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CN109709805B - A Robust Rendezvous Trajectory Design Method for Spacecraft Considering Uncertainties - Google Patents

A Robust Rendezvous Trajectory Design Method for Spacecraft Considering Uncertainties Download PDF

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CN109709805B
CN109709805B CN201811612847.XA CN201811612847A CN109709805B CN 109709805 B CN109709805 B CN 109709805B CN 201811612847 A CN201811612847 A CN 201811612847A CN 109709805 B CN109709805 B CN 109709805B
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罗建军
靳锴
马卫华
王明明
党朝辉
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Northwestern Polytechnical University
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Abstract

本发明涉及一种考虑不确定性因素的航天器鲁棒交会轨迹设计方法，利用协方差分析方法在快速、精确构建不确定因素传播方程的特点，分析不确定因素对标称轨迹的影响；将分析结果作为优化问题的约束条件，构建鲁棒优化问题；通过遗传算法进行求解，从而实现鲁棒交会轨迹设计。从而将传统的确定系统的最优交会问题转化为考虑不确定因素的鲁棒交会问题，并通过遗传算法进行求解，实现鲁棒交会轨迹设计的目的。

Figure 201811612847

The invention relates to a method for designing a robust rendezvous trajectory of a spacecraft considering uncertainty factors, which utilizes the characteristics of a covariance analysis method to rapidly and accurately construct a propagation equation of uncertain factors, and analyzes the influence of uncertain factors on a nominal trajectory; The analysis result is used as the constraint condition of the optimization problem to construct a robust optimization problem; it is solved by genetic algorithm to realize the robust intersection trajectory design. Therefore, the traditional optimal rendezvous problem of deterministic system is transformed into a robust rendezvous problem considering uncertain factors, and is solved by genetic algorithm to achieve the purpose of robust rendezvous trajectory design.

Figure 201811612847

Description

Spacecraft robust intersection trajectory design method considering uncertainty factors
Technical Field
The invention belongs to the field of space flight dynamics and control, and relates to a spacecraft robust intersection trajectory design method considering uncertainty factors.
Background
Since the 21 st century, with the development of aerospace technology, space technology gradually shifted from the first of entering space, exploring space to utilizing space, space operation. Space rendezvous is used as the basis for the space operation task executed by the spacecraft, and refers to the technology that two or more spacecrafts meet with each other according to preset positions and time on a space orbit. For half a century, mankind has completed complex space activities such as space station construction, manned lunar landing, deep space exploration and the like based on rendezvous technology.
In the design of meeting tracks, the scholars develop extensive research. In Clhessy W.H.terminal Guidance System for Satellite Rendezvous [ J ]. Aerospace Sci,1960,27(9): 653-. For the nonlinear problem in the intersection, the document Handlsman M, Lion P.M. primer vector on fixed-time impulse vectors [ J ] Aerospace Sci,1968,6(1):11-19, Handelsman proposes a principal vector method, which was widely applied to the nonlinear pulse intersection trajectory optimization problem later. The documents direct N.M.O., Division N.F.D., Center N.J.S.history of Space Shuttle Rendezvous [ J ]. Journal of Space and jacks, 2011,43(5):944 and 959, describe the technical challenges encountered in the Spacecraft Rendezvous problem in the last three decades and describe the Rendezvous and access operations and Space tasks of multiple Spacecraft. The documents Wofenden D.C., Geller D.K., visualizing the Road to Autonomous Orbitronzeous Rendervous [ J ]. Journal of space and rocks, 2007,44(4): 898-. In a recent study, the document Ping Lu, Xinfu Liu. Autonomous project Planning for Redezvus and Proximaty Operations by Conic Optimization [ J ]. Journal of guide Control and Dynamics,2013,36(2):375 and 389, an autonomous Rendezvous method based on a second-order cone Planning is proposed. The method comprises the steps of firstly converting an optimal control problem of relative motion into a series of second-order cone planning problems through lossless relaxation, then solving a nominal track, introducing a perturbation term into a differential equation, and obtaining an optimal track considering perturbation through iterative optimization.
However, the research work carried out above is based on deterministic systems. In the actual rendezvous process, a large number of uncertain factors exist in the navigation, guidance and control system and the environment where the spacecraft is located, and the precision of the rendezvous task is seriously influenced by the uncertain factors. In response to this problem, expert scholars have conducted some research. Fujimoto K, Scheers D.J., Alfriend K.Analytical Nonlinear amplification of uncertain in the Two-Body protocol [ J ]. Journal of uncertain Control Dynamics,2012,35(2):497-509. the method using state transition tensor was used to analyze the influence of uncertain factors on the rendezvous mission, giving an uncertain factor analysis Nonlinear Propagation equation. The documents Journal B.A., Parrish N., Doostan A.Postmanapeur condensation behaviour Estimation Using Sparse polymeric char Expansions [ J ]. Journal of Guidance Control and Dynamics 2015,38(8):1-13, a Polynomial Chaos based method was proposed to solve the stochastic differential equation to obtain the propagation equation of the uncertainty along the designed trajectory. The document Deaconu G, Louembet C, Th etron A. minimizing the Effects of Navigation Uncertainties on the space recovery Dynamics [ J ]. Journal of Guidance Control and Dynamics,2014,37(2): 695-. The documents Luo Y Z, Yang Z, Li H N. Robust optimization of nonlinear interactive rendezvous with uncertainties [ J ]. Science China (Physics, Mechanics and advancement), 2014,57(4):731 and 740. the influence of the uncertain factors on the rendezvous trajectory is analyzed and introduced into the optimization problem as an optimization target, thereby realizing the design of the robust rendezvous trajectory. Documents Xiong F, Xiong Y, Xue B. transport Optimization under uncertain Chaos Expansion [ C ]// AIAA guide, Navigation, and Control reference, 2015,993 + 999. modeling the initial error and uncertain factors existing in the system, converting the random system Optimization problem into a determined system Optimization problem, and solving by a Polynomial Chaos method to obtain a robust track. These methods are generally slow in computation speed and introduce uncertainty in an open-loop manner, which is not consistent with the actual situation.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a spacecraft robust intersection track design method considering uncertainty factors, an uncertainty factor propagation equation based on covariance analysis is established, and the influence of the uncertainty factors on a nominal track is analyzed; constructing a robust track design problem by using the analysis result as a constraint condition of an optimization problem; and solving through a genetic algorithm, thereby realizing the design of a robust rendezvous track.
Technical scheme
A spacecraft robust intersection trajectory design method considering uncertainty factors is characterized by comprising the following steps:
step 1, establishing an uncertain factor propagation equation in a spacecraft rendezvous mission:
Figure BDA0001925183100000031
Figure BDA0001925183100000032
the above-mentioned
Figure BDA0001925183100000033
SηMeasuring the noise covariance, SωAs covariance of disturbance acceleration, RvFor measuring noise covariance
FxIs an equation of dynamics
Figure BDA0001925183100000034
For the jacobian matrix of x,
Figure BDA0001925183100000035
is an equation of dynamics
Figure BDA0001925183100000036
To pair
Figure BDA0001925183100000037
The jacobian matrix of (a) is,
Figure BDA0001925183100000038
by
Figure BDA0001925183100000039
To pair
Figure BDA00019251831000000310
Jacobian matrix of
Figure BDA00019251831000000311
Navigation equation
Figure BDA00019251831000000312
To pair
Figure BDA00019251831000000313
A Jacobian matrix of;
Figure BDA00019251831000000314
navigation equation
Figure BDA00019251831000000315
To pair
Figure BDA00019251831000000316
A Jacobian matrix of;
Figure BDA00019251831000000317
equation of inertia measurement
Figure BDA00019251831000000318
To pair
Figure BDA00019251831000000319
A Jacobian matrix of;
Cxequation of inertia measurement
Figure BDA00019251831000000320
A Jacobian matrix for x;
Figure BDA00019251831000000321
is the kalman filter gain.
HkNon-inertial measurement model pair xkJacobian matrix of
B is a noise input matrix
Step 2, constructing a robust rendezvous trajectory optimization problem:
after considering the uncertainty factor, the robust rendezvous trajectory design problem is expressed as:
Figure BDA0001925183100000041
Figure BDA0001925183100000042
x(t0)＝x0
x(tf)＝xd
Figure BDA0001925183100000043
Figure BDA0001925183100000044
Figure BDA0001925183100000045
Figure BDA0001925183100000046
Figure BDA0001925183100000047
wherein:
Figure BDA0001925183100000048
x0as initial relative state of spacecraft, xfRelative state of spacecraft ends, xdFor spacecraft to expect end relative states, MrAnd MvTo be made byMapping of state deviation to position and speed deviation;
Figure BDA0001925183100000049
and
Figure BDA00019251831000000410
task position and speed accuracy requirements.
And 3, solving the robust track by adopting a genetic algorithm:
step 1, initializing the rendezvous task, and determining the initial relative state x of the task0State x relative to desired endd；
Step 2, initializing genetic algorithm parameters, and aiming at the problem of robust intersection tracks, designing an initial population number of 100, a maximum algebra of 300, a cross probability of 0.92 and a variation probability of 0.1;
step 3, assigning values to the rendezvous population;
step 4, solving Kalman filtering gain to obtain navigation information;
step 5, solving the uncertain factor propagation equation of the spacecraft established in the Step 1 by adopting a covariance theory;
step 6, calculating robustness parameter sigma in intersection track optimization problemrAnd σvAt σrAnd σvScreening populations meeting task constraint conditions;
step 7, calculating a fitness function:
Figure BDA00019251831000000411
and Step 8, returning to Step 3 until the fitness function converges.
Advantageous effects
The spacecraft robust intersection trajectory design method considering the uncertainty factors, which is provided by the invention, utilizes the characteristic that the covariance analysis method is used for quickly and accurately constructing the uncertainty factor propagation equation, and analyzes the influence of the uncertainty factors on the nominal trajectory; constructing a robust optimization problem by using the analysis result as a constraint condition of the optimization problem; and solving through a genetic algorithm, thereby realizing the design of a robust rendezvous track. Therefore, the optimal rendezvous problem of the traditional determination system is converted into the robust rendezvous problem considering uncertain factors, and the robust rendezvous track is designed by solving through a genetic algorithm.
The invention has the beneficial effects that: a spacecraft robust intersection trajectory design method based on covariance analysis and a genetic algorithm is provided. The method utilizes a covariance analysis theory, can establish a propagation equation of uncertain factors, analyzes the influence of the uncertain factors on a nominal track, and constructs a robust optimization problem by taking an analysis result as a constraint condition of the optimization problem; solving the problem through a genetic algorithm, and designing to obtain a robust intersection track capable of effectively inhibiting the influence of uncertain factors.
Drawings
FIG. 1: the method is a rendezvous track pulse command obtained under the condition of considering uncertain factors. As can be seen from the figure. The meeting process is performed with 3 times of pulse control, and the maneuvering time is 41s,1310s and 3000s respectively. The required velocity increment was 7.5213 m/s.
FIG. 2: the trajectory satisfies an initial relative state constraint and an expected terminal relative state constraint for a three-dimensional intersection trajectory in a target spacecraft orbit coordinate system.
Fig. 3 is a graph showing the accuracy of the end position obtained by performing 100 monte carlo simulations for each of the two methods. Wherein, the x represents the distribution of the terminal position of the robust intersection track designed by the method provided by the patent under the uncertain disturbance, and the statistical property of the robust intersection track meets the task robustness requirement and is smaller than that of the traditional method. And the 'o' represents the state distribution of the terminal position of the optimal track designed by the traditional method under the uncertainty factor, which does not meet the task robustness requirement.
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
in order to verify the effectiveness of the proposed robust trajectory design method, the proposed robust trajectory design method is applied to a rendezvous task containing uncertainty factors, and the following simulation is performed. The uncertainty factors of the tasks are shown in table 1, and the task targets are shown in table 2.
TABLE 1 uncertainty factors/disturbance parameters
Figure BDA0001925183100000061
TABLE 2 task goals
Figure BDA0001925183100000062
The steps in solving the problem include the following three:
step one, establishing an uncertain factor propagation equation in a spacecraft rendezvous mission
First, the equation of the relative motion dynamics considering the uncertainty factor can be expressed as
Figure BDA0001925183100000063
Figure BDA0001925183100000071
Wherein r is the relative position of the spacecraft, v is the relative velocityc，vtAnd rc，rtRespectively representing the velocity and position of the tracking spacecraft and the target spacecraft, mu being the gravitational constant, rcAnd rtRepresenting the tracking spacecraft and target spacecraft position scalars,
Figure BDA0001925183100000072
for the control command, omega disturbance acceleration, obtained by solving the navigation state by the control rate, satisfies E [ omega (t) omegaT(τ)]＝Sω(t) δ (t- τ) in which E [ · is]For the desired operator, δ (t- τ) is the Dirac function, SωIs the covariance of the disturbance acceleration.
For the convenience of derivation, the kinetic equations are written in a generalized form
Figure BDA0001925183100000073
Where x is the spacecraft state including relative velocity and position.
The navigation equation at this time is
Figure BDA0001925183100000074
Wherein the inertia measurement model is
Figure BDA0001925183100000075
Wherein
Figure BDA0001925183100000076
For continuous measurements, η is the measurement noise associated with the sensor, satisfying Eη (t) ηT(τ)]＝Sη(t)δ(t-τ)，SηThe noise covariance is measured.
The non-inertial measurement model is
Figure BDA0001925183100000077
Wherein
Figure BDA0001925183100000078
As discrete measured values, vkFor measurement noise associated with the sensor, the method satisfies
Figure BDA0001925183100000079
RvTo measure the noise covariance, δkk′In order to be a function of the dirac function,
Figure BDA00019251831000000710
is the kalman filter gain.
Linearizing the kinetic equation and the navigation equation along the nominal track to obtain
Figure BDA00019251831000000711
Figure BDA0001925183100000081
Wherein
Figure BDA0001925183100000082
By
Figure BDA0001925183100000083
Determination of FωIs a jacobian matrix determined by equation (2).
Defining extended states
Figure BDA0001925183100000084
Thus, propagation and update equations for the extended states can be derived
Figure BDA0001925183100000085
Wherein
Figure BDA0001925183100000086
Definition Ca＝E[XXT]The propagation and updating equation of the uncertain factors can be obtained by adopting the Labrunitz theorem on the formula (9)
Figure BDA0001925183100000087
Step two, constructing a robust rendezvous trajectory optimization problem
After considering the uncertainty factor, the robust rendezvous trajectory design problem can be expressed as:
Figure BDA0001925183100000088
wherein
Figure BDA0001925183100000091
Figure BDA0001925183100000092
Figure BDA0001925183100000093
x0As initial relative state of spacecraft, xfRelative state of spacecraft ends, xdFor spacecraft to expect end relative states, MrAnd MvIs a mapping from true state deviations to position and velocity deviations.
Thirdly, solving the robust track by adopting a genetic algorithm
The genetic algorithm has loose mathematical requirements on the solved optimization problem, and due to the evolution characteristic, the discrete or continuous target function and constraint condition in any form can be effectively processed in linear or nonlinear way; the ergodicity of the evolutionary operator enables the genetic algorithm to perform a probabilistic global search very efficiently. Based on the advantages, the robust track design problem is solved by adopting a genetic algorithm.
Step 1, initializing the rendezvous task, and determining the initial relative state x of the task0State x relative to desired endd；
Step 2, initializing genetic algorithm parameters, and aiming at the problem of robust intersection tracks, designing an initial population number of 100, a maximum algebra of 300, a cross probability of 0.92 and a variation probability of 0.1;
step 3, assigning values to the rendezvous population;
step 4, solving Kalman filtering gain to obtain navigation information;
step 5, solving the uncertain factor propagation equation of the spacecraft established in the Step 1 by adopting a covariance theory;
step 6, calculating robustness parameter sigma in intersection track optimization problemrAnd σvAt σrAnd σvScreening populations meeting task constraint conditions;
step 7, calculating a fitness function:
Figure BDA0001925183100000094
and Step 8, returning to Step 3 until the fitness function converges.
In the method, an uncertain factor propagation equation based on covariance analysis is established, and the influence of uncertain factors on a nominal track is analyzed; constructing a robust track design problem by using the analysis result as a constraint condition of an optimization problem; and solving through a genetic algorithm, thereby realizing the design of a robust rendezvous track.

Claims (1)

1. A spacecraft robust intersection trajectory design method considering uncertainty factors is characterized by comprising the following steps:
step 1, establishing an uncertain factor propagation equation in a spacecraft rendezvous mission:
Figure FDA0002780894380000011
Figure FDA0002780894380000012
the above-mentioned
Figure FDA0002780894380000013
SηMeasuring the noise covariance, SωAs covariance of disturbance acceleration, RvFor measuring noise covariance
FxIs an equation of dynamics
Figure FDA0002780894380000014
For the jacobian matrix of x,
Figure FDA0002780894380000015
is an equation of dynamics
Figure FDA0002780894380000016
To pair
Figure FDA0002780894380000017
The jacobian matrix of (a) is,
Figure FDA0002780894380000018
by
Figure FDA0002780894380000019
To pair
Figure FDA00027808943800000110
Jacobian matrix of
Figure FDA00027808943800000111
Navigation equation
Figure FDA00027808943800000112
To pair
Figure FDA00027808943800000113
A Jacobian matrix of;
Figure FDA00027808943800000114
navigation equation
Figure FDA00027808943800000115
To pair
Figure FDA00027808943800000116
A Jacobian matrix of;
Figure FDA00027808943800000117
equation of inertia measurement
Figure FDA00027808943800000118
To pair
Figure FDA00027808943800000119
A Jacobian matrix of;
Cxequation of inertia measurement
Figure FDA00027808943800000120
A Jacobian matrix for x;
Figure FDA00027808943800000121
is the Kalman filter gain;
Hknon-inertial measurement model pair xkJacobian matrix of
B is a noise input matrix
Step 2, constructing a robust rendezvous trajectory optimization problem:
after considering the uncertainty factor, the robust rendezvous trajectory design problem is expressed as:
Figure FDA00027808943800000122
Figure FDA00027808943800000123
x(t0)＝x0
x(tf)＝xd
Figure FDA00027808943800000124
Figure FDA00027808943800000125
Figure FDA00027808943800000126
Figure FDA00027808943800000127
Figure FDA00027808943800000128
wherein:
Figure FDA0002780894380000021
x0as initial relative state of spacecraft, xfRelative state of spacecraft ends, xdFor spacecraft to expect end relative states, MrAnd MvMapping from true state deviation to position and speed deviation;
Figure FDA0002780894380000022
and
Figure FDA0002780894380000023
task position and speed accuracy requirements;
and 3, solving the robust track by adopting a genetic algorithm:
step 1, initializing the rendezvous task, and determining the initial relative state x of the task0State x relative to desired endd；
Step 2, initializing genetic algorithm parameters, and aiming at the problem of robust intersection tracks, designing an initial population number of 100, a maximum algebra of 300, a cross probability of 0.92 and a variation probability of 0.1;
step 3, assigning values to the rendezvous population;
step 4, solving Kalman filtering gain to obtain navigation information;
step 5, solving the uncertain factor propagation equation of the spacecraft established in the Step 1 by adopting a covariance theory;
step 6, calculating robustness parameter sigma in intersection track optimization problemrAnd σvAt σrAnd σvScreening populations meeting task constraint conditions;
step 7, calculating a fitness function:
Figure FDA0002780894380000024
and Step 8, returning to Step 3 until the fitness function converges.
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