grade
Several parameters, it is track restrained to meet, realize more geometrical characteristic mixed tracks splicing of overall track.This method is in face of routine
The constraint of track three classes breaches and only meets rail boundary constraint currently based on fixed shaped tracks design method, can not handle tool
There is the defect of point constraint and track thrust restricted problem in track.
Detailed description of the invention
Fig. 1 is the spacecraft motion model figure in the present invention under two-body gravitational field；
Fig. 2 is flow diagram of the present invention.
Specific embodiment
Technical solution of the present invention is further illustrated in the following with reference to the drawings and specific embodiments.
The present invention provides a kind of continuous thrust orbit design method of the spacecraft of oriented mission, this method is based on Multiple Shape
Overall track is separated into several segments for task by the Track desigh theory of hybrid junction, by point in specific more complicated track
Constraint is converted into the boundary point constraint of every track section；Then every track section is all carried out using a certain geometry track
Approximation makes it meet the constraint of rail boundary point, then converts fourier grade for the obtained track with certain geometry
Number form formula solves fourier series parameter, so that track meets point constraint in track；The track of discrete all segmentations is handled
Later, the track of whole section of Multiple Shape hybrid junction can be obtained.Its specific step are as follows:
Step S1 is established kinematical equation of the spacecraft under polar coordinate system, is assumed using shape under two-body gravitational field
Method provides the fitted shapes equation for meeting the spacecraft movement of spacecraft mission requirements.
Under two-body gravitational field, expression-form of the spacecraft equation of motion under polar coordinate system in plane are as follows:
As shown in Figure 1, r is spacecraft orbit radius vector, θ indicates spacecraft polar angle in orbit, and α is that thrust is cut with track
The angle of line, β are spacecraft speed and the tangential angle of track, and f is the thrust acceleration of spacecraft, and μ is gravitational constant.
It is obtained by formula (1):
In order to simplify Track desigh, taking thrust direction is the direction along spacecraft speed, then has:
Formula (3) are simplified are as follows:
F (r, r ', r ", θ ', θ ")=r2(θ′r″-r′θ″)+θ′(μ-2rr′2)-(rθ′3)=0 (7)
The thrust size of spacecraft realization track are as follows:
For the Track desigh with task time constraint and track editor, the shape based on seven inverse polynomials can be used
Assuming that method is fitted trade shape, to obtain the variation of orbit radius r.Overall track is fitted to following shape by this method
Formula:
When not having the constraint of track task time, track is using six inverse polynomial form descriptions；When there is track task
Between when constraining, track is using seven inverse polynomial forms descriptions.
Step S2 is converted into track variable bound for the task of spacecraft is track restrained, specifically includes rail boundary value about
Point constraint and thrust size constraint in beam, track.
Step S3, by the task track of spacecraft it is discrete be several segments, using Fourier expansion method solve meet
The track of the track variable bound.
As shown in Fig. 2, task track is divided into several segments track, the shape of every track section can be different.It is assumed that will
Overall track it is discrete become n section, each section representated by track geometry function be fi(ri,θi), if the shape of overall track
Shape is F (r, θ), then has:
The each section of track with geometrical characteristic is described using the Fourier space form of finite term, finally by integral rails
Road is expressed as the track of a finite term Fourier space, and wherein the coefficient of Fourier space is as the task period changes.
It is expressed as in addition, will have figurate curve as the form of finite term Fourier space；It is past due to the track of fixed shape
It is past to be difficult to meet the constraint of track thrust size, if shape will be fixed as to the initial of finite term Fourier expansion formula parameter
Then thrust constraint is changed into nonlinear restriction by estimation, can thus set solving with the track under thrust constraint
Meter, conversion meets orbit equation constraint, and there are the finite term Fourier coefficient Solve problems of nonlinear restriction, and the problem can
To use nonlinear restriction planing method to solve well.
Include: using the detailed process that Fourier expansion method solves the track for meeting the track variable bound
Step S31 designs every section of track using Method On Shape, so that it is met boundary value constraint, while determination changes a section track
Discrete point；S32 converts finite term Fourier for every section of track in the case where this section of track meets and put constraint in track
Progression form, and determine its coefficient；Step S33 determines the arrow of every section of track in the case where this section of track meets thrust constraint
Diameter, polar angle and its finite term fourier function.
When carrying out shape hypothesis to every track section, determining geometric shape parameters meet the boundary value constraint of two o'clock.
Finite term Fourier space form is converted by specific geometric shape parameters, is provided just for the coefficient of Fourier expansion formula
Begin to estimate.In the specific geometry of determination, it is assumed that the independent variable of curve is time constant, and radius vector and polar angle are time variables
Function.Form is as follows:
When coefficient of N number of discrete point to determine Fourier space in the curve of selected fixed form, coefficient undetermined has
It 2N+1, if independent variable is become θ, can not solve completely, therefore can only select independent variable is that the time is normal
Number.After fixed geometry curve has been determined, a certain number of discrete points are chosen on curve, it is assumed that of discrete point
Number is N number of.Here it is assumed that the shape of track is six order polynomial inverse functions, other shapes of Fourier coefficient determines method therewith
It is identical.Shape function are as follows:
It is constrained by rail boundary value, then can determine the coefficient (a, b, c, d, e, f, g) of shape function, it thus can be true
The polar angle of curve and the relationship of polar diameter are made, finite term Fourier space form is converted in order to which form parameter will be fixed, must also
(12) formula must be converted to the function of time.The wherein relationship of polar angle and time are as follows:
θ (t)=a1t3+b1t2+c1t+d1 (13)
Polar angle function coefficients (a can be determined by rail boundary constraint1,b1,c1,d1), it is assumed that track starting point condition is
(θ,θ1',θ″1), termination condition be (θ, θ 'f,θ″f), whole section of track time-consuming t, then the coefficient of polar angle function are as follows:
R=f (t) is obtained by formula (11), then has following relationship:
θ (t)=g (t) → r=f (t) (15)
Wherein.
Finite term Fourier space form formula (11) is converted by formula (14) by the function of fixed shape.From formula
(14) N-1 discrete point is selected in, it is assumed that meet following formula on the discrete point:
Formula (16) is also denoted as following matrix form:
Wherein
The time of known entire task orbit time and discrete point, radius vector, polar angle (being determined by Method On Shape) the case where
Under, matrix A .C is that the matrix function determined by a variable (sets N number of freedom to N-1 discrete point in note equation (17)
Variable), the coefficient of finite term Fourier space, the boundary constraint of optimization problem can be thus acquired by optimizing the variable
It is all constraints met in step 2, optimization aim is fuel consumed by overall track is motor-driven.The optimization problem can adopt
It is solved with the Fmin in matlab.After optimized parameter has been determined, A.C matrix is just obtained, and bringing equation (18) into can obtain
To Matrix C.It finally brings these coefficients into equation (12) and equation (8), the track for meeting task restriction can be obtained.
Claims (8)
1. a kind of continuous thrust orbit design method of the spacecraft of oriented mission, which comprises the following steps:
Step S1 establishes kinematical equation of the spacecraft under polar coordinate system under two-body gravitational field, assumes method using shape
Provide the fitted shapes equation for meeting the spacecraft movement of spacecraft mission requirements；
Step S2 is converted into track variable bound for the task of spacecraft is track restrained, specifically includes the constraint of rail boundary value, rail
Point constraint and thrust size constraint in road；
Step S3, by the task track of spacecraft it is discrete be several segments, using Fourier expansion method solve meet described in
The track of track variable bound.
2. the continuous thrust orbit design method of the spacecraft of oriented mission according to claim 1, which is characterized in that described
It is using the detailed process that Fourier expansion method solves the track for meeting the track variable bound in step S3: step
S31 designs every section of track using Method On Shape, so that it is met boundary value constraint, while determining the discrete point for changing section track；Step
S32 converts finite term Fourier space form for every section of track in the case where this section of track meets and put constraint in track,
And determine its coefficient；Step S33, in the case where this section of track meets thrust constraint, determine the radius vector of every section of track, polar angle and
Its finite term fourier function.
3. the continuous thrust orbit design method of the spacecraft of oriented mission according to claim 2, which is characterized in that described
In step S32, certain section of track is unsatisfactory in track in the case where point constraint, step S31 is carried out, until this section of track meets track
Interior point constraint.
4. the continuous thrust orbit design method of the spacecraft of oriented mission according to claim 2, which is characterized in that described
Geometric shape parameters are converted into finite term Fourier space form in step S33 are as follows:
5. the continuous thrust orbit design method of the spacecraft of oriented mission according to claim 2, which is characterized in that described
Certain section of track is unsatisfactory for thrust constraint in step S33, carries out step S32, until this section of track meets thrust constraint.
6. the continuous thrust orbit design method of the spacecraft of oriented mission according to claim 1, which is characterized in that described
The kinematical equation of spacecraft in step S1 are as follows:
；
Wherein r is spacecraft orbit radius vector, and θ indicates spacecraft polar angle in orbit, and α is the angle of thrust and track tangential,
β is spacecraft speed and the tangential angle of track, and f is the thrust acceleration of spacecraft, and μ is gravitational constant.
7. the continuous thrust orbit design method of the spacecraft of oriented mission according to claim 1, which is characterized in that described
The fitted shapes equation of spacecraft movement is in step S1
8. the continuous thrust orbit design method of the spacecraft of oriented mission according to claim 1, which is characterized in that described
The task track of spacecraft is separated into n sections in step S3, and the geometric shape parameters of every section of track are fi(ri,θi), task track
Shape is
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103226631A (en) * | 2013-03-29 | 2013-07-31 | 南京航空航天大学 | Method for rapidly designing and optimizing low-thrust transfer orbit |
| CN106628257A (en) * | 2016-09-28 | 2017-05-10 | 西北工业大学 | Method for keeping relative motion orbit of near-earth spacecraft in earth's perturbation gravitational field |
| CN107211287A (en) * | 2014-08-29 | 2017-09-26 | 峰鸟航空科技公司 | The system and method that regional air transport network is realized using hybrid electrically aircraft |
| US20180106898A1 (en) * | 2015-01-02 | 2018-04-19 | Reservoir Labs, Inc. | Systems and methods for efficient targeting |
-
2018
- 2018-07-26 CN CN201810837031.0A patent/CN109145391A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103226631A (en) * | 2013-03-29 | 2013-07-31 | 南京航空航天大学 | Method for rapidly designing and optimizing low-thrust transfer orbit |
| CN107211287A (en) * | 2014-08-29 | 2017-09-26 | 峰鸟航空科技公司 | The system and method that regional air transport network is realized using hybrid electrically aircraft |
| US20180106898A1 (en) * | 2015-01-02 | 2018-04-19 | Reservoir Labs, Inc. | Systems and methods for efficient targeting |
| CN106628257A (en) * | 2016-09-28 | 2017-05-10 | 西北工业大学 | Method for keeping relative motion orbit of near-earth spacecraft in earth's perturbation gravitational field |
Non-Patent Citations (6)
| Title |
|---|
| FANG, Q ET AL: "A Shape-Based Method for Continuous Low-Thrust Trajectory Design between Circular Coplanar Orbits", 《INTERNATIONAL JOURNAL OF AEROSPACE ENGINEERING》 * |
| SHI MINGMING ET AL: "Using Fourier Shape-Based Method For the Construction of Moon to Mars Transfer Orbit", 《2014 INTERNATIONAL CONFERENCE ON MECHATRONICS AND CONTROL (ICMC)》 * |
| 方群 等: "混合推力作用下基于傅里叶级数展开的", 《西北工业大学学报》 * |
| 曾奎 等: "基于傅里叶级数的小推力航天器快速轨迹设计", 《自动化学报》 * |
| 曾奎 等: "基于多项式设计法的小推力轨迹设计", 《国防科技大学学报》 * |
| 王雪峰: "基于傅立叶级数展开的航天器连续推力机动轨道设计", 《中国优秀硕士学位论文全文数据库电子期刊 工程科技II辑》 * |
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