CN108958064B - Attitude guidance law error judgment method and system and electronic equipment - Google Patents
Attitude guidance law error judgment method and system and electronic equipment Download PDFInfo
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Abstract
The invention provides a method, a system and electronic equipment for judging attitude guidance law errors, which comprises the steps of setting a transverse drift ellipse with the relative motion track of a spacecraft and a reference spacecraft in an orbital plane as twice as long as a long half shaft and a short half shaft in an LVLH coordinate system of the reference spacecraft, and obtaining a relational expression of attitude guidance law parameters and relative positions according to a C-W equation; setting relative motion trajectories of the accompanying spacecraft relative to the reference spacecraft into a quasi-straight line and a transverse drift ellipse from front to back, and acquiring simulated relative motion data of the accompanying spacecraft corresponding to the two groups of motion trajectories; and estimating attitude guide law parameters according to the two groups of simulated relative motion data without errors and with errors and the relative orbit prediction data, and calculating the errors of the expected pitch angle and the simulated pitch angle. The method, the system and the electronic equipment for judging the attitude guidance law error are carried out by calculating the expected pitch angle error, and provide a basis for engineering application.
Description
Technical Field
The invention relates to the technical field of satellite relative motion in orbital dynamics, in particular to a method and a system for judging attitude guidance law errors and electronic equipment.
Background
With the continuous development of aerospace technology and the continuous expansion of the application field of spacecrafts, the distributed satellite system has been shifted from concept to practical application. The plurality of micro-nano satellites with function distribution and information interconnection can replace large satellites to carry out space missions through cooperative control. The system has strong flexibility and system damage resistance, has obvious advantages in the aspects of development period and development cost, and has wide application prospect for a plurality of micro-nano satellites with function distribution and information interconnection. Currently, research on related technologies and application modes of distributed satellite systems are actively carried out in all countries in the world.
The relative distance between the flying spacecrafts in formation flight is short, and the analysis can be carried out under a relative motion framework. The following two methods are commonly used to describe relative motion:
(1) kinematics method based on number of orbits of two spacecrafts
The method takes the absolute orbit number of two spacecrafts as input, has higher calculation precision, but needs high-precision numerical integration, has larger calculation amount and poor disturbance resistance.
(2) Dynamics method based on relative position and speed of two spacecrafts, also called C-W equation method
When perturbation influence is ignored and the reference spacecraft is a circular orbit, the C-W equation can obtain an analytic solution through linearization processing. The C-W equation analytic solution takes the relative state of two spacecrafts as input, has clear physical meaning, small calculated amount and strong robustness, and is very suitable for analyzing the relative motion problem that the reference spacecraft is a circular orbit and the formation distance is short (the ratio of the relative distance to the nominal orbit radius does not exceed the eccentricity magnitude of the reference spacecraft).
However, the spacecraft flying in orbit cannot be a standard circular orbit, the distance cannot be kept at a short distance all the time, a relative motion fitting method suitable for a long distance and small in error needs to be explored according to a relative motion rule, and relative motion related physical quantities required by a task are obtained and serve as a basis for engineering design.
Disclosure of Invention
In view of the above disadvantages of the prior art, an object of the present invention is to provide a method, a system, and an electronic device for determining an error of an attitude guidance law, which are used for accurately estimating a parameter solution of a C-W equation by using a parameter estimation method of a least square optimal estimation theory according to a high resolution imaging pitch attitude adjustment requirement of a close-range spacecraft, deriving an attitude guidance law oriented with respect to a target spacecraft, and analyzing an expected pitch angle error calculated by the attitude guidance law according to an empirical model of a prediction error of a relative orbit and an orbit prediction accuracy of an in-orbit actual orbit, thereby providing a basis for engineering application.
In order to achieve the above objects and other related objects, the present invention provides a method for determining attitude guidance law errors for close-range spacecraft coplanar formation, comprising the steps of: setting a transverse drift ellipse with the long half axis being twice as long as the short half axis in an LVLH coordinate system of the reference spacecraft along with the relative motion track of the spacecraft relative to the reference spacecraft in the orbit surface, and acquiring the relative position x and y and the attitude guidance law parameter x according to a C-W equationc0,yc0The relation of Θ and b, wherein (x)c0,yc0) Is the center of the ellipse at the initial moment, b is the minor semi-axis of the ellipse, and theta is the phase of the reference spacecraft on the ellipse; setting relative motion trajectories of the accompanying spacecraft relative to the reference spacecraft into a quasi-straight line and a transverse drift ellipse from front to back, and acquiring simulated relative motion data of the accompanying spacecraft corresponding to the two groups of motion trajectories; based on attitude guidance law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of simulation relative motion datac0,yc0Theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle; error correction is carried out on two groups of simulated relative motion data according to the relative orbit prediction error empirical model, and the error correction is based on the attitude leading law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of corrected simulated relative motion datac0,yc0E, theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of corrected simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle; based on attitude guidance law parametersxc0,yc0The relation between theta and b and the relative position x and y and the relative orbit forecast data corresponding to the two groups of motion tracks estimate the attitude guidance law parameter x according to the least square estimation principlec0,yc0Theta and b, and calculating to obtain expected pitch angles at each moment corresponding to two groups of relative track forecast data; and calculating the actual pitch angle at each corresponding moment according to the two groups of post-orbit determination data corresponding to the two groups of motion tracks, and calculating the difference value between the expected pitch angle and the actual pitch angle.
In an embodiment of the present invention, the relative position x, y and the attitude guidance law parameter xc0,yc0The relation Θ, b is:
wherein n is the average motion angular velocity of the absolute orbit of the reference spacecraft, and t is the time from the initial moment.
In an embodiment of the present invention, the desired Pitch angle Pitch is calculated according to the following formula:
Pitch＝π+γ
γ ═ arctan (x/y) or γ ═ pi + arctan (x/y)
Wherein γ is selected from
And
is determined by the sign of (a), xc0,yc0And theta and b are estimated values obtained according to the least square estimation principle.
In an embodiment of the present invention, the relative orbit prediction error model is a linear plus trigonometric function model, and a period of the trigonometric function is an orbit period of the reference spacecraft.
Meanwhile, the invention also provides an attitude guidance law error judgment system suitable for close-range spacecraft coplanar formation, which comprises an expression acquisition module, a data acquisition module, a first processing module, a second processing module and a third processing module;
the expression acquisition module is used for setting a transverse drift ellipse with a long half axis twice as long as a short half axis in an LVLH coordinate system with a relative motion track of the spacecraft relative to a reference spacecraft as the reference spacecraft in an orbital plane, and acquiring relative positions x and y and attitude guidance law parameters x according to a C-W equationc0,yc0The relation of Θ and b, wherein (x)c0,yc0) Is the center of the ellipse at the initial moment, b is the minor semi-axis of the ellipse, and theta is the phase of the reference spacecraft on the ellipse;
the data acquisition module is used for setting the relative motion trajectories of the accompanying spacecraft relative to the reference spacecraft into a quasi-straight line and a transverse drift ellipse from front to back and acquiring simulated relative motion data of the accompanying spacecraft corresponding to the two groups of motion trajectories;
the first processing module is used for guiding law parameter x based on attitudec0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of simulation relative motion datac0,yc0Theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle;
the second processing module is used for carrying out error correction on two groups of simulated relative motion data according to the relative orbit prediction error empirical model and based on the attitude leading law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of corrected simulated relative motion datac0,yc0E, theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of corrected simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle;
the third processing module is used for guiding law parameter x based on the attitudec0,yc0The relation between theta and b and the relative position x and y and the relative orbit forecast data corresponding to the two groups of motion tracks estimate the attitude guidance law parameter x according to the least square estimation principlec0,yc0Theta and b, and calculating to obtain expected pitch angles at each moment corresponding to two groups of relative track forecast data; and calculating the actual pitch angle at each corresponding moment according to the two groups of post-orbit determination data corresponding to the two groups of motion tracks, and calculating the difference value between the expected pitch angle and the actual pitch angle.
In an embodiment of the present invention, the relative position x, y and the attitude guidance law parameter xc0,yc0The relation Θ, b is:
wherein n is the average motion angular velocity of the absolute orbit of the reference spacecraft, and t is the time from the initial moment.
In an embodiment of the present invention, in the first processing module, the second processing module and the third processing module, the desired Pitch angle Pitch is calculated according to the following formula:
Pitch＝π+γ
γ ═ arctan (x/y) or γ ═ pi + arctan (x/y)
Wherein γ is selected from
And
is determined by the sign of (a), xc0,yc0And theta and b are estimated values obtained according to the least square estimation principle.
In an embodiment of the invention, in the second processing module, the relative orbit prediction error model is a model of a linear plus trigonometric function, and a cycle of the trigonometric function is an orbit cycle of the reference spacecraft.
In addition, the invention also provides electronic equipment comprising any attitude guidance law error judgment system suitable for close-range spacecraft coplanar formation.
As described above, the attitude guidance law error determination method, system and electronic device according to the present invention have the following advantages:
(1) according to the high-resolution imaging pitching attitude adjustment requirement of the close-range spacecraft, a parameter estimation method of a least square optimal estimation theory is adopted to accurately estimate the parameter solution of the C-W equation, and an attitude guidance law oriented relative to the target spacecraft is deduced;
(2) and analyzing the expected pitch angle error obtained by the attitude guidance law calculation aiming at the prediction error empirical model of the relative track and the actual track prediction precision of the on-track, thereby providing a basis for engineering application.
Drawings
FIG. 1 is a flow chart of a method for determining attitude guidance law errors for close range spacecraft coplanar formation according to the present invention;
FIG. 2 is a schematic view of the elliptical trajectory associated with the relative motion of the spacecraft and the reference spacecraft in the orbital plane in accordance with the present invention;
FIG. 3 is a schematic phase diagram of the relative motion of the companion spacecraft and the reference spacecraft of the present invention in the orbital plane;
FIG. 4 is a schematic diagram of the LVLH system with respect to the motion coordinate system;
FIG. 5 is a schematic view of a desired pitch angle;
FIG. 6 is a graph showing a desired pitch angle for error free linear motion in an embodiment of the present invention;
FIG. 7 is a schematic diagram illustrating a comparison between a parameter estimation relative motion trajectory and a simulation relative motion trajectory corresponding to an error-free quasi-linear motion according to an embodiment of the present invention;
FIG. 8 is a graph illustrating a difference between an estimated expected pitch angle and a simulated pitch angle for a parameter without error in a linear motion according to an embodiment of the present invention;
FIG. 9 is a graph showing lateral and radial errors of a parametric estimated relative motion trajectory versus a simulated relative motion trajectory for error-free quasi-linear motion in an embodiment of the present invention;
FIG. 10 is a graph showing the expected pitch angle for relative motion with an error-free elliptical minor semi-axis of 160m in an embodiment of the invention;
FIG. 11 is a schematic diagram showing a comparison between a parameter estimation relative motion trajectory and a simulation relative motion trajectory corresponding to a relative motion with an error-free ellipse minor semi-axis of 160m according to an embodiment of the present invention;
FIG. 12 is a graph illustrating a difference between an estimated expected pitch angle and a simulated pitch angle for a relative motion with an error-free elliptical stub shaft of 160m according to an embodiment of the present invention;
FIG. 13 is a graph showing the lateral and radial errors of a parametric estimated relative motion trajectory versus a simulated relative motion trajectory for a relative motion with an error-free elliptical minor semi-axis of 160m in an embodiment of the present invention;
FIG. 14 is a graph showing a desired pitch angle for an embodiment of the present invention with an error quasi-linear motion;
FIG. 15 is a diagram illustrating a comparison between a parameter estimation relative motion trajectory corresponding to an error quasi-linear motion and a true relative motion trajectory according to an embodiment of the present invention;
FIG. 16 is a graph illustrating a difference between an estimated desired pitch angle and a simulated pitch angle for a parameter corresponding to an erroneous quasi-linear motion in an embodiment of the present invention;
FIG. 17 is a graph showing lateral and radial errors of a parameter estimated relative motion trajectory and a simulated relative motion trajectory corresponding to an erroneous quasi-linear motion in an embodiment of the present invention;
FIG. 18 is a graph showing the expected pitch angle for relative motion with an error elliptical minor semi-axis of 160m in an embodiment of the invention;
FIG. 19 is a schematic diagram showing a comparison between a parameter estimation relative motion trajectory and a simulation relative motion trajectory corresponding to a relative motion with an error ellipse having a minor semi-axis of 160m according to an embodiment of the present invention;
FIG. 20 is a graph showing a difference between a parameter estimated desired pitch angle and a simulated pitch angle for a relative motion having an error elliptical minor semi-axis of 160m in an embodiment of the present invention;
FIG. 21 is a graph showing lateral and radial errors of a parametric estimated relative motion trajectory versus a simulated relative motion trajectory for a relative motion having an error ellipse minor semi-axis of 160m in an embodiment of the present invention;
FIG. 22 is a graph showing true pitch angle for post-hoc fine tracking data in an embodiment of the present invention;
fig. 23 is a schematic diagram illustrating a comparison between a parameter estimation relative motion trajectory corresponding to relative orbit prediction data and post-event precise orbit determination data and a real relative motion trajectory according to an embodiment of the present invention;
FIG. 24 is a graph showing a difference between an estimated expected pitch angle and a true pitch angle for parameters corresponding to pre-track data and post-fine tracking data according to an embodiment of the present invention;
FIG. 25 is a graph showing lateral and radial errors of a parametric estimated relative motion trajectory versus a true relative motion trajectory for relative trajectory prediction data and post-hoc fine tracking data in an embodiment of the present invention;
FIG. 26 is a schematic structural diagram of an attitude guidance law parameter generation system suitable for close-range spacecraft coplanar formation according to the present invention;
fig. 27 is a schematic structural diagram of an electronic device according to the present invention.
Description of the element reference numerals
1 expression acquisition module
2 data acquisition module
3 first processing module
4 second processing module
5 third processing Module
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It is to be noted that the features in the following embodiments and examples may be combined with each other without conflict.
It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention, and the drawings only show the components related to the present invention rather than the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
As shown in fig. 1, the method for determining attitude guidance law errors applicable to close-range spacecraft coplanar formation of the present invention includes the following steps:
s1, setting a transverse drift ellipse with the longer half axis being twice as long as the shorter half axis in an LVLH coordinate system with the relative motion trail of the spacecraft relative to the reference spacecraft as the reference spacecraft in the orbital plane, and acquiring the relative position x and y and the attitude guidance law parameter x according to a C-W equationc0,yc0The relation of Θ and b, wherein (x)c0,yc0) The center of the ellipse at the initial moment, b the minor semi-axis of the ellipse, and theta the phase of the reference spacecraft on the ellipse.
As shown in fig. 2 and 3, the elliptical trajectory in the orbital plane that accompanies the motion of the spacecraft relative to the reference spacecraft can be represented by:
wherein (x)c,yc) Is the center of the ellipse, and b is the minor semi-axis of the ellipse. x is the number ofc＝xc0，yc＝yc0-1.5nxc0t, n are reference spacecraftOf absolute tracksAverage angular velocity of motion, (x)c0,yc0) Is the ellipse center at the initial time, and t is the time since the initial time.
The LVLH coordinate system is a Local Vertical Local Horizontal coordinate system, the centroid of a certain spacecraft in the space is taken as an origin, the direction of the geocentric pointing to the spacecraft is taken as an x-axis, the normal direction of an orbit plane is taken as a z-axis, and the y-axis, the x-axis and the z-axis form a right-hand coordinate system. As shown in fig. 4, the x-axis in the LVLH coordinate system is oriented radially towards the sky, wherein the direction pointing from the geocentric to the centroid of the reference spacecraft is radial; the y axis is perpendicular to the x axis in the track plane and is transverse along the flight direction; the z-axis conforms to the right hand rule, normal to the orbital plane.
Thus, the relative position x, y and the attitude-guidance law parameter xc0,yc0The relationship Θ, b is represented by the following formula:
where, θ is the initial phase of the reference spacecraft on the ellipse.
And step S2, setting the relative motion trajectories of the accompanying spacecraft relative to the reference spacecraft into a quasi-straight line and a transverse drift ellipse from front to back, and acquiring simulated relative motion data of the accompanying spacecraft corresponding to the two groups of motion trajectories.
Specifically, two sets of relative motion trajectories are set as a quasi-straight line from front to back and a transverse drift ellipse, and two sets of simulated relative motion position and speed data, referred to as relative motion data for short, of the accompanying spacecraft corresponding to the two relative motion trajectories within a certain time period of relative motion are obtained to be used as the basis data of subsequent simulation analysis.
Step S3, guiding law parameter x based on posturec0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of simulation relative motion datac0,yc0And theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle.
Specifically, according to the relation between the attitude guidance law parameters and the relative motion data and the simulated relative motion data, the least square parameter estimation method is adopted to obtain the attitude guidance law parameters x according to the minimum residual error principlec0,yc0Θ, b; and calculating to obtain an estimated value of the relative motion data according to the attitude guidance law parameters, and further obtaining an expected pitch angle required by attitude control. According to the difference between the expected pitch angle and the simulated pitch angle, the least square estimation theory can be analyzed to conduct law parameters in attitude guidanceA role in number estimation. And the simulation pitch angle is obtained by calculating simulation relative motion data.
As shown in fig. 5, the desired pitch angle, i.e. the angle along the-x axis with the apparent axis of the load of the spacecraft pointing towards the body, is calculated according to the following equation:
Pitch＝π+γ
wherein, gamma is arctan (x/y) or gamma pi + arctan (x/y), and the value of gamma is selected from
And
are determined together.
Step S4, error correction is carried out on the two groups of simulated relative motion data according to the relative orbit prediction error empirical model, and the error correction is based on the attitude leading law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of corrected simulated relative motion datac0,yc0And theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of corrected simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle.
Specifically, according to the relative orbit prediction error empirical model, errors are added to two groups of simulated relative motion data, and then the difference value between the expected pitch angle and the simulated pitch angle is calculated in the same manner. By comparing with the result without error, the robustness of the attitude guide law parameter estimation theory can be analyzed.
According to engineering experience, the relation between the relative orbit prediction error and time is given, and a relative orbit prediction error model is established. The relative orbit prediction error model is a linear + trigonometric function empirical model, wherein the period of the trigonometric function is the orbit period.
Step S5, guiding law parameter x based on posturec0,yc0The relation between theta and b and the relative position x and y and the relative orbit forecast data corresponding to the two groups of motion tracks estimate the attitude guidance law parameter x according to the least square estimation principlec0,yc0Theta and b, and calculating to obtain expected pitch angles at each moment corresponding to two groups of relative track forecast data; and calculating the actual pitch angle at each corresponding moment according to the two groups of post-orbit determination data corresponding to the two groups of motion tracks, and calculating the difference value between the expected pitch angle and the actual pitch angle.
Wherein, the error caused by the attitude guidance law is obtained by comparing the difference between the expected pitch angle and the actual pitch angle.
Therefore, the attitude guidance law error judgment method suitable for close-range spacecraft coplanar formation calculates the difference between the expected pitch angle and the simulated/actual pitch angle through the following three types of input, thereby providing a conclusion of engineering application:
(1) two groups of simulated relative motion data of a quasi-straight line and a transverse drift ellipse which are accompanied with the self-forward and self-backward motion of the spacecraft;
(2) according to the relative orbit prediction error empirical model, adding errors to the two groups of simulated relative motion data to obtain relative motion data containing errors;
(3) two sets of relative orbit forecast data and post-precision orbit determination data.
The method for judging the attitude guidance law error suitable for the close-range spacecraft coplanar formation is further described below by combining a specific embodiment.
In 2016, 13 minutes and 47 seconds at 9, 15 and 22 days, and a TG-2 satellite enters the orbit along with TG-2; after 38 days of rail storage, 31 minutes 0 seconds was successfully released from TG-2 at 2016, 10, 23, 7, and the sheng mission of the space wedding photographer, whose TG-2 and SZ-11 combination, began. In 2016, 10 months, 30 days, 5 hours, 54 minutes and 16 seconds, the successful flying of about 1.4km above the combination is realized by accurate orbit control of TG-2 satellites for 7 times, high-definition imaging of the combination is completed, and 900 pieces of wedding photos are shot.
And taking the TG-2 satellite as an accompanying spacecraft and the assembly as a reference spacecraft, calculating corresponding attitude guidance law parameters in the flying photographing process of the assembly for the TG-2 satellite to obtain the final on-orbit expected pitch angle error so as to provide a basis for engineering application. Aiming at the requirement of a TG-2 satellite flying combination body, according to the fact that the movement of the TG-2 satellite relative to the combination body is in-plane movement of a track, the height of the TG-2 satellite track is about 1.46km higher than that of the combination body, two groups of quasi-straight lines with front and back relative movement and a fluctuation curve with a relative movement ellipse short semi-axis of 160m are set, two groups of simulation relative movement data 120min before and 90min after a flying moment are given, and the two groups of simulation relative movement data are used as the data of the basis of subsequent simulation analysis.
And (3) deriving relative motion position and speed data before and after control by using an HPOP orbit extrapolation model (considering all perturbation) of STK software, and taking the relative motion position and speed data as a basis for estimating attitude guidance law parameters.
The empirical model of the relative orbit prediction error is shown as follows:
1. relative motion data based on error-free simulation
a. The result of estimating the attitude guidance law parameters of the simulation data of the error-free quasi-linear motion is
xc0＝-1463.246218127131m
yc0＝-17900.84783337577m
Θ＝4.238784462530427rad
b＝54.59450495536964m
Wherein the expected pitch angle is shown in fig. 6, the parameter estimation relative track and the real relative track are shown in fig. 7, the difference between the parameter estimation expected pitch angle and the simulation pitch angle is shown in fig. 8, and the transverse and radial errors of the parameter estimation relative track and the simulation relative track are shown in fig. 9.
b. The estimation result of the attitude guidance law parameters of the simulation data of relative motion with the error-free ellipse minor semi-axis of 160m is
xc0＝-1463.673145480557m
yc0＝-18108.07121033077m
Θ＝2.029183483729073rad
b＝161.2360679716028m
Wherein the expected pitch angle is shown in fig. 10, the difference between the parameter estimation relative trajectory and the simulated relative trajectory is shown in fig. 11, the difference between the parameter estimation expected pitch angle and the simulated pitch angle is shown in fig. 12, and the lateral and radial errors of the parameter estimation relative trajectory and the simulated relative trajectory are shown in fig. 13.
2. Simulated relative motion data with errors
a. The estimation result of the attitude guidance law parameters of the quasi-linear motion simulation data with the error is
xc0＝-1464.490714356118m
yc0＝-17900.67669131771m
Θ＝4.234450195813123rad
b＝53.68400543336465m
Wherein the expected pitch angle is shown in fig. 14, the difference between the parameter estimated relative trajectory and the simulated relative trajectory is shown in fig. 15, the difference between the parameter estimated expected pitch angle and the simulated pitch angle is shown in fig. 16, and the lateral and radial errors between the parameter estimated relative trajectory and the real relative trajectory are shown in fig. 17.
b. The estimation result of the attitude guidance law parameters of the simulation data of the relative motion with the error ellipse and the minor semi-axis of 160m is
xc0＝-1464.917641617445m
yc0＝-18107.90010651827m
Θ＝2.025524539809740rad
b＝161.9671171786372m
Wherein the expected pitch angle is shown in fig. 18, the difference between the parameter estimated relative trajectory and the simulated relative trajectory is shown in fig. 19, the difference between the parameter estimated expected pitch angle and the simulated pitch angle is shown in fig. 20, and the lateral and radial errors of the parameter estimated relative trajectory and the simulated relative trajectory are shown in fig. 21.
3. Forecasting orbit and post-event precision orbit determination data in orbit flying process
In this embodiment, two sets of relative motion data 120min to 90min before the time of the flight are given, and the track forecast time (90 min after the time of the flight) can be estimated to be about 5 hours according to the on-track guidance law calculation and the experience of the upper note. According to the experience of the prediction error of the actual on-orbit, the maximum error of the relative orbit prediction corresponding to 5 hours is about 21m, the relative orbit prediction does not diffuse within the first 1.5 hours (about 1 orbit), and the corresponding prediction error model parameter is
Δxσ＝Δr×8％＝21×8％＝1.7m
Δyσ＝Δxσ
Δy0＝0
Therefore, the estimation result of the guidance law parameters for forecasting the orbit attitude in the process of the on-orbit flying is
xc0＝-1407.093235535373m
yc0＝-17148.77536192946m
Θ＝2.249255219230809rad
b＝20.91089797730896m
Wherein the desired pitch angle is shown in fig. 22. The parameter estimation relative trajectory and the true relative trajectory are shown in fig. 23. The difference between the parameter estimate desired pitch angle and the true pitch angle is shown in fig. 24. The lateral and radial errors of the parameter estimated relative trajectory from the true relative trajectory are shown in fig. 25.
As shown in fig. 26, the attitude guidance law error determination system suitable for close-range spacecraft coplanar formation of the present invention includes an expression obtaining module 1, a data obtaining module 2, a first processing module 3, a second processing module 4, and a third processing module 5.
The expression obtaining module 1 is used for setting a transverse drift ellipse with a long semi-axis being twice as long as a short semi-axis in an LVLH coordinate system with a relative motion track of the spacecraft relative to a reference spacecraft as the reference spacecraft in an orbit surface, and obtaining relative positions x and y and attitude guidance law parameters x according to a C-W equationc0,yc0The relation of Θ and b, wherein (x)c0,yc0) The center of the ellipse at the initial moment, b the minor semi-axis of the ellipse, and theta the phase of the reference spacecraft on the ellipse.
As shown in fig. 2 and 3, the elliptical trajectory in the orbital plane that accompanies the motion of the spacecraft relative to the reference spacecraft can be represented by:
wherein (x)c,yc) Is the center of the ellipse, and b is the minor semi-axis of the ellipse. x is the number ofc＝xc0，yc＝yc0-1.5nxc0t, n is the average angular velocity of motion of the absolute orbit of the reference spacecraft, (x)c0,yc0) Is the ellipse center at the initial time, and t is the time since the initial time.
The LVLH coordinate system is a Local Vertical Local Horizontal coordinate system, the centroid of a certain spacecraft in the space is taken as an origin, the direction of the geocentric pointing to the spacecraft is taken as an x-axis, the normal direction of an orbit plane is taken as a z-axis, and the y-axis, the x-axis and the z-axis form a right-hand coordinate system. As shown in fig. 4, the x-axis in the LVLH coordinate system is oriented radially towards the sky, wherein the direction pointing from the geocentric to the centroid of the reference spacecraft is radial; the y axis is perpendicular to the x axis in the track plane and is transverse along the flight direction; the z-axis conforms to the right hand rule, normal to the orbital plane.
Thus, the relative position x, y and the attitude-guidance law parameter xc0,yc0The relationship Θ, b is represented by the following formula:
where, θ is the initial phase of the reference spacecraft on the ellipse.
The data acquisition module 2 is used for setting the relative motion trajectories of the accompanying spacecraft relative to the reference spacecraft into a quasi-straight line and a transverse drift ellipse from front to back, and acquiring simulated relative motion data of the accompanying spacecraft corresponding to the two groups of motion trajectories.
Specifically, two sets of relative motion trajectories are set as a quasi-straight line from front to back and a transverse drift ellipse, and two sets of simulated relative motion position and speed data, referred to as relative motion data for short, of the accompanying spacecraft corresponding to the two relative motion trajectories within a certain time period of relative motion are obtained to be used as the basis data of subsequent simulation analysis.
The first processing module 3 is connected with the expression obtaining module 1 and the data obtaining module 2 and is used for obtaining the attitude guidance law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of simulation relative motion datac0,yc0And theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle.
Specifically, according to the relation between the attitude guidance law parameters and the relative motion data and the simulated relative motion data, the least square parameter estimation method is adopted to obtain the attitude guidance law parameters x according to the minimum residual error principlec0,yc0Θ, b; and calculating to obtain an estimated value of the relative motion data according to the attitude guidance law parameters, and further obtaining an expected pitch angle required by attitude control. According to the difference between the expected pitch angle and the simulated pitch angle, the effect of the least square estimation theory in the estimation of the attitude guidance law parameters can be analyzed. And the simulation pitch angle is obtained by calculating simulation relative motion data.
As shown in fig. 5, the desired pitch angle, i.e. the angle along the-x axis with the apparent axis of the load of the spacecraft pointing towards the body, is calculated according to the following equation:
Pitch＝π+γ
wherein, gamma is arctan (x/y) or gamma pi + arctan (x/y), and the value of gamma is selected from
And
are determined together.
The second processing module 4 is connected with the expression obtaining module 1 and the data obtaining module 2, and is used for performing error correction on the two groups of simulated relative motion data according to the relative orbit prediction error empirical model and based on the attitude guidance law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of corrected simulated relative motion datac0,yc0And theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of corrected simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle.
Specifically, according to the relative orbit prediction error empirical model, errors are added to two groups of simulated relative motion data, and then the difference value between the expected pitch angle and the simulated pitch angle is calculated in the same manner. By comparing with the result without error, the robustness of the attitude guide law parameter estimation theory can be analyzed.
According to engineering experience, the relation between the relative orbit prediction error and time is given, and a relative orbit prediction error model is established. The relative orbit prediction error model is a linear + trigonometric function empirical model, wherein the period of the trigonometric function is the orbit period.
The third processing module 5 is connected with the expression obtaining module 1 and the data obtaining module 2 and is used for obtaining the attitude guidance law parameter xc0,yc0Theta, b and phaseEstimating attitude guide law parameters x according to the least square estimation principle for the relational expression of the positions x and y and the relative orbit forecast data corresponding to the two groups of motion tracksc0,yc0Theta and b, and calculating to obtain expected pitch angles at each moment corresponding to two groups of relative track forecast data; and calculating the actual pitch angle at each corresponding moment according to the two groups of post-orbit determination data corresponding to the two groups of motion tracks, and calculating the difference value between the expected pitch angle and the actual pitch angle.
Wherein, the error caused by the attitude guidance law is obtained by comparing the difference between the expected pitch angle and the actual pitch angle.
Therefore, the attitude guidance law error judgment system suitable for close-range spacecraft coplanar formation calculates the difference between the expected pitch angle and the simulated/actual pitch angle through the following three types of input, so that the conclusion of engineering application can be provided:
(1) two groups of simulated relative motion data of a quasi-straight line and a transverse drift ellipse which are accompanied with the self-forward and self-backward motion of the spacecraft;
(2) according to the relative orbit prediction error empirical model, adding errors to the two groups of simulated relative motion data to obtain relative motion data containing errors;
(3) two sets of relative orbit forecast data and post-precision orbit determination data.
As shown in fig. 27, the electronic device of the present invention includes the above-mentioned attitude guidance law error determination system suitable for close-range spacecraft coplanar formation.
In summary, the present invention provides a method, a system and an electronic device for determining an attitude guidance law error. Therefore, the invention effectively overcomes various defects in the prior art and has high industrial utilization value.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.
Claims (9)
1. An attitude guidance law error judgment method suitable for close-range spacecraft coplanar formation is characterized by comprising the following steps: the method comprises the following steps:
setting a transverse drift ellipse with the long half axis being twice as long as the short half axis in an LVLH coordinate system of the reference spacecraft along with the relative motion track of the spacecraft relative to the reference spacecraft in the orbit surface, and acquiring the relative position x and y and the attitude guidance law parameter x according to a C-W equationc0,yc0The relation of Θ and b, wherein (x)c0,yc0) Is the center of the ellipse at the initial moment, b is the minor semi-axis of the ellipse, and theta is the phase of the reference spacecraft on the ellipse;
setting relative motion trajectories of the accompanying spacecraft relative to the reference spacecraft into a quasi-straight line and a transverse drift ellipse from front to back, and acquiring simulated relative motion data of the accompanying spacecraft corresponding to the two groups of motion trajectories;
based on attitude guidance law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of simulation relative motion datac0,yc0Theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle;
error correction is carried out on two groups of simulated relative motion data according to the relative orbit prediction error empirical model, and the error correction is based on the attitude leading law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of corrected simulated relative motion datac0,yc0E, theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of corrected simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle;
based on attitude guidance law parameter xc0,yc0The relational expression of theta, b and relative position x, y and the relative orbit forecast data corresponding to two groups of motion tracks estimate the attitude according to the least square estimation principleAttitude leading law parameter xc0,yc0Theta and b, and calculating to obtain expected pitch angles at each moment corresponding to two groups of relative track forecast data; and calculating the actual pitch angle at each corresponding moment according to the two groups of post-orbit determination data corresponding to the two groups of motion tracks, and calculating the difference value between the expected pitch angle and the actual pitch angle.
2. The attitude guidance law error judgment method suitable for close-range spacecraft coplanar formation according to claim 1, characterized by comprising the following steps: relative position x, y and attitude guidance law parameter xc0,yc0The relation Θ, b is:
wherein n is the average motion angular velocity of the absolute orbit of the reference spacecraft, and t is the time from the initial moment.
3. The attitude guidance law error judgment method suitable for close-range spacecraft coplanar formation according to claim 2, characterized by comprising the following steps: the desired Pitch angle Pitch is calculated according to:
Pitch＝π+γ
γ ═ arctan (x/y) or γ ═ pi + arctan (x/y)
Wherein γ is selected from
And
is determined by the sign of (a), xc0,yc0And theta and b are estimated values obtained according to the least square estimation principle.
4. The attitude guidance law error judgment method suitable for close-range spacecraft coplanar formation according to claim 1, characterized by comprising the following steps: the relative orbit prediction error empirical model is a model of a linear plus trigonometric function, and the period of the trigonometric function is the orbit period of the reference spacecraft.
5. The utility model provides an attitude guidance law error judgment system suitable for close range spacecraft coplane formation which characterized in that: the system comprises an expression acquisition module, a data acquisition module, a first processing module, a second processing module and a third processing module;
the expression acquisition module is used for setting a transverse drift ellipse with a long half axis twice as long as a short half axis in an LVLH coordinate system with a relative motion track of the spacecraft relative to a reference spacecraft as the reference spacecraft in an orbital plane, and acquiring relative positions x and y and attitude guidance law parameters x according to a C-W equationc0,yc0The relation of Θ and b, wherein (x)c0,yc0) Is the center of the ellipse at the initial moment, b is the minor semi-axis of the ellipse, and theta is the phase of the reference spacecraft on the ellipse;
the data acquisition module is used for setting the relative motion trajectories of the accompanying spacecraft relative to the reference spacecraft into a quasi-straight line and a transverse drift ellipse from front to back and acquiring simulated relative motion data of the accompanying spacecraft corresponding to the two groups of motion trajectories;
the first processing module is used for guiding law parameter x based on attitudec0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of simulation relative motion datac0,yc0Theta and b, and calculating to obtain an expected pitch angle at each moment corresponding to the two groups of simulated relative motion data and a difference value between the expected pitch angle and the simulated pitch angle;
the second processing module is used for carrying out error correction on two groups of simulated relative motion data according to the relative orbit prediction error empirical model and based on the attitude leading law parameter xc0,yc0Estimating the attitude guidance law parameter x according to the least square estimation principle by using the relational expression of theta, b and relative position x, y and two groups of corrected simulated relative motion datac0,yc0Theta, b, and calculating to obtain the period of each time corresponding to the two groups of corrected simulated relative motion dataThe expected pitch angle and the difference value of the expected pitch angle and the simulated pitch angle;
the third processing module is used for guiding law parameter x based on the attitudec0,yc0The relation between theta and b and the relative position x and y and the relative orbit forecast data corresponding to the two groups of motion tracks estimate the attitude guidance law parameter x according to the least square estimation principlec0,yc0Theta and b, and calculating to obtain expected pitch angles at each moment corresponding to two groups of relative track forecast data; and calculating the actual pitch angle at each corresponding moment according to the two groups of post-orbit determination data corresponding to the two groups of motion tracks, and calculating the difference value between the expected pitch angle and the actual pitch angle.
6. The attitude guidance law error determination system suitable for close range spacecraft coplanar formation according to claim 5, wherein: relative position x, y and attitude guidance law parameter xc0,yc0The relation Θ, b is:
wherein n is the average motion angular velocity of the absolute orbit of the reference spacecraft, and t is the time from the initial moment.
7. The attitude guidance law error determination system suitable for close range spacecraft coplanar formation according to claim 6, wherein: the desired pitch angle in the first, second and third process modules
Pitch is calculated according to:
Pitch＝π+γ
γ ═ arctan (x/y) or γ ═ pi + arctan (x/y)
Wherein γ is selected from
And
is determined by the sign of (a), xc0,yc0And theta and b are estimated values obtained according to the least square estimation principle.
8. The attitude guidance law error determination system suitable for close range spacecraft coplanar formation according to claim 5, wherein: in the second processing module, the empirical model of the relative orbit prediction error is a model of a linear plus trigonometric function, and the period of the trigonometric function is the orbit period of the reference spacecraft.
9. An electronic device, characterized in that: attitude guidance law error determination system suitable for close-range spacecraft coplanar formation according to one of claims 5 to 8.
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Citations (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH04283615A (en) * | 1991-03-13 | 1992-10-08 | Tokimec Inc | Gyroscope apparatus |
| EP0999128A1 (en) * | 1998-11-06 | 2000-05-10 | Société Européenne des Satellites | Method for determining the yaw angle of a satellite |
| EP2685214A2 (en) * | 2012-07-10 | 2014-01-15 | Honeywell International Inc. | Multiple truth reference system and method |
| CN103728980A (en) * | 2014-01-08 | 2014-04-16 | 哈尔滨工业大学 | Spacecraft relative orbit control method |
| CN103852082A (en) * | 2012-11-30 | 2014-06-11 | 上海航天控制工程研究所 | Inter-satellite measurement and gyro attitude orbit integrated smoothing estimation method |
| CN104765373A (en) * | 2015-01-30 | 2015-07-08 | 北京控制工程研究所 | On-satellite relative motion state acquiring method |
| CN105094139A (en) * | 2015-07-24 | 2015-11-25 | 上海微小卫星工程中心 | Elliptical short half shaft control method of close-range spacecraft coplanar ellipse formation |
| CN105159304A (en) * | 2015-06-26 | 2015-12-16 | 哈尔滨工业大学 | Finite time fault-tolerant control method for approaching and tracking space non-cooperative target |
| CN105222788A (en) * | 2015-09-30 | 2016-01-06 | 清华大学 | The automatic correcting method of the aircraft course deviation shift error of feature based coupling |
| CN105678061A (en) * | 2015-12-31 | 2016-06-15 | 中国人民解放军国防科学技术大学 | Space station safe region design method capable of satisfying passive safety requirement |
| CN106227225A (en) * | 2016-08-25 | 2016-12-14 | 上海微小卫星工程中心 | Spacecraft coplanar formation accompanying flying configuration control method |
| CN106297422A (en) * | 2016-10-09 | 2017-01-04 | 中国人民解放军国防科学技术大学 | A kind of non-linear relevant path forecasting procedure based on least square |
| CN106384152A (en) * | 2016-09-09 | 2017-02-08 | 哈尔滨工业大学 | PF space non-cooperative target track prediction method based on firefly group optimization |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8344303B2 (en) * | 2010-11-01 | 2013-01-01 | Honeywell International Inc. | Projectile 3D attitude from 3-axis magnetometer and single-axis accelerometer |
| US8756001B2 (en) * | 2011-02-28 | 2014-06-17 | Trusted Positioning Inc. | Method and apparatus for improved navigation of a moving platform |
-
2017
- 2017-05-17 CN CN201710345816.1A patent/CN108958064B/en active Active
Patent Citations (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH04283615A (en) * | 1991-03-13 | 1992-10-08 | Tokimec Inc | Gyroscope apparatus |
| EP0999128A1 (en) * | 1998-11-06 | 2000-05-10 | Société Européenne des Satellites | Method for determining the yaw angle of a satellite |
| EP2685214A2 (en) * | 2012-07-10 | 2014-01-15 | Honeywell International Inc. | Multiple truth reference system and method |
| CN103852082A (en) * | 2012-11-30 | 2014-06-11 | 上海航天控制工程研究所 | Inter-satellite measurement and gyro attitude orbit integrated smoothing estimation method |
| CN103728980A (en) * | 2014-01-08 | 2014-04-16 | 哈尔滨工业大学 | Spacecraft relative orbit control method |
| CN104765373A (en) * | 2015-01-30 | 2015-07-08 | 北京控制工程研究所 | On-satellite relative motion state acquiring method |
| CN105159304A (en) * | 2015-06-26 | 2015-12-16 | 哈尔滨工业大学 | Finite time fault-tolerant control method for approaching and tracking space non-cooperative target |
| CN105094139A (en) * | 2015-07-24 | 2015-11-25 | 上海微小卫星工程中心 | Elliptical short half shaft control method of close-range spacecraft coplanar ellipse formation |
| CN105222788A (en) * | 2015-09-30 | 2016-01-06 | 清华大学 | The automatic correcting method of the aircraft course deviation shift error of feature based coupling |
| CN105678061A (en) * | 2015-12-31 | 2016-06-15 | 中国人民解放军国防科学技术大学 | Space station safe region design method capable of satisfying passive safety requirement |
| CN106227225A (en) * | 2016-08-25 | 2016-12-14 | 上海微小卫星工程中心 | Spacecraft coplanar formation accompanying flying configuration control method |
| CN106384152A (en) * | 2016-09-09 | 2017-02-08 | 哈尔滨工业大学 | PF space non-cooperative target track prediction method based on firefly group optimization |
| CN106297422A (en) * | 2016-10-09 | 2017-01-04 | 中国人民解放军国防科学技术大学 | A kind of non-linear relevant path forecasting procedure based on least square |
Non-Patent Citations (3)
| Title |
|---|
| Analysis of Manned Spacecraft Attitude Variation to Relay Terminal Antenna Pointing Error;Zheng Jun;《2015 7th International Conference on Intelligent Human-Machine Systems and Cybernetics》;20150827;全文 * |
| 基于C-W方程的近程导引制导与控制方法;刘胜;《上海航天》;20140228;全文 * |
| 空间目标轨道预报误差与碰撞概率问题研究;白显宗;《中国博士学位论文全文数据库 工程科技Ⅱ辑》;20141215;全文 * |
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