CN108562292A - The interspace transfer track optimizing method of solar sail based on the adaptive pseudo- spectrometries of hp - Google Patents
The interspace transfer track optimizing method of solar sail based on the adaptive pseudo- spectrometries of hp Download PDFInfo
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- G—PHYSICS
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- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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- G—PHYSICS
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Abstract
The present invention proposes a kind of interspace transfer track optimizing method of solar sail based on the adaptive pseudo- spectrometries of hp, when being navigated by water from certain planetary orbit to another planetary orbit suitable for solar sail, seek an optimal transfer track, keep the time of its Orbit Transformation minimum, the technical problem slow for solving convergence rate existing in the prior art realizes that step includes：Establish the interspace transfer movement equation of solar sail under polar coordinate system；Build the optimal control problem of the interspace transfer track of solar sail；Using hp, adaptively the pseudo- spectrometry optimal control problem for shifting track interspace to solar sail optimizes, and obtains the Optimal Flight Route of the interspace transfer of solar sail.The present invention is adaptively adjusted the meshes number of respective bins or polynomial order according to the requirement of computational accuracy, to, with point number and more reasonably with point distribution, reduce calculation amount with less, be effectively improved convergence rate.
Description
Technical field
The invention belongs to field of deep space exploration, are related to a kind of solar sail transfer track optimizing method, and in particular to one
Kind of the interspace transfer track optimizing method of solar sail based on the adaptive pseudo- spectrometries of hp, is suitable for solar sail and is navigated by water from certain planetary orbit
When to another planetary orbit, seek an optimal transfer track, keeps the time of its Orbit Transformation minimum.
Background technology
With the complexity of survey of deep space task and the increase of space length, traditional propulsion mode has been difficult to meet it
It is required that.Solar sail is a kind of novel spacecraft generating thrust in large area light thin film surface reflection using solar photon,
Power resources are natural solar energy, need not consume chemical fuel.Therefore, navigation service life of the solar sail in space does not receive
Limit the restriction of fuel.In addition, continuous low thrust, portable construction, it is of low cost, transmitting risk is small the features such as so that solar sail exists
There is prodigious advantage in terms of the macrocyclic space mission such as survey of deep space, interplanetary flight.
The key technology that solar sail is related to includes：Structure design, material selection, the fold storage of solar sail and expansion,
Gesture stability, track optimizing etc..Wherein, the track optimizing of spacecraft can realize that reducing the fuel of spacecraft in orbit disappears
Consumption extends in-orbit life-span, increases and executes the optimal performance indexs such as task ability.For execute survey of deep space task solar sail and
Speech, since it is transferred to, the time span of target track is very big, very it is necessary to be optimized to the track that it is navigated by water, contracting
Short its shifts duration.
Solar sail it is interspace transfer optimal trajectory generation be substantially to solve for it is non-linear, carry state constraint and control constraints
Dynamic optimum control problem, solve it is extremely difficult.Currently, the interspace transfer track optimizing method of solar sail is broadly divided into indirectly
Method and direct method.It includes that derivation optimality condition is difficult, convergence radius is small and association's state variable initial value conjecture is tired that indirect method, which exists,
Difficult disadvantage, therefore, the operation of indirect method is relatively difficult.The basic thought of direct method be by continuous solar sail it is interspace transfer most
Excellent control problem discretization is simultaneously converted to NLP problems, then by optimization algorithm to performance indicator direct searching optimization.Direct method has just
Valuation susceptibility is low, is not required to derive First Order Optimality Condition, is easy to the advantages of sequencing, therefore the application relative to indirect method is more
It is extensive.Such as：2013, Naiming Qi were delivered in the phase of volume 34 the 5th of Journal of Astronautics
《Electric Sail Trajectory Optimization and Performance Analysis》, disclose one kind and adopt
Shift the method that track optimizes from the earth to Mars to solar sail with Gauss puppets spectrometry.This method has initially set up pole seat
Then the solar sail equation of motion under mark system constructs the optimal control problem of the solar sail earth-Mars transfer track, finally
Solution is optimized to the optimal control problem using Gauss puppets spectrometry.Gauss puppets spectrometry can also realize that solar sail is interspace
The optimization problem of track is shifted, but a point distribution form is matched due to it and is fixed, generally requires the interpolation polynomial ability compared with higher-dimension
Ideal approximate solution is obtained, calculation amount is larger, causes convergence rate slower.
Invention content
It is an object of the invention to overcome the shortcomings of above-mentioned prior art, it is proposed that a kind of based on the adaptive pseudo- spectrometries of hp
The interspace transfer track optimizing method of solar sail, the technical problem slow for solving convergence rate existing in the prior art.
To achieve the above object, the technical solution that the present invention takes includes the following steps：
(1) the interspace transfer movement equation of solar sail under polar coordinate system is established：
(1a) assumes that solar sail is the ideal plane of fully reflective solar photon, calculates solar photon and acts on solar sail face
On solar pressure Fs；
The sun radially and tangentially solar photon acted on solar sail face of (1b) along solar sail interplanetary transfer orbit
Light pressure FsDecomposed, obtain solar light pressure track radial direction acceleration magnitude arIt is big with the acceleration of tangential direction
Small aθ；
(1c) using the sun and solar sail as particle, the radial optical pressure acceleration a obtained by step (1b)rWith tangential light
Press acceleration aθ, establish the interspace transfer movement equation of solar sail under polar coordinate system；
(2) optimal control problem of the interspace transfer track of structure solar sail：
It is constrained for state differential equation by the interspace transfer movement of step (1) solar sail is equations turned, and by solar sail
Emit the quantity of state x of position0As primary condition, meets state differential equation constraint in state variable x and terminal is entered the orbit constraint
When, optimal control variable u so that performance indicator J minimalizations；
Wherein, state variable x takes the radial velocity v of solar sailrWith tangential velocity vθAnd step (1) the solar sail star
Angle Position θ of the solar sail with sun distance r and solar sail relative to the sun in the transfer movement equation of border；Control variable u takes
Pitch angle α in the interspace transfer movement equation of step (1) described solar sail；Performance indicator J takes the time of the interspace transfer of solar sail；
(3) using hp, adaptively the pseudo- spectrometry optimal control problem for shifting track interspace to solar sail in step (2) carries out
Optimization, obtains the Optimal Flight Route of the interspace transfer of solar sail：
Total section number that the interspace transfer track of solar sail is arranged in (3a) is K, current interval k, { k | 1≤k≤K }, often
The initial points of matching in a section are M, and M >=1, error threshold ε, relative curvature threshold value is rmax；
(3b) with turning to NLP problems by optimal control problem is discrete on point, and solves it in each section, obtains
To the corresponding state variable value x (τ) of a flight path and control variable value u (τ)；
(3c) calculates the maximum residul difference in each section by state variable value x (τ) and control variable value u (τ)And root
According toWith the magnitude relationship of ε, whether the flight path that judgment step (3b) obtains is optimal trajectory, if all sectionsThe flight path that then step (3b) obtains is optimal trajectory, and optimization terminates, if there are certain sectionsMeter
Calculate the relative curvature in these sectionsAnd execute step (3d)；
(3d) updatesSection with point a number：
Judge these sectionsAnd rmaxMagnitude relationship, ifThen redefine corresponding section matches a point number
NkIfIt is then n by corresponding interval divisionkA subinterval, and it will be set as M with point number in each subinterval,
It obtains new the matching in these sections and puts number and distribution, and execute step (3b), carry out next iteration.
Compared with prior art, the present invention having the following advantages that：
The present invention is due to when solving the optimal control problem of the interspace transfer track of solar sail, using the adaptive pseudo- spectrometries of hp
As method for solving, this method is adaptively adjusted the meshes number or multinomial of respective bins according to the requirement of computational accuracy
Order, to it is less with point number and more reasonably match point be distributed, reduce calculation amount, compared with prior art,
It is effectively improved convergence rate.
Description of the drawings
Fig. 1 is the implementation flow chart of the present invention；
Fig. 2 is the schematic diagram that solar pressure is radially and tangentially decomposed along the solar sail earth-Mars transfer orbit.
Specific implementation mode
The specific embodiment that track optimizing is shifted below in conjunction with attached drawing and the solar sail earth-Mars, makees into one the present invention
Step is described in detail.
Referring to Fig.1, a kind of solar sail earth-Mars based on the adaptive pseudo- spectrometries of hp shifts track optimizing method, including
Following steps：
Step 1 establishes the solar sail earth-Mars transfer movement equation under polar coordinate system：
Step 1a) assume that solar sail is the ideal plane of fully reflective solar photon, it calculates solar photon and acts on the sun
Solar pressure F on sail faces, expression formula is：
Wherein, m is the quality of solar sail；β is the illuminance of solar sail；μ is solar gravitation coefficient；R is for solar sail and too
The distance of sun；R is incident ray unit vector；N is solar sail unit normal vector.
Step 1b) along the solar sail earth-Mars transfer orbit solar sail face radially and tangentially is acted on to solar photon
On solar pressure FsIt is decomposed, as shown in Fig. 2, solar pressure FsDirection perpendicular to ideal sail face, α is the sun
Angle between incident ray unit vector r and solar sail unit normal vector n obtains solar light pressure adding in track radial direction
Velocity magnitude arWith the acceleration magnitude a of tangential directionθ, expression formula is respectively：
Wherein, β is the illuminance of solar sail；μ is solar gravitation coefficient；R is solar sail at a distance from the sun；α is the sun
The pitch angle of sail.
Step 1c) using the sun and solar sail as particle, by step 1b) obtained radial optical pressure acceleration arWith it is tangential
Optical pressure acceleration aθ, the solar sail earth-Mars transfer movement equation under polar coordinate system is established, expression formula is：
Wherein, r is solar sail at a distance from the sun；θ is Angle Position of the solar sail relative to the sun；μ is solar gravitation system
Number；arAnd aθRespectively acceleration magnitude of the solar light pressure in the earth-Mars transfer orbit radially and tangentially direction.
The optimal control problem of step 2, the structure solar sail earth-Mars transfer track：
It is constrained for state differential equation by the step 1) the solar sail earth-Mars transfer movement is equations turned, and it will too
Quantity of state x of the positive sail in Earth's orbit0As primary condition.In state variable x=[r, θ, vr,vθ]TMeet state differential equation
Constraint and terminal enter the orbit constraint when, optimize the pitch angle α of solar sail so that performance indicator J minimalizations.Wherein, state differential
Equation constraint expression formula be：
Primary condition x0For：
r0=1, vr0=0, vθ0=1, θ0=0.1
Terminal, which is entered the orbit, is constrained to the quantity of state x that solar sail enters Mars trackf：
Performance indicator J is the time of the solar sail earth-Mars transfer, and expression formula is：
Wherein, r is solar sail at a distance from the sun；θ is Angle Position of the solar sail relative to the sun；vrAnd vθRespectively too
The radial velocity and tangential velocity of positive sail；arAnd aθRespectively solar light pressure is radially and tangentially square in the earth-Mars transfer orbit
To acceleration magnitude；μ is solar gravitation coefficient；t0For the initial time of sun sail；tfEnter Mars track for solar sail
At the time of.
Step 3, using hp, adaptively pseudo- spectrometry shifts the solar sail earth in step 2)-Mars the optimum control of track
Problem optimizes, and obtains the Optimal Flight Route of the solar sail earth-Mars transfer：
Step 3a) total section number of the setting solar sail earth-Mars transfer track is K, current interval k, k | 1≤
K≤K }, the initial points of matching in each section are M, and M >=1, error threshold ε, relative curvature threshold value is rmax；
Step 3b) matching on point in each section, the discrete NLP that turns to of optimal control problem is asked using Radau puppets spectrometry
Topic, and it is solved, obtain the corresponding state variable value x (τ) of a flight path and control variable value u (τ)；
Step 3c) by state variable value x (τ) and control variable value u (τ), calculate the maximum residul difference in each section
Its expression formula is：
According toWith the magnitude relationship of ε, judgment step 3b) whether obtained flight path be optimal trajectory, if all areas
BetweenThen step 3b) obtained flight path is optimal trajectory, optimization terminates；If there are certain sections
Calculate the relative curvature in these sectionsAnd execute step 3d), expression formula is：
Wherein,For s-th of sampled pointThe first differential residual error of i-th of state variable at place；It is sampled for s-th
PointJ-th of path constraint residual error at place；WithMaximum curvature and average curvature in respectively all sampled points.S
State variable first differential residual error at a sampled pointPath constraint residual errorAnd curvature κ(k)Expression formula difference
For：
Wherein, f constrains for state differential equation；C is path constraint；For the state variable value at s-th of sampled point；For the control variable value at s-th of sampled point.
Step 3d) updateSection with point a number：
Judge these sectionsAnd rmaxMagnitude relationship, ifIllustrate that this section of track is smoother, then again really
Surely correspond to section matches a point number Nk, expression formula is：
IfIllustrate that this section of track is excessively shaken, is then n by corresponding interval divisionkA subinterval, expression formula
For：
And will be in each subinterval be set as M with a point number, obtain these sections it is new with point number and distribution, and hold
Row step 3b), carry out next iteration.Wherein, M is that initial the matching in each section is counted；Ceil () expressions round up；ε
For error threshold；For the maximum residul difference in each section；A is the integer more than 0, is an adjustable factors；B is whole more than 0
Number is an adjustable factors.
The technique effect of the present invention is further illustrated below in conjunction with emulation experiment：
1, simulated conditions：
The present invention and the existing optimization Simulation for shifting track to the solar sail earth-Mars using Gauss puppets spectrometry are all
In the hardware environment and MATLAB R2014a of Intel (R) Core (TM) i5-3230M processors of dominant frequency 2.6GHZ, memory 4GB
Software environment under carry out.In the emulation of the present invention, illuminance β=0.17 of solar sail；Solar sail pose adjustment is to connect
Continuous, pitch angle α meets：It is set as 10 with a required precision-6。
2, analysis of simulation result：
The present invention and the existing optimization Simulation for shifting track to the solar sail earth-Mars using Gauss puppets spectrometry, institute
Being taken with point number and calculating for using is as shown in table 1：
Table 1
Present invention uses 52 it can be seen from the comparing result in table 1 to match point, takes 7.611s, and Gauss puppets are composed
Method has used 60 to match point, takes 18.402s.What the present invention used takes less, the convergence speed of optimization with point number and calculating
Degree also faster, this is because the present invention solar sail earth-Mars is shifted track concussion region be divided into it is multiple more smooth
Section, optimal trajectory is approached with low order interpolation polynomial in each section, it is complete using high-order relative to Gauss puppet spectrometries
Office's approximation by polynomi-als, is reduced on number and calculation amount.
Claims (8)
1. a kind of interspace transfer track optimizing method of solar sail based on the adaptive pseudo- spectrometries of hp, it is characterised in that including walking as follows
Suddenly：
(1) the interspace transfer movement equation of solar sail under polar coordinate system is established：
(1a) assumes that solar sail is the ideal plane of fully reflective solar photon, calculates solar photon and acts on solar sail face
Solar pressure Fs；
The solar light pressure radially and tangentially solar photon acted on solar sail face of (1b) along solar sail interplanetary transfer orbit
Power FsDecomposed, obtain solar light pressure track radial direction acceleration magnitude arWith the acceleration magnitude a of tangential directionθ；
(1c) using the sun and solar sail as particle, the radial optical pressure acceleration a obtained by step (1b)rAdd with tangential optical pressure
Speed aθ, establish the interspace transfer movement equation of solar sail under polar coordinate system；
(2) optimal control problem of the interspace transfer track of structure solar sail：
It is constrained for state differential equation by the interspace transfer movement of step (1) solar sail is equations turned, and solar sail is emitted
The quantity of state x of position0As primary condition, state variable x meet state differential equation constraint and terminal enter the orbit constraint when, it is excellent
Change control variable u so that performance indicator J minimalizations；
Wherein, state variable x takes the radial velocity v of solar sailrWith tangential velocity vθAnd interspace turn of step (1) described solar sail
Angle Position θ of the solar sail with sun distance r and solar sail relative to the sun in shifting movement equation；Control variable u takes step
(1) the pitch angle α in the interspace transfer movement equation of the solar sail；Performance indicator J takes the time of the interspace transfer of solar sail；
(3) using hp, adaptively the pseudo- spectrometry optimal control problem for shifting track interspace to solar sail in step (2) optimizes,
Obtain the Optimal Flight Route of the interspace transfer of solar sail：
Total section number that the interspace transfer track of solar sail is arranged in (3a) is K, current interval k, { k | 1≤k≤K }, Mei Gequ
Between it is initial be M with points, M >=1, error threshold ε, relative curvature threshold value is rmax；
(3b) with turning to NLP problems by optimal control problem is discrete on point, and solves it in each section, obtains one
The corresponding state variable value x (τ) of flight path and control variable value u (τ)；
(3c) calculates the maximum residul difference in each section by state variable value x (τ) and control variable value u (τ)And according toWith the magnitude relationship of ε, whether the flight path that judgment step (3b) obtains is optimal trajectory, if all sectionsThe flight path that then step (3b) obtains is optimal trajectory, and optimization terminates, if there are certain sectionsMeter
Calculate the relative curvature in these sectionsAnd execute step (3d)；
(3d) updatesSection with point a number：
Judge these sectionsAnd rmaxMagnitude relationship, ifThen redefine corresponding section matches a point number Nk,
IfIt is then n by corresponding interval divisionkA subinterval, and it will be set as M with point number in each subinterval, it obtains
Number and distribution are put in new the matching in these sections, and execute step (3b), carry out next iteration.
2. the solar sail interspace transfer track optimizing method according to claim 1 based on the adaptive pseudo- spectrometries of hp, special
Sign is：Solar pressure F described in step (1a)s, expression formula is：
Wherein, m is the quality of solar sail；β is the illuminance of solar sail；μ is solar gravitation coefficient；R is solar sail and the sun
Distance；R is incident ray unit vector；N is solar sail unit normal vector.
3. the solar sail interspace transfer track optimizing method according to claim 1 based on the adaptive pseudo- spectrometries of hp, special
Sign is：Solar light pressure described in step (1b) is in track radial direction acceleration magnitude arWith tangential direction acceleration magnitude aθ,
Its expression formula is respectively：
Wherein, β is the illuminance of solar sail；μ is solar gravitation coefficient；R is solar sail at a distance from the sun；α is solar sail
Pitch angle.
4. the solar sail interspace transfer track optimizing method according to claim 1 based on the adaptive pseudo- spectrometries of hp, special
Sign is：The interspace transfer movement equation of solar sail described in step (1c), expression formula are：
Wherein, r is solar sail at a distance from the sun；θ is Angle Position of the solar sail relative to the sun；μ is solar gravitation coefficient；ar
And aθRespectively acceleration magnitude of the solar light pressure in track radially and tangentially direction.
5. the solar sail interspace transfer track optimizing method according to claim 1 based on the adaptive pseudo- spectrometries of hp, special
Sign is：In the optimal control problem of the interspace transfer track of structure solar sail described in step (2), state differential equation constraint and
Performance indicator J, expression formula are respectively：
Wherein, r is solar sail at a distance from the sun；θ is Angle Position of the solar sail relative to the sun；vrAnd vθRespectively solar sail
Radial velocity and tangential velocity；arAnd aθRespectively acceleration magnitude of the solar light pressure in track radially and tangentially direction；μ is
Solar gravitation coefficient；t0For the initial time of sun sail；tfAt the time of entering target track for solar sail.
6. the solar sail interspace transfer track optimizing method according to claim 1 based on the adaptive pseudo- spectrometries of hp, special
Sign is：Step (3b) is described to turn to NLP problems by optimal control problem is discrete, using Radau puppet spectrometries.
7. the solar sail interspace transfer track optimizing method according to claim 1 based on the adaptive pseudo- spectrometries of hp, special
Sign is：Maximum residul difference described in step (3c)And relative curvatureIts expression formula is respectively：
Wherein,For s-th of sampled pointThe first differential residual error of i-th of state variable at place；For s-th of sampled point
J-th of path constraint residual error at place；WithMaximum curvature and average curvature in respectively all sampled points.
8. the solar sail interspace transfer track optimizing method according to claim 1 based on the adaptive pseudo- spectrometries of hp, special
Sign is：Corresponding section is redefined described in step (3d) matches a point number NkIt is n with interval division will be corresponded tokA subinterval,
Expression formula is respectively：
Wherein, M is that initial the matching in each section is counted；Ceil () expressions round up；ε is error threshold；For each area
Between maximum residul difference；A is the integer more than 0, is an adjustable factors；B is the integer more than 0, is an adjustable factors.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111191358A (en) * | 2019-12-24 | 2020-05-22 | 南京理工大学 | Air-breathing supersonic missile trajectory optimization design method |
| WO2020191712A1 (en) * | 2019-03-28 | 2020-10-01 | Baidu.Com Times Technology (Beijing) Co., Ltd. | A map-less and camera-based lane markings sampling method for level-3 autonomous driving vehicles |
| CN114004035A (en) * | 2021-12-13 | 2022-02-01 | 哈尔滨工业大学（威海） | Target tracking control method for unmanned surface vehicle |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103112600A (en) * | 2013-03-04 | 2013-05-22 | 北京理工大学 | Interplanetary transfer orbit design method |
| CN105930550A (en) * | 2016-04-01 | 2016-09-07 | 方洋旺 | Method for optimizing boost-skip trajectory of air-breathing hypersonic missile |
-
2017
- 2017-11-24 CN CN201711187855.XA patent/CN108562292B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103112600A (en) * | 2013-03-04 | 2013-05-22 | 北京理工大学 | Interplanetary transfer orbit design method |
| CN105930550A (en) * | 2016-04-01 | 2016-09-07 | 方洋旺 | Method for optimizing boost-skip trajectory of air-breathing hypersonic missile |
Non-Patent Citations (4)
| Title |
|---|
| MINXIU KONG ETAL.: "Optimal Point-to-point Motion Planning of Flexible Parallel Manipulator with Adaptive Gauss Pseudo-spectral Method", 《2014 IEEE/ASME INTERNATIONAL CONFERENCE ON ADVANCED INTELLIGENT MECHATRONICS(AIM)》 * |
| 董雪仰等: "航天器太阳帆板展开过程最优控制的自适应Gauss伪谱法", 《应用数学和力学》 * |
| 邱文杰等: "基于hp自适应伪谱法的飞行器多阶段轨迹优化", 《北京理工大学学报》 * |
| 钱航等: "太阳帆航天器行星际轨道转移优化算法", 《空间控制技术与应用》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2020191712A1 (en) * | 2019-03-28 | 2020-10-01 | Baidu.Com Times Technology (Beijing) Co., Ltd. | A map-less and camera-based lane markings sampling method for level-3 autonomous driving vehicles |
| CN112041637A (en) * | 2019-03-28 | 2020-12-04 | 百度时代网络技术（北京）有限公司 | Map-less and camera-based lane marker sampling method for 3-level autonomous vehicles |
| CN112041637B (en) * | 2019-03-28 | 2021-11-19 | 百度时代网络技术（北京）有限公司 | Map-less and camera-based lane marker sampling method for 3-level autonomous vehicles |
| US11267476B2 (en) | 2019-03-28 | 2022-03-08 | Baidu Usa Llc | Map-less and camera-based lane markings sampling method for level-3 autonomous driving vehicles |
| CN111191358A (en) * | 2019-12-24 | 2020-05-22 | 南京理工大学 | Air-breathing supersonic missile trajectory optimization design method |
| CN111191358B (en) * | 2019-12-24 | 2022-06-24 | 南京理工大学 | Air-breathing supersonic missile trajectory optimization design method |
| CN114004035A (en) * | 2021-12-13 | 2022-02-01 | 哈尔滨工业大学（威海） | Target tracking control method for unmanned surface vehicle |
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