CN109709805A - A kind of spacecraft robust intersection trajectory design method considering uncertain factor - Google Patents
A kind of spacecraft robust intersection trajectory design method considering uncertain factor Download PDFInfo
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Abstract
The present invention relates to a kind of spacecraft robusts for considering uncertain factor to intersect trajectory design method, using Covariance Analysis Technique quick, the accurate building uncertain factor propagation equation the characteristics of, influence of the analysis uncertain factor to nominal trajectory；Using analysis result as the constraint condition of optimization problem, robust optimization problem is constructed；It is solved by genetic algorithm, to realize that robust intersects Trajectory Design.Consider that the robust of uncertain factor intersects problem to convert the Optimal Rendezvous problem of traditional determination system to, and solved by genetic algorithm, realizes the purpose of robust intersection Trajectory Design.
Description
Technical field
The invention belongs to space travel dynamic and control fields, are related to a kind of spacecraft Shandong for considering uncertain factor
Stick intersects trajectory design method.
Background technique
Since 21 century, with the development of space technology, space technology gradually enters space, exploration space turn from initial
To utilization space, spatial operation.Space intersection executes the basis of spatial operation task as spacecraft, refers to two or two
On spacecraft on space orbit by the technology that predetermined position and time meet.Since half a century, the mankind are to intersect technology
Based on complete space station build, the complicated solar-system operation such as manned moon landing and deep space exploration.
In terms of intersecting Trajectory Design, scholar has carried out wide hair research.Document Clohessy W.H.Terminal
Guidance System for Satellite Rendezvous[J].Aerospace Sci,1960,27(9):653-658.
In, Clohessy proposes Clohessy-Wiltshire equation to describe the relative motion between spacecraft 1960, from
And be various track optimizing technology and methods application provide the foundation.The nonlinear problem being directed in intersection, document
Handelsman M.,Lion P.M.Primer vector on fixed-time impulsive trajectories[J]
.Aerospace Sci, 1968,6 (1): Handelsman proposes master vector method in 11-19., and this method is extensively sent out later
Track optimizing problem is intersected applied to nonlinear pulse formula.Document Directorate N.M.O., Division N.F.D.,
Center N.J.S.History of Space Shuttle Rendezvous[J].Journal of Spacecraft and
Rockets, 2011,43 (5): 944-959. is described nearest 30 years, technological challenge encountered in Spacecraft Rendezvous problem,
And describe the intersection and Proximity operation and space tasks of multinomial spacecraft.Document Woffinden D.C., Geller
D.K.Navigating the Road to Autonomous Orbital Rendezvous[J].Journal of
Spacecraft and Rockets, 2007,44 (4): 898-909. to the engineering, task and technical background of orbital rendezvous with
Development process has carried out comprehensive introduction.In a recent study, document Ping Lu, Xinfu Liu.Autonomous
Trajectory Planning for Rendezvous and Proximity Operations by Conic
Optimization[J].Journal of Guidance Control and Dynamics,2013,36(2):375-389.
Propose a kind of autonomous rendezvous method based on Second-order cone programming.This method is first by lossless relaxation, most by relative motion
Then excellent control problem conversion solves nominal trajectory, then perturbing term is introduced differential for a series of Second-order cone programming problem
Among equation, obtain considering the optimal trajectory of perturbation by iteration optimization.
However, above-mentioned carried out research work is based on deterministic system.During actually intersection, navigation, guidance
With in control system and spacecraft local environment there is a large amount of uncertain factor, these factors drastically influence intersection appoint
The precision of business.For this problem, experts and scholars have carried out some research.Document Fujimoto K., Scheeres D.J.,
Alfriend K T.Analytical Nonlinear Propagation of Uncertainty in the Two-Body
Problem [J] .Journal of Guidance Control Dynamics, 2012,35 (2): 497-509. adoption status turns
The method for moving tensor, the influence to uncertain factor to intersection task are analyzed, and it is non-thread to give uncertain factor parsing
Spread through sex intercourse equation.Document Jones B.A., Parrish N., Doostan A.Postmaneuver Collision
Probability Estimation Using Sparse Polynomial Chaos Expansions[J].Journal of
Guidance Control and Dynamics, 2015,38 (8): 1-13. proposes the method based on polynomial chaos, solves
Stochastic differential equation, to obtain uncertain factor along the propagation equation of designed track.Document Deaconu G., Louembet
C.,Théron A.Minimizing the Effects of Navigation Uncertainties on the
Spacecraft Rendezvous Precision[J].Journal of Guidance Control and Dynamics,
2014,37 (2): 695-700. describes a kind of method based on sequence feedback, realizes and is considering uncertain factor feelings of navigating
Intersection Trajectory Design under condition.Document Luo Y Z, Yang Z, Li H N.Robust optimization of nonlinear
impulsive rendezvous with uncertainty[J].Science China(Physics,Mechanics and
Astronomy), 2014,57 (4): influence of the 731-740. to uncertain factor to intersection track is analyzed, and is made
It is introduced among optimization problem for optimization aim, to realize the design of robust intersection track.Document Xiong F, Xiong
Y,Xue B.Trajectory Optimization under Uncertainty based on Polynomial Chaos
Expansion [C] //AIAA Guidance, Navigation, and Control Conference, 2015,993-999. pairs
Initial error with there are uncertain factors to be modeled in system, convert determining system optimization for stochastic system optimization problem and ask
Topic, and solve to obtain robust track using polynomial chaos method.The universal calculating speed of these methods is slower, and in an open-loop manner
Uncertain factor is introduced, is not inconsistent with actual conditions.
Summary of the invention
Technical problems to be solved
In order to avoid the shortcomings of the prior art, the present invention proposes a kind of spacecraft robust for considering uncertain factor
Trajectory design method is intersected, the uncertain factor propagation equation based on the analysis of covariance is established, analyzes uncertain factor to nominal
The influence of track；Using analysis result as the constraint condition of optimization problem, robust Trajectory Design problem is constructed；Pass through genetic algorithm
It is solved, to realize that robust intersects Trajectory Design.
Technical solution
A kind of spacecraft robust intersection trajectory design method considering uncertain factor, it is characterised in that steps are as follows:
Step 1 establishes uncertain factor propagation equation in Spacecraft Rendezvous task:
It is described
SηMeasure noise covariance, SωFor the covariance of disturbance acceleration, RvTo measure noise covariance
FxFor kinetics equationTo the Jacobian matrix of x,
For kinetics equationIt is rightJacobian matrix,
ByIt is rightJacobian matrix
Navigation equationIt is rightJacobian matrix；
Navigation equationIt is rightJacobian matrix；
Inertia measurement equationIt is rightJacobian matrix；
CxInertia measurement equationTo the Jacobian matrix of x；
For Kalman filtering gain.
HkNon-inertial measurement model is to xkJacobian matrix
B is noise inputs matrix
Step 2, building robust intersect track optimizing problem:
After considering uncertain factor, robust intersects Trajectory Design problem representation are as follows:
x(t0)=x0
x(tf)=xd
Wherein:
x0For the initial relative status of spacecraft, xfFor spacecraft end relative status, xdIt is expected end with respect to shape for spacecraft
State, MrWith MvFor by the mapping of time of day deviation to position and velocity deviation；WithTask location and velocity accuracy need
It asks.
Step 3 solves robust track using genetic algorithm:
1. pairs of intersection tasks of Step initialize, and determine the initial relative status x of task0With desired end relative status
xd；
Step 2. initializes genetic algorithm parameter, intersects trajectory problem for robust, design initial population number is 100, most
Advanced algebra is 300, crossover probability 0.92, mutation probability 0.1；
3. pairs of intersection population assignment of Step；
Step 4. solves Kalman filtering gain, obtains navigation information；
The spacecraft uncertain factor propagation equation that Step 5. is established using covariance theory solution procedure 1；
Step 6. calculates the robustness parameter σ in intersection track optimizing problemrWith σv, with σrWith σvMeet task for screening
The population of constraint condition；
Step 7. calculates fitness function:
Step 8. returns to Step 3, until fitness function is restrained.
Beneficial effect
A kind of spacecraft robust considering uncertain factor proposed by the present invention intersects trajectory design method, utilizes association side
Poor analysis method analyzes uncertain factor to nominal trajectory quick, the accurate building uncertain factor propagation equation the characteristics of
It influences；Using analysis result as the constraint condition of optimization problem, robust optimization problem is constructed；It is solved by genetic algorithm,
To realize that robust intersects Trajectory Design.To by the Optimal Rendezvous problem of traditional determination system be converted into consideration it is uncertain because
The robust of element intersects problem, and is solved by genetic algorithm, realizes the purpose of robust intersection Trajectory Design.
It a kind of is intersected based on the analysis of covariance with the spacecraft robust of genetic algorithm the beneficial effects of the present invention are: proposing
Trajectory design method.This method is theoretical using the analysis of covariance, can establish the propagation equation of uncertain factor, and analysis is uncertain
Factor is influenced caused by nominal trajectory, and using analysis result as the constraint condition of optimization problem, is constructed robust optimal and asked
Topic；Problem is solved by genetic algorithm, design obtains the robust that can effectively inhibit uncertain factor to influence intersection rail
Mark.
Detailed description of the invention
Fig. 1: to consider the intersection track pulse command obtained in the case of uncertain factor.As seen from the figure.The intersection
The control of 3 subpulses is carried out altogether in the process, the time kept in reserve is respectively 41s, 1310s, 3000s.Required speed increment is
7.5213m/s。
Fig. 2: for the three-dimensional intersection track under passive space vehicle orbital coordinate system, which meets initial relative status about
Beam and desired end relative status constrain.
Fig. 3 is that two methods carry out the terminal position accuracy comparison figure that 100 Monte Carlo simulations obtain respectively.Wherein
"×" indicates the robust intersection track of patent proposed method design in uncertain disturbances lower end position distribution, statistics
Characteristic meets task robustness requirement, and is less than conventional method." o " indicates the optimal trajectory of conventional method design in uncertainty
The distribution of factor lower end location status, is unsatisfactory for task robustness requirement.
Specific embodiment
Now in conjunction with embodiment, attached drawing, the invention will be further described:
Validity for the robust trajectory design method to proposition is verified, and is applied to comprising uncertain factor
Intersection task, emulated as follows.Wherein the uncertain factor of task is as shown in table 1, and task object is as shown in table 2.
1 uncertain factor of table/disturbance parameter
2 task object of table
Step in solving the problems, such as includes following three:
Step 1: establishing the uncertain factor propagation equation in Spacecraft Rendezvous task
Firstly, considering that the dynamics of relative motion equation of uncertain factor can be expressed as
Wherein r is spacecraft relative position, and v is relative velocity, vc, vtWith rc, rtRespectively indicate pursuit spacecraft and target
The speed of spacecraft and position, μ are gravitational constant, rcWith rtIndicate pursuit spacecraft and passive space vehicle position scalar,For the control instruction solved by navigational state by control rate, ω disturbance acceleration meets E [ω (t) ωT
(τ)]=Sω(t) δ (t- τ), wherein E [] is expectation operator, and δ (t- τ) is Dirac function, SωFor the association side of disturbance acceleration
Difference.
For convenience of derivation, kinetics equation is write as generalized form
Wherein x is the spacecraft state for including relative velocity and position.
Navigation equation is at this time
Wherein inertia measurement model is
WhereinFor continuous measurements, η is measurement noise relevant to sensor, meets E [η (t) ηT(τ)]=Sη(t)δ
(t- τ), SηMeasure noise covariance.
Non-inertial measurement model is
WhereinFor discrete measured values, νkFor measurement noise relevant to sensor, meetRvFor
Measure noise covariance, δkk′For Dirac function,For Kalman filtering gain.
Kinetics equation and navigation equation are linearized along nominal trajectory, it is available
WhereinByIt determines, FωIt is the Jacobian matrix determined by formula (2).
Define extended mode
Thus it is possible to propagation and the renewal equation of the state that is expanded
Wherein
Define Ca=E [XXT], Leibniz theorem is used to formula (9), available uncertain factor is propagated and update side
Journey
Step 2: building robust intersects track optimizing problem
After considering uncertain factor, robust intersection Trajectory Design problem can be indicated are as follows:
Wherein
x0For the initial relative status of spacecraft, xfFor spacecraft end relative status, xdIt is expected end with respect to shape for spacecraft
State, MrWith MvFor by the mapping of time of day deviation to position and velocity deviation.
Step 3: being solved using genetic algorithm to robust track
Genetic algorithm is more loose to required majorization of solutions problem mathematical requirement, and due to evolution characteristic, for any shape
The objective function and constraint condition of formula, it is no matter linear or non-linear, it is discrete or continuously can be carried out being effectively treated；Into
Change the global search that the ergodic of operator enables genetic algorithm effectively to carry out probability meaning.Based on the above advantage,
Robust Trajectory Design problem is solved using genetic algorithm.
1. pairs of intersection tasks of Step initialize, and determine the initial relative status x of task0With desired end relative status
xd；
Step 2. initializes genetic algorithm parameter, intersects trajectory problem for robust, design initial population number is 100, most
Advanced algebra is 300, crossover probability 0.92, mutation probability 0.1；
3. pairs of intersection population assignment of Step；
Step 4. solves Kalman filtering gain, obtains navigation information；
The spacecraft uncertain factor propagation equation that Step 5. is established using covariance theory solution procedure 1；
Step 6. calculates the robustness parameter σ in intersection track optimizing problemrWith σv, with σrWith σvMeet task for screening
The population of constraint condition；
Step 7. calculates fitness function:
Step 8. returns to Step 3, until fitness function is restrained.
The uncertain factor propagation equation based on the analysis of covariance is established in this method, analyzes uncertain factor to nominal rail
The influence of mark；Using analysis result as the constraint condition of optimization problem, robust Trajectory Design problem is constructed；By genetic algorithm into
Row solves, to realize that robust intersects Trajectory Design.
Claims (1)
1. a kind of spacecraft robust for considering uncertain factor intersects trajectory design method, it is characterised in that steps are as follows:
Step 1 establishes uncertain factor propagation equation in Spacecraft Rendezvous task:
It is described
SηMeasure noise covariance, SωFor the covariance of disturbance acceleration, RvTo measure noise covariance
FxFor kinetics equationTo the Jacobian matrix of x,
For kinetics equationIt is rightJacobian matrix,
ByIt is rightJacobian matrix
Navigation equationIt is rightJacobian matrix；
Navigation equationIt is rightJacobian matrix；
Inertia measurement equationIt is rightJacobian matrix；
CxInertia measurement equationTo the Jacobian matrix of x；
For Kalman filtering gain.
HkNon-inertial measurement model is to xkJacobian matrix
B is noise inputs matrix
Step 2, building robust intersect track optimizing problem:
After considering uncertain factor, robust intersects Trajectory Design problem representation are as follows:
x(t0)=x0
x(tf)=xd
Wherein:
x0For the initial relative status of spacecraft, xfFor spacecraft end relative status, xdEnd relative status, M it is expected for spacecraftr
With MvFor by the mapping of time of day deviation to position and velocity deviation；WithTask location and velocity accuracy demand.
Step 3 solves robust track using genetic algorithm:
1. pairs of intersection tasks of Step initialize, and determine the initial relative status x of task0With desired end relative status xd；
Step 2. initializes genetic algorithm parameter, intersects trajectory problem for robust, and design initial population number is 100, maximum generation
Number is 300, crossover probability 0.92, mutation probability 0.1；
3. pairs of intersection population assignment of Step；
Step 4. solves Kalman filtering gain, obtains navigation information；
The spacecraft uncertain factor propagation equation that Step 5. is established using covariance theory solution procedure 1；
Step 6. calculates the robustness parameter σ in intersection track optimizing problemrWith σv, with σrWith σvMeet task restriction for screening
The population of condition；
Step 7. calculates fitness function:
Step 8. returns to Step 3, until fitness function is restrained.
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