CN113741197B - Single-approach three-pulse control method and system for high-rail target - Google Patents
Single-approach three-pulse control method and system for high-rail target Download PDFInfo
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Abstract
The application provides a single approach three-pulse control method and a system for a high-track target, comprising the following steps: describing the relative motion of two stars by adopting a CW equation according to the minimum distance, speed and time of the approaching task, and constructing a relative track of the terminal; according to the number of the two-star orbit, calculating an initial relative orbit of the tracked star under the Hill coordinate system; under the Hill coordinate system, optimizing and calculating three pulse parameters by adopting an analytic method according to the initial relative track and the terminal relative track; and (3) re-optimizing according to a numerical method by adopting an orbit dynamics model according to the analysis and calculation result, and finally obtaining an optimal solution. The method realizes the trade-off among orbit precision, calculated amount and design efficiency, can quickly and effectively perform three-pulse preliminary by adopting a simplified orbit model, and then uses the solution as an initial value guess of a high-precision multi-body model, thereby effectively reducing iteration times, reducing calculated amount and ensuring the robustness of numerical iteration.
Description
Technical Field
The application relates to the field of spacecraft orbit design and optimization, in particular to a single approach three-pulse control method and system for a high-orbit target.
Background
In the on-orbit operation task of a spacecraft, single approach is an important component of relative motion control. In the approaching process, a plurality of pulses are required to be applied to form the effect of short-distance fly-by targets, so that imaging of the fault condition of the targets is realized. Because the fly-over distance is short and the task is more frequent, the control precision in a single approach process is required to be high, the fuel consumption is required to be small, conditions are created for executing the task for multiple times, and the research on optimal multi-pulse approach of the fuel has great significance.
At present, some researches are carried out on the relative motion design of a spacecraft, and the main problems related to orbit control are as follows:
in the Chinese patent document with the publication number of CN104249816B, a gesture track cooperative control method for non-cooperative target hovering around is disclosed, and a real-time closed-loop LQG track control law is adopted for a relative motion process of hovering around firstly, so that the actual track motion of a tracked star relative to a target star in a flying around stage and the deviation amount of a designed general flying around track, and the relative position and relative speed of the tracked star relative to a hovering target point in a hovering stage are controlled, and the control precision is high and the fuel consumption is low. The gesture collaborative design method in the flying around process focused by the patent has great difference from the approaching control of the patent, and the related design method cannot be used.
In the Chinese patent document with the publication number of CN104309822B, a parameter optimization-based spacecraft monopulse drop-shaped fly-around trajectory hover control method is disclosed, the problem that the existing fixed-point hover method requires continuous control quantity, the existing monopulse drop-shaped fly-around method realizes hover, and the problem of fuel consumption of a tracking spacecraft hovering on a target spacecraft orbit plane due to longer hover time is not considered. The hover control in the process of winding and flying focused by the patent is very different from the approach control of the patent, and the related design method cannot be used.
In the Chinese patent document with the publication number of CN106628257B, a method for maintaining the relative motion orbit of a near-earth spacecraft in the earth perturbation gravitational field is disclosed, the relative motion of a near-earth orbit satellite under the influence of the earth flat perturbation is modeled, and a periodic solution estimation scheme based on a time discrete method is provided, so that the initial condition of the periodic relative motion can be simply and effectively estimated more accurately, and the change of the dynamic characteristic of the relative motion of the near-earth spacecraft under the influence of the earth gravitational perturbation can be quantitatively studied. The control of the holding in the winding process concerned by the patent is very different from the control of the approaching of the patent, and the related design method cannot be used.
In the chinese patent document with publication number CN110954104a, a spacecraft approach operation path planning method is disclosed, comprising: determining the type of obstacle in the path planning; carrying out algorithm description and constraint analysis on the approaching path planning problem of the spacecraft to generate a sampling state space; carrying out ovalization treatment on the sampling state space; carrying out security analysis on the sampling state space after the ovalization treatment; applying a path planning algorithm based on sampling to the sampling state space after security analysis to obtain a discrete sampling state sequence; and carrying out continuous processing on the discrete sampling state sequence to obtain a path of spacecraft approaching operation.
Disclosure of Invention
Aiming at the defects in the prior art, the application aims to provide a single approach three-pulse control method and system for a high-track target.
The application provides a single approach three-pulse control method of a high-orbit target, which comprises the following steps:
step S1: describing the relative motion of two stars by adopting a CW equation according to the minimum distance, speed and time of the approaching task, and constructing a relative track of the terminal;
step S2: according to the number of the two-star orbit, calculating an initial relative orbit of the tracked star under the Hill coordinate system;
step S3: under the Hill coordinate system, optimizing and calculating three pulse parameters by adopting an analytic method according to the initial relative track and the terminal relative track;
step S4: and (3) re-optimizing according to a numerical method by adopting an orbit dynamics model according to the analysis and calculation result, and finally obtaining an optimal solution.
Preferably, the step S1 includes:
step S1.1: assuming that the eccentricity of a target star orbit is zero, defining an origin of a Hill coordinate system as a target star centroid, wherein an X axis points radially, a Z axis is normal to a track surface, and a Y axis and other two axes form a right-hand coordinate system;
step S1.2: establishing a CW equation under a Hill coordinate system, and defining a single approach track by adopting a water drop configuration;
step S1.3: and calculating a water drop configuration track set meeting the constraint according to the minimum distance, speed and time of the approaching task, and preferably determining one of the water drop configuration track sets as a terminal relative track.
Preferably, the step S2 includes:
step S2.1: calculating to obtain rectangular coordinates of the positions and the speeds of the two stars and relative positions and speed vectors of the two stars according to the instantaneous number of the orbit of the two stars under the J2000.0 geocentric coordinate system;
step S2.2: according to the position and the speed vector of the target star, calculating a conversion matrix from a J2000.0 geocentric coordinate system to a Hill coordinate system;
step S2.3: and calculating the projection of the relative positions and the velocity vectors of the two stars under the Hill coordinate system by utilizing a conversion matrix from the J2000.0 geocentric coordinate system to the Hill coordinate system, obtaining initial motion parameters of the tracked star under the Hill coordinate system, and finally obtaining an initial relative orbit.
Preferably, the step S3 includes:
step S3.1: according to the initial relative orbit and the terminal relative orbit parameters, adopting a CW equation analysis model to calculate three characteristic parameters of the elliptical semi-minor axis, the instantaneous elliptical center position Y-direction coordinate and the elliptical drift rate of the two initial and final relative orbits;
step S3.2: setting three pulse positions to be positioned at characteristic points with zero radial speed, wherein the phase difference of the three pulses is 180 degrees, and the pulse directions are all along the Y axis;
step S3.3: the semi-minor axis of ellipse of the relative orbit of the initial and final, Y-direction coordinates of the instantaneous ellipse center position and ellipse drift rate are established, three equation sets described by the three pulse sizes are established, the pulse sizes are obtained through solving and calculating, and the positions, the sizes and the directions of the three pulses can be obtained.
Preferably, the step S4 includes:
step S4.1: according to the analysis and calculation result, an intermediate track for transferring the initial relative track to the terminal relative track can be obtained;
step S4.2: setting the position and the speed vector of the tail end of the middle track as terminal conditions, wherein the total number of the variables is 4;
step S4.3: setting a total of 5 variables of the flight time delta tk after the kth pulse acts and the three pulse size as optimization variables;
step S4.4: and recursion is carried out by using a high-precision orbit model, a three-pulse analytic solution is used as an initial value guess, a least square method is adopted for targeting iteration, and finally an optimal solution is obtained.
The application provides a single approach three-pulse control system of a high-track target, which comprises the following steps:
module M1: describing the relative motion of two stars by adopting a CW equation according to the minimum distance, speed and time of the approaching task, and constructing a relative track of the terminal;
module M2: according to the number of the two-star orbit, calculating an initial relative orbit of the tracked star under the Hill coordinate system;
module M3: under the Hill coordinate system, according to the initial relative track and the terminal relative track, adopting an analytic system to optimize and calculate three pulse parameters;
module M4: and (3) adopting an orbit dynamics model according to the analysis and calculation result, and re-optimizing according to a numerical system to finally obtain an optimal solution.
Preferably, the module M1 comprises:
module M1.1: assuming that the eccentricity of a target star orbit is zero, defining an origin of a Hill coordinate system as a target star centroid, wherein an X axis points radially, a Z axis is normal to a track surface, and a Y axis and other two axes form a right-hand coordinate system;
module M1.2: establishing a CW equation under a Hill coordinate system, and defining a single approach track by adopting a water drop configuration;
module M1.3: and calculating a water drop configuration track set meeting the constraint according to the minimum distance, speed and time of the approaching task, and preferably determining one of the water drop configuration track sets as a terminal relative track.
Preferably, the module M2 comprises:
module M2.1: calculating to obtain rectangular coordinates of the positions and the speeds of the two stars and relative positions and speed vectors of the two stars according to the instantaneous number of the orbit of the two stars under the J2000.0 geocentric coordinate system;
module M2.2: according to the position and the speed vector of the target star, calculating a conversion matrix from a J2000.0 geocentric coordinate system to a Hill coordinate system;
module M2.3: and calculating the projection of the relative positions and the velocity vectors of the two stars under the Hill coordinate system by utilizing a conversion matrix from the J2000.0 geocentric coordinate system to the Hill coordinate system, obtaining initial motion parameters of the tracked star under the Hill coordinate system, and finally obtaining an initial relative orbit.
Preferably, the module M3 includes:
module M3.1: according to the initial relative orbit and the terminal relative orbit parameters, adopting a CW equation analysis model to calculate three characteristic parameters of the elliptical semi-minor axis, the instantaneous elliptical center position Y-direction coordinate and the elliptical drift rate of the two initial and final relative orbits;
module M3.2: setting three pulse positions to be positioned at characteristic points with zero radial speed, wherein the phase difference of the three pulses is 180 degrees, and the pulse directions are all along the Y axis;
module M3.3: the semi-minor axis of ellipse of the relative orbit of the initial and final, Y-direction coordinates of the instantaneous ellipse center position and ellipse drift rate are established, three equation sets described by the three pulse sizes are established, the pulse sizes are obtained through solving and calculating, and the positions, the sizes and the directions of the three pulses can be obtained.
Preferably, the module M4 includes:
module M4.1: according to the analysis and calculation result, an intermediate track for transferring the initial relative track to the terminal relative track can be obtained;
module M4.2: setting the position and the speed vector of the tail end of the middle track as terminal conditions, wherein the total number of the variables is 4;
module M4.3: setting a total of 5 variables of the flight time delta tk after the kth pulse acts and the three pulse size as optimization variables;
module M4.4: and recursion is carried out by using a high-precision orbit model, a three-pulse analytic solution is used as an initial value guess, a least square method is adopted for targeting iteration, and finally an optimal solution is obtained.
Compared with the prior art, the application has the following beneficial effects:
1. the method realizes the trade-off among track precision, calculated amount and design efficiency;
2. the application adopts a simplified orbit model, can quickly and effectively perform three-pulse preliminary, and then uses the solution as an initial value guess of a high-precision multi-body model;
3. the application can effectively reduce the iteration times, reduce the calculated amount and ensure the robustness of numerical iteration.
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Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
FIG. 1 is a flow chart of the method of the present application;
fig. 2 shows the initial and final relative tracks and the intermediate track according to an embodiment of the present application.
Detailed Description
The present application will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present application, but are not intended to limit the application in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present application.
A single approach three-pulse control method for a high-orbit target can effectively consider the requirements of an actual task on approach distance, speed and time, and three pulses obtained by an analysis method can rapidly evaluate the feasibility of an approach process, and meanwhile, the pulse solution can provide an initial value for a high-precision model and an effective method for rapidly obtaining a high-precision numerical solution. The method realizes trade-off among orbit precision, calculated amount and design efficiency, can quickly and effectively perform three-pulse preliminary by adopting a simplified orbit model, and then uses the solution as an initial value guess of a high-precision multi-body model, thereby effectively reducing iteration times, reducing calculated amount and ensuring the robustness of numerical iteration.
The method comprises the following steps:
step S1: and describing the relative motion of two stars by adopting a CW equation according to the minimum distance, speed and time of the approaching task, and constructing a relative track of the terminal.
The step S1 specifically comprises the following steps:
step S1.1: assuming that the eccentricity of a target star orbit is zero, defining an origin of a Hill coordinate system as a target star centroid, wherein an X axis points radially, a Z axis is normal to a track surface, and a Y axis and other two axes form a right-hand coordinate system;
step S1.2: establishing CW equations in Hill coordinate system
In the method, in the process of the application,the average orbital angular velocity of the target star is μ the gravitational constant, a c For the semi-major axis of the target star, x, y, and z are the components of the relative position vector on the three axes of the HILL coordinate system. Defining a single approach trajectory by adopting a water drop configuration based on a CW equation;
step S1.3: and calculating a water drop configuration track set meeting the constraint according to the minimum distance, speed and time of the approaching task, and preferably determining one of the water drop configuration track sets as a terminal relative track.
Step S2: and calculating the initial relative orbit of the tracking star under the Hill coordinate system according to the number of the orbits of the two stars.
The step S2 specifically comprises the following steps:
step S2.1: calculating and obtaining rectangular coordinates of positions and speeds of two stars in a coordinate system according to the instantaneous root number of the orbits of the two stars in the J2000.0 geocentric coordinate system, and representing relative positions r and speed vectors v of the two stars as follows
r＝r t -r c
v＝v t -v c
Step S2.2: according to the position and speed vector of the target star, calculating a conversion matrix from a J2000.0 geocentric coordinate system to a Hill coordinate system
M j2000-hill ＝[R T N] T
In the method, in the process of the application,r c and v c The position and velocity vectors are the target star J2000.0 geocentric coordinate system.
Step S2.3: calculating the projection of the relative position and speed vector of two satellites under the Hill coordinate system by using a conversion matrix from the J2000.0 geocentric coordinate system to the Hill coordinate system, and obtaining the initial motion parameter r of the tracked satellites under the Hill coordinate system hill ＝M j2000-hill r，v hill ＝M j2000-hill v-ω hill X r, finally obtaining initial relative track, wherein
Step S3: and under the Hill coordinate system, optimizing and calculating three pulse parameters by adopting an analytic method according to the initial relative track and the terminal relative track.
The step S3 specifically comprises the following steps:
step S3.1: according to the initial relative orbit and the terminal relative orbit parameters, adopting a CW equation analysis model to calculate three characteristic parameters of the elliptical semi-minor axis, the instantaneous elliptical center position Y-direction coordinate and the elliptical drift rate of the two initial and final relative orbits;
step S3.2: setting three pulse positions to be positioned at characteristic points with zero radial speed, wherein the phase difference of the three pulses is 180 degrees, and the pulse directions are all along the Y axis;
step S3.3: the semi-minor axis of ellipse of the relative orbit of the initial and final, the Y-direction coordinate of the instantaneous ellipse center position and the ellipse drift rate, three equation sets described by the three pulse sizes are established,
ΔV 1 ＝-n(a 0 -a 1 )/2
ΔV 2 ＝n(a 1 -a 2 )/2
ΔV 3 ＝-n(a 2 -a 3 )/2
wherein a is 0 、a 1 、a 2 A 3 The pulse size is obtained by solving and calculating the intermediate configuration parameters, so that the position, the size and the direction of the three pulses can be obtained.
Step S4: according to the analysis and calculation result, adopting an orbit dynamics model, re-optimizing according to a numerical method, and finally obtaining an optimal solution, wherein the specific model is as follows
Wherein a is T To consider the three-dimensional perturbation acceleration after the earth attraction and the moon attraction, a N A is the non-spherical perturbation acceleration of the earth caused by the irregular sphere of the earth P For earth tide perturbation acceleration, a A For the earth outer layer atmospheric perturbation acceleration, a S Is the light pressure perturbation acceleration caused by sunlight.
The step S4 specifically comprises the following steps:
step S4.1: according to the analysis and calculation result, an intermediate track for transferring the initial relative track to the terminal relative track can be obtained;
step S4.2: setting the position d of the end of the intermediate rail f Velocity vector v xf 、v yf V zf A total of 4 variables as terminal conditions;
step S4.3: setting a total of 5 variables of the flight time delta tk after the kth pulse acts and the three pulse size as optimization variables;
step S4.4: and recursion is carried out by using a high-precision orbit model, a three-pulse analytic solution is used as an initial value guess, a least square method is adopted for targeting iteration, and finally an optimal solution is obtained.
Those skilled in the art will appreciate that the application provides a system and its individual devices, modules, units, etc. that can be implemented entirely by logic programming of method steps, in addition to being implemented as pure computer readable program code, in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc. Therefore, the system and various devices, modules and units thereof provided by the application can be regarded as a hardware component, and the devices, modules and units for realizing various functions included in the system can also be regarded as structures in the hardware component; means, modules, and units for implementing the various functions may also be considered as either software modules for implementing the methods or structures within hardware components.
In the description of the present application, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are merely for convenience in describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present application.
The foregoing describes specific embodiments of the present application. It is to be understood that the application is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the application. The embodiments of the application and the features of the embodiments may be combined with each other arbitrarily without conflict.
Claims (6)
1. The single approach three-pulse control method for the high-track target is characterized by comprising the following steps of:
step S1: describing the relative motion of two stars by adopting a CW equation according to the minimum distance, speed and time of the approaching task, and constructing a relative track of the terminal;
wherein the two stars are a tracking star and a target star;
step S2: according to the number of the two-star orbit, calculating an initial relative orbit of the tracked star under the Hill coordinate system;
step S3: under the Hill coordinate system, optimizing and calculating three pulse parameters by adopting an analytic method according to the initial relative track and the terminal relative track;
step S4: according to the analysis and calculation result, adopting an orbit dynamics model, and carrying out re-optimization according to a numerical method to finally obtain an optimal solution;
the step S3 includes:
step S3.1: according to the initial relative orbit and the terminal relative orbit parameters, adopting a CW equation analysis model to calculate three characteristic parameters of the elliptical semi-minor axis, the instantaneous elliptical center position Y-direction coordinate and the elliptical drift rate of the two initial and final relative orbits;
step S3.2: setting three pulse positions to be positioned at characteristic points with zero radial speed, wherein the phase difference of the three pulses is 180 degrees, and the pulse directions are all along the Y axis;
step S3.3: according to the ellipse semi-short axis of the relative orbit of the initial and final, the Y-direction coordinate of the instantaneous ellipse center position and the ellipse drift rate, three equation sets described by the three pulse sizes are established, the pulse sizes are obtained by solving and calculating, and the position, the size and the direction of the three pulses can be obtained;
the step S4 includes:
step S4.1: according to the analysis and calculation result, an intermediate track for transferring the initial relative track to the terminal relative track can be obtained;
step S4.2: setting the position and the speed vector of the tail end of the middle track as terminal conditions, wherein the total number of the variables is 4;
wherein the four variables are the position d of the end of the middle track f Velocity vector v xf 、v yf V zf ；
Step S4.3: setting a total of 5 variables of the flight time delta tk after the kth pulse acts and the three pulse size as optimization variables;
step S4.4: and recursion is carried out by using a high-precision orbit model, a three-pulse analytic solution is used as an initial value guess, a least square method is adopted for targeting iteration, and finally an optimal solution is obtained.
2. The single approach three pulse control method of a high rail target according to claim 1, characterized in that: the step S1 includes:
step S1.1: assuming that the eccentricity of a target star orbit is zero, defining an origin of a Hill coordinate system as a target star centroid, wherein an X axis points radially, a Z axis is normal to a track surface, and a Y axis and other two axes form a right-hand coordinate system;
step S1.2: establishing a CW equation under a Hill coordinate system, and defining a single approach track by adopting a water drop configuration;
step S1.3: and calculating a water drop configuration track set meeting the constraint according to the minimum distance, speed and time of the approaching task, and preferably determining one of the water drop configuration track sets as a terminal relative track.
3. The single approach three pulse control method of a high rail target according to claim 1, characterized in that: the step S2 includes:
step S2.1: calculating to obtain rectangular coordinates of the positions and the speeds of the two stars and relative positions and speed vectors of the two stars according to the instantaneous number of the orbit of the two stars under the J2000.0 geocentric coordinate system;
step S2.2: according to the position and the speed vector of the target star, calculating a conversion matrix from a J2000.0 geocentric coordinate system to a Hill coordinate system;
step S2.3: and calculating the projection of the relative positions and the velocity vectors of the two stars under the Hill coordinate system by utilizing a conversion matrix from the J2000.0 geocentric coordinate system to the Hill coordinate system, obtaining initial motion parameters of the tracked star under the Hill coordinate system, and finally obtaining an initial relative orbit.
4. A single approach three pulse control system for a high track target, comprising the steps of:
module M1: describing the relative motion of two stars by adopting a CW equation according to the minimum distance, speed and time of the approaching task, and constructing a relative track of the terminal;
wherein the two stars are a tracking star and a target star;
module M2: according to the number of the two-star orbit, calculating an initial relative orbit of the tracked star under the Hill coordinate system;
module M3: under the Hill coordinate system, according to the initial relative track and the terminal relative track, adopting an analytic system to optimize and calculate three pulse parameters;
module M4: adopting an orbit dynamics model according to the analysis and calculation result, re-optimizing according to a numerical system, and finally obtaining an optimal solution;
the module M3 includes:
module M3.1: according to the initial relative orbit and the terminal relative orbit parameters, adopting a CW equation analysis model to calculate three characteristic parameters of the elliptical semi-minor axis, the instantaneous elliptical center position Y-direction coordinate and the elliptical drift rate of the two initial and final relative orbits;
module M3.2: setting three pulse positions to be positioned at characteristic points with zero radial speed, wherein the phase difference of the three pulses is 180 degrees, and the pulse directions are all along the Y axis;
module M3.3: according to the ellipse semi-short axis of the relative orbit of the initial and final, the Y-direction coordinate of the instantaneous ellipse center position and the ellipse drift rate, three equation sets described by the three pulse sizes are established, the pulse sizes are obtained by solving and calculating, and the position, the size and the direction of the three pulses can be obtained;
the module M4 includes:
module M4.1: according to the analysis and calculation result, an intermediate track for transferring the initial relative track to the terminal relative track can be obtained;
module M4.2: setting the position and the speed vector of the tail end of the middle track as terminal conditions, wherein the total number of the variables is 4;
wherein the four variables are the position d of the end of the middle track f Velocity vector v xf 、v yf V zf ；
Module M4.3: setting a total of 5 variables of the flight time delta tk after the kth pulse acts and the three pulse size as optimization variables;
module M4.4: and recursion is carried out by using a high-precision orbit model, a three-pulse analytic solution is used as an initial value guess, a least square method is adopted for targeting iteration, and finally an optimal solution is obtained.
5. The single approach three pulse control system of a high rail target of claim 4, wherein: the module M1 includes:
module M1.1: assuming that the eccentricity of a target star orbit is zero, defining an origin of a Hill coordinate system as a target star centroid, wherein an X axis points radially, a Z axis is normal to a track surface, and a Y axis and other two axes form a right-hand coordinate system;
module M1.2: establishing a CW equation under a Hill coordinate system, and defining a single approach track by adopting a water drop configuration;
module M1.3: and calculating a water drop configuration track set meeting the constraint according to the minimum distance, speed and time of the approaching task, and preferably determining one of the water drop configuration track sets as a terminal relative track.
6. The single approach three pulse control system of a high rail target of claim 4, wherein: the module M2 includes:
module M2.1: calculating to obtain rectangular coordinates of the positions and the speeds of the two stars and relative positions and speed vectors of the two stars according to the instantaneous number of the orbit of the two stars under the J2000.0 geocentric coordinate system;
module M2.2: according to the position and the speed vector of the target star, calculating a conversion matrix from a J2000.0 geocentric coordinate system to a Hill coordinate system;
module M2.3: and calculating the projection of the relative positions and the velocity vectors of the two stars under the Hill coordinate system by utilizing a conversion matrix from the J2000.0 geocentric coordinate system to the Hill coordinate system, obtaining initial motion parameters of the tracked star under the Hill coordinate system, and finally obtaining an initial relative orbit.
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| RU2561490C1 (en) * | 2014-04-30 | 2015-08-27 | Федеральное государственное унитарное предприятие "Центральный научно-исследовательский институт машиностроения" (ФГУП ЦНИИмаш) | Control over spacecraft deorbit from earth artificial satellite orbit |
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| CN113268809A (en) * | 2021-04-26 | 2021-08-17 | 上海卫星工程研究所 | Design method and system for solar system marginal detection electric propulsion transfer orbit |
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